Water and Environmental Engineering Department of Chemical Engineering
Modeling Anaerobic Digestion -Validation and calibration of the Siegrist model with uncertainty and sensitivity analysis
Master Thesis by
Oscar Lidholm & Elin Ossiansson November 2008
Vattenförsörjnings- och Avloppsteknik Institutionen för Kemiteknik Lunds Universitet
Water and Environmental Engineering Department of Chemical Engineering Lund University, Sweden
Modeling Anaerobic Digestion Master Thesis number: 2008-12 by
Oscar Lidholm & Elin Ossiansson Water and Environmental Engineering Department of Chemical Engineering Lund University
November 2008
Supervisor: Professor Jes la Cour Jansen Examiner: Associate Professor Karin Jönsson
Picture on front page: 1
Postal address: P.O Box 124 221 00 Lund Sweden
Figure 26 Examples of scatter plots for the Aalborg household waste experiment; gas production vs. TS (left) and gas production vs. kH (right) from MC analysis on characterization and model parameters respectively (Figure 26).
Visiting address: Getingevägen 60
Telephone: +46 46-222 82 85SE+46 46-222 00 00 Telefax: +46 46-222 45 26 Web address: www.vateknik.lth.se
Summary Anaerobic digestion is a complex system of biochemical and physical processes. Due to the complexity of the process, it has traditionally been treated as a black box system, and optimization has been based on experience or trial and error methods. As experiments of anaerobic digestion processes are expensive and time consuming, modeling can provide a useful tool for process understanding and optimization. Models have potentials for revealing non-linear behaviors of the system and to quantify the performance of alternative operational setups. The aim of this work was to evaluate the uncertainty, sensitivity and applicability of a model for anaerobic digestion of mixed sludge published by Siegrist et al (2002) on pilot and full scale processes. Experimental data from two pilot scale experiments on household waste and one experiment on mixed sludge published in Davidsson (2007) were used for validation of the model. The household waste experiments were operated at meso- and thermophilic temperature respectively, and the sludge experiment was conducted at mesophilic temperature. For the household waste experiments, characterizations of the substrates were available and the hydrolysis dynamics was determined from batch experiments. The results from the validation showed that the steady state gas production could be predicted in the household waste simulations, but not to the same extent in the sludge reactor simulation. The ammonium correlated better for the sludge validation than for the household waste experiments, but VFA concentrations needed to be calibrated for all simulations. To assess the quality of the simulations, uncertainty analysis is required. The effect of measurement uncertainty on the model predictions was evaluated using Monte Carlo methods. It was concluded that measurement errors could explain some of the discrepancy between simulations and data, but that further calibration was needed. It was also concluded that the household waste characterization measurements reduced the prediction uncertainty substantially, compared to using a general waste composition. The gas production and ammonium proved to be highly affected by the quality of the input data while the alkalinity and VFA were less influenced. To deepen the understanding of the process, and to find the parameters best suited for calibration, sensitivity analysis was conducted. The importance of individual input and model parameters were quantified with a variance-based method with Monte Carlo sampling, measuring the effect of individual parameter variations on the total variance of outputs. This method needed to be supplemented with scatter plots, to enable visual evaluation of the correlation between parameters and output. A drawback of the sensitivity analysis was the lack of reliable distributions for the model parameters, which produced unreliable results. It was concluded that better defined distributions would provide a better ground for finding parameters for calibration. The most important parameters to determine the gas production were the degradability and the hydrolysis rate constant. The VFA and alkalinity, on the other hand, were dependent on the model parameters connected to propionate degradation and acetoclastic methanogenesis. To calibrate the VFA concentrations, the half saturation constants were changed substantially. This implies different mass transfer conditions than suggested in the model implementation by Siegrist et al. (2002). The precision for ammonium prediction could not be improved without recalibration of the feed protein content. It was therefore concluded that a revision of the model structure was needed for a successful validation. A slower hydrolysis rate for protein than for e.g. sugar would be required. After calibration, the model precision was I
improved significantly for the mixed sludge, while the precision for the household waste simulations could not be improved to the same extent. The full scale operation at Käppala waste water treatment plant on Lidingö was simulated to validate the model and evaluate various process designs. Data of flows and VS measurements were used as input to the model, complemented with literature values for the characterization of the sludge. The simulation gave predictions of gas production and alkalinity with acceptable accuracy. To evaluate different reactor setups and pretreatment options, simulations were tested and evaluated with respect to gas production, sludge reduction and economical viability. The simulations with different scenarios indicated that there are economical incitements to operate reactors in series, at thermophilic temperature, and to use enzymatic pretreatment of waste activated sludge.
II
Sammanfattning Anaerob nedbrytning är ett komplext system av biokemiska och fysiska processer. På grund av systemets komplexitet har det traditionellt blivit betraktat som ett s.k. black box system, och optimering har baserats på erfarenhet och praktiska försök. Eftersom experiment är både kostsamma och tidsödande kan modellering vara ett användbart verktyg för ökad förståelse och processoptimering. Modeller har potentialen att exponera olinjärheter i systemet och att kvantifiera prestandan för alternativa utformningar av processer. Målet med det här arbetet var att utvärdera osäkerheten, känsligheten och användbarheten för en modell av anaerob nedbrytning av blandslam publicerad av Siegrist et al (2002). Modellen applicerades på rötning av hushållsavfall i pilotskala och rötning av blandslam i pilot- och fullskala. Data från två experiment i pilotskala med hushållsavfall och ett experiment med blandslam, publicerade i Davidsson (2007), användes för validering av modellen. Hushållsavfallet rötades mesofilt och termofilt, och blandslammet rötades vid mesofil temperatur. Karaktäriseringar för hushållsavfallen fanns att tillgå, och hydrolyskonstanten för ett av hushållsavfallen och för blandslammet bestämdes med data från flaskförsök. Resultaten från valideringen visade att gasproduktionen vid stabil drift kunde simuleras med god träffsäkerhet, medan träffsäkerheten för simuleringen med blandslam inte var lika god. Mätningar och simuleringar för ammonium korrelerade bättre för valideringen med blandslam än för hushållsavfallen, medan koncentrationen av flyktiga organiska syror (FOS) behövde kalibreras för samtliga fall. Osäkerhetsanalys fordrades för att bedöma kvaliteten av simuleringarna. Effekten av mätosäkerheter på modellens prediktioner utvärderades med en Monte-Carlo metod. Slutsatsen var att mätosäkerhet kunde förklara en del av skillnaderna mellan simuleringar och data, men att kalibrering av parametrar behövdes för att öka korrelationen. Det kunde även observeras att en uppmätt karaktärisering väsentligen kunde minska osäkerheten i utdata jämför med att använda en generell karaktärisering för hushållsavfall. Gasproduktionen och ammonium visade sig vara mycket påverkade av kvaliteten hos indata, medan alkaliniteten och FOS var mindre påverkade. För att öka förståelsen av processen och hitta de parametrar som är bäst lämpade för kalibrering genomfördes en känslighetsanalys. Vikten av inflödes- och modellparametrarna kvantifierades med en variansbaserad metod, och prover renderade med Monte-Carlo metoden användes. Denna metod behövde kompletteras med punktdiagram för att visualisera korrelationen mellan parametrarna och utdata. En nackdel med känslighetsanalysen var avsaknaden av trovärdiga fördelningar för modellparametrarna, vilket ledde till otillförlitliga resultat. Bättre definierade intervall för modellparametrarna skulle möjliggöra en mer tillförlitlig känslighetsanalys och därmed ge bättre grund för att hitta lämpliga parametrar att kalibrera. De viktigaste parametrarna för att bestämma gasproduktionen var nedbrytbarheten och hydrolyskonstanten. Alkaliniteten och FOS var å andra sidan beroende av modellparametrarna kopplade till acetogenes av propionsyra och acetoklastisk metanogenes. Halvmättnadskonstanterna för dessa processer ökades avsevärt i kalibreringen, vilket visar på förändrade betingelser för masstransport än vid modellkalibreringen av Siegrist et al. Träffsäkerheten för ammoniumprediktionen kunde inte förbättras utan att kalibrera proteininnehållet i substratet. Slutsatsen av detta var att en lägre hydrolyshastighet för protein än för t.ex. kolhydrater skulle krävas för en lyckad validering. Efter kalibreringen ökade korrelationen avsevärt för simuleringen av blandslam, medan precisionen för simuleringarna med hushållsavfall inte kunde förbättras i samma utsträckning. III
Fullskaleprocessen på Käppala reningsverk på Lidingö simulerades för att validera modellen och jämföra olika processdesign. Data för flöden och VS användes som indata i modellen, och kompletterades med karaktäriseringar av primär och sekundärslam från litteraturen. Simuleringarna gav en godtagbar träffsäkerhet för gasproduktionen och alkaliniteten. Olika processkonstruktioner simulerades och utvärderades med avseende på gasproduktion, VSreduktion och ekonomisk nytta. Simuleringarna av de olika scenarierna påvisade att det finns ekonomiska incitament att införa seriell drift, termofil rötning och att använda enzymer för förbehandling av sekundärslam.
IV
Acknowledgements This Master Thesis project would not have been possible without the valuable assistance from our supervisors, Jes la Cour Jansen and Michael Recktenwald (Kemira Recycling Competence Center). The cooperation has been a pleasure, and owing to your competence we have gained a lot of insights to the field of anaerobic digestion. Mattias Alveteg has been very helpful when we accoutered programming and modeling problems. The experimental data received from Åsa Davidsson, was used extensively in this dissertation. Many thanks for assisting us also with supplementary information. We would also like to recognize Andreas Thunberg for providing us with information on the full scale process at Käppala WWTP. Hansreudi Siegrist helped us with the implementation of the model, something we are very grateful for. We would also like to thank our competent opponent, Niklas Borg, and the other folks at the department for good company at the coffee breaks. Last, but not least, thank you Emma and Fredric for your loving support.
V
VI
Abbreviations and symbols Waste Water Treatment Plant Long-Chain Fatty Acids Volatile Fatty Acids Gas-liquid transfer coefficient Continuously Stirred Tank Reactor Upflow Anaerobic Sludge Blanket Total solids Volatile solids Person Equivalents Chemical oxygen demand Solubilized COD Extracellular Polymeric Substances Waste Activated Sludge Anaerobic Digestion Model no. 1 Sludge Retention Time Hydraulic Retention Time Ordinary Differential Equations Vector of liquid phase state variables Liquid concentrations Protons Hydrogen Methane Carbon dioxide Hydrogen carbonate Ammonium ions Ammonia Acetate Acetic acid Propionate Propionic acid Dissolved amino acids Dissolved sugars Dissolved long chain fatty acid Dissolved inert COD Particulate degradable COD Amino acid fermenters Sugar fermenters Long chain fatty acid degraders Propionate degraders Acetotrophic methanogens Hydrogenotrophic methanogens Inert particulate matter Partial pressures in gas bubbles Hydrogen Methane Carbon dioxide Volumetric flow Volume
WWTP LCFA VFA k La CSTR UASB TS VS p.e. COD SCOD EPS WAS ADM1 SRT HRT ODE xi
d-1
g/m3 g/m3
d d
SH SH2 SCH4 SCO2 SHCO3 SNH4 SNH3 Sac Shac Spro Shpro Saa Ssu Sfa Sin XS Xaa Xsu Xfa Xpro Xac XH2 Xin
mol/m3 mg COD/m3 g COD/m3 mol/m3
pH2 pCH4 pCO2 q V
bar
VII
g COD/m3
m3/d m3
Vector of inflow concentrations Vector of outflow concentrations Vector of reaction rates Vector of reaction rates including gas stripping reactions Vector of gas stripping rates Stoichiometric matrix Stoichiometric coefficient Vector of reaction rates for all processes Hydrolysis rate constant Maximum growth rate Half saturation constant for growth Decay rate Inhibition of process Inhibition constant Chemical equilibrium rate constant Acidity constant Partial pressure Molecular weight Gas constant Temperature Proportional constant Differential Algebraic Equations Uncertainty Analysis Probability Density Function Monte Carlo Stochastic Differential Equations Latin Hypercube Sampling Number of realizations Cumulative Distribution Function Sensitivity Analysis Model coefficient of determination Model value for output parameter θ Simulated value for output parameter θ
cin cout r rtot rstripping T ѵ ρ
d-1 d-1 g COD/m3 d-1
I KI /
p MG R T Kp DAE UA PDE MC SDE LHS N CDF SA R2
VIII
bar g COD/mol bar m3 mol-1 K-1
Contents 1. Introduction ............................................................................................................................ 1 2. Theoretical background to anaerobic digestion ..................................................................... 3 3. Overview of existing models.................................................................................................. 7 4. Mathematical structure of the Siegrist model ........................................................................ 9 5. Numerical aspects ................................................................................................................ 13 6. System identification ............................................................................................................ 15 7. Model validation .................................................................................................................. 17 8. Uncertainty analysis ............................................................................................................. 33 9. Sensitivity analysis ............................................................................................................... 45 10. Sensitivity analysis of the Siegrist model .......................................................................... 49 11. Calibration of the model parameters .................................................................................. 59 12. Industrial scale application ................................................................................................. 71 13. Conclusions ........................................................................................................................ 77 14. Suggestions for further research ......................................................................................... 79 References ................................................................................................................................ 81 Appendices ................................................................................................................................... Article ...........................................................................................................................................
IX
X
1. Introduction 1.2. Background Increasing awareness of global warming and rising energy prices have led to a growing interest for renewable energy during recent years. Biogas, consisting mainly of methane, is an energy carrier with many advantages. It can be produced from a variety of substrates, preferably from different types of wastes, in the process of anaerobic digestion. The technique is widely used at waste water treatment plants (WWTPs) for reducing the waste volume and stabilizing the sludge produced from waste water treatment. The process can also be applied to treat e.g. household and agricultural waste, turning them into valuable resources and solving a waste handling problem. Greenhouse gas reduction is not only attained by the replacement of fossil fuels, but digesting household waste, sludge and manure prevents direct emission of the strong greenhouse gases methane and nitrous oxide to the atmosphere. The residues from the digestion process can be used as fertilizer on farmland, and the carbon dioxide produced from the methane combustion is thus taken up by plants. Plants which once again can be used for biogas production, thus the carbon cycle is closed.
1.3. Why model anaerobic digestion? To increase the biogas production capacity at WWTPs, different alternatives can be considered. Serial digestion and thermophilic temperature are possible measures for improved process efficiency. Another technique is to increase the degradation of the sludge with different methods of sludge pretreatment. At many facilities, the possibilities of including other wastes than sludge, e.g. household waste is considered as a way to increase the biogas production. Before implementation of a new process design, it is essential to evaluate the alternatives. Pilot plant and lab scale experiments are important tools, but costly and time consuming. Mathematical models can serve as useful tools to deepen the understanding of complex systems, and to facilitate operation and design of the process. If the behavior of a system can be predicted, the production can be optimized and process failure can be prevented. More effective processes could lead to a better competitiveness for biogas as an energy carrier. Despite of these motivations modeling has rarely been applied on anaerobic digestion (Batstone, et al., 2003). The obstacles for introducing modeling to the industry are among others that the models of anaerobic digestion are complex and require extensive input data, and that the performance of the models on full scale processes has not yet been tested (Batstone, 2006). It is therefore interesting to perform validations and uncertainty/sensitivity analysis of the models to gain knowledge that will facilitate model application.
1.4. The aim of this work The aim of this work was to evaluate the uncertainty, sensitivity and applicability of a mathematical model on pilot scale digestion of sludge and household waste. The model for anaerobic digestion of mixed sludge, published by Siegrist et al. (2002) was also used for studying the potentials of simulating a full scale process with different operational settings and pretreatments. Some of the questions that needed to be answered were: What input data is required to use the model with desirable accuracy? Which model parameters are most influential? Is the model suitable for simulating household waste digestion? Can the results from a sensitivity analysis be used for calibration of model parameters? Can the model predict the operation at a full scale digester, and how can the model be used to evaluate different process designs? 1
Central methods for investigating these questions were uncertainty and sensitivity analysis.
1.5. Outline of the report An introduction to anaerobic digestion is given in section 2, and an overview of models can be found in section 3. A presentation of the Siegrist model (section 4) is then followed by a discussion on the numerical aspects of the implementation (section 5). In section 6, the reader will be introduced to system identification of models. The first validation of the model, including description of the data, input parameters, results and reflections is presented in section 7. The uncertainty analysis, section 8, includes introduction, results and reflections. In section 9, a literature study on sensitivity analysis is provided as in introduction to section 10, where the results from the sensitivity analysis on the studied examples are presented. These results were used in the calibration of parameters (section 11). Examples of application on full scale digesters, in section 12, give an insight on the practical benefits from model use. Last, but not least, are the conclusions and proposals for further studies in section 13 and 14. The last part of the report includes the appendices and the unpublished article “Application, uncertainty and sensitivity of the anaerobic digestion model by Siegrist et al. (2002) on household waste digestion”.
2
2. Theoretical background to anaerobic digestion 2.1. Biochemical reactions Anaerobic degradation of organic material to methane and carbon dioxide is a complex system of biochemical reactions. The reactions are commonly divided into four groups of processes; hydrolysis, acidogenesis, acetogenesis and methanogenesis (Figure 1), each step involving a specific group of microorganisms. To obtain a stable and efficient process all four reaction steps need to function, as the processes are connected. Degradable particulate organic material (XS) Proteins Carbohydrates Lipids 30% 17% 5% 48% 1) Hydrolysis
3% 20%
Inert diss. COD (Sin)
Amino acids (Saa), Sugars (Ssu) 50% Fermentation of 2) amino acids 3) sugars 29%
12%
Long chain fatty acids (Sfa) 45%
Propionate (Spro)
4) Anaerobic oxid. of Sfa
5) Anaerobic oxid. of Spro 5% 7% 9% 31%
Hydrogen (SH2)
Acetate (Sac) 6) Acetotrophic methanogenesis
14%
67%
28%
7) Hydrogenotrophic methanogenesis
Methane (SCH4)
Figure 1 Overview of the biochemical reactions in anaerobic digestion with flows expressed as percent of COD (from Siegrist et al 2002 based on Gujer et al 1983)
2.1.1. Hydrolysis In this context hydrolysis refers to the group of reactions that degrades particulate organic matter, consisting of complex carbohydrates, proteins and lipids to soluble monomers. The end products are dissolved amino acids, sugars, long-chain fatty acids (LCFA) and dissolved inert organic matter. The process can be subdivided into biological, chemical and physical hydrolysis. Biological hydrolysis occurs when microorganisms excrete enzymes such as lipase, protease and sucrase that attack the substrate. Chemical hydrolysis is often due to weak acids or bases, which can be added to increase the hydrolysis rate. It can also be effective to mechanically facilitate the disintegration of particulate matter by treatment with ultrasound or with thermal treatment. These processes are examples of physical hydrolysis. Hydrolysis is often rate limiting when the particulate matter is not readily degradable or in systems with high loading rates (Davidsson, 2007). Even though the dynamics of hydrolysis of some individual substrates are known, the process is often described as a simple first-order process due to extensive variations in substrate composition (Batstone, 2006).
3
2.1.2. Acidogenesis Acidogenesis refers to the fermentation of dissolved sugars, amino acids and LCFA to volatile fatty acids (VFA), carbon dioxide and hydrogen. These processes are energetically favorable for the microorganisms, and are seldom rate limiting. 2.1.3. Acetogenesis The VFA produced from acidogenesis consist of short chained fatty acids like acetate, propionate and butyrate. During acetogenesis, a group of strict anaerobe Achaea oxidizes VFA of higher order than acetate to acetate and hydrogen, which can be used to produce methane in the methanogenesis. The energetic yields for these reactions are negative, and the microorganisms need to co-metabolize with methane producing bacteria in order to make this degradation step energetically feasible. Acetogens are easily inhibited by environmental factors like pH, NH3, etc., and can thus be rate limiting and a source of instability to the process. Accumulation of VFA is an indication of process failure. The dissolved hydrogen concentration is a crucial parameter as it determines the energetic yield from the reaction where VFA are degraded to acetate and hydrogen (Nilsson et al, 2007). 2.1.4. Methanogenesis Methane producing bacteria can be divided into two groups; acetotrophic methanogens and hydrogenotrophic methanogens. Acetotrophic methanogens produces methane and carbon dioxide from acetic acid, and hydrogenotrophic methanogens produces methane from hydrogen and carbon dioxide. Methanogenesis requires neutral pH, otherwise the gas production is inhibited (Reith, et al., 2003). 2.1.5. Environmental requirements The microbial processes are dependent on suitable environmental factors when it comes to e.g. pH, temperature, nutrient levels and the levels of toxicants. The processes will be inhibited if the requirements are not met. The reactor temperature is generally mesophilic (35±5 °C) or thermophilic (55±5°C). These temperature ranges provide optimal conditions for different populations of microorganisms. The reactions in a mesophilic reactor are not as fast as in the thermophilic case, but mesophilic reactors are more stable and not as sensitive to ammonia inhibition. Problems with instability are most likely to occur if easily degradable substrates are digested in a thermophilic digester (Davidsson, 2007).
2.2. Physicochemical processes 2.2.1. Equilibrium processes Important equilibrium reactions in anaerobic digestion systems are the acid-base reactions of VFA, ammonium and the carbonate system. VFA affect the alkalinity and pH of the system, which in turn can have inhibitory effects on the processes. Ammonia inhibition occurs mainly at high pH, when the deprotonated ammonia is favored. 2.2.2. Gas stripping The liquid-gas transfer is a crucial parameter for a bioreactor. A typical anaerobic digester consists of a mixture of liquid phase, particles and gas bubbles. In a simplified manner, the transport of dissolved gas to gas bubbles can be modeled as a two-phase system using stationary liquid-film theory. All mass transport resistance is then assumed to be in the liquid phase, and the kinetics is based on the overall transfer coefficient, kLa, which includes the liquid-gas film area, the diffusivity of the specimen and the layer thickness. The kLa value also depends e.g. on the degree of stirring and the temperature. The high concentrations of dissolved gases in anaerobic digesters often led to supersaturation of the liquid. The effect of 4
particles that work as catalysts for the gas stripping process is neglected in the two-phase system.
2.3. Reactor configuration A key parameter for the reactor operation is the loading rate. Anaerobic stabilization ponds are often used for low rate systems, which are often modeled as continuously stirred tank reactors (CSTR) with liquid inflow and outflow streams and a separate gas collection system. Examples of high-rate reactors are upflow anaerobic sludge blanket (UASB), expanded granular sludge bed (EGSB) and anaerobic sequencing batch reactor (ASBR). The benefits of these high rate reactors are for example less space requirements and odor problems, and a more effective process (Batstone, 2006). The effectiveness of the reactors can be enhanced by increasing the plug flow characteristics and by increasing the biomass retention. Two-step digestion where the fermentation and methanogenesis occur in different reactors can also be applied. The aim for this configuration is to make the process more stable, since the process variables can be adapted for the fermenters and methanogens respectively. The first step is usually thermophilic and the second step mesophilic (Blumensaat F, 2005). Thus, the concentration of inhibitory ammonia can be kept lower in the second reactor where the bacteria are more sensitive (Davidsson, 2007).
2.4. Substrate characterization Total solids (TS), volatile solids (VS), total and solubilized chemical oxygen demand (COD, SCOD) are common parameters to measure in the incoming substrate at digestion facilities. If the fractions of fat, protein and carbohydrates are known, the theoretical methane yield can be determined using the Buswell formula (eq. 2.1) (Buswell, et al., 1930). (2.1) mole per mole The methane production capacity can thus be expressed as organic compound, . If combining the Buswell formula with the oxygen demand of the organic substance, the theoretical methane production potential per unit of COD can be determined. The oxygen demand can be expressed as (eq. 2.2). mol O2 per mole organic substance
(2.2)
The average elemental compositions of the organic compounds used in this project are presented in Table 1. These compositions were calculated for household waste samples in Højlund Christensen et al. (2003). Fat is a beneficial substrate with a much higher biogas potential than both sugars and proteins; furthermore it gives a higher methane ratio. High amounts of protein can on the other hand cause disturbances in the process due to a higher ammonia concentration (Davidsson, 2007). Table 1 Average composition of organic compounds (Højlund Christensen, et al., 2003)
Compound Fat Protein Carbohydrates
Elemental composition C57H104O6 C5H7NO2 C6H10O5
The theoretical methane yield can be used as an indicator of the quality of the substrate, but digestion tests needs to be carried out to determine the practical biogas potential. The ratio of degradable COD to total COD (inert + degradable) will in this text be denoted as the 5
degradability of the substrate. The inert fraction can consist of complex structures of the mentioned organics, fibers, extracellular polymeric substances (EPS) etc. The processes covered in this project include digestion of sludge from wastewater treatment plants and household waste. The sewage sludge from a waste water plant can be subdivided into primary, secondary and tertiary sludge. Primary sludge is the residue after the mechanical treatment stage at the plant, often including a chemical precipitation process. The secondary sludge, or waste activated sludge (WAS) usually contains more inert organic material from dead bacteria and is more difficult to degrade than the primary sludge (Davidsson, 2007). High sludge age at the activated sludge process leads to more inert material and hence lower degradation potential in the anaerobic digestion process. Household waste has a large potential for anaerobic digestion. With improved collection systems, urban waste could be added to the existing digesters at the wastewater plants, and increase the methane production. Other commonly used substrates are grease trap waste, manure, food processing residuals or crops (Davidsson, 2007).
2.5. Sludge pre-treatment Pre-treatment can be applied to increase the degradability and dewatering properties of the WAS. This can be done by physical treatments like thermal treatment or ultrasonication or with chemical treatment, e.g. by acid or base addition or addition of enzymes (Davidsson, 2007). During these treatments, the flocs are disintegrated and both intracellular and extracellular materials are extracted (Eskicioglu C, 2006). After thermal pre-treatment experiments carried out by Eskicioglu (2006) the soluble COD increased with over 350 %, and the digestibility with over 450 %. The rate of the digestion was however lower than for the control sample, possibly due to denaturation of enzymes during the pre-treatment (Wawrzynczyk, 2007). It has been shown that thermal treatment in combination with enzyme addition gives a high methane yield (Davidsson, 2007).
6
3. Overview of models Anaerobic digestion has traditionally been treated as a black box system due to the complexity of the process. To facilitate design, system analysis, operational analysis and control, a mathematical model describing the processes is required (Batstone, 2006). The different purposes require different ranges of accuracy and model complexity. A complex, non-linear model with focus on the biochemical reactions is well suited when the understanding of the process is important, e.g. for operational analysis or for research purposes. These models can facilitate optimization of operational stability and efficiency. When implementing model-based control on a system, a linear and well parameterized model is needed with measurable key parameters as input signals. For design purposes, the model should focus on hydraulics and particle structure (Batstone, 2006). An example of such a model is presented in Elmitwalli et al. (2003).
3.1. ADM1 Researchers have strived for a standardization of model structure and parameterization over the last couple of years (Batstone, 2006). The most widely used model for anaerobic digestion is the Anaerobic Digestion Model no. 1 (ADM1), developed by a task group for the International Water Association (IWA) and published in 2002 (Batstone, et al., 2002). This model has often been used as a framework model enabling researchers to focus on modifications for specific purposes. The model includes kinetics for disintegration of homogenous particles to carbohydrates, proteins and lipids, and hydrolysis of these particles to sugars, amino acids and LCFA. The disintegration process is often rate limiting, and modeled with first order kinetics with respect to the concentration of particulate matter. Acidogenesis and acetogenesis are also accounted for, including the dynamics of the VFA acetate, propionate, valerate and butyrate. Methanogenesis from acetate and hydrogen/CO2 to biogas is included. Inhibition functions of the metabolic activity by ammonia, pH, acetate and hydrogen, and nitrogen limitation are included. The model also describes gas-liquid transfer and ion association and -dissociation. Implemented as a system of differential equations, there are 32 dynamic concentration state variables, and as a set of differential and algebraic equations, 26 state variables and 8 implicit algebraic equations are used (Batstone, et al., 2002). Examples of known excluded processes in ADM1 are lactate formation, sulphate reduction, nitrate reduction, LCFA inhibition, competitive uptake of H2 and CO2 and chemical and biological precipitation (Blumensaat F, 2005). The benefits from using a model to evaluate and optimize anaerobic processes are not fully recognized by the industry. ADM1 is not widely used due to the lack of implementation in a commercial program, and due to the low number of case studies (Batstone, et al., 2003). In Batstone, et al. (2003), two examples of ADM1 application were demonstrated to clarify the advantages from modeling. Process modifications in the industry were evaluated, and the model predictions were considered to be of high accuracy.
3.2. The Siegrist model 3.2.1. Comparison with ADM1 The ADM1 model has been regarded as too complex for practical applications (Batstone, et al., 2003). In parallel to the ADM1 model, Siegrist, et al., (2002) published a slightly more simplified model oriented towards mixed sludge treatment. The main differences are the exclusion of valerate and butyrate as state variables. The hydrolysis rate is modeled as a single step process with first order kinetics with respect to the concentration of particulate matter, furthermore, the uptake and decay rates are higher than in the ADM1 model. The two 7
models were constructed with different approaches, the Siegrist model parameters are based on experiments, whereas the ADM1 uses review consensus (Batstone, 2006). The Siegrist model was calibrated with lab scale experiments and validated with full-scale experiments. The incoming sewage sludge used to calibrate the Siegrist model was a mixture of primary, secondary and tertiary sludge from a municipal treatment plant (Siegrist, et al., 2002). The particulate matter, which is lumped together in the Siegrist model, is divided in sugars, fatty acids, proteins and inert material with different hydrolysis constants in ADM1. The particulate substrate composition can however be defined in the stoichiometry of the hydrolysis. 3.2.2. Model assumptions and limitations of the Siegrist model Anaerobic digestion is a complex process, and could not be modeled without many simplifications and without neglecting many processes. Apart from the assumptions regarding the processes already mentioned in 3.2.1, there are several others to declare, some of them are stated below: •
•
•
•
The fixed stoichiometry in the microbial processes is problematic, especially the fermentation of sugars (Batstone, et al., 2006). Increased temperature can increase maintenance and thus alter the stoichiometry. According to the liquid film theory, mass transfer resistance is assumed to lie only on the liquid side (Nielsen, et al., 2004). The kLa value is only dependent on temperature in the model, but in reality it is affected by several other parameters. Although the mass has been reduced in the digestion, the liquid phase is considered to be dilute and the volume is assumed to be constant. This assumption is however widely used (Batstone, 2006). The reactor is assumed to be completely mixed and the sludge retention time (SRT) is equal to the hydraulic retention time (HRT).
Due to the many assumptions in the model, there are limitations to what can be modeled, some of them are: • •
A rapid change in reactor temperature from mesophilic to thermophilic cannot be predicted due to the change in the microbial population (Siegrist, et al., 2002). Since all parameters are calibrated for sewage sludge digestion, a change in substrate may not be modeled well. The particle size of the substrate is not included in the model.
8
4. Mathematical structure of the Siegrist model In this section the mathematical structure of the model is presented, as it was implemented in Matlab. For further reading, see Siegrist et al. (2002).
4.1. Model structure The model is based on a system of ordinary differential equations (ODE) for the vector of state variables x, (eq. 4.1). (4.1)
,
The state variables (xi) of the system are presented in Table 2. The model includes 23 state variables of liquid phase concentrations (with units g COD/m3, mol/m3 and g N/m3), and three state variables describing the pressures of gases in the rising gas bubbles (measured in bar). Table 2 State variables of the system
State variable Liquid concentrations 1. Protons 2. Hydrogen 3. Methane 4. Carbon dioxide 5. Hydrogen carbonate 6. Ammonium ions 7. Ammonia 8. Acetate 9. Acetic acid 10. Propionate 11. Propionic acid 12. Dissolved amino acids 13. Dissolved sugars 14. Dissolved long chain fatty acid 15. Dissolved inert COD 16. Particulate degradable COD 17. Amino acid fermenters 18. Sugar fermenters 19. Long chain fatty acid degraders 20. Propionate degraders 21. Acetotrophic methanogens 22. Hydrogenotrophic methanogens 23. Inert particulate matter Partial pressures in gas bubbles 24. Hydrogen 25. Methane 26. Carbon dioxide
Notation
Unit
SH SH2 SCH4 SCO2 SHCO3 SNH4 SNH3 Sac Shac Spro Shpro Saa Ssu Sfa Sin XS Xaa Xsu Xfa Xpro Xac XH2 Xin
mol/m3 mg COD/m3 g COD/m3 mol/m3 mol/m3 mol/m3 mol/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3 g COD/m3
pH2 pCH4 pCO2
bar bar bar
4.2. Liquid phase differentials The liquid phase differentials are expressed as for a CSTR (eq. 4.2). In the case of a pulse-fed digester, the digester is modeled as batch reactor with instant feeding and withdrawal. (4.2)
9
The liquid phase system includes 17 reactions j (gas stripping not included) with individual reaction rates ρj. The processes and related state variables are listed in Table 3 (compare with Figure 1). The kinetics will be presented in the following sections. Table 3 Liquid phase processes included in the model with process number (j) and reactants (i)
j 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
i XS Saa Ssu Sfa Spro Sac SH2 Xaa Xsu Xfa Xpro Xac XH2 SCO2, SHCO2 SNH3, SNH4 Sac, Shac Spro, Shpro
Process Hydrolysis Fermentation of amino acids Fermentation of sugars Anaerobic oxidation of LCFA Propionate oxidation Acetotrophic methanogenesis Hydrogenotrophic methanogenesis Decay of amino acid fermenters Decay of sugar fermenters Decay of LCFA oxidizers Decay of propionate oxidizers Decay of acetotrophic methanogens Decay of hydrogenotrophic methanogens Equilibrium of CO2/HCO3 Equilibrium of NH3/NH4 Equilibrium of Ac/HAc Equilibrium of Pro/HPro
The stoichiometric coefficients ѵj,i of the reactions j with respect to the state variables i are sorted as rows in a stoichiometric matrix, T, (see Appendix I). The stoichiometry is based on the conservation of COD, nitrogen and electrons, and that the N/COD ratio in e.g. proteins should remain unchanged (Appendix I). The 23 columns in T each represent one of the liquid phase state variables (xi). The state variable reaction rates rreaction for the liquid phase reactions could thus be written as in equation 4.3. ·
(4.3)
In equation 4.3 rreaction is a column vector expressing the reaction rates of the 23 state variables, and ρ is a vector with the reaction rates for all processes. For the stripping of the dissolved gases H2, CO2 and CH4 (state variables 2-4), the rates (rstripping) were calculated separately (section 4.3.) and added to the vector rreaction to get the total reaction rate rtot. The concentration in the feed was expressed by the vector cin and the outflow concentration vector cout also represented the state variables. 4.2.1. Kinetics of microbial reactions The hydrolysis rate is described with a first order expression with respect to the concentration of particulate organic matter (eq. 4.4). (4.4) Processes 2-7 (Table 3) are functions of the reactants, inhibitory substances and model parameters. These processes are modeled with first order kinetics with respect to the biomass
10
concentration Xi (state variables 17-22 in Table 2) and with Monod kinetics with respect to the substrate concentration (eq. 4.5). ,
,
(4.5)
,
The inhibition factors, modeled with Monod kinetics, are described with equation 4.6. , ,
,
(4.6)
, ,
x is here the inhibiting variables pH, acetate, ammonia or hydrogen. z is 2 for pH and NH3 inhibition but otherwise 1. All processes calculated from (eq. 4.5) are slowed down by low pH values. The anaerobic oxidation of LCFA and propionate are the most sensitive processes, inhibited by high acetate and hydrogen concentrations and by low pH values. Propionate oxidation is also inhibited by a high ammonia concentration, as is the acetotrophic methanogenesis. The hydrogen inhibition of the hydrogen producing processes is due to the thermodynamics of the reactions. The biomass decay (Table 3) is modeled as first order reactions with respect to the biomass concentrations (eq. 4.7). 80 % of the decayed biomass is assumed to become XS and the rest Xin. (4.7)
,
4.2.2. Protonation- deprotonation The equilibriums of CO2/HCO3 and NH4/NH3 and protonations of acetate and propionate were modeled as pseudo-equilibrium processes as in eq. 4.7-4.10. To achieve a more stable model, the ammonia and VFA were protonated with CO2 instead of a proton (Siegrist, et al., 2002). (4.7) (4.8) (4.9) (4.10)
/ / /
/
/ /
/ /
/
/
4.3. Gas-stripping model The kinetics of the mass transfer of dissolved gases from liquid to gas phase was based on stationary film theory (eq. 4.11). These reaction rates were added to the liquid reaction rate vector r (eq. 4.3). (4.11)
,
The interfacial concentration SS,i was expressed with Henry’s law (eq. 4.12). (4.12)
,
To calculate the pressure differentials in the gas bubbles leaving the liquid, the common gas law was used. As the molecules leave the liquid phase a pressure is induced in the gas bubbles. The outflow of gas from the bubbles was modeled with a pressure control loop, which kept the pressure close to the ambient pressure using the proportional constant Kp. The 11
differentials for the pressures in the bubbles were calculated with equation 4.13. It is important that Kp is high enough to keep the pressure offset low and at the same time not too high to avoid numerical instability (Siegrist, et al., 2002). (4.13) The biogas flow for 25 °C and atmospheric pressure for the whole reactor was calculated with equation 4.15. (4.14)
4.4. Temperature dependency The temperature dependencies of all constants were described with exponential expressions like in equation 4.15. (4.15) All constants were listed as values at standard temperature (T0 = 35°C), and then multiplied with the factor from equation 4.15 to get the actual values. θ are constants determined from experiments with varying temperature.
12
5. Numerical aspects 5.1. Modeling methods for avoiding numerical problems ADM1 is a very stiff model, with time constants varying from seconds to months (Rosen C, 2006). The pH calculations are the fastest processes, e.g. the protonation/deprotonation of VFA and equilibrium of CO2/HCO3 and NH3/NH4. The problem of stiffness in the model can be reduced if the fastest processes are assumed to be at equilibrium, (dx/dt=0). This means that a system of Differential Algebraic Equations (DAE) has been created, a system which is readily solved with a DAE solver, e.g. ode15s in Matlab. Rosen C, (2006) showed that the differences between the results from the ODE system and the DAE system were minor. Another benchmarking made by (Blumensaat F, 2005) proved that the ODE solvers in Aquasim (ASIM) and Matlab (ode15s) gave very similar results for their adapted ADM1 model. The results from the implementation of Siegrist model in Matlab made in this report and the same model implemented in ASIM are therefore not expected to differ significantly. In the model by Siegrist et al, the problem of stiffness has been addressed differently from the DAE system; the fastest processes have been slowed down instead. The reaction rate constants of the equilibrium processes are chosen to be large enough to make the processes faster than the other reactions, but they are very slow compared to the real process rates. The hydrogen conversions are also very fast and the retention time is lower than for the other substrates, which leads to a very low concentration of hydrogen. To avoid long simulation times, the hydrogen concentration is artificially increased 1000 times, thus slowing down the response time. The authors claim that this does not affect the result, since the response time still is much shorter than for the other state variables. Another trick that has been used to increase model stability and create a fast interaction between the acids and bases is to assume that NH3 is protonated with CO2.
5.2. Numerical methods in the Matlab implementation Since the model is stiff, the preferred integration method is ode15s which is the stiff ODEsolver in Matlab. Numerical problems are not to be expected when performing the simulation and the solver is usually fast. When a pulse-fed reactor is fed at several times, the simulation time is slower, but still within seconds and not minutes.
13
14
6. System identification The goal of system identifiability analysis is to check that the model structure and parameterization is adequate from a mathematical point of view. For nonlinear models, system identification is complicated, and an analysis lies beyond the scope of this work. Nonetheless, it is important to be aware of the problems that non-identifiable parameters may cause when calibrating the model and conducting sensitivity analysis.
6.1. Parameter identifiability If a parameter is identifiable, it can be uniquely determined. If a parameter is globally identifiable only one unique solution exists for the parameter value, whereas an infinite number of solutions exist for an unidentifiable parameter. A model with unidentifiable parameters can produce the exact same result with many combinations of parameters, e.g. can the product of two unidentifiable parameters be identifiable. Calibrating the parameter values from measurements is not possible for a model with unidentifiable parameters (Jeppsson, 1996). Practical identifiability, on the other hand, depends on the quality of the measured data. Measurements from similar conditions produce many different parameter results which gives a poor parameter precision. Practical identifiability can be assessed by studying the joint probability distributions with Monte Carlo analysis (see 8.1.1). Functional relationships may exist between starting values of dynamical variables and parameters, or between model parameters.
6.2. Examples of identifiability analysis Identifiability analysis for dynamic models of anaerobic digestion was carried out by Müller, et al., (2002). Two mathematical models were tested, one with simple Monod structure, and one with inhibition and decay coefficients included. For nonlinear models, there are not many available techniques for structural identifiability analysis; Taylor series expansion and a differential-algebraic method are among the few. The problem is that the methods work well for simpler models, but for more complex model they tend to fail. Even a simple Monod model could not be evaluated with the methods, so the authors developed a new method based on the covariance matrix of the probability distributions. If there is a functional relationship between some of the parameters, the joint probability distributions have a correlation and the covariance matrix will not be of full rank. This method assumes a white noise, which may not always be the case. These methods will however not be employed in this report.
15
16
7. Model validation To enable model validation and calibration of the Siegrist model, data from pilot-scale experiments and a full-scale process were collected. The aim was to evaluate the usability of the model for different applications, e.g. simulation of the full-scale operation at a WWTP or pilot plant reactors with varying substrates and temperatures. The input parameters that needed to be determined before running the simulations were operational settings, such as the times of feeding, feed volumes, temperature of the reactor and the properties of the feed. The constituents of the feed needed to be transformed into units used in the model (mainly based on COD), and the characteristics of the particulate degradable organic matter (XS) needed to be determined. As the available data differed for the data sets, the methods for computing these calculations varied. Where data was missing, values from the literature or standard values from the implementation by Siegrist, et al., (2002) were used instead.
7.1. Process descriptions 7.1.1. Methods for pilot and lab scale experiments Pilot and lab scale data was collected from experiments where the biogas potentials of household wastes were studied. The experiments were carried out by Åsa Davidsson within the frame of a Danish-Swedish project (Højlund Christensen, et al., 2003) and a project for the city of Malmö (la Cour Jansen, et al., 2004). Two sets of continuous data from experiments on household wastes were used for validation, with waste from Aalborg, Denmark, and from the city district Västra Hamnen in Malmö. Continuous data from a pilot scale reactor fed with a mixture of primary sludge and WAS from Sjölunda WWTP in Malmö was used as well. For the experiments on the Sjölunda sludge and on the household waste from Västra Hamnen, lab scale batch tests were also available. Here a short description follows of the continuous and batch experiments, for more detailed information, see Davidsson, 2007. The continuous experiments were performed in stirred and heated 35 liter reactors (20 liters effective volume) with a connected gas collection tank of 77 liters. The reactors were operated at mesophilic conditions (Sjölunda sludge, Västra Hamnen household waste) or thermophilic conditions (Aalborg household waste). The experiments were running over 2-3 months and the operation was divided into three phases, start-up, continuous operation and post digestion. During the start-up phase 10 liters of inoculum was added to the reactor and the volume was gradually increased by increasing the daily feeding until a volume of 20 liters was reached. Then the continuous phase followed, where the reactors were operated with daily feeding and effluent withdrawal at constant HRT (15 days for household waste and 13.3 days for sludge). After achieving a stable process, the feeding and effluent withdrawals were eventually stopped and the post-digestion phase started. For the Sjölunda sludge process no start-up phase was needed, since the inoculum was collected at a full scale digester fed with the same sludge. No post digestion phase data was available for the reactor with household waste from Västra Hamnen. The lab analyses of the continuous processes consisted of daily measurements of the gas production, methane content, temperature and pH. Weekly analyses of the residue were HCO3, VFA, TS, VS, COD, N-tot and NH4-N. For the household waste experiments, the substrate was stored as frozen samples, and was considered to have constant composition. For the Sjölunda sludge experiment, the same batch of substrate was used for 4-20 days, and a new analysis of TS and VS was made for each batch. Characterization of the household 17
wastes was conducted within the projects, and included data of TS, VS, fat, protein, fiber, sugar, ash and ammonium content. Calculations were needed for these values to be converted to input parameters for the model, and these will be presented separately for each substrate. For the Sjölunda sludge, there was no feed characterization made specifically for the experiment. The batch experiments were conducted in 2 liter glass bottles filled to about 30 % with a mixture of inoculum and substrate (Davidsson, 2007). No withdrawal of liquid was conducted during the test period, but gas was collected and analyzed for methane content a few times per week. The bottles were stored for 30-50 days in 35°C to assure that the maximum total methane production for the waste was reached. The resulting methane potentials, however, varied more than acceptable for double samples, and were not used in the validation. The uncertainty can be due to difficulties in taking homogenous samples, described in (la Cour Jansen, et al., 2004), or insecurities in the lab method. 7.1.2. The process at Käppala WWTP Käppala WWTP in Lidingö receives 500 000 person equivalents (p.e.) and has two treatment lines, one old and one new. The old line has chemical phosphorus removal while the new line is equipped with biological phosphorus removal. Both lines include an activated sludge process with a sludge age of 8-10 days. The amount of primary sludge is stable throughout the year, but the WAS volume increases during the winter due to low temperature which leads to slow degradation. After the primary sludge is dewatered, it flows into the first digester, called R100. This digester is mesophilic (35 °C) and the HRT is kept at 15 d. The outflow from R100 is further digested in R200, together with the dewatered WAS. R200 is also mesophilic, but with a HRT of only 10 days (Figure 2). Both reactors are stirred, but there are problems with clogging of the impellers and the stirring speed is only about 5-6 rpm.
Figure 2 The digestion process at Käppala WWTP
7.2. Determination of the hydrolysis constants The hydrolysis constants for the household waste from Västra Hamnen and the Sjölunda sludge were calibrated from the batch experiments described in 7.1.1. The dynamics of the biogas production during these batch tests was used to determine the hydrolysis constants. It was assumed that the hydrolysis step was rate limiting, and that there were no inhibition effects on the microbial reactions. Under this assumption, a first order differential model for the hydrolysis could be set up. After transferring the values to logarithm scale and applying linear regression, kH was represented by the first order derivative. kH was determined to 0.33 18
d-1 for the Sjölunda sludge and 0.20 d-1 for the Västra Hamnen household waste (Figure 3). As no batch experiment was conducted for the Aalborg household waste, the hydrolysis constant from Västra Hamnen household waste was used. 4 Duplicate 1
4
Gas production, [Nml/Day]
Gas production, [Nml/Day]
5
Duplicate 2 3
kh=0.33
2 1 0
3.5
Triplicate 1
3
Triplicate 2 Triplicate 3 kh=0.2
2.5 2 1.5 1 0.5 0
-1
0
10
20 Tim e, [Days]
30
-0.5
40
0
10
20 30 Tim e, [Days]
40
50
Figure 3 Calibration of kH with batch experiment with Sjölunda sludge (left) and household waste from Västra Hamnen household waste (right)
7.3. Household waste experiment 1 - Aalborg household waste The Aalborg household waste substrate originated from source sorted household waste from the city of Aalborg in Denmark. The waste had been pretreated with a waste separator prior to the experiments (Højlund Christensen, et al., 2003). To be able to use the data for model validation, the experimental data needed to be translated into units used in the model. Manual calibration was made for the initial value of ammonium and VFA, as no data was available of the inoculum used in the experiment. The hydrolysis constant was given from the batch experiments (see 7.2.), but for the other model parameters default values from Siegrist et al. (2002) was used. 7.3.1. Feed composition The feed properties used as inputs to the model were the concentrations of particulate organic material (XS and Xin), dissolved organics (Ssu, Sfa, Saa, Sin) and other dissolved components (SH, SNH4, SHCO3, etc). The composition of the particulate organic matter was also calculated. The degradable particulate organic material, XS, degrades into fractions of dissolved amino acids, sugars, fatty acids and inert material during the hydrolysis process. The reaction also produces small amounts of dissolved CO2 and consumes small amounts of dissolved HCO3. The reaction with stoichiometric coefficients can be written as in equation 7.1, and the default stoichiometric coefficients from (Siegrist, et al., 2002) are presented in Appendix I (T-matrix). ѵ
ѵ
,
ѵ
,
ѵ
,
,
ѵ
ѵ
,
,
0
(7.1)
Omitting the production of CO2 and consumption of HCO3 and introducing new notation resulted in the simplified hydrolysis reaction described by equation 7.2. ѵ
ѵ
ѵ
(7.2)
ѵ
19
The content of sugar, fat and proteins in XS could hence be described with the stoichiometric coefficients ѵi for the hydrolysis process. All species were given in COD-fractions, and due to the conservation of COD, the hydrolysis could be written as in equation 7.3. ѵsu + ѵaa + ѵfa + ѵin = 1
(7.3)
Characterization data for fat, protein, fiber, sugar, starch, VFA and ammonium content for the waste is presented in Table 4 as percentages of TS. The soluble and particulate fractions of TS were determined by centrifugation (Højlund Christensen, et al., 2003). Table 4 Crude data used for validation of the Aalborg household waste experiment (Højlund Christensen, et al., 2003)
Characterization parameter TS Protein Sugar Starch Fat Fibers Ammonium VFA Soluble TS
Value 5 17 7 18 18 11 0.32 0.14 23
Unit % % of TS % of TS % of TS % of TS % of TS % of TS % of TS % of TS
To convert the data into units used in the model (g COD/m3, g N/m3) the Buswell formula was used (eq.2.2). The average chemical compositions were needed (Table 1), for fibers it was assumed to be C5H10O5. To enable validation to the VFA levels in the reactor, some processing of the data were needed. The analysis method used measured the total VFA level expressed as acetate. Under the assumption that the measured VFA consisted of 2/3 acetate and 1/3 propionate on a COD basis, the input variables, Sac and Spro, could be calculated from the data. The degradable organics were assumed to be the sum of protein, fat, sugar, starch and fibers (cellulose). The sugar, starch and fibers were lumped into a sugar fraction to comply with the model structure. 23 % of the degradable organics XS were dissolved components (Ssu, Sfa, Saa, Sin) with the same distribution as XS. The stoichiometric coefficients for the hydrolysis were calculated as ratios of protein, sugar and fat to the total COD in XS (ѵin was set to zero). These ratios were also assumed to determine the composition of the soluble degradable organics in the feed. For remaining input parameters, standard values from Siegrist et al. (2002) were used. The calculated input parameters are presented in Table 5. Table 5 Input values from the feed characterization for the Aalborg household waste simulation
Characterization parameter Total degradable organic matter Degradable particulate organic matter Protein fraction XS Sugar fraction XS Fat fraction XS Inert fraction of hydrolyzed XS Ammonium
Notation Saa+ Ssu+ Sfa+ Xs Xs ѵaa ѵsu ѵfa ѵin SNH4
20
Value
Unit
58 193 45 071 0.21 0.35 0.45 0 160
g COD/m3 g COD/m3 g N/m3
7.3.2. Initial state variables The inoculum was collected from a digester at a WWTP in Kalmar. As there were no analysis data for the inoculum, standard values were applied for the first simulation. Then comparing with data, it became evident that the concentrations of ammonium and VFA were higher than first assumed, and these levels were iteratively increased to fit to data. The concentration of ammonium in the inoculum was set to 3500 g N/m3 and the VFA content to 720 g COD/m3. 7.3.3. Results The simulation of the experiment included all feeding and withdrawals, simulated as new initial states for the ODE-solver on these occasions. The feeding was hence made in pulses, which was closer to reality than if the reactor would be modeled as a continuous reactor. The frequent oscillations of some outputs were due to this fed-batch mode of operation. The measured biogas was considered to be dry since it was measured at around 10 °C, which corresponded to a partial pressure of less than 15 mbar for water. The simulated gas production (Figure 4) was overestimated compared to the measurements during the first 50 days, but correlated better during the stable period and the post-digestion phase. The sharp decrease in biogas production after 10 days was due to lower feeding volumes; it was seen during the experiment that the pH dropped (Figure 6), and the feeding rate was therefore decreased to prevent overload. The methane content was also overestimated during the first part of the time series, and the drop in methane fraction when the feeding was stopped can not be seen in the simulation (Figure 4). For the steady state phase, the simulated result was well correlated to data. 0.05
100 Sim ulated dry biogas production
Sim ulated CH4
0.04
0.03
0.02
0.01
0
Measured CH4
80
Percent [%]
Production rate [m3/day]
Measured biogas production
60
40
20
0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 4 Measured and simulated biogas production (left) and methane content (right) from continuous experiment with Aalborg household waste
The totals VFA, however, were undervalued in the simulation and are 300-400 gCOD/m3 below the measured values (Figure 5). The fluctuations in the measured values of HCO3 were not captured in the simulated result, but the predictions were in the same range as the measurements (Figure 5).
21
1600 1400
Measured VFAs
60 Concentraion [mol/m3]
Concentration [g COD/m3]
70
Sim ulated VFAs
1200 1000 800 600 400
40 Sim ulated HCO3
30
Measured HCO3 20 10
200 0
50
0 0
20
40 60 Tim e [days]
80
0
20
40 60 Tim e [days]
80
Figure 5 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with Aalborg household waste
The high initial ammonium content was washed out during the start-up of the reactor, but seemed to reach a stable concentration during the steady state phase (Figure 6). It was observed that the model estimation of the final value was poor, while the dynamics of the start up phase is reflected in the simulation. The measured pH was fluctuating (Figure 6), and differed from the more stable simulated values. The values were however in the same range. 3500
8 Sim ulated NH4 m odelled
7
Measured NH4
6
2500
5
Sim ulated pH
2000 pH
Concentration [g N/m3]
3000
Measured pH
4
1500 3 1000
2
500
1
0 0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 6 Measured and simulated ammonium concentration and pH from continuous experiment with Aalborg household waste
7.3.4. Discussion The inoculum used in the experiment was taken from a full scale sludge fed digester. Thus, the microorganisms were not used to degrading food waste, and all processes could be assumed to be slower in the beginning of the experiment. As the state of the biomass is not a state variable in the model, the start-up phase can probably not be modeled very well with constant parameters during the whole experiment. It would however be possible to lower the hydrolysis constant during the start-up phase to improve the validation. The problem with such measures is that the value of kH would need calibration to data and that the theoretical background is not fully clear. Another explanation for the poor correlation to the measured results can be that inhibition from the high ammonium concentration in the reactor was underestimated in the model. A higher inhibition would cause accumulation of VFA, due to reduced methanogenesis rate and 22
a drop in pH. These trends could be seen in the data, as well as a lower methane fraction of the biogas. The model parameters were not calibrated for household waste, thus it is likely that the validation would be more successful with recalibrated parameters. Calibration of the model parameters is the subject of section 11.
7.4. Household waste experiment 2 – Västra Hamnen household waste The operation of the pilot scale experiment on substrate from Västra Hamnen was similar to the previously described experiment. In this case the reactor was kept at mesophilic conditions, and batch experiments were also available. At the 20th and 21st day of the experiment, 50 g of HCO3 was added to the reactor to increase pH; this is also done for the simulated reactor. 7.4.1. Feed composition The same methodology as for the Aalborg household waste characterization was applied. The available data is presented in Table 6, and the calculated input values in Table 7. Values for the soluble fraction of TS and the VFA concentration of the feed were not available, so the same values were used as in the Aalborg household waste simulation. Table 6 Crude data used for validation of the Västra Hamnen household waste experiment (Højlund Christensen, et al., 2003)
Characterization parameter TS Protein Sugar Starch Fat Fibers Ammonium
Value 5 17 4.3 7 11.6 14 0.027
Unit % % of TS % of TS % of TS % of TS % of TS % of TS
Table 7 Input values from the feed characterization for the Västra Hamnen household waste simulation
Characterization parameter Total degradable organic matter Degradable particulate organic matter Protein fraction of XS Sugar fraction of XS Fat fraction of XS Inert fraction of hydrolyzed XS Ammonium
Notation Saa+ Ssu+ Sfat+ Xs Xs ѵaa ѵsu ѵfat ѵin SNH4
Value 42 248 32 721 0.28 0.32 0.40 0 13.5
Unit g COD/m3 g COD/m3 g N/m3
7.4.2. Initial state variables The same methodology as for the Aalborg household waste simulation was used, the initial ammonium concentration was set to 835 g N/m3 and the total VFA to 300 g COD/m3. 7.4.3. Results Both the simulated biogas production and the simulated methane content follow the experimental values more closely during the start up phase than for the Aalborg household waste experiments (Figure 7). After day 15 there is a major drop in methane content from 60 to 40 %, and a rise in VFA concentration (Figure 8). The measured alkalinity was declining during this period, but increased after the addition of HCO3 after 20 days (Figure 8). The model simulation did not predict this minor reactor breakdown, and even though the VFA concentration increased, the methane content in the gas, alkalinity and pH remained 23
practically unchanged. The measured ammonium concentration was declining during the whole experiment, while the simulated ammonium remained fairly constant (Figure 9). 0.05
100 Sim ulated CH4
Measured biogas production
0.04
0.03
0.02
0.01
0
Measured CH4
80
Percent [%]
Production rate [m3/day]
Sim ulated dry biogas production
60
40
20
0
10
20 30 Tim e [days]
40
0
50
0
10
20 30 Tim e [days]
40
50
350
140 Sim ulated VFAs
300
120
Measured VFAs Concentraion [mol/m3]
VFAs as acetate equivalents [g COD/m3]
Figure 7 Measured and simulated biogas production (left) and methane content (right) from continuous experiment with Västra Hamnen household waste
250 200 150 100 50 0
100 80 60 40 Sim ulated HCO3 20
0
10
20
30 40 Tim e [days]
50
0
60
Measured HCO3
0
10
20
30 40 Tim e [days]
50
60
Figure 8 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with Västra Hamnen household waste 1000
8
6 600 pH
Concentration [g N/m3]
7 800
400
5
Sim ulated pH
4
Measured pH
3 Sim ulated NH4 m odelled
200
2
Measured NH4 1
0
0
10
20
30 40 Tim e [days]
50
0
60
0
10
20 30 Tim e [days]
40
50
Figure 9 Measured and simulated ammonium concentration (left) and pH (right) from continuous experiment with Västra Hamnen household waste
24
7.4.6. Discussion The validation of the gas production was acceptable, whereas the validations of the other parameters were less successful. One of the purposes of modeling is to be able to prevent reactor failures, and it can be concluded that the result was poor in this case. The experiment was designed to keep the feed characteristics constant by freezing daily portions from the same batch of feed, so it is unlikely that the problems in the reactor around day 20 was caused by changes in the input. It is possible that the reason was a too high loading rate during the start up phase, which led to consumption of alkalinity in the fermentation. The poor correlation for ammonium indicates that the characterization of the waste might not be reliable; the protein content or the hydrolysis rate seems to have been overestimated which led to a higher ammonium concentration in the simulated result than for the measurements. VFA were quickly produced and consumed, which gave large daily variations and made it difficult to measure and validate the model. For the inhibition constants and reaction rate of the methanogenesis, it is important that the VFA are in the right range. Methods for calibrating the VFA concentration will be developed in the following sections.
7.5. Sludge experiment: Sjölunda mixed sludge The model was originally calibrated with a mixture of primary and secondary sludge by Siegrist et al. (2002). Hence, default values from the original implementation were assumed to apply for this experiment when no better guess could be made. 7.5.1. Feed composition The feeding of the Sjölunda sludge reactor was made from batches of sludge that were used up after 4-15 days. These batches were analyzed for TS and VS but no analyses for protein, fat or carbohydrate content were made. Therefore, the alterative characterization method proposed by Siegrist et al. (2002) was used. The only parameters needed for the characterization was the ammonium concentration in the reactor at steady state, the COD reduction and the ratio of CH4 to CO2 in the produced biogas. The degraded particulate organic matter, XS,red, was calculated from the experimental values for influent VS and mean effluent VS at steady state (29 g/l and 14 g/l respectively). To calculate the COD content of the degraded VS, the default characterization from Siegrist et al. (2002) was used, and the resulting conversion factor was calculated to 1.9 g COD/g VS. The mean ammonium concentration in the digester (SNH4 = 860 g N/m3) was used for calculating the stoichiometric coefficient for protein in the hydrolysis (ѵaa) with equation 7.4. The N-content of protein, iNH4, was given the value 0.1 (Siegrist, et al., 2002), for results from the characterization, see Table 8.
(7.4)
,
The fat content (ѵfa) was calculated from the relation between the real methane fraction in the biogas and the theoretical methane content rendered from fat, protein and sugar (eq. 7.5). The real methane fraction in the biogas at steady state (xCH4,XS = 0.65), could be calculated from the known CO2 pressure and HCO3 concentration in the reactor with the equations in the carbonate system (see Appendix II). The fractions of methane from anaerobic digestion of sugar, protein and fat (xCH4,su = 0.5, xCH4,aa = 0.68 and xCH4,fa = 0.7) were found in VAV (1981). ѵ
,
ѵ
,
1
ѵ
ѵ
,
,
25
(7.5)
The stoichiometric parameter for sugar, (ѵsu) was calculated from the COD balance, in equation 7.6. A standard value of 0.05 for the inert fraction (ѵin) was used. The results of the characterization (Table 8) does not differ substantially from the characterization by Siegrist, et al., (2002) shown in Figure 1. ѵ
1
(7.6)
ѵ – ѵ – ѵ
The total COD in the inflow was determined using the COD/VS ratio calculated from the characterization and the Buswell formula (equation 2.2). The batch experiments resulted in a degradability of 23 % and 54 %, indicating an unreliable method. The degradability based on data for the continuous process, varied between 40-55 %, the ultimate degradability, however, was assumed to be 60 % in the simulation. The soluble part of incoming COD was assumed to be 30 %, and the fractions of the dissolved components were assumed to be the same as for the hydrolysis stoichiometry. The ammonium concentration was suggested by the experimenter, Åsa Davidsson, (2008). Table 8 Input values from characterization of the Sjölunda sludge
Characterization parameter Total degradable organic matter (mean value) Degradable particulate organic matter (mean value) Protein fraction of XS Sugar fraction of XS Fat fraction of XS Inert fraction of XS Ammonium
Notation Saa+ Ssu+ Sfa+ Xs Xs ѵaa ѵsu ѵfa ѵin SNH4
Value 30 785 21 549 0.34 0.16 0.45 0.05 45
Unit g COD/m3 g COD/m3 g N/m3
7.5.2. Initial state variables The inoculum was collected from a full scale continuous reactor, fed with the sludge used for the experiment. Steady state values after running the model could hence be used as initial values. 7.5.3. Results There was no start up phase as for the household waste experiments, since the inoculum was taken from a reactor with the same feed and with similar operational settings. This resulted in a gas production that was rather stable during the whole experimental period, both for the measurements and simulation. The variations of the measured gas production were however more pronounced than for the simulation, and the simulated values were also significantly lower than the measurements. The modeled methane content in the gas seemed to be slightly overrated (Figure 10). Both the measured and simulated VFA concentrations vary over a wide range, but the measured values were generally higher (Figure 11). The validation of alkalinity and ammonium were more successful (Figure 11 and Figure 12), while the simulated values of pH were slightly higher than the measured values (Figure 12).
26
0.05
100 Sim ulated CH4
Measured biogas production
0.04
0.03
0.02
0.01
0
Measured CH4
80
Percent [%]
Production rate [m3/day]
Sim ulated dry biogas production
60
40
20
0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
400
80 Sim ulated VFAs
350
70
Measured VFAs Concentraion [mol/m3]
VFAs as acetate equivalents [g COD/m3]
Figure 10 Measured and simulated biogas production (left) and methane content (right) from continuous experiment with Sjölunda sludge
300 250 200 150 100 50 0
60 50 Sim ulated HCO3 40
Measured HCO3
30 20 10
0
20
40 60 Tim e [days]
80
0
100
0
20
40 60 Tim e [days]
80
100
Figure 11 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with Sjölunda sludge 1500
8 Sim ulated NH4 m odelled
7 6
1000
5 pH
Concentration [g N/m3]
Measured NH4
Sim ulated pH Measured pH
4 3
500
2 1 0
0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 12 Measured and simulated ammonium concentration (left) and pH (right) from continuous experiment on Sjölunda sludge
7.5.4. Discussion The degradability of the Sjölunda sludge used for the simulation was higher than measured, and the hydrolysis constant was calibrated from the batch experiment. Despite this, the gas 27
production was lower for the simulation than for the measured data. It is possible that the assumption of a non-inhibitory condition during the batch test was wrong. In that case, the hydrolysis constant, kH, should have been higher for the simulation, which would have led to more biogas and probably lower methane content in the gas. Another important parameter is the ultimate degradability, which could have been higher than assumed. The uncertainty of the characterization is higher for this simulation than for the household wastes since it is not based on direct measurements. It would have been interesting to compare the results from the characterization with measured data to evaluate the credibility of the method. On the other hand, the default model parameters are probably more suitable for this validation than for the household wastes given that they are calibrated for a similar substrate.
7.6. Full scale digester at Käppala WWTP (Lidingö) Validation of the model to a full scale digester was made with data kindly provided by Kemira Recycling Competence Center (Helsingborg) to evaluate the practical applicability of the model. The time-scale is different from the pilot and lab scale experiments, and thus the initial values are of less interest. The reactors were modeled as CSTRs and the stiffness of the model was reduced compared to the previous simulations of pulse-fed reactors. For the model validation, data for R100 and R200 from January to June 2006, and from October 2006 to December 2007 was used. For each week, data of mean values for flows and biogas production were available, as well as measurements of pH, VFA and VS/TS. The reactors were modeled with weekly variations of inflow parameters, as well as of flows and reactor volumes. Typical values for sludge variables can be found in Table 9. The mean concentrations for each week from the simulation of R100 were used as input values to R200. This method does not fully reflect the dynamics of R100, and the mass balance is not fully closed but the accuracy of the simulation is still considered to be good enough considering the quality of input data. A simulation with new input values at each time step would be very time consuming, and it was seen in the simulations for R100 that the changes in concentration for each week appeared to be linear. Table 9 Typical values for sludge variables at Käppala WWTP
Variables
Unit
Primary sludge
Digested primary sludge
WAS
TS VS pH VFA Alkalinity
% % of TS
4.5-6.5 80-85 -
2-2.5 65-70 7.1 50-80 3000
4-6 65-70 -
mg/l mg CaCO3/l
Digested primary sludge and WAS 2.5-3 2.5-3 7.2 80-120 3500-4500
7.6.1 Feed composition Since no measurements of the protein, fat and carbohydrate content in the sludge was made, typical values were therefore sought after in the literature. A well defined characterization for a primary sludge from the Netherlands which was published by Miron et al. (2000) was chosen for input values to the model. The fractions expressed as percentages of VS (Table 10) gave all inflow characteristics when converted into g COD/m3 (with the Buswell formula, equation 2.2) or g N/m3 (Table 11). Alkalinity and pH were set to 5 mol/m3 and 7 respectively. The measured degradability in R100 was 60-70 % with a fairly high HRT, hence the degradable fraction in the inflow was assumed to be 70 %.
28
No data on the properties of the WAS was available from Käppala, thus a characterization from the literature (Chen, et al., 2007) was used for the substrate for R200. This characterization was obtained from a waste water treatment plant in Shanghai with a sludge age of 7 days (Table 10) and was converted to g COD/m3 as for the primary sludge (Table 11). The ammonium concentration in the inflow was assumed to be the same as for the Sjölunda sludge, and the VFA concentration were assumed to be low (100 g/m3) with a distribution of 2/3 acetate and 1/3 propionate on a COD basis. The alkalinity was set to 5 mol/m3, which is the value proposed in Siegrist et al. (2002), and the pH of the sludge was found in Chen et al. (2007) (Table 11). Table 10 Characterization of primary sludge and WAS
Characterization parameter VS (mean value) COD to VS ratio Protein Amino acids Sugar Dissolved carbohydrates Fat LCFA
Primary sludge 4.7 1.64 18 1.7 45 0.65 21 13
WAS 3.5 1.24 83 0 15 0 1.3 0
Unit % g COD/g VS % of COD % of COD % of COD % of COD % of COD % of COD
Table 11 Input parameters for primary sludge and WAS
Characterization parameter Mean total degradable organic matter Mean degradable particulate organic matter Protein fraction of XS Sugar fraction of XS Fat fraction of XS Inert fraction of hydrolyzed XS Mean ammonium VFA HCO3 pH
Notation Saa+ Ssu+ Sfa+ Xs Xs ѵaa ѵsu ѵfa ѵin SNH4 Shac+Shpro SHCO3 -log(SH)
R100 52 000 45 000 0.22 0.54 0.25 0 410 5000 10 7
R200 21 000 70 0.83 0.15 0.013 0 45 100 5 6.8
Unit g COD/m3 g COD/m3 g N/m3 g COD/m3 mol/m3
7.6.3. Hydrolysis constant A hydrolysis constant of 0.4 d-1 for primary sludge was found in a review by Vavilin et al. (2008). A lower value of 0.15 d-1 was assumed for the WAS. Only primary sludge is hydrolyzed in R100, and in R200 it was assumed that only the WAS was hydrolyzed. 7.6.4. Initial state variables Owing to the long time scale for the simulation, the initial values for R100 were of little importance for this simulation, and were therefore set to steady state values to avoid stiffness in the simulation. The initial values for R100 were also used for R200. 7.6.5. Results The biogas production was integrated for each time step and divided with the time difference to enable a comparison with the measured data. The result from the simulation of the biogas production in R100 shows that the correlation is fair, except for some outliers (Figure 13). The variations in the modeled gas production are due to changes in TS and flow rate, and it seems that these variations can explain the variations in measured values to some extent. The residual analysis of the gas production in R100 in Figure 13 shows that the model 29
underestimates the gas production in the beginning of the time series. It is also shown in the normal probability plot that the residuals seem to be normal distributed with a mean slightly lower than 0. 4
4
1 [m3/day]
2
1.5
x 10
0 -1 -2 0
1
Measured, R100 Sim ulated, R200 Measured, R200
0.5
0
200
400 600 Tim e [days] Norm al Probability Plot
Sim ulated, R100
Probability
Wet biogas production [m3/day]
x 10
0
100
200
300 400 Tim e [days]
0.75 0.50 0.25 0.10 -10000
500
800
-5000
0
5000
Data
Figure 13 Simulated and measured biogas production for R100 and R200 (left) with residuals and normal probability plot for R100 (right)
Measured, R100
250
Sim ulated, R100 Measured, R200
200
Sim ulated, R200
150
100
50
0
0
200
400 Tim e [days]
100 Concentration [mol/m3]
Total VFAs as acetate equivalents,[gCOD/m3]
The simulation results of R200 depend on the effluent from R100 and the quality of the characterization of the WAS. Despite the underestimation of biogas production in R100, the biogas production in R200 correlates well during the last part of the time series (Figure 13) while it is underestimated during the first part. As for the biogas production in R100, the trends and variations seem to be reflected in the modeled results for R200. The simulated VFA are underestimated in the simulations, but are in the same order of magnitude as the measured values (Figure 14). It has been observed previously in validations of ADM1 that the VFA correlate worse than the other parameters (Tartakovsky et al. (2008), Jeong et al. (2005)). The simulated alkalinity, on the other hand, correlates well with the measured values (Figure 14). The pH is stable around 7.1 for both the simulation and the measured values, while the ammonium is variable and higher in R200 (Figure 15).
80
60 Sim ulated HCO3 40
Mesured HCO3 Sim ulated HCO3R200
20
Measured HCO3
0
600
0
100
200
300 400 Tim e [days]
Figure 14 Simulated and measured VFA (left) and HCO3 (right) for R100 and R200
30
500
600
700
1600
7
1500 Concentration [g N/m3]
8
6 Sim ulated, R100
pH
5
Measured, R100
4
Sim ulated, R200 Measured, R200
3 2 1 0
1400 1300 1200 1100 1000 900
Sim ulated NH4, R100
800 0
100
200
300 400 Tim e [days]
500
600
700
700
Sim ulated NH4 R200 0
200
400 Tim e [days]
600
800
Figure 15 Simulated and measured pH (left) and ammonium (right) for R100 and R200
7.6.6. Discussion Although the characterization was obtained from the literature and not from direct measurements, the simulations correlated fairly well with the experimental data. A major problem with the validation is the lack of data for ammonium in the reactor, which means that the real inhibitory effect of free ammonia is unknown. It is possible that the VFA concentration in R200 was underestimated in the simulation due to the underestimation of ammonia, which led to a higher rate of acetotrophic methanogenesis and thus a lower acetate concentration. The fluctuations in the biogas production could not be entirely explained by the model. This was not expected, however, since the model did not include the daily and seasonal variations in sludge composition. These variations are due to changes in the waste water treatment processes and to variability in the inflow to the WWTP. Despite this lack of information, the model could predict some of the observed trends. The result could hopefully be improved if a better characterization and more data were available. The model parameters were calibrated for a mixed sludge reactor, and the microbial population in the reactor may be different for the reactors with digestion of household waste. Therefore, a recalibration of the model parameters could possibly improve the model fit.
31
32
8. Uncertainty analysis In this section, uncertainty analysis (UA) of the model is conducted to enable evaluation of the accuracy and credibility of the model output. The uncertainty of the model is evaluated using Monte Carlo methods, with known or assumed distributions of the input parameters to the model. In section 7, measured values were used as inputs for the simulations. A good fit to the measured output values were considered as a successful validation, and if the correlation was poor the validation was considered to be a failure. In this section, the measurement errors will be taken into consideration, to evaluate the quality of the model predictions. If the uncertainty of the model output is high, then better analysis methods may be required to produce a satisfying fit to data. Another topic that will be addressed in this section is the benefit from extensive characterization of household waste. The variabilities of 40 different household wastes were used to describe a general characterization. The quality of model predictions with or without measurements could then be compared, in order to evaluate the importance of a detailed characterization.
8.1. Introduction to uncertainty analysis A complex natural system like anaerobic digestion is impossible to perfectly predict, thus the uncertainty is an important measure of the reliability of the prediction. The prediction uncertainty will depend on the uncertainty of the model structure, parameters and measurements and on the mathematical uncertainty as in Figure 16. The mathematical uncertainty arises from the processes where the equations are solved numerically. Model structure uncertainty can have different sources, e.g. excluded processes or a false representation of the system. Uncertainty from model structure can change with time if the excluded processes change with time. An example in the anaerobic digestion model is the inhibition from H2S, which most likely varies with time but is excluded in the model (Kops, et al., 1996). The model structure can be mathematically verified only if the parameters can be identified (see section 6). The model structure is assumed to be valid for this case, even if system identification is not likely to be successful. Indications of the lack of identifiable parameters for the model were discussed in section 6.2. Real Prediction Uncertainty
Model Uncertainty
Determined Prediction Uncertainty
Mathematical Uncertainty Measurement Uncertainty
Parameter Uncertainty
Figure 16 Correlation between uncertainties (adapted from Kops et al, 1996)
33
The parameter and measurement uncertainties are in focus in this analysis. Uncertainty in input parameters propagates through the model and affects the model output. The statistical probability of parameters and measurements can often be described with probability density functions (PDEs), with e.g. normal, uniform, or triangular distribution. To be able to determine the uncertainty in the model prediction, the PDEs are used as input in the Monte Carlo analysis. 8.1.1 Monte Carlo analysis If the PDEs of the parameters are known, it is possible to generate random numbers from these and use as input to the model. The procedure where a set of generated random numbers are used as input to a model is called Monte Carlo (MC) analysis. The distribution of the output from a MC analysis can be used to quantify the uncertainty of the prediction. This method has many benefits and is widely used; one of the most important advantages is that it can be applied for non-linear models. The method enables analysis of the model for a span of input parameters, i.e. global sensitivity analysis, which will be discussed in section 9. The sampling of input values is commonly made from the entire spectrum of the PDEs independently for each input variable, called simple random sampling, or brute force sampling. If an infinite number of samples are generated, the resulting set of outputs will give the PDE of the model output. In reality, however, a number of runs are chosen that is large enough to ensure that the result is not changed notably by increasing the number of runs. This sampling method is commonly used, since it is relatively easy to conduct and to understand. One drawback with the method is that a large number of simulations often are required, which can be very time consuming. The ordinary MC method does not include variation of the parameters with time, which is a disadvantage (Kops, et al., 1996). In wastewater treatment plants, input parameters are known to vary with time, for example flow rates and concentrations of phosphorous and nitrogen. An alternative to MC simulation is therefore produce stochastic MC input variables at each time step, a method called MC with stochastic parameters. Another method is the stochastic differential equations method (SDE) where a noise term is added to the ODE system which ads the uncertainty for each time step (Kops, et al., 1996). These methods are rarely used, they have the drawback of being slower than MC and they require further assumptions regarding the quantity of the noise. 8.1.2. Latin Hypercube Sampling (LHS) To reduce the number of simulations needed in the MC analysis, Latin hypercube sampling (LHS) can be applied. This method divides each parameter PDE into equiprobable intervals, and combinations of input values are chosen from these intervals so that as much as possible of the parameter space is covered (Figure 17). An underlying assumption in this method is that all parameters are independent and could be paired as such, but in real life it is fairly common with correlated parameters. If the parameters are correlated the LHS sampling can produce unlikely input combinations.
34
1
0.8
0.8
Probability X 1
Cumulative Probability
1
0.6
0.4
0.2
0.6
0.4
0.2
0
0
-2
-1
0
1
2
0
0.2
X1
0.4
0.6
0.8
1
Probability X 2
Cumulative Probability
1
0.8
0.6
0.4
0.2
0 -2
-1
0
1
2
X2
Figure 17 Visualization of the LHS sampling method (Minasny, 2004)
When generating the MC samples, it is important to verify that the number of realizations, N, is large enough not to affect to result. If the total mean or variance of the output is changed when increasing N, it is not sufficiently large. To evaluate the benefits of the LHS sampling methods, a comparison between the simple random method and LHS sampling was conducted (Figure 18 and Figure 19). The LHS method produced results converged faster to the final value, and fluctuated less. This method was hence chosen for the analyses in this work. The choice of N is a trade-off between desired accuracy of the result and the time available for the simulations. N was chosen to be 5000 for all simulations, a value large enough to produce sufficiently consistent results but still low enough to keep the required simulation time within hours and not days. -3
0.05 3
x 10
2.8 Standard deviation
Mean gasproduction
0.0499 0.0498 0.0497 0.0496
2.4
2.2
0.0495 0.0494
2.6
0
2000
4000 6000 8000 Num ber of runs (N)
10000
2
0
2000
4000
6000 N
8000
10000
Figure 18 Mean (left) and variance (right) for steady state gas production as a function of N for a continuous process when using simple random MC sampling
35
-3
0.05 3
x 10
2.8 Standard deviation
Mean gasproduction
0.0499 0.0498 0.0497 0.0496
2.4
2.2
0.0495 0.0494
2.6
0
2000
4000 6000 8000 Num ber of runs (N)
10000
2
0
2000
4000
6000
8000
10000
N
Figure 19 Mean (left) and variance (right) for steady state gas production as a function of N for a continuous process when using LHS sampling
8.2 Measurement uncertainty of the household waste simulations 8.2.1. Methods for the uncertainty analysis The uncertainties of the simulations of household waste experiments from section 7 were analyzed with MC method. The uncertainty from the model structure and parameters is hard to quantify as stated in 6.1., and was omitted in this work. Focus of the analysis was instead on the impact of the measurement quality on the model predictions. The standard deviations of the measurements for the characterization of the waste were found in the literature, and are presented in Table 12. The measurement errors were assumed to be normally distributed. Values for some parameters were not found, either because they were measured with unknown instruments, as in the case of pH and pressure, or because they were impossible to measure, as in the case of HCO3. For these cases, high values for uncertainty were assumed. Table 12 Standard deviations for measurements of input parameters
Input parameter TS Soluble COD Protein Fat Starch Sugar Fibers pH NH4-N Acetate Propionate Temperature Pressure Feed flow rate N
Aalborg household waste 5.0 23 17 18 18 7 11 7.4 0.32 48.7 34.3 53.3 1.02 1.33
Västra Hamnen household waste 5.0 23N 17 12 7 4 14 7.2 0.027 48.7N 34.3 N 35.4 1.03 1.33
Unit
σ (%)
% % % of TS % of TS % of TS % of TS % of TS
2.5S 20U 0.97J 3.5 J 3.4 J 18 J 4.7 J 2U 3L 10 U 10 U 2U 2U 2U
% of TS g COD/m3 g COD/m3 °C bar l/d
No available data, the same values as for Aalborg household waste were used in the simulations, Estimated value, S (SIS, 1981), J (la Cour Jansen, et al., 2004), L(Dr Lange®)
U
The uncertainty of the measurements for the target output parameters gas production, VFA, alkalinity and ammonium are presented in Table 13. The gas production was the key parameter of interest and the measurements were considered to be very reliable (a relative standard deviation of 2 % was estimated for the measurements). Measurement variability for 36
VFA was unknown, and the method for determination was considered less unreliable. Uncertainties for the ammonium and alkalinity measurements were found in laboratory documentation. Table 13 Standard deviations for measurements of output parameters
Output parameter
σ (%)
Gas production VFA NH4-N HCO3
2U 10U 3L 3.5S2
U
Estimated value, L(Dr Lange®),S2 (SIS, 1994)
The experiments were modeled as pulse-fed reactors in section 7, but the stiffness of these simulations led to long simulation times. MC simulations of these models would be very time consuming for a sufficient number of realizations. Instead the reactors are approximated to CSTRs with flows and volumes as in the steady state phase (see section 7.1.1.). One drawback for this method is that the results from the uncertainty analysis cannot be fully compared with the experimental data. The advantage is, apart from the short simulation time, that the results will be more useful for real processes which are fed with shorter intervals. To ensure that the samples are well distributed, the LHS sampling technique was used in Matlab (Minasny, 2004). With normally distributed samples, it was possible to get negative values for the concentrations; in that case they were set to 0. 8.2.2. Results of the measurement uncertainty analysis The resulting distributions of the model outputs from the MC analysis on the Aalborg household waste simulation are presented as cumulative distribution functions (CDFs) in Figure 20. The median for the simulated output is found on the x axis for F(x)=0.5, and the 95% confidence interval between F(x)=0.025 and F(x)=0.975. Although the inputs to the model are normally distributed, it can be seen that the output are not, since the CFDs are not fully symmetrical. Especially for the alkalinity, where it can be seen that the higher output values are more spread out than the lower values (F(x)=0.5 is not in the middle of the curve). The biogas production, however seem to be normally distributed.
37
Em pirical CDF
Em pirical CDF
0.8
0.8
0.6
0.6 F(x)
1
F(x)
1
0.4
0.4
0.2
0.2
0
0.035
0.04
0.045
0 100
0.05
150
x Em pirical CDF 1
0.8
0.8
0.6
0.6
250
F(x)
F(x)
1
200 x Em pirical CDF
0.4
0.4
0.2
0.2
0
900
950 x
0 50
1000
60
70
80
90
100
x
Figure 20 CDF of the model outputs for the Aalborg household waste simulation, gas production (upper left), VFA (upper right), NH4-N (lower left) and HCO3 (lower right)
Intervals of the modeled outputs from the Aalborg household waste simulation with a confidence level of 95% are presented in Figure 21. These are results from Monte Carlo simulations, and are compared to data with measurement errors also presented with confidence intervals. The confidence intervals for the gas production and alkalinity are the broadest, which means that the measurement errors are most influential on these parameters. When the confidence intervals overlap, the validation error can be explained by measurement error. If not, the explanation for the lack of fit is to be found elsewhere since it is highly unlikely that measurement error is the cause. Most of the data points for the gas production are within the interval, except for the first time period. The alkalinity has a broad interval and all data points overlap the simulated confidence intervals. For the VFA and the ammonium; none of the measurements are included in the interval.
38
0.06
1200
0.05
1000
Concentration [g COD/m3]
Production rate [m3/day]
VFAs m odelled
0.04 0.03 Biogas production m odelled
0.02
95 % confidence interval 95 % confidence interval
0.01
95 % confidence interval 95 % confidence interval VFAs m easured
800 600 400 200
Biogas production m easured 0 40
45
50
55 60 Tim e [days]
65
0 40
70
50
55 60 Tim e [days]
65
70
100
80 Concentraion [mol/m3]
Concentration [g N/m3]
1500
45
1000
500
NH4 m odelled 95 % confidence interval 95 % confidence interval
60
40 HCO3 m odelled 95 % confidence interval 95 % confidence interval
20
HCO3 m easured
NH4 m easured 0 40
45
50
55 60 Tim e [days]
65
0 40
70
45
50
55 60 Tim e [days]
65
70
Figure 21 Plots of the confidence intervals of the model outputs ammonium and alkalinity with respect to measurement errors for the Aalborg household waste simulation
The same method for uncertainty analysis was applied on the Västra Hamnen household waste simulation from section 7.4., and the results from the simulations are presented in Figure 22. There are many measurements for the gas production which are far from the confidence interval, while the VFA measurements are all within the interval. The lack of fit for ammonium and alkalinity cannot be explained by measurement error. 0.06
1200
0.05
95 % confidence interval 95 % confidence interval
0.04
Biogas production m easured
VFAs m odelled Concentration [g COD/m3]
Production rate [m3/day]
Biogas production m odelled
0.03 0.02 0.01 0 30
35
40 Tim e [days]
45
50
39
1000
95 % confidence interval 95 % confidence interval VFAs m easured
800 600 400 200 0 30
35
40 Tim e [days]
45
50
200 NH4 m odelled
HCO3 m odelled
95 % confidence interval 95 % confidence interval
95 % confidence interval 95 % confidence interval
Concentraion [mol/m3]
Concentration [g N/m3]
1500
NH4 m easured
1000
500
0 30
35
40 Tim e [days]
45
50
150
HCO3 m easured
100
50
0 30
35
40 Tim e [days]
45
50
Figure 22 Plots of the confidence intervals of the model outputs with respect to measurement errors for the Västra Hamnen household waste simulation
8.2.3. Discussion A considerable measurement uncertainty is naturally not desirable since it means that the model cannot predict the parameters better than the confidence interval, even if the model parameters were improved by calibration. The only way to reduce measurement uncertainly is, of course, to improve the analytical method for determination of these inputs. If the parameters that influence the uncertainty the most are determined, the measurements that need improvement can be found. Even so, there is also the uncertainty of sampling, which is harder to quantify but further broadens the confidence interval of the result. It can seem unpromising that so many measurements are outside of the confidence interval for the household waste simulations, but it is in fact promising in one way; it allows the correlation to be improved by calibration of the model parameters. Sensitivity analysis and model calibration is discussed in section 9 and 10.
8.3. Variability of feed composition 8.3.1 Method To enable comparison of the prediction accuracy when using the characterization from measurements and when using a general composition of household waste, the variation of data from 40 samples was analyzed. The general characterization was calculated from the literature and based on household waste collected in Danish cities ( Table 14). This comparison is interesting since measurements of proteins, fibers, fat and other constituents in the substrate are costly and thus seldom carried out. If the uncertainty of the model results mainly depends on accurate measurement of these parameters, it means that these measurements are needed for a satisfactory simulation. The 40 measurements were regarded as normally distributed, which was a well-grounded assumption e.g. for the fat content (compare with Figure 23). The standard deviations of the parameters can be found in Table 14. It is worth noting that the fractions of the different constituents are assumed not to be correlated, although it is likely that they are correlated in reality. The total amount of the constituents makes up the degradable part of TS.
40
Table 14 Means and standard deviations for household waste
Characterization parameter
General household waste values
Unit
σ (% Rel std (%) of TS)
TS Protein Sugar Starch Fat Fibers Soluble COD
26.4A 14.9 6M 15M 13.8 18.5 13.9
% % of TS % of TS % of TS % of TS % of TS %
6.5 1.37 3 5 1.65 3.69 8.3
24.6B 9.2H 50 H 33.3H 12.0 H 20.0 H 59.7B
Before dilution, uncertainty is equal to measurement uncertainty after dilution, MMean values from (Hansen, et al., 2007) and σ from assuming that 95 % of measurements are within the range of 2σ, B (Højlund Christensen, et al., 2003), H (Hansen, et al., 2007)
Probability
A
0.99 0.98 0.95 0.90 0.75 0.50 0.25 0.10 0.05 0.02 0.01 10
11
12
13
14
15
16
17
5
0 10
12
14
16
18
Figure 23 Normal probability plot and histogram for fat fractions in data from (Hansen, et al., 2007)
8.3.2. Results and discussion The uncertainties of the model predictions when using the general characterization instead of measurements were determined for the Aalborg and Västra Hamnen household waste simulations. This analysis was conducted simply by changing the means and distributions of the characterizations from 8.2. to the values in Table 14. A comparison between the resulting variances and the variances due to measurement errors is presented in Table 15. This table shows that the variance increases almost 10-fold when it comes to gas production and ammonium. The predictions of VFA and HCO3 are not as influenced of the quality of the input data. Table 15 Variance of model predictions from analysis with varying characterization parameters Parameter Unit Aalborg Aalborg Västra Västra household waste household waste Hamnen Hamnen with measured with general household waste household waste characterization characterization with measured with general characterization characterization 2.3x10-5 m3/d 4.1x10-6 1.2x10-6 Gas production 1.5x10-5 422 506 VFA gCOD/m3 22.4 13.3 gN/m3 428 5.8x103 NH4 493 6.1x103 3 52.9 82 HCO3 mol/m 59.5 92.7
41
The confidence intervals of the model outputs presented in Figure 24 and Figure 25, show that the confidence interval for biogas production is significantly broader when the variability of the characterization parameters are used instead of the measurement uncertainty. This implies that the measurements of the substrate are important to reduce the uncertainty of the results for household waste. One can hence expect that the difference in gas production from different household wastes can be significant if the fractions of the feed are non-correlated. Figure 24 and Figure 25 also show that the levels of ammonium and alkalinity in the reactor are affected by the content in the waste, while the VFA seem to be largely unaffected in the same range. Measurements of the specific household waste would therefore not be expected to improve the correlation of the simulation for VFA. The confidence intervals for the general composition also reveal that there are values that cannot be explained by varying the waste composition. This implies that the model parameterization or structure needs to be revised. To be able to calibrate the model, the influence of individual parameter on outputs needs to be investigated. This is the subject of section 9 and 10. 0.05
1200
0.04
Concentration [g COD/m3]
Production rate [m3/day]
VFAs m odelled
0.03
0.02 Biogas production m odelled 95 % confidence interval 95 % confidence interval
0.01
1000
95 % confidence interval 95 % confidence interval VFAs m easured
800 600 400 200
Biogas production m easured 0 40
45
50
55 60 Tim e [days]
65
0 40
70
50
55 60 Tim e [days]
65
70
100
80 Concentraion [mol/m3]
Concentration [g N/m3]
1500
45
1000
500
NH4 m odelled 95 % confidence interval 95 % confidence interval
60
40 HCO3 m odelled 95 % confidence interval 95 % confidence interval
20
NH4 m easured 0 40
45
50
55 60 Tim e [days]
HCO3 m easured 65
70
0 40
45
50
55 60 Tim e [days]
Figure 24 Aalborg household waste simulation with general waste composition
42
65
70
0.06
1200
0.05
95 % confidence interval 95 % confidence interval
0.04
Biogas production m easured
VFAs m odelled Concentration [g COD/m3]
Production rate [m3/day]
Biogas production m odelled
0.03 0.02 0.01 0 30
35
40 Tim e [days]
45
1000
VFAs m easured
800 600 400 200 0 30
50
1500
95 % confidence interval 95 % confidence interval
35
40 Tim e [days]
HCO3 m odelled
95 % confidence interval 95 % confidence interval
Concentraion [mol/m3]
Concentration [g N/m3]
50
200 NH4 m odelled
NH4 m easured
1000
500
0 30
45
35
40 Tim e [days]
45
50
95 % confidence interval 95 % confidence interval
150
HCO3 m easured
100
50
0 30
35
40 Tim e [days]
Figure 25 Västra Hamnen household waste simulation with general waste composition
43
45
50
44
9. Sensitivity analysis In the uncertainty analysis from the previous section the overall uncertainty of the model output due to uncertainties in input was studied. In this section the sources of the variations in output is investigated to find the input parameters which the model is sensitive to. Sensitivity analysis (SA) can be conducted to find the input parameters that are most important to measure to minimize the prediction uncertainty. SA can also be used to test the model stability and to find the model parameters that are most suitable for model calibration. If a parameter has a negligible impact on the output, then the efforts to determine that parameter might be reconsidered. For some applications, like control, it is desirable to simplify the model as much as possible, and if the result is insensitive to a parameter, it can be excluded from the model. The parameter for which the output is most sensitive to is probably the best control signal. Another obvious purpose of SA is to improve the understanding of the system. Large ODE systems are not easily understood, and the SA can help to quantify the contribution of different parts of the system to the output result and give hints on what parts of the process that needs special consideration. A specific goal of the SA in this case was to find key parameters that could be used to calibrate the pilot scale simulations from section 7. First, a general presentation of different methods for sensitivity analysis is made, in section 9.1. and 9.2., then previous SA on anaerobic digestion models from the literature are presented in 9.3. The sensitivity analysis on the pilot scale simulations from section 7 are found in section 10.
9.1. Local SA methods Local methods evaluate linear perturbations for the output for a specific set of parameters. Thus, the result applies for this set of parameters, but may not be applicable for other values. For linear models without correlation between parameters, these methods are useful. 9.1.1. Sensitivity functions A common SA method is to study the partial derivative of an output variable with respect to a certain input parameter. This derivative is called the sensitivity function δ, and can be interpreted as the linear change in output due to the change in the input parameter. The sensitivity function can be computed continuously during the simulation time, to study the dynamics of the sensitivity of the output to the parameter. The absolute change in an input variable x per unit change in the parameter θ is presented in (eq. 9.1) (Jeppsson, 1996). (9.1) The definition in equation 9.1 gives a result that strongly depends on the units of the parameter, and often the relative change in parameter is more interesting to compute (eq. 9.2). The derivative of the variable x with respect to the parameter θ is here multiplied with the parameter value. Here the sensitivity function depends on the parameter on a relative basis, and sensitivity functions for different parameters can easily be compared. θ
(9.2)
When analyzing the sensitivity functions for different parameters dependencies between parameters can be detected. If parameters have similar but inverse sensitivity functions they can be non-identifiable, i.e. a change in one parameter can be compensated by a change in another. The best identifiability is achieved when sensitivity functions have different behavior 45
and when they differ significantly from zero. As sensitivity functions give a linear sensitivity analysis they are valid only locally for the specific parameter values that were used.
9.2. Global methods Models of complex systems such as the anaerobic digestion process are usually nonlinear. Using local SA methods to analyze these models can be questionable, since the results only are valid for the set of parameters that were analyzed. For other parameter values, the sensitivity analysis may not be accurate. For nonlinear models, global methods are preferred, that evaluate the sensitivity for a broader spectrum of input parameters. This analysis will not be as straightforward as the linear methods, though. Here three examples of useful methods for nonlinear SA are presented.
0.06
0.06
0.05
0.05 Gas production rate [m 3/d]
Gas production rate [m3/d]
9.2.1. Scatter plots A natural first step when analyzing a model is to study plots of outputs vs. input for a qualitative analysis of the model behavior. Dependencies and nonlinearities can be detected, and the understanding of the system can be improved. A MC generated sample of inputs and the corresponding outputs can be used for this analysis. Figure 26 shows an example of how scatter plots can be used for SA.
0.04
0.03
0.02
0.01
0 0.044
0.046
0.048
0.05 TS [%]
0.052
0.054
0.056
0.04
0.03
0.02
0.01
0 0.1
0.15
0.2
0.25
0.3
-1
k H [d ]
Figure 26 Examples of scatter plots for the Aalborg household waste experiment; gas production vs. TS (left) and gas production vs. kH (right) from MC analysis on characterization and model parameters respectively
The qualitative sensitivity analysis from these plots indicates that the TS content in the feed has an impact on the biogas flow from the reactor, and a nonlinear correlation between kH and gas production was detected. 9.2.2. Standardized regression coefficients Another common SA method is to use the output from a set of MC sampled parameters for linear regression with respect to the different parameters. The standardized regression coefficients are a measure of the sensitivity of the output to the specific parameters. The model coefficient of determination, R2, can be used to determine the precision of the model. For R2 values close to 1, the regression model is valid and the regression coefficients are a good measure of the sensitivity. If R2 is low, on the other hand, it indicates a nonlinear model, with a poor correlation to the linear regression. In these cases, a nonlinear approach to SA is
46
preferred. This analysis hence can quantify the degree of nonlinearity, and if the linear behavior is dominant, give a measure of the degree of sensitivity. 9.2.3. Variance-based methods Scatter plots represent a qualitative method, and is a very useful for revealing nonlinearities and finding correlations between inputs and outputs. To be able to quantify the sensitivity of input parameters, and to compare sensitivities for different parameters, more sophisticated methods are required. The method that was chosen for the main part of the SA in this project is based on the correlation between the variance of input parameters and the variance of outputs for steady state simulations. The variance in the parameters will lead to a variance in output, and an important parameter will have a bigger impact on the output variance than a parameter that the model is less sensitive to. If, for example, the inputs are generated with MC methods from PDEs as in section 8.2., the outputs will be determined with a total variance. This is the same variance that was used for determining the uncertainties of the predictions. In the case of sensitivity analysis, the source of the variance is of interest. The variance that each parameter adds to the total output variance is the measure of sensitivity that is sought. For a linear model, without correlation effects, the total uncertainty could be decomposed into fractions of variances assigned to each parameter. The contributions of variance for one parameter at a time could simply be calculated, and the total output variance would be the sum of these. For a nonlinear model, the total variance cannot be decomposed in this simple manner due to correlation effects. Instead, the difference between the total output variance and the output variance when one parameter was held constant was chosen as an estimator of the correlation between variance in input and output. This value also represents the possible reduction in uncertainty that would be gained if a parameter would be determined without uncertainty.
9.3. Sensitivity analysis of anaerobic digestion models in the literature Linear sensitivity analysis is the most commonly used method for analyzing the parameter sensitivity in anaerobic digestion models, in fact no examples of SA based on MC simulations were found in the literature. Tartakovsky et al. (2008) developed a distributed version of ADM1 for simulation of an UASB reactor and performed a sensitivity analysis on the model parameters. They used sensitivity functions to find the most sensitive parameters, which were used to calibrate the model. The sensitivity analysis showed that specific uptake rates and half saturation constants for acetate and propionate and butyrate/valerate had the strongest impact on reactor COD concentration, acetate and propionate, while kLa affected the methane percentage. The measurements had high variability, but model correlation with “reasonable accuracy” was achieved. COD predictions were better than VFA predictions; the authors suggested that the model underestimated inhibition of fermentation from free acid, thus overestimating the VFA. Another method for SA was used by Jeong et al (2005) as they analyzed the sensitivity of ADM1 using bottle tests with glucose and acetate as substrate. ADM1 was simplified as the decay processes for microorganisms, inhibition from pH and free ammonia and the gas-liquid transfer for methane were ignored. The sensitivity analysis was carried out by varying one parameter at a time over a chosen interval, and then calculating the mean of the absolute differences between the standard parameter setting result and the model result with altered parameter value for each time step. The benefit from this method compared to sensitivity functions was that different intervals of variance could be chosen for the parameters, and that the non-linearity of the output could be revealed in that range. Yield of product on substrate and Monod maximum specific uptake rates proved to be significant parameters, while yield of 47
biomass on substrate were less important. Correlation with the model for methane concentration was good after calibration, but worse for acetate which the authors explain with adsorption and storage by the microorganisms. The question which arose from the results of this SA was whether the chosen intervals of variance are reasonable, for example the yield of product on substrate varied with 30 %, a figure which was not supported in the article. An example of SA for the purpose of parameter reduction can be found in Noykova (2000) where an SA is made on an older and simpler model than ADM1. The only output in the SA was the biogas flow, and logarithmic or relative sensitivity functions were used (eq. 9.3) (9.3) The analytical equation to calculate Tij could not be adapted for non-linear systems, therefore simulation results were required. µmax for methanogens proved to be the most significant parameter, as were the yield coefficient for methane and inhibition coefficient for methanogens. Decay rates, on the other hand, had little impact on the results and could be neglected. The simplified model with four optimized parameters had a reasonable fit. When reducing a model, it is important to be aware that the conditions under which the model could be used become narrower. The process needed to be very stable for the reduced model to be useful.
9.4. Discussion If a model prediction is sensitive to a specific parameter, this parameter will also contribute more to the uncertainty of the prediction. Uncertainty and sensitivity analysis therefore go hand in hand. All sensitivity analyses on anaerobic digestion found in the literature were based on local methods. These analyses were easy to perform and to grasp. Sensitivity functions, for example, give a general sensitivity analysis in the sense that the parameters are always changed 100 %. The result should however be treated with caution. Some parameters are not at all likely to vary as much as 100 %, while others could vary more than that. The non-linear behavior and correlation effects of the model are also excluded using this method. It is known that both ADM1 and the Siegrist model are non-linear and it is doubtable whether sensitivity functions are a suitable method. All sensitivity analyses found in the literature only included model parameters and not inflow parameters, although they are interesting as well. It is for example not useful to put much effort info calibrating the model parameters if the level of detail is not supported by the data. Furthermore, it could be interesting to compare the relative importance of input parameters for various operational settings. Increase knowledge of the model sensitivity for all parameters would enhance model application and ensure that measurements are made for the most influential input parameters. Global MC methods are preferred over local methods when it comes to analyzing nonlinear models. It is however important to stress that sensitivity or uncertainty analysis using MC methods are performed for a certain case, with chosen ranges for the parameters, and that the results only are valid for that particular parameter space. The analysis will not be reliable if the probability density functions of the parameters are chosen poorly. One of the drawbacks of MC-based methods is of course the extensive computational force that is required.
48
10. Sensitivity analysis of the Siegrist model As discussed in chapter 9, a global and variance-based method was considered most suitable for SA of the validation simulations of section 7. The chosen method quantified the reduction of variance in output when one parameter was kept constant compared to when all parameters were varying. The background to the sampling method and distributions for characterization parameters can be found in chapter 8. The sensitivity analysis was conducted by first rendering a LHS sample of 5000 parameter sets. Steady state simulations were run for the LHS sample, giving the total variance, and also for the same parameter sets but where one parameter at a time was kept at a constant value (at the mean value). The sensitivity measure for each parameter was expressed as the relation between the variance when the parameter was held constant to the total variance. A low value for this relative sensitivity means that the output is very sensitive to the parameter. SA was conducted for the validation simulations of the pilot scale experiments presented in section 7. Each of these experiments were now simulated as steady state simulations, and analyzed for three different categories of parameters. One of the purposes of the SA was to find the parameters that were important to measure in order to reduce the output uncertainty. This was achieved by calculating the sensitivity to the measured parameters, using known and estimated measurement errors as parameter distributions. Another aim for the SA was to find the parameters that would be most suitable for calibration. In this case, the sensitivity to the model parameters was studied, using rectangular distributions for these parameters with a range of 50 % to 150 % of the default values. This means that all values in this interval were assumed to be equally probable. This use of general intervals was applied due to the lack of information, and does not always reveal what parameters that was best suited for calibration. The reason for this was partly that some parameters are more variable by nature than others, and may be changed to a higher extent. The sensitivity measure for some parameters could also be explained with a high rate of unstable simulations, due to e.g. washout. These parameters will not always be good for calibration purposes. The SA therefore needed to be supplemented with scatter plots to study relationships between parameter value and output more closely. The sensitivity of the measured parameters and model parameters were also studied when all input and model parameters were allowed to vary simultaneously. This could display the relative importance of the measured parameters compared with the model parameter. The values used in the model were given for 35°C, and recalculated for the actual reactor temperature with the equations for temperature dependency (see equation 4.16).
10.1. Aalborg household waste experiment For this first example, all results are presented in the text, but for the other cases only the most interesting results are shown, and the rest are found in Appendix III. 10.1.1. Sensitivity of input parameters The first step of the sensitivity analysis for this thermophilic digester was to find measurement uncertainties for the input parameters, described as standard deviations. The standard deviations and rank of the uncertainties were presented in Table 16. The resulting relative sensitivity for each parameter with respect to different output parameters is also presented here. Rank 1 is given to the parameter that lowers output variance the most when kept at a constant value.
49
Table 16 Results of SA, UA and variability of measured parameters for the Aalborg household waste simulation Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.23 0.17 0.18 0.07 0.18 0.11 7.4 10 160 48.7 34.3 55.3 1.33 1.02
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Sensitivity (Gas)
Sensitivity (VFA)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank 12 2 14 9 3 10 8 13 1 11 4 4 13 6 6
rank relative 1 0.74 8 0.98 10 1.00 6 0.95 4 0.88 7 0.97 9 0.99 14 1.00 11 1.00 13 1.00 15 1.00 12 1.00 5 0.90 3 0.87 2 0.78
rank relative 4 0.95 3 0.95 7 0.99 11 1.00 5 0.98 8 1.00 10 1.00 14 1.00 2 0.59 9 1.00 15 1.00 13 1.00 1 0.49 12 1.00 6 0.98
rank 1 3 2 6 7 9 11 14 4 5 13 15 12 8 10
rank relative 3 0.97 2 0.95 4 0.99 8 1.00 5 1.00 13 1.00 7 1.00 11 1.00 1 0.080 12 1.00 9 1.00 10 1.00 15 1.00 6 1.00 14 1.00
σ (%) 2.5S 20U 0.97J 3.5J 18J 3.4J 4.7J 2U 100 U 3L 10 U 10 U 2U 2U 2U
relative 0.42 0.93 0.84 0.97 0.97 0.99 1.00 1.00 0.93 0.95 1.00 1.00 1.00 0.98 1.00
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Højlund Christensen, et al., 2003), H (Hansen, et al., 2007)
The results from the sensitivity analysis show that the gas production is most sensitive to the TS and flow of the feed and to the pressure in the reactor. The temperature and starch content are also influential (rank 5 and 4), but the other parameters seem to be measured well enough or have an insignificant effect on the variability for the gas production. The alkalinity, which was given the highest uncertainty, is still irrelevant for the gas production. It can also be concluded that the hydrolysis is not limiting, since the solubility of the waste also is insignificant for the variance in gas production. The VFA, on the other hand, are very much affected by the temperature and by the unknown inflow of carbonate alkalinity. The measurement uncertainty for protein that was used in this analysis was very low. This resulted in a higher contribution of the TS in the feed to the variance of the ammonium levels in the reactor than for the protein content (compare 0.42 and 0.84). The carbonate alkalinity in the reactor was mainly affected by the inflow concentration of HCO3, and not by the other constituents of the feed. 10.1.2. Model parameter sensitivity The results from the sensitivity analysis on model parameters are presented in Table 17. In the first column the parameters are listed. The sensitivity analysis did not include the chemical equilibrium constants, since these were considered to be well defined. The parameters included maximum growth rate constants for the processes (µmax,j), death rate constants (kd,j), half saturation constants (KSi), inhibition constants (KIac), kLa for CO2 (which decides the kLa for H2 and CH4 as well) and hydrolysis constant (kH).
50
Table 17 Results of SA of model parameters for the Aalborg household waste simulation
Parameter at 35 °C
Mean
Unit
µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.2
d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 1.00 14 1.00 16 0.99 2 1.00 24 1.00 7 1.00 5 1.00 17 1.00 18 1.00 4 1.00 13 1.00 23 1.00 11 1.00 15 1.00 21 0.99 3 1.00 22 1.00 6 1.00 8 1.00 25 1.00 10 1.00 12 1.00 19 1.00 9 1.00 27 1.00 26 1.00 20 0.019 1
Sensitivity (VFA) rank relative 1.01 27 1.00 17 1.00 24 0.35 1 0.72 4 0.80 6 1.00 23 1.00 22 1.00 26 0.64 3 0.86 8 0.96 13 1.00 21 1.00 18 1.00 16 0.98 15 0.95 11 0.90 9 0.98 14 1.00 20 0.80 5 1.00 19 0.91 10 0.47 2 0.85 7 1.00 25 0.96 12
Sensitivity (NH4-N) rank relative 0.99 2 1.00 21 0.99 17 0.99 5 0.99 8 0.99 6 11 1.00 27 1.00 10 0.99 12 1.00 3 0.99 7 0.99 13 1.00 22 1.00 26 1.00 20 1.00 25 1.00 15 1.00 18 1.00 24 1.00 14 1.00 23 1.00 16 1.00 4 0.99 9 0.99 19 1.00 1 0.051
Sensitivity (HCO3) rank relative 1.00 19 1.00 22 1.00 16 0.80 3 0.75 2 0.93 8 1.00 20 1.00 25 1.00 27 0.88 7 0.88 6 0.99 13 1.00 18 1.00 23 1.00 17 0.99 15 0.96 10 0.97 12 0.99 14 1.00 21 0.94 9 1.00 24 0.96 11 0.85 4 0.86 5 1.00 26 0.57 1
The gas production seemed to be virtually insensitive to all model parameters except the hydrolysis constant, which indicates that the hydrolysis could get rate-limiting for certain values of kH (Table 17). The non-linear correlation between kH and gas production is illustrated in Figure 26 (in section 9.2.1). It can be noted that the hydrolysis was irrelevant for the VFA concentrations, as were the rates of fermentation (processes 3, 4 and 5). The VFA were instead linked to the constants for propionate degradation (process 6; rank 1, 2 and 3) and the acetoclastic methanogenesis (process 7, rank 4). The high sensitivity for the maximum growth rates could be explained with a high rate of washout of propionate degraders when the parameters reached critical values. Figure 27 shows an example where reactor instability can be detected for low values for µmax6. These parameters would not be suited for calibration, since it would result in unstable reactors. Instead the half saturation constants for processes that determine the VFA levels should be considered for calibration of VFA. This result could not be found in the sensitivity analysis, and a better approach for the SA would hence have been to either use realistic variations for the parameters, or to sort out values when bacteria were washed out. This analysis was not performed in this project due to lack of time.
51
Concentration [g COD/m 3]
5000
4000
3000
2000
1000
0 0.2
0.4
0.6
0.8
1
µ max6
Figure 27 Scatter plot with VFA levels as function of µmax6
The ammonium is primarily produced in the fermentation of proteins, a process which is fast and limited by the rate of the hydrolysis. Therefore, the hydrolysis constant was far more important for the ammonium concentration than the other model parameters. The carbonate alkalinity is mostly produced in the methanogenesis (process 7 and 8), consequently the maximum rates of these reactions proved to be important. The most significant parameter, however, was the hydrolysis constant. It affects alkalinity by consumption in the hydrolysis, but moreover it decides the rates of the other processes, of which many include uptake or production of alkalinity. A relative sensitivity higher than 1 is unlikely, but it can be seen for the VFA and µmax3. It can happen if more extreme values are produced for the run where one variable is kept constant than for the run where all parameters vary. If the distributions for the model parameters were known and the number of runs was increased, this problem would probably not occur to the same extent. It could be shown that TS contributed to a great deal to the uncertainty for the gas production, although it was measured with a standard deviation of 2.5 %. kH stands out as an important parameter for gas production, ammonium and alkalinity when it varies between 0.1 and 0.3. It is possible that the real variability is even higher which makes it clear that kH is essential to measure or approximate with sufficient accuracy. This is also practical; kH is easier to measure than many of the other constants. The uncertainty of the biogas production can namely be reduced by measuring three easy variables: kH, TS and the gas pressure. Moreover, measuring the TS and pressure is inexpensive and already implemented at many plants. Reducing the uncertainty for the alkalinity is more complicated; the most significant variable HCO3 in the feed is immeasurable. Numerical calibration of the feed alkalinity is therefore required to find a suitable inflow concentration (section 11).
10.2. Västra Hamnen household waste experiment This reactor was run with the same operational settings as for the Aalborg household waste experiment, but with mesophilic temperature instead of thermophilic. The SA could hence reveal if the importance of certain parameters change with the temperature. 10.2.1. Sensitivity of input parameters The results from the SA on measured parameters are presented in Table 18. It was shown that the sensitive parameters for the biogas production rate were similar to the Aalborg household 52
waste simulation, while the results for the VFA were more interesting. In this case, the carbonate alkalinity was the most important parameter, followed by the TS and solubilisation of TS. The temperature, which was the most important parameter for the Aalborg household waste reactor was rather unimportant for the mesophilic reactor. This is probably due to the exponential expressions for temperature dependence (compare eq. 4.15), which cause the parameters to change more in the thermophilic interval than in the mesophilic. It is clear that these nonlinearities in the model were exposed by the SA. The sensitivities for ammonium and carbonate alkalinity are virtually the same as for the thermophilic reactor. Table 18 Results of SA, UA and variability of measured parameters for the Västra Hamnen household waste simulation Parameter at 35 °C
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.23 0.17 0.12 0.04 0.07 0.14 7.21 10 13.5 48.7 34.3 35.4 1.33 1.03
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Sensitivity (Gas)
Sensitivity (VFA)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank σ (%) 12 2.5S 20U 2 0.97J 14 3.5J 9 18J 3 3.4J 10 4.7J 8 2U 13 100 U 1 3L 11 10 U 4 10 U 4 2U 13 2U 6 2U 6
rank relative 1 0.69 5 0.93 10 1.00 7 0.95 4 0.90 9 0.99 6 0.95 12 1.00 15 1.00 13 1.00 14 1.00 11 1.00 8 0.99 3 0.87 2 0.79
rank relative 3 0.88 2 0.88 6 0.97 10 1.00 7 0.98 11 1.00 9 0.99 14 1.00 1 0.29 12 1.00 15 1.00 13 1.00 4 0.93 8 0.99 5 0.96
rank relative 1 0.46 2 0.76 3 0.86 6 0.98 7 0.98 9 1.00 8 0.99 13 1.00 15 1.00 10 1.00 12 1.00 14 1.00 4 0.97 5 0.97 11 1.00
rank relative 3 0.97 2 0.95 4 0.99 13 1.00 7 1.00 14 1.00 8 1.00 11 1.00 1 0.074 12 1.00 10 1.00 9 1.00 6 1.00 5 1.00 15 1.00
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Højlund Christensen, et al., 2003), H (Hansen, et al., 2007)
10.2.2. Model parameter sensitivity The most influential parameters from the SA with model parameters for the Västra Hamnen household waste simulation are presented in Table 19. The sensitivity for the gas production was different for mesophilic conditions; kH is still the most influential parameter, but there were also other parameters that affected the output variance. The maximum growth rate of the acetoclastic methanogens (ranked 2) and the inhibition of the same process (rank 3) were ranked higher for this reactor. This was probably due to the fact that this process was slower under mesophilic conditions, and washout of biomass occurred for more parameter settings. The maximum growth rate of the acetoclastic methanogens was therefore ranked high for the VFA and carbonate concentrations, which was not the case in the thermophilic reactor. The acetoclastic methanogenesis is important for the reactor stability; these results therefore indicate that the stability for the mesophilic Västra Hamnen household waste digester should be lower than for the thermophilic Aalborg household waste digester. However, this finding could not be reasonable since the opposite is known by experience. The drawback of this method for a poor precision of the parameter distributions is exposed again, and it is clear that the results need to be evaluated before conclusions are drawn. Table 19 Results from SA of model parameters for the Västra Hamnen household waste simulation
Parameter at 35 °C
Mean
Unit
µmax7 KIH,58 KINH3,7 kLaCO2 kH
0.37 5e-4 17 200 0.2
d-1 mol/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 2 0.78 4 0.86 3 0.78 17 1.00 1 0.21
Sensitivity (VFA) rank relative 1 0.09 3 0.52 2 0.14 20 1.00 6 0.88
53
Sensitivity (NH4-N) rank relative 2 0.98 5 0.99 3 0.98 24 1.00 1 0.024
Sensitivity (HCO3) rank relative 1 0.41 5 0.81 2 0.47 21 1.00 3 0.65
10.3. Sjölunda sludge experiment 10.3.1. Sensitivity of input parameters For the Sjölunda sludge, the uncertainty of the feed characterization method was unknown, and instead guessed standard deviations of 20 % were used (Table 20). The results from this SA were in other words less reliable than for the household wastes. Table 20 Results of SA, UA and variability of measured parameters for the Sjölunda sludge simulation Parameter at 35 °C
Mean
Unit
Uncertainty
Variability
Sensitivity (Gas)
Sensitivity (VFA)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank relative rank relative rank σ (%) rank σ (%) rank relative rank relative 12 TS 0.039 8 4 kg/kg 2.5S 0.99 5 0.99 3 0.99 7 1.00 0.53J 10 VS 0.75 13 10 g/TS 1.00 8 1.00 5 1.00 12 1.00 20U Soluble TS 0.3 2 8 1.00 12 1.00 6 1.00 5 0.99 20 U Protein 0.34 2 2 gCOD/gXS 0.97 1 0.46 1 0.43 2 0.78 U gCOD/gXS 20 Fat 0.45 2 13 1.01 4 0.97 13 1.00 4 0.98 gCOD/gXS 20 U Inert 0.05 2 3 0.98 6 0.99 12 1.00 6 1.00 2U pH 7.13 9 11 1.00 10 1.00 11 1.00 9 1.00 3 U mol/m 100 HCO3 12 1 5 0.99 3 0.90 4 1.00 1 0.69 NH4-N gN/m3 3L 45 7 12 1.00 9 1.00 8 1.00 10 1.00 Temperature °C 2U 0.6 34 9 9 1.00 13 1.00 10 1.00 11 1.00 U 2 Flow l/d 0 1.5 9 6 0.99 11 1.00 7 1.00 8 1.00 2U Pressure bar 0.9 1.02 9 7 0.99 7 1.00 9 1.00 13 1.00 20 U Degradability 0.6 gCOD/gCOD 2 1 0.13 2 0.48 2 0.60 3 0.81 S (SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Højlund Christensen, et al., 2003), H (Hansen, et al., 2007)
The most influential input parameters for the sludge simulation were the degradability and protein content (Table 20), which indicated that ammonia inhibition became important for high protein levels, and that the degradability of the substrate is fundamental to measure. The composition of the waste did not affect the gas flow as much as the degradability, which indicated that the characterization was less important to measure. The VFA are affected by the degradability, which could not be seen for the household wastes, probably because of the broadened intervals for the inputs. 10.3.2. Model parameter sensitivity The results of interest from the model parameter SA are presented in Table 21. The gas production was mostly dependent on the rate of the acetoclastic methanogenesis which implied that it was the rate-limiting process. One could suspect that the lower bound for the growth rate was too low and that this led to washout of bacteria. The degradability was so low that the biogas production could not be increased much by a faster hydrolysis in this range. For shorter HRT or higher degradability, the hydrolysis rate would be rate limiting and kH would have contributed more to the uncertainty of the result. The instability of the reactor led to a high sensitivity for all outputs to KINH3,7 and µmax7, parameters determining the ammonia inhibition and growth rate of acetoclastic methanogens. The scatter plot in Figure 28 shows that the frequency of reactor failure was higher for low values on µmax,7. Table 21 Results of SA of model parameters for the Sjölunda sludge simulation
Parameter at 35 °C
Mean
Unit
µmax7 KINH3,7 kH
0.37 17 0.2
d-1 gN/m3 d-1
Sensitivity (Gas) rank relative 1 0.19 2 0.53 6 0.94
Sensitivity (VFA) rank relative 1 0.25 2 0.54 26 1.03
54
Sensitivity (NH4-N) rank relative 1 0.38 3 0.60 2 0.60
Sensitivity (HCO3) rank relative 1 0.24 2 0.51 27 1.03
Gas production rate [m 3/d]
0.02
0.015
0.01
0.005
0
0.2
0.3
0.4 µ max7 [d
0.5
-1
]
Figure 28 Gas production rate vs. µmax from MC simulation with varying model parameters
10.4. Aalborg household waste experiment with general characterization In this case the same reactor settings were used as for the previous simulation on Aalborg household waste, but with the general feed characterization from section 8.3. The distributions for the characterization variables hence reflect the variability of the parameters when collected from different sites. The previous SA investigated the relative decrease in output uncertainty that would be achieved if the characterization variables were determined without measurement errors. In this case, the SA is conducted to analyze the output uncertainties if no characterization measurements were made at all. The SA methodology is the same as in previous sections, but with other means and standard deviations for the characterization. It should be noted that the variability of the fractions are caused both by real variability in the waste, but also by measurement errors. 10.4.1. Sensitivity of input parameters The results from the SA with varying input parameters are presented in Table 22. When throwing a glance at the results, it may first seem like the starch was a more important fraction of the substrate than the other constituents. But it can also be seen that the starch content in the waste had a high variability, and consequently the high values for starch would increase the degradability of the waste. This was a consequence of the determination of degradable fraction from the sum of protein, carbohydrates, fibers and fat. The increased uncertainty for the biogas production seen in 8.3. for the unmeasured substrate can in fact be explained by the varying degradability of the waste. When plotting the gas production as a function of degradablility, this relationship is clearly shown (Figure 29). The protein content of the feed was not very variable and does not affect the biogas production as much, but had an impact on the concentrations of VFA, ammonium and alkalinity, three parameters that are of major importance for the reactor stability.
55
Table 22 Results of SA, UA and variability of measured parameters for the general thermophilic household waste simulation Parameter at 35 °C
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.14 0.15 0.14 0.06 0.15 0.19 7.4 10 160 48.7 34.3 55.3 1.33 1.02
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Variability
Sensitivity (Gas)
Sensitivity (VFA)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank 5 6 1 4 2 2 6 6 6
rank 1 7 6 3 2 4 -
rank 5 10 7 4 3 1 2 14 11 13 15 12 9 8 6
rank relative 8 0.98 5 0.95 1 0.60 10 1.00 6 0.96 4 0.88 7 0.96 14 1.00 3 0.77 11 1.00 15 1.00 13 1.00 2 0.66 12 1.00 9 0.99
rank relative 2 0.96 7 0.99 1 0.13 5 0.99 4 0.98 3 0.96 6 0.99 12 1.00 10 1.00 8 1.00 11 1.00 13 1.00 15 1.00 9 1.00 14 1.00
rank relative 4 0.98 3 0.94 2 0.70 8 1.00 6 0.99 5 0.99 7 0.99 11 1.00 1 0.39 13 1.00 12 1.00 10 1.00 15 1.00 9 1.00 14 1.00
σ (%) 2.5S 2U 100 U 3L 10 U 10 U 2U 2U 2U
σ (%) 59.7B 9.2H 12.0H 33.3H 50H 20.0H -
relative 0.96 1.00 0.98 0.92 0.85 0.55 0.83 1.00 1.00 1.00 1.00 1.00 0.99 0.98 0.97
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Højlund Christensen, et al., 2003), H (Hansen, et al., 2007)
0.06
Gas production [m3/d]
0.05 0.04 0.03 0.02 0.01 0
0
0.1 0.2 0.3 0.4 0.5 0.6 Non-degradable fraction of TS Figure 29 The gas production vs. the degradability of the substrate from the simulation of the Aalborg household waste with general characterization
10.4.2. Model parameter sensitivity kH is still the highest ranked model parameter, and in general it seems that the broadened distributions of the feed fractions has no significant impact on the sensitivity for the parameters (Table 23). It could be expected that the broader span for the protein could increase the importance of the ammonia inhibition constants for the VFA, but this was not the case. Instead, the decay rate for the propionate degraders turned out to be more important. The amount of propionate depends on the amount of sugars and proteins; fat does not lead to propionate production in the model. When the span of sugars and proteins are broadened, the propionate production is increased, and the slow process of propionate degradation becomes even more important for the total VFA concentration than it already was for the measured characterization. Another interesting difference is the increased sensitivity for KIH2,6 (the half saturation concentration for H2 inhibition of propionate degradation) which means that the thermodynamics of the process is affected by the variable substrate. The hydrogenotrophic methanogenesis (process 8) is affected if the fat content is too high and the hydrogen level is increased, or if the growth rate of the bacteria is too low. This can also be seen in the SA, as the sensitivity for µmax8 and KIH,58 are increased as well.
56
Table 23 Results of SA of model parameters for the general thermophilic household waste simulation
Parameter at 35 °C
Mean
Unit
µmax3 µmax5 µmax6 µmax7 KIH2,6 kH
4 0.6 0.6 0.37 1 0.34
d-1 d-1 d-1 d-1 mgCOD/m3 d-1
Sensitivity (Gas) rank relative 19 1.00 2 0.98 4 0.98 8 0.98 9 0.98 1 0.04
Sensitivity (VFA) rank relative 26 1.01 16 1.00 1 0.34 6 0.68 5 0.65 14 0.98
Sensitivity (NH4-N) rank relative 2 0.98 17 1.00 9 0.99 12 1.00 14 1.00 1 0.08
Sensitivity (HCO3) rank relative 16 0.99 14 0.98 3 0.78 2 0.72 8 0.88 1 0.58
10.5. Västra Hamnen household waste experiment with general characterization 10.5.1. Sensitivity of input parameters This SA was conducted using the same characterization as in the previous example, but with operational settings as in the Västra Hamnen household waste simulation (mesophilic). The results (Table 24) show that the ranking of the parameters remains mainly unchanged compared to the Aalborg household waste reactor. The same pattern can be observed for the gas production, but the sensitivity for the VFA is slightly altered and the importance for the protein is higher than in the thermophilic reactor. Table 24 Results of SA, UA and variability of measured parameters for the general mesophilic household waste simulation Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.14 0.15 0.14 0.06 0.15 0.11 7.2 10 13.5 48.7 34.3 35.4 1.33 1.03
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Variability
Sensitivity (Gas)
Sensitivity (VFA)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank 5 6 1 4 2 2 6 6 6
rank 1 6 5 3 2 4 8 7
rank 5 9 7 4 3 1 2 14 11 13 15 12 10 8 6
rank relative 8 0.96 4 0.90 1 0.38 11 1.00 6 0.94 3 0.81 7 0.94 15 1.00 2 0.70 12 1.00 14 1.00 13 1.00 5 0.91 9 0.98 10 1.00
rank relative 3 0.96 5 0.98 1 0.17 7 0.98 4 0.98 2 0.94 6 0.98 12 1.00 15 1.00 10 1.00 11 1.00 13 1.00 9 1.00 8 1.00 14 1.00
rank relative 5 0.99 3 0.93 2 0.72 8 1.00 6 0.99 4 0.98 7 0.99 12 1.00 1 0.39 13 1.00 14 1.00 11 1.00 10 1.00 9 1.00 15 1.00
σ (%) 2.5S 2U 100 U 3L 10 U 10 U 2U 2U 2U
σ (%) 59.7B 9.2H 12.0H 33.3H 50H 20.0H 1.4A 1.6A
relative 0.96 0.99 0.98 0.92 0.84 0.54 0.83 1.00 1.00 1.00 1.00 1.00 1.00 0.98 0.97
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Højlund Christensen, et al., 2003), H (Hansen, et al., 2007)
10.5.1. Model parameters As for most other cases, kH stands out as the first parameter to be calibrated (Table 25). This can be seen by the much lowered variances in the gas production, ammonium and alkalinity. If kH is varying, the VFA will have more extreme values than if it is kept constant (relative sensitivity >1), the same applies for the KSac. The reason for these odd values could be the extreme values for VFA that are produced by some combinations. It is also possible that the VFA have not converged to the steady state values during the simulation time.
57
Table 25 Results of SA of model parameters for the general mesophilic household waste simulation
Parameter
Mean
Unit
µmax7 kd13 KIH,58 KINH3,7 kH
0.37 0.05 5e-4 17 0.34
d-1 d-1 mol/m3 gN/m3 d-1
Sensitivity (Gas) rank relative 4 0.87 3 0.87 2 0.86 5 0.87 1 0.19
Sensitivity (VFA) rank relative 1 0.44 4 0.52 2 0.45 3 0.52 26 1.12
Sensitivity (NH4-N) rank relative 3 0.98 2 0.97 5 0.98 4 0.98 1 0.06
Sensitivity (HCO3) rank relative 2 0.72 5 0.77 3 0.76 4 0.76 1 0.52
10.5. Discussion on SA As discussed earlier, using spans of ± 50 % when varying model parameters produces misleading results. The ranges of variability for the model parameters were not available, and a realistic uncertainty or sensitivity analysis was not feasible to conduct within this project. Although the quality of the SA results may be disputable, it could still give interesting information on the system. For example: even if the relation between the importance of input and model parameters may be incorrect, the difference in this relationship can still be compared for different modes of operation, for example mesophilic and thermophilic conditions. In the results from the uncertainty analysis it was revealed that the outputs were affected differently by the changes in input data. The SA could provide some clues on what one should measure to reduce uncertainty but also give a deeper understanding of the process and of the mathematics of the model. Nonetheless, it was clear that the method was useful to find interesting parameters but it needed to be supplemented with scatter plots to avoid false conclusions from the results.
10.6. Summary of the SA The most important findings from the SA were: •
The hydrolysis rate constant kH and the degradability are important input parameters for the biogas production for the household waste digesters.
•
In the Sjölunda sludge digester, the degradability of the substrate was so low that the hydrolysis constant was unimportant for the studied HRT.
•
The VFA concentration is much more affected by the model parameters linked to propionate degradation and acetoclastic methanogenesis than by the input parameters.
•
The sensitivities for the parameters differ between a mesophilic and thermophilic digester; the model parameters are more important for the gas production in a mesophilic digester.
•
If the protein content in a household waste is not measured, this contributes to the uncertainty for the ammonium, VFA and alkalinity.
•
The SA method can give some information on which parameters are suitable for calibration, but it is important to consider reasonable distributions of the model parameters and to study scatter plots before performing a calibration based in the SA results.
58
11. Calibration of the model parameters In this part of the thesis, some parameters are calibrated to improve the fit of model predictions to data. The calibration is made for the pilot scale simulations for which sensitivity analysis was conducted in the previous section. The results from the SA will be used for choosing suitable parameters for calibration of different output variables. As far as possible, changes in the parameterization are motivated with a physical explanation.
11.1. Method for calibration Most of the calibrations were conducted by minimizing the sum of absolute errors for model predictions, θi, compared to measured data (eq. 11.1). The sums of absolute errors were simply plotted as functions of the calibration variable, and the calibration value for which the error function was minimized was chosen. Compared to using optimizers in Matlab such as fmincon and fminsearch this method has lower precision, but it is faster, and gives a graphical presentation of the error which makes it easier to avoid local minimums as solutions. The magnitude of the error and non linear behaviors are also revealed with this method. The startup phases of the pilot scale reactors on household waste were not stable, and were therefore excluded when performing the calibration. ∑
,
(11.1)
,
The first step in the calibration procedure for the Västra Hamnen household waste and Sjölunda sludge simulations was to calibrate the alkalinity of the feed. This was done first of all, because the sensitivity analysis showed that the reactor alkalinity was sensitive to this parameter, and because it is immeasurable in these types of wastes. Many processes in the digestion involve uptake and production of alkalinity, and it would not be desirable that the lack of calibration for inflow alkalinity affected the calibration of other parameters. For the Aalborg household waste, this method could not be applied since the dependency between the alkalinity and the VFA needed to be considered. The VFA were sensitive to the inflow alkalinity while the alkalinity in the digester was sensitive to the parameters in propionate degradation and acetoclastic methanogenesis which are important for the VFA concentration. It was thus impossible to calibrate the parameters apart from each other; a numerical method for minimizing the errors for several parameters at a time was required here. An optimization with fminsearch was therefore conducted. The same relation existed for the Västra Hamnen household waste simulation but in that case it did not cause a problem in the calibration because the alkalinity in the reactor was much too high compared to the measured values. If the calibrations were conducted simultaneously, the alkalinity in the inflow would still need to be reduced substantially. The other model parameters to be calibrated differed from case to case, but for all cases the biogas production was an interesting output parameter to include in the calibration process, e.g. for calibration of kH. In the sensitivity analysis, it was concluded that the VFA concentration mostly depended on the parameters connected to the propionate degradation and the acetoclastic methanogenesis. These parameters were calibrated to minimize the sum of errors for VFA predictions.
59
11.2. Aalborg household waste experiment 11.2.1. Hydrolysis constant kH The SA showed that kH was more important for determining the gas production, alkalinity and ammonium concentration than any of the other model parameters. It was not calibrated from batch experiment, but assumed to be the same as for the Västra Hamnen household waste and was therefore an interesting candidate for calibration. Due to the high relative error for ammonium, it would have had a major impact on the optimization if it was included in the objective function for the calibration. A trial to calibrate kH from the ammonium measurements only revealed that the kH would have to be so low that the hydrolysis almost stopped to lower the error for ammonium. It was therefore concluded that the relative error for ammonium cannot be reduced by calibration of kH. The gas production, on the other hand, the most economically important output, could probably be used successfully to calibrate kH . It was therefore chosen as output for the calibration. The result (Table 26) showed that the former value which was determined by experiments should be reduced slightly to improve the model fit to the data. 11.2.2. Protein content The deviation from the measured values for the simulation of ammonium is problematic since ammonia is important for inhibition of propionate degradation and acetotrophic methanogenesis. kH could not be used in the calibration, since it was calibrated from the gas production rate, although it was the most important parameter for the ammonium concentration. This means that either the protein measurement was unsuccessful, or the hydrolysis model could not describe the degradation of protein properly. For the ammonium to correlate with the measured values, the protein content in the feed would have to be 9 % on a weight basis instead of the measured value 17 % (Table 26). It is unlikely that the measurement of protein would deviate so much from the real value. A more plausible explanation is that the protein was hydrolyzed slower than the other fractions in the substrate, but to include this in the model, an alteration of the hydrolysis model would be required. Throughout this work, however, a fixed model structure was used, and in the further calibration the calibrated value for protein content was used instead. This was used because it is important to have reasonable values of ammonium to calibrate the processes that are affected by ammonia inhibition. To compensate for the error in inflow COD as the protein content is reduced, the weight was added to the sugar content in order to retain the biogas production. 11.2.3. Parameters for propionate degradation, acetotrophic methanogenesis and inflow alkalinity Both the VFA and the alkalinity were sensitive to µmax7, µmax6 (growth rates of propionate degraders and acetotrophic methanogens) and KINH3,6, (inhibition constant for propionate degradation). The SA thus indicated that these parameters could be used for calibration of these outputs. However, as discussed in 10.1.2 the high sensitivity to these parameters was mainly due to a frequent washout of bacteria when these parameters reached extreme levels. When trying to calibrate the VFA using growth rates, the result showed that the fit to the measured values only could be improved slightly, and that instability occurred when changing the values further. A better result was achieved when calibration with half saturation constants instead, which were calibrated by Siegrist et al. by measuring propionate and acetate for different HRTs in a mixed sludge digester. The fit to data could be improved more in this case, but the changes in parameter values were high for optimal fit. In Figure 30, a comparison between a calibration of VFA with µmax7 and KS,ac is shown. When increasing the 60
7000
7000
6000
6000 Sum of absolute errors
Sum of absolute errors
half saturation constant, the Monod kinetics produces the same reaction rate at a higher substrate concentration. Thus, the gas production should not be affected from the calibration, which made the calibration process less complicated.
5000 4000 3000 2000 1000 0
5000 4000 3000 2000 1000 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0
50
100
150
200
250
KSac
µ max7
Figure 30 Example of calibration of VFA using µmax7 (left) and KS,ac (right)
VFA needed most calibration for the household waste experiments. It is possible that the accessibility of the substrate for the propionate degraders and acetotrophic methanogens was lower for the household waste digester, which could give a physical explanation for calibrating KS,pro and KS,ac. For the Aalborg household waste simulation both parameters were first calibrated independently with the graphical method, and it was seen that they should be increased many times to lower the error for the VFA, to 220 and 240 g COD/m3 respectively. The shape of the curve for the total VFA was more similar to the measured values for the calibration of KS,ac than for KS,pro, which means that KS,ac probably is altered more than KS,pro for the substrate. It was thus decided that KS,pro should be set to 100 g COD/m3 and that calibration of KS,ac should account for the rest of the output error. As was discussed in 11.1., the inflow alkalinity and VFA are correlated and must be calibrated simultaneously. With the start guesses 180 g COD /m3 for KS,ac and 30 mol/m3for SHCO3, the optimizer fminsearch converged well, but the results (Table 26) differed much from the values suggested by Siegrist et al. (2002). The half saturation concentration for acetate would have to be increased more than six fold to minimize the error. On the other hand, it has been seen in calibration of ADM1 that the half saturation constants for propionate and acetate uptake were 297 and 582 g/m3 respectively (Jeong, et al., 2005). The suggested values in ADM, 100 and 150 (Jeong, et al., 2005) were also much higher than the values in the Siegrist model. The substrate uptake rate in ADM1, which is equivalent to the maximum growth rate parameter in the Siegrist model has been shown to be important and was calibrated to much lower values by Tartakovsky et al. ( 2008). This indicates that the uptake rate of VFA is variable, Tartakovsky, et al., (2008) suggested that the content of intert material in the substrate could affect the the mass transfer. The resulting VFA levels after calibration (Figure 32) shows that the steady state concentration could be modeled, but that the fit to data in the start-up phase was poor.
61
Table 26 Values for former and calibrated parameters for the Aalborg household waste simulation
Parameter
Unit
Former value
Calibrated value
Output θ
kH
d-1
0.20
0.15
Dry gas production
Protein content KS,pro for 35 °C
g/g TS g COD/m3
0.17 20
0.09 100*
Ammonium in reactor VFA in reactor
KS,ac for 35 °C
g COD/m3
40
260
VFA in reactor+ Reactor alkalinity
Inflow SHCO3
mol/m3
5
42
VFA in reactor+ Reactor alkalinity
*Assumed value
An important issue when calibrating the model was the problem with parameter identifiability which was discussed in section 6. There are many combinations of for example µmax6, kd,12, KS,pro and KINH3,6 that give the same reaction rate for the propionate degradation which means that a correct calibration is impossible. This problem could easily be dealt with by using one parameter at a time for the calibration, and that strategy was employed in this work. The alternatives would have been to make guesses for parameter combinations or simply to avoid calibrating these parameters. 11.2.4. Simulation results with calibrated parameters The gas production and methane content were not changed notably after the calibration (compare Figure 31 with Figure 4), and the start up phase was still not correlating well. Considering that the calibration was performed for the steady state phase, this was not surprising. The lower biogas production rate in the start-up phase was probably due to that the microorganisms were not adapted to the substrate, and lacked specific enzymes for the hydrolysis. When modeling a slower hydrolysis in the beginning, the measured gas production correlated better to measurements. An example of how this could be modeled iteratively is shown in Figure 34. The VFA were over predicted during the start-up with calibrated parameters, and the correlation for alkalinity was poorer (Figure 32). The calibration improved the correlation for ammonium and pH (Figure 33). 0.06
100
Biogas production modelled
CH4 m odelled
Biogas production measured
CH4 m easured
80
0.04 Percent [%]
Production rate [m3/day]
0.05
0.03 0.02
40
20
0.01 0
60
0
20
40 60 Time [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 31 Measured and simulated biogas production (left) and methane content (right) from continuous experiment with Aalborg household waste after model calibration
62
3500
80 VFAs m odelled
70
VFAs m easured Concentraion [mol/m3]
Concentration [g COD/m3]
3000 2500 2000 1500 1000 500 0
60 50 40 HCO3 m odelled
30
HCO3 m easured 20 10
0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 32 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with Aalborg household waste after model calibration 3500
8 NH4 m odelled
7
NH4 m easured
6
2500
pH m odelled 5
pH m easured
2000 pH
Concentration [g N/m3]
3000
4
1500 3 1000
2
500 0
1 0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 33 Measured and simulated ammonium concentration and pH from continuous experiment with Aalborg household waste after model calibration 0.06
0.16 Biogas production m odelled
0.14
Biogas production m easured
0.12 0.04
0.1 k H [d-1]
Production rate [m3/day]
0.05
0.03
0.08 0.06
0.02
0.04 0.01 0
0.02 0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 34 Measured and simulated biogas production (left) with kH increased stepwise as in the figure to the right
63
11.3. Västra Hamnen household waste experiment 11.3.1. Inflow alkalinity As seen in section 7.4.3., the simulated alkalinity during the steady state operation was too high. The calibration of inflow alkalinity showed that it should be as low as possible, but even if it was set to zero, large errors remained. The calibration was hence not successful, and other possible calibration parameters were examined. The calibration of the reactor alkalinity was however considered good enough since the deviations were small enough to have only minor impact on the result. It was clear that the variations in alkalinity could not be modeled very well; the UA showed that the uncertainty of alkalinity is high which means that detailed calibration is impossible. 11.3.2. Hydrolysis constant kH It was revealed in the SA that kH had a significant impact on both the gas production and on the ammonium concentration in the reactor. Only the error in gas production was used for the calibration, however, since this parameter was prioritized because of the stronger correlation to the other processes in the system. If both the gas production and ammonium levels in the reactor were to be calibrated, the model would have to be expanded to include an individual hydrolysis constant for particulate protein, as discussed for the calibration of the Aalborg household waste simulation. It turned out that the value used previously in the simulations gave the best fit to data (Table 27), which showed that the batch experiment produced a reasonable value. The value for the hydrolysis rate constant when calibrating the ammonium levels was low (kH = 0.02), which indicated that the degradation of the protein fraction of the particles was ten times slower than the other constituents. 11.3.3. Protein content of feed The ammonium concentration in the reactor was also dependent on the protein content of the feed, and could be calibrated with this value. The value for protein content that gave the optimal fit to data was 10 % instead of 17 % of TS (Table 27). The measurements are not expected to be this poor for protein, thus indicating that it rather is the hydrolysis of protein that is slower. The result, however, had the same effect on the amount of degraded protein in the reactor, and hence the ammonia inhibition will be better modeled with this new value. The seven percent of particles that was withdrawn from the total degradable TS was added to the sugar fraction to compensate for the loss of degradable matter. 11.3.4. Half saturation constant for acetotrophic methanogenesis, KS,ac For calibration the VFA in the reactor, the sensitivity analysis indicated that the growth rate of aceticlastic methanogens and the inhibition of this process were suitable as calibration parameters. The high sensitivity could however be explained by the high rate of washout of bacteria, as discussed in the previous section. Using the half saturation constant Ks,ac turned out to be more successful, and is easier to motivate from a biological point of view, see 11.2.3. The required value for best fit to data KS,ac=190 (Table 27), was lower than the value calibrated for the Aalborg household waste. It could probably have been useful to calibrate more parameters than only one in this case, but this was not prioritized. 11.3.5. Simulation results with calibrated values The resulting simulation results are shown in Figure 35 - Figure 37. Compared to the first crude validation in 8.4., the gas production was more stable but otherwise not much changed. The correlation for ammonium was much better after the calibration of the protein content, but it can also be noted that the initial value probably was higher than the average in the Sjölunda sludge digester. The modeled VFA were variable, but the range of variation was 64
now closer to the measured values. It seemed that the drop in methane content in the gas could and pH not be reflected in the results after calibration. Table 27 Values for former and calibrated parameters for the Västra Hamnen household waste simulation
Parameter
Unit
Former value
Calibrated value
Output θ
Inflow SHCO3
mol/m3
10
0
Reactor alkalinity
-1
kH
d
Protein content of feed Ks,ac
g/g TS d-1
0.20
0.20
Dry gas production
0.17 40
0.10 190
Ammonium in reactor VFA in reactor
0.05
100 Sim ulated CH4
Measured biogas production
0.04
0.03
0.02
0.01
0
Measured CH4
80
Percent [%]
Production rate [m3/day]
Sim ulated dry biogas production
60
40
20
0
10
20 30 Tim e [days]
40
0
50
0
10
20 30 Tim e [days]
40
50
400
Concentration of HCO3 120
Sim ulated VFAs
350
Measured VFAs 100
300
Concentraion [mol/m3]
VFAs as acetate equivalents [g COD/m3]
Figure 35 Measured and simulated biogas production (left) and methane content (right) from continuous experiment with Västra Hamnen household waste after model calibration
250 200 150 100 50 0
80 60 40 20
Sim ulated HCO3 Measured HCO3
0
10
20 30 Tim e [days]
40
0
50
0
10
20 30 Tim e [days]
40
50
Figure 36 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with Västra Hamnen household waste after model calibration
65
1000
pH 8 Measured pH 7.5
600 pH
Concentration [g N/m3]
Sim ulated pH 800
7
400 Sim ulated NH4 m odelled 200
0
6.5
Measured NH4
0
10
20 30 Tim e [days]
40
6
50
0
10
20 30 Tim e [days]
40
50
Figure 37 Measured and simulated ammonium concentration and pH from continuous experiment with Västra Hamnen household waste after model calibration
11.4. Sjölunda sludge 11.4.1. Inflow alkalinity The inflow alkalinity was calibrated with the graphical method, and it was shown that the calibrated value was the same as the former used assumed value (Table 28). 11.4.2. Degradability In the sensitivity analysis, it was concluded that the gas production was more sensitive to the degradability of the substrate than to the model parameters connected to the acetoclastic methanogenesis and propionate degradation. Furthermore, the model parameters had already been calibrated while the ultimate degradability of the sludge was more or less assumed. It was thus decided to use the gas production to calibrate the degradability of the substrate. The result, (Table 28) is reasonable for mixed sludge. As seen in section 8, the measurement uncertainty of VFA is low, but the sampling uncertainty is probably more significant. The correlation for VFA concentration (Figure 39) was therefore considered to be good enough after the calibration of degradability; no further calibrations were needed for the parameters in propionate degradation and acetate methanogenesis. Table 28 Values for former and calibrated parameters for the Aalborg household waste simulation
Parameter
Unit
Former value
Calibrated value
Output θ
Inflow SHCO3
mol/m3
10
10
Reactor alkalinity
Degradability
gCOD/gCOD
0.60
0.72
Dry gas production
66
11.4.3. Simulation results calibrated parameters The resulting simulation results from the calibration of the Sjölunda sludge experiments are presented in Figure 38 - Figure 40. It can be seen that the calibration of degradability significantly improved the correlation for the gas production. Overall, the quality of the predictions is higher for the sludge than for the household wastes, which further emphasize the importance of parameter calibration for household wastes. For mixed sludge, however, these simulation results show that results with high accuracy can be achieved with only minor calibration if the characterization method of Siegrist, et al., (2002) is used. 0.05
100 Sim ulated CH4
Measured biogas production
0.04
0.03
0.02
0.01
0
Measured CH4
80
Percent [%]
Production rate [m3/day]
Sim ulated dry biogas production
60
40
20
0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
500 100
Sim ulated VFAs Measured VFAs
400
80 Concentraion [mol/m3]
VFAs as acetate equivalents [g COD/m3]
Figure 38 Measured and simulated biogas production (left) and methane content (right) from continuous experiment with Sjölunda sludge digestion after model calibration
300
200
100
0
0
20
40 60 Tim e [days]
80
100
60
Sim ulated HCO3
40
Measured HCO3 20
0
0
20
40 60 Tim e [days]
80
Figure 39 Measured and simulated VFA (left) and HCO3 concentrations (right) from continuous experiment with Aalborg household waste after model calibration
67
1500
8 Sim ulated NH4 m odelled
7 6 Sim ulated pH
1000
5 pH
Concentration [g N/m3]
Measured NH4
Measured pH
4 3
500
2 1 0
0
20
40 60 Tim e [days]
0
80
0
20
40 60 Tim e [days]
80
Figure 40 Measured and simulated ammonium concentration and pH from continuous experiment with Aalborg household waste after model calibration
11.5. Discussion on the calibration From the SA in section 10 it was concluded that the most important output variable, the gas production rate, could be used to calibrate kH. In section 11, it was shown that the values of kH which were calibrated from batch experiments were good approximations. It was however impossible to get a good fit to data in the start-up phase for the Aalborg household waste simulation with a constant kH, indicating that the hydrolysis was slower before the microorganisms had adapted to the new substrate. When it came to the ammonium levels in the reactor, however, the only way to improve the fit to data with a fixed kH was to drastically change the protein content in the feed. It is unlikely that the measurements would be of such low quality. Furthermore, the mean protein content in the tested household wasted was 15 % (Table 22 in 10.4.), which is much higher than the values that were needed to achieve an acceptable correlation to the measurement. If the model is to be used successfully for household waste digestion, it is essential to calibrate the protein content with the ammonium concentration in the reactor or to extend the hydrolysis model. Both methods produce reasonable results, but the second option has a theoretical background and is therefore preferable. The hydrolysis description applied in ADM1 (Batstone, et al., 2002) includes different hydrolysis rate for all constituents, and could be used in further studies. The hydrolysis rate for protein would in that case be approximately ten times slower that the average particular organic component. For the Sjölunda sludge, the correlation of modeled ammonium to data was much better, but this was not surprising since the protein was calculated from the ammonium in the digester. It is possible that the real protein content in the mixed sludge was higher, which would mean that the hydrolysis of protein is slower in this case as well. A measurement of the protein in the Sjölunda sludge would confirm if this theory is likely. Another option is that the hydrolysis description in the model is less suitable for household waste than for mixed sludge. Household waste includes meat and other components with high protein content and may in other words be less available for hydrolysis than the protein in the mixed sludge. This can depend on the particle size which is affected by the pretreatment method, and on the protein characteristics. Protein in the primary sludge is readily available, and the protein in the WAS becomes available after cell lysis, together with the other substrates. As suspected in the first validation of the model (7.4.6. and 7.6.6.), the model parameters for the household wastes needed to be recalibrated to improve the correlation for VFA. The lack 68
of identifiability and the correlation between the parameters were however problematic for calibration of model and inflow parameters. It was concluded that the SA did not give the best calibration values, but that the half saturation constants was better suited for calibration purposes. As discussed in 11.2.3., half saturation constants of VFA seem to vary considerably for different substrates and it was not surprising that these parameters needed recalibration for household wastes. The VFA are thus less likely to be successfully modeled without calibration than other outputs, which was also indicated in the crude validation (7.3.3. and 7.4.3.). Since the sampling uncertainty is suspected to be high for VFA, it is also possible that the model results are more credible than the measurements if the measurements are slightly lower than the simulated values. However, as long as simulated VFA levels do not exceed levels that are inhibitory to the methanogenesis, the correlation for biogas will still be acceptable.
69
70
12. Industrial scale application In this section, the model will be used for evaluation of a full scale process at Käppala WWTP; various process designs will be assessed and discussed. A simple economical analysis is made to compare the economical benefits for the process designs.
12.1. Example with Käppala digesters Käppala WWTP which receives 500 000 p.e. has two mesophilic digestion chambers, R100 and R200 (Figure 2, section 7.2.1.). The primary sludge is digested separately in R100 to avoid filamentous bacteria clogging the upper part of the digester and causing reactor overflow. The digested primary sludge is mixed with the WAS in R200, for typical characteristics of the inflow and validation to data, see section 7.2.1. With the current setup the biogas production from R200 is low and it could possibly be improved with thermophilic temperature, different process design or pretreatment of the WAS. Experimental trials to compare different solutions would be both expensive and time consuming. Nonetheless, different alternatives for reactor setup and process variables can be tested on the full scale process, which has been done on some occasions. The drawback of such full scale experiments is that they are can be costly e.g. if the VS reduction is poor or if practical problems arise. Simulating different alternatives for process setups can be a useful tool for discovering possibilities and problems quickly and inexpensively. Several possibilities for the process are explored in this section, including thermophilic digestion and pretreatment of the WAS. Some parameters are not included in the model, like the dewaterability of the sludge, which will raise the costs for handling of the remaining sludge, or the amount of filamentous bacteria. The results can however be used to evaluate the potentials of the different setups. 12.1.1. Simulated cases A) Original design described in 7.1.2., mesophilic (35 °C)
The retention time for the primary sludge is very long for this design, 15+10 days while the WAS has a shorter retention time of 10 days. B) Original setup, thermophilic (55 °C)
The degradability in thermophilic digestion has proved to increase with 7.6 % compared to mesophilic digestion (Song, et al., 2004). A representative retention time for mesophilic digestion is 25 days, while it is about 15 days for thermophilic digestion. Consequently, the temperature dependency of kH (see 4.4) resulted in an increase for the WAS kH from 0.15 to 0.24 d-1, and 0.4 to 0.65 d-1 for the primary sludge kH. The digester volumes and thus retention times were kept constant. C) The digesters in series, mesophilic (35 °C)
For this case, the sludge is mixed and flows first into R100 and then R200 (Figure 41). The total retention time for the primary sludge is reduced in this case, from 25 to 20 days total but it is increased for the WAS from 10 to 20 days total. D) The digesters in series, thermophilic (55 °C)
The same reactor design as in case C is used, but with thermophilic temperature 55 °C. The degradability and kH are the same as for case B. E) The digesters in series, enzyme addition mesophilic (35 °C)
Sludge pretreatments have been proved to increase the gas production significantly as discussed in section 2.5. Many treatment methods require expensive investments in 71
form of vessels, heat exchangers, pumps etc. Enzymatic treatment has the advantage of low investment costs; the enzymes are simply poured into the digester. The solubilisation and degradability of the primary sludge are not notably improved by enzyme addition; the substrate is already highly degradable and hydrolysable. The WAS, on the other hand, is not readily degradable unless the EPS are degraded (Recktenwald, 2008). Solubilisation of WAS with a dose of 60 mg/g TS increased to 0.41 g SCOD/g TS (Wawrzynczyk, 2007); recalculated for the characterization of the WAS this means a solubilisation of 49 % on a COD basis. The degradability of WAS with enzyme pretreatment was calculated from the increased methane production from batch tests, which increased with 60 % (Wawrzynczyk, 2007). It should be noted that the enzymatic dose of 60 mg/L in the laboratory scale tests is significantly higher than the dose of 0.25 mg/L which is used for full scale processes (Recktenwald, 2008). The laboratory scale data was used due to lack of known input variables for full scale digesters with enzymatic pretreatment. F) One reactor with the volume VR100+ VR200 In many WWTPs, there is only one digester in which both the primary sludge and WAS are digested (Figure 42). The total retention time is 20 days for both flows, the same as for case D.
Figure 41 Reactors in series, cases C, D and E
Waste activated sludge Primary sludge
To dewatering
R100+R200
Figure 42 The digester in case F
72
12.1.2. Method Data from 2007 for flows and VS content of the primary sludge and WAS were used. All initial values and parameters for case A can be found in section 7.6. The allocation for calculating the characterization of the substrate and kH was made on a basis of mass VS of primary sludge and WAS into the reactor. 12.1.3. Results and discussion With thermophilic temperature, (cases B and D) the methane content in the gas is 3 percentage points lower than for the mesophilic cases (A and C), but it can also be seen that the methane production is increased with 9 percentage points compared to mesophilic digestion (Table 29). Enzyme addition is also an effective measure to improve the methane production, an increase of 11 % was reached compared to the first case. The methane production in the single digester (case F) is the lowest; 5 % lower than for case A. The increase of ammonium for the thermophilic digesters compared to the mesophilic is small, only 100 and 200 g COD/m3 for case B-A and D-C (Table 30). The risk for ammonia inhibition, however, increases more compared to the mesophilic cases and it was seen that the inhibition was more important in case D than case C. The alkalinity was mainly unaffected by the temperature (compare case A-B and C-D) but varied for different process designs (compare A-B and C-D). The enzymatic treatment in case E increased solubilization which led to a fast acidogenesis and high concentration of VFA (Table 30). Although the concentration reached over 3000 g COD/m3, the gas production was still high, this indicated that VFA inhibition was not a substantial problem for the gas production (Table 29). Furthermore, it is worth noting that the VFA concentrations for cases A and B are similar in R100 and R200, while the VFA level is higher in R100 when the digesters are run in series (cases C and D). The thermophilic cases B and D showed higher VFA concentration than the mesophilic cases A and C. The total COD reduction could be increased 3 percentage points compared to case A by running the process in series, and 7 percentage points by introducing thermophilic digestion (Table 30). Enzymatic treatment and thermophilic digestion in series give the highest VS reduction, 0.64 and 0.65 respectively. Table 29 Biogas production for R100 and R200 with different process designs for 2007 Total Total Total Mean Case Total dry gas methane methane methane dry gas R200 R100 R200 content R100 in dry gas [106 m3] [106 m3] [106 m3] [106 m3] Original setup, A 5.1 1.1 3.2 0.79 0.64 B, 55 °C 5.9 1.3 3.5 0.83 0.61 C, series mesophilic 5.6 1.6 3.2 0.97 0.58 D, series thermophilic 6.8 1.4 3.7 0.78 0.55 E, Enzyme treatment, series 5.9 1.8 3.3 1.1 0.57 F, one digester 6.6 3.8 0.58
73
Total dry gas production in R100 and R200 [106 m3]
Total methane production [106 m3]
Relative change in total methane production
6.3 7.2 7.2 8.2 7.7 6.6
4.0 4.3 4.2 4.5 4.4 3.8
0% 9% 5% 14 % 11 % -5%
Table 30 Process variables for R100 and R200 with different process designs Mean Mean Mean Mean VFA Case Mean NH4-N HCO3 HCO3 R100 NH4-N R200 R100 R200 R100 Original setup, A B, 55 °C C, series mesophilic D, series thermophilic E, Enzyme treatment, series F, one digester
Mean VFA R200
[g N/m3]
[g N/m3]
[mol/m3]
[mol/m3]
[g COD/m3]
[g COD/m3]
Total COD reduction after R100
1100 1200 1400 1600 1600 1500
1300 1400 1600 1800 1800 -
68 71 80 92 8 94
87 88 110 110 200 -
66 200 780 870 3500 580
49 220 170 330 1800 -
0.30 0.38 0.45 0.54 0.50 0.53
Total COD reduction after R200
0.56 0.63 0.59 0.65 0.64 -
It is common in WWTPs to run the digesters in parallel instead of series to facilitate the control of the process, but it can be seen that this is not the best process design if increased gas production, VS degradation and stabilization is the goal (Table 29 and Table 30). Apparently, the process rates are increased with serial digestion. This is due to higher concentrations of the substrates in R100 than in a single digester where the feed is more diluted. The substrates are more easily available for the biomass, and the substrate uptake rate is increased. Although the retention time for R100 in the case of serial operation (C) is half of the retention time with one big digester (F), it can be seen in Table 29 that the biogas production in R100 for case C is much higher than half than for case F. It is understandable that many WWTP prefer parallel digestion, but it could be preferable to implement serial digestion with improved process control. Enzyme addition was beneficial for increasing the VS degradation and methane production, but resulted in a high VFA concentration which could lead to inhibition of the methanogenesis and propionate degradation (case E). The VFA increased during the winter due to the higher production of WAS, and the total effect from the enzyme addition became more pronounced. Problems with high VFA levels could be avoided if the dose of enzymes was adapted to the amount of WAS, or if the active volume was increased. However, the dose of enzymes used in the simulation was, as mentioned, too high to be economically defendable. If enzyme addition was introduced, the dose would be significantly lower and the VFA concentrations would not reach the levels shown in (Table 30). The drawback of a lower dose could be that the methane production would not be increased as much as the 11 % for case E. The effect from enzyme dosing is also dependent on the sludge characteristics, e.g. ratio municipal/industrial waste water, sludge genesis, season and sludge age. In order to evaluate the process with enzyme dosing with less uncertainty, experimental results of the sludge from Käppala would be needed. The literature values used for case E in this simulation produce results that are less credible than for the other cases.
12.2. Economical evaluation 12.2.1. Method A simple economical analysis of the results from section 12.1. was conducted for the quantification of the economical benefits for the process designs. The cost for investments and running costs for the processes would be dependent on the individual factors for the WWTPs and were not included here. A switch from mesophilic to thermophilic digestion may for example require new heat exchangers in some cases, and the cost depends on the reactor configuration. The fee for the handling of the dewatered sludge and the income from selling the methane gas are similar for all WWTP in Sweden and were therefore included in the economical analysis. 74
The fee for handling of the sludge is 300 SEK per m3, and considering the amounts of sludge produced each year this is a significant cost for the WWTPs. After dewatering, the TS content is stable at around 25 % and the total amount sludge can therefore be calculated from the mass of TS out from digester R200. In this case the VS reduction is assumed to be equal to the COD reduction shown in (Table 30), and the outgoing VS is simply calculated from the total influent mass of VS. Total amount of ashes out from digester R200 during the year is calculated from the data of TS and VS in incoming flows (equation 12.1), and summarized with outgoing VS for each case. The total outgoing TS is transformed to a volume assuming that the densities of the dewatered sludge and water are 1 ton/m3. The WWTP sells the methane gas for 5 SEK /m3 in these calculations.
∑
∑
1.61 · 10
1.25 · 10
3.58 · 10
(12.1)
12.2.2. Results and discussion For cases B-E, it is possible to earn and save money if the yearly costs for investments and continuous expenses compared to case A are lower than the total change shown in the outmost right column (Table 31). For case F, it is only possible if the expenses are lower than the total change compared to case A. It is less expensive to run a single digester with the double volume, but it is also associated with poorer mixing and heating due to the upscaling. For most WWTPs, it would probably be economically favorable to choose serial digestion. If the WWTP is equipped with several digesters run in parallel, it is both simple and inexpensive to convert the process. The economical benefit would be around 3 million SEK per year for a WWTP similar to Käppala (compare case C and case F). At Käppala WWTP, the problems with filamentous bacteria means that case A is chosen instead of case C. With improved control of the activated sludge process, Käppala could have applied serial digestion and saved 1.5 million SEK 2007 from reduced fees and increased income from biogas. The cost for changing from case A to C is practically zero. The most economically favorable option is thermophilic digestion in series, which would have spared Käppala 4 million SEK 2007, enzymatic treatment is next with 3.4 million SEK. A comparison between these measures would require a detailed analysis of the process at Käppala and of the costs for investments and maintenance. As mentioned before, the effect of enzyme addition on the Käppala sludge would need to be studied closer, the degradability and solubilization could be both lower and higher than the literature values. A lower enzyme dose would mean less effect, but the sludge at Käppala could be more or less suitable for enzymatic treatment than the sludge studied in the literature. It is however likely that the investment costs for enzymatic treatment are lower than for conversion to thermophilic digestion; the equipment for enzyme dosing is about 50 000 - 100 000 SEK depending on the reactor configuration (Recktenwald, 2008). Improved heat exchangers, revetment of the reactor and new pumps which could have been required for thermophilic digestion are expensive. Furthermore, thermophilic digestion has the drawback of being less stable than mesophilic digestion, which means that the risk for expensive process failures is higher.
75
Table 31 Change in cost for sludge handling and income from methane production for the cases Income from Outgoing Fee for Total change Case Outgoing methane volume of sludge compared to mass of TS production handling sludge case A compared to compared to case A [103 m3/yr] case A [106 kg /yr]
6
[106 SEK /yr]
[106 SEK /yr]
0 1.8 1.0 2.7 2.2 -1.1
0 2.9 1.5 4.0 3.4 -1.5
[10 SEK/yr] A Original setup, B, 55 °C C, series mesophilic D, series thermophilic E, Enzyme treatment, series F, one digester
9.09 8.22 8.72 7.97 8.09 9.47
36 33 35 32 32 38
0 1.1 0.45 1.4 1.2 -0.45
The increase in income from selling the methane gas is higher than the savings from the sludge handling fee for all cases. The price for the gas is however variable and less predictable compared to the sludge handling fee which could make it hazardous to introduce expensive equipment with high continuous costs. Political decisions and public awareness of climate change are important to make the methane gas competitive compared to other alternatives and to enhance investments to increase biogas production. The economical analysis showed that there are many options for process design that could be economically beneficial if the investment and maintenance costs do not exceed the profit from decreased sludge handling fees and increased income. The model can be a useful tool to evaluate different process designs and choose interesting options for further investigations. It is of course still essential to perform pilot plant experiments, but the number of experiments could be reduced if the least appealing alternatives are sorted out after simulations. The process variables VFA and alkalinity give indications on the stability of the processes and a comparison between those can be useful when assessing the stability of the process. Unwanted side-effects of a process configuration can thus be found by simulations and not by expensive pilot plant experiments. Important variables, like the formation of mercaptans which causes odor problem and the dewaterability of the remaining sludge, are not included in the model. These neglected factors, and the problem with filamentous bacteria described above, could be affected by the alterations of the process. This needs to be taken into account when evaluating the simulation results.
76
13. Conclusions The first part of this dissertation was aimed at giving the reader a background of the process of anaerobic digestion, and to summarize the prior research in the field of modeling anaerobic digestion. It was stated that models have not been widely used in this field, and due to the complex microbiologic and physiochemical processes, they are difficult to parameterize and impossible to identify mathematically. For household waste experiments, it was possible to get accurate predictions of steady state gas production, but the correlation for ammonia was less satisfying. Simulations of the sludge experiment produced the opposite result. VFA concentrations were difficult to model in all three cases. In the household waste experiments, the inoculums were not adapted to the substrates. The startup phase before adaptation proved to be difficult to simulate with the current model structure. Validation of the model to the full scale process at Käppala proved to be successful, considering the lack of data for the feed characterization. It was shown in the uncertainty analysis that measurement errors could not be used to explain the discrepancy between the simulations and data. The output uncertainties when using a general characterization of household waste were significantly higher than when conducting measurements for gas production and ammonia, while VFA and alkalinity were less affected by input data. The global, variance based method chosen for the sensitivity analysis was useful for the inflow variables, but as the distributions of model parameters were unknown, the analysis needed to be supplemented with scatter plots to study the correlations between parameters and output. The results from the sensitivity analysis indicated that to determine the gas production, information of degradability and hydrolysis rate of the sludge were needed, in addition to the actual flows and sludge concentrations. The batch experiments used for determination of the hydrolysis rate constant proved to give reasonable values. For better precision for VFA predictions, the parameters connected to propionate degradation and acetoclastic methanogenesis were essential. A revision of the model structure is needed for a successful calibration of ammonium. In the model by Siegrist, particulate organic matter is lumped. To be able to calibrate the experiments on household waste digestion, a slower degradation of particulate protein would be required. To calibrate the VFA concentrations, the half saturation constants were changed substantially. This implies different mass transfer conditions than suggested in the model implementation by Siegrist et al. The model proved to be a promising tool for testing different process designs for a full scale process. The productivity could be improved by running the reactors in series, at thermophilic temperature and by implementing enzymatic pretreatment.
77
78
14. Suggestions for further research It was concluded that the degradability and hydrolysis rate are more important to measure than the individual constituents of a substrate, when it comes to prediction of biogas production rate. This could be due to the relative stability of the simulated systems, without significant problems with inhibited processes. It would be interesting to validate the model at more critical states, to evaluate the ability of the model to simulate reactor instability. The Siegrist model was primarily developed for modeling mixed sludge digestion. In this dissertation the model was applied on household waste digestion, but not without complications. A changed hydrolysis model would be required for this task, as in the more complex model ADM1. Further research is however needed to determine the hydrolysis kinetics and other process parameters for different wastes, as there is scarce information available in the literature. It was seen in the validation and SA of the household wastes that the precision for VFA correlation was poor and that a calibration of parameters connected to propionate degradation and acetoclastic methanogenesis was necessary to improve the model fit. It would be beneficial to increase the knowledge about the uptake rates for VFA; is it dependent of the fraction of inert material or particle size in the reactor or is it a related to the microbial species? If the relations between the parameters µmax, KS , and KI for propionate degradation and acetoclastic methanogenesis could be expressed as functions of the substrate characteristics, this would allow application of the model to various substrates without recalibration of these parameters. More research about the theoretical background for these parameters could therefore be valuable. It was shown in 11.2.4. that an upstart phase cannot be modeled well with the Siegrist model. Siegrist, et al., (2002) also stressed that a simulation of a transition between mesophilic and thermophilic digestion could not be performed with accuracy. An inclusion of a state variable describing the physiological state of the biomass may solve this problem. More research on this subject would be interesting, although it must be admitted that such a variable would be difficult and expensive to verify with measurements. More studies are required to specify the distributions of the model parameters. This would enable a more useful SA and it would be possible to get a better ground for allocation of resources to determine model parameters, and to deepen the understanding of the processes. In some cases, it could be used for simplification of the model if several parameters are proven to be irrelevant.
79
80
References Batstone, D. J. (2006). Mathematical modelling of anaerobic reactors treating domestic. Reviews in Environmental Science and Bio/Technology , 5, 57–71. Batstone, D. J. (2006). Mathematical modelling of anaerobic reactors treating domestic wastewater: rational criteria for model use. Reviews in Environmental Science and Bio/Technology 5:57–71 , 5:57– 71. Batstone, D. J., Keller, J., Angelidaki, I., Kalyuzhnyi, S. V., Pavlostathis, S. G., Rozzi, A., et al. (2002). The IWA Anaerobic Digestion Model No 1 (ADM1). 45, 65-73. Batstone, D., & Keller, J. (2003). Industrial applications of the IWA anaerobic digestion model No. 1 (ADM1). Water science and technology , 47, 199-206. Batstone, J., Keller, J., & Steyer, J. P. (2006). A review of ADM1 extensions, applications, and analysis: 2002-2005. Water Science and Technology , 54, 1-10. Bernard, O., Polit, M., Hadj-Sadok, Z., Pengov, M., Dochain, D., & Estaben, M. (2001). Advanced monitoring and control of anaerobic wastewater treatment plants: software sensors and controllers for an anaerobic digester. Water Science and Technology , 43(7), 175-182. Blumensaat F, K. J. (2005). Modelling of two-stage anaerobic digestion using the IWA Anaerobic Digestion Model No. 1 (ADM1). Water Research , 39, 171–183. Buswell, E. G., & Neave, S. L. (1930). Laboratory studies of sludge digestion. Illinois Division of State Water Survey , Bulletin no. 30. Chen, Y., Jiang, S., Yuan, H., & Guowei, G. (2007). Hydrolysis and acidification of waste activated sludge at different pHs. Water Research , 41, 683-689. Davidsson, Å. (2008) Interview, August 6 Davidsson, Å. (2007). Increase of biogas production at wastewater treatment plants. Doctoral Disseration, ISBN 978-91-7422-143-5, Lund University. Elmitwalli, T., Sayed, S., Groendijk, L., van Lier, J., Zeeman, G., & Lettinga, G. (2003). Decentralised treatment of concentrated sewage at low temperature in a two-step anaerobic system: two upflowhybrid septic tanks. Water Science and Technology , 48(6), 219-226. Eskicioglu C, K. J. (2006). Characerization of soluble organic matter of wast activated sludge before and after thermal pretreatment . 40 (3725-3736). Gujer, W., & Zehnder, A. J. (1983). Conversion processes in anaerobic digestion. Water Science and Technology , 15 (8/9); 127-167. Hansen, T. L., la Cour Jansen, J., Spliid, H., Davidsson, Å., & Christensen, T. H. (2007). Composition of source-sorted municipal organic waste collected in Danish cities. Waste Management , 27; 510– 518. Hansen, T. L., Schmidt, J. E., Angelidaki, I., Marca, E., la Cour Jansen, J., Mosback, H., et al. (2003). Method for determination of methane potentials of solid organic waste. 24:4; 393-400. Højlund Christensen, T., la Cour Jansen, J., & Jørgensen, O. (2003). Datarapport om sammensætning og biogaspotentiale i organisk dagrenovation. Miljøstyrelsen (Danish Environmental Board). Højlund Christensen, T., la Cour Jansen, J., Kjems Toudal, J., & Gruvberger, C. (2003). Basisdokumentation for biogaspotentialet i organisk dagrenovation. Miljøprojekt Nr. 815, Miljøstyrelsen (Danish Environmental Board). Jeong, H.-S., Suh, C.-W., Lim, J.-L., Lee, S.-H., & Shin, H.-S. (2005). Analysis and application of ADM1 for anaerobic methane production. Bioprocess Biosyst Eng , 27; 81–89. Jeppsson, U. (1996). Modelling aspects of waste water treatment processes. Doctoral Disseration, ISBN 91-88934-00-4, Lund University.
81
Kops, S. G., & Vanrolleghem, P. A. (1996). An evaluation of Methodologies for uncertainty analysis in biological waste water treatment. Unknown publisher. la Cour Jansen, J., Gruvberger, C., Hanner, N., Aspegren, H., & Svärd, Å. (2004). Digestion of sludge and organic waste in the sustainability concept for Malmö, Sweden. Water Science and Technology , 49:10 163-169. la Cour Jansen, J., Spliid, H., Lund Hansen, T., & Svärd, Å. (2004). Assessment of sampling and chemical analysis of source-separated organic household waste. Waste Management , 24; 541-549. Minasny, B. (2004, 1 11). (reference from internet 2009-07-16 9.00 page creator Budiman Minasny, University of sidney). (The Mathworks) Retrieved July 16, 2008, from www.mathworks.com/matlabcentral: http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=4352&objectType=file Miron, Y., Zeeman, G., van Lier, J. B., & Lettinga, G. (2000). The role of sludge retention time in the hydrolysis and acidification of lipids, carbohydrates and protein during digestion of primary sludge in CSTR systems. Water Reserch , 34:5 1705-1713. Muller, T. G., Noykova, N., Gyllenberg, M., & Timmer, J. (2002). Parameter identification in dynamical models of anaerobic waste water treatment. Mathematical biosciences , 177; 147-160. Nielsen, J., Villadsen, J., & Lidén, G. (2004). Bioreaction Engineering Principles. Springer. Nilsson et al, I. (2007). Environmental biotechnology. Department of biotechnology, Lund University. P54, V. (1984). Enkla analysmetoder för driftkontroll vid avloppsreningsverk. Svenska Vatten- och avloppsverksföreningen. Recktenwald, M. (2008, November 3). Ingeneer, Kemira Recycling Competence Center in Helsingborg. Lund. Reith, J. H., Wijffels, R. H., & Barten, H. (2003). Status and perspectives of biological methane and hydrogen production. The Hague: Smiet offset. Rosen C, V. D. (2006). Implementing ADM1 for plant-wide benchmark simulations in Matlab/Simulink. Water Science & Technology , 54, 11–19. Siegrist, H., Vogt, D., Garcia-Heras, J. L., & Gujer, W. (2002). Mathematical model for meso- and thermophilic anaerobic sewage sludge digestion. Environmental Science and Technology , 36, 11131123. SIS. (1994). Bestämning av karbonatalkalinitet SS-EN ISO 9963-2. Standardiseringskommisionen i Sverige. SIS. (1981). Svensk Standard SS 02 81 13. SIS Standardiseringskommisionen i Sverige. Song, Y.-C., Kwon, S.-J., & Woo, J.-H. (2004). Mesophilic and thermophilic temperature co-phase anaerobicdigestion compared with single-stage mesophilic- and thermophilic digestion of sewage sludge. Water Research , 38, 1653–1662. VAV. (1981). Rötning av kommunalt slam, P42. Vatten- och avloppsverksföreningen (VAV) AB. Vavilin, V. A., Fernandez, B., Palatsi, J., & Flotats, X. (2008). Hydrolysis kinetics in anaerobic degradation of particulate organic material: An overwiev. Waste Management , 28; 939-951. Wawrzynczyk, J. (2007). Enzymatic treatment of wastewater sludge. Doctoral Disseration, ISBN 97891-628-7246-5, Lund University.
82
Appendix I
Process number
Matrix of stoichiometric coefficients T (with default values for ѵj,i): State variable (see table 2) SH SH2 SCH4 SCO2 1 2 3 4 1 0 0 0 0.0004 2 0 0.96 0 0.043 3 0 0.96 0 0.91 4 0 6.7 0 0.199 5 0 8.2 0 0.162 6 0 0 0 -0.006 7 0 -22 39 -0.353 8 0 0 21 0 9 0 0 0 0 10 0 0 0 0 11 0 0 0 0 12 0 0 0 0 13 0 0 0 0 14 -1 0 0 1 15 0 0 0 -1 16 0 0 0 -1 17 0 0 0 -1
SHCO3 5 -0.0005 -0.022 -0.07 -0.202 0.004 0.618 -0.006 0.003 0.003 0.003 0.003 0.003 0.003 -1 1 1 1
SNH4 6 0 0.587 -0.08 -0.08 -0.08 -0.08 -0.08 0.045 0.045 0.045 0.045 0.045 0.045 0 14 0 0
SNH3 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -14 0 0
Sac 8 0 3.29 3.29 14.3 10.8 -40 0 0 0 0 0 0 0 0 0 -64 0
Shac 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 64 0
Spro 10 0 1.42 1.42 0 -20 0 0 0 0 0 0 0 0 0 0 0 -112
Shpro 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 112
Saa 12 0.3 -6.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Ssu 13 0.2 0 -6.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Sfa 14 0.45 0 0 -22 0 0 0 0 0 0 0 0 0 0 0 0 0
Sin 15 0.05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Xs 16 -1 0 0 0 0 0 0 0.8 0.8 0.8 0.8 0.8 0.8 0 0 0 0
Xaa 17 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0
Xsu 18 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
Xfa 19 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0
Xpro 20 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0
Xac 21 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0
XH2 22 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0
Xin 23 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0 0 0 0
Conservation matrix with respect to mass conservation of theoretical COD (1), conservation of N/COD ratio or N/N ratio (2), charge per g of COD, N or mol (3) and mol of C/g of COD or mol:
cxzxcz
State variable 1 2 3 4
SH 1 0 0 1 0
SH2 2 1 0 0 0
SCH4 3 1 0 0 0.0156
SCO2 4 0 0 0 1
SHCO3 5 0 0 -1 1
SNH4 6 0 1 -1/14 0
SNH3 7 0 1 0 0
Sac 8 1 0 -1/64 0.0313
Shac 9 1 0 0 0
Spro 10 1 0 -1/112 0.0268
Shpro 11 1 0 0 0
I
Saa 12 1 0.1 0 0.029
Ssu 13 1 0 0 0.031
Sfa 14 1 0 -0.0012 0.0216
Sin 15 1 0.02 0 0.03
Xs 16 1 0.031 0 0.026
Xaa 17 0 1 0 0.03
Xsu 18 0 0 0 0
Xfa 19 1 0.08 0 0
Xpro 20 0 0 0 0
Xac 21 0 0 0 0
XH2 22 0 0 0 0
Xin 23 1 0.05 0 0.03
II
Appendix II Calculation of the Sjölunda sludge characterization %calculating the amount of CO2 in the carbonate system pH=7.14; H=10^-pH; %kmol/m3 HCO3m=4000/61000; %kmol/m3, the mean value in the digester at stable operation T=35+273; %K kHCO3=10^(6.53-2906/T-0.0238*T); %equilibrium constant CO2 to HCO3 kH2CO3=10^(14.82-3401/T-0.0327*T); %equilibrium constant HCO3 to H2CO3 kH=10^(-12.59+2198/T+0.0126*T); %henry's constant for CO2 pCH4=0.65; %bar, measured in reactor pCO2=1-pCH4; H2CO3=kH*pCO2 HCO3=kH2CO3*kH*pCO2/ HCO3 are alike CO3=HCO3*kHCO3/H
%The measured and calculated values for
moles_in_liquid=1.5*(H2CO3+HCO3+CO3) %moles of carbon in the carbonate system leaving the reactor 1.5 is the outtake volume moles_in_gas=(21.8e-3*pCO2)/(0.082e-3*(273+18)) %moles leaving as gas, caluclated from mean flow of gas and general gas law CO2tot=moles_in_gas+moles_in_liquid %moles leaving as gas and liquid CH4=(21.8e-3*pCH4)/(0.082e-3*(273+18)) %moles leaving as gas, caluclated from mean flow of gas and general gas law part_in_liquid=moles_in_liquid/(moles_in_liquid+moles_in_gas) realCO2fraction=CO2tot/(CH4+CO2tot) produced by the biomass from the substrate realCH4fraction=CH4/(CH4+CO2tot) produced by the biomass from the substrate
% The fraction of CO2 % The fraction of CH4
%Calculation of theroretical protein fraction from hansreudi method iN=0.1; %g N/g COD taken from the stoichiometric matrix SNH4=834; %mean value in reactor for stable operation %COD-reduction ds.VSred=ds.indata.ch.VS*0.45; ds.CODred=1e6*ds.VSred*1.9; 1e6 to get g/m3 XST=mean(ds.CODred); vaa=SNH4/(iN*XST)
%45 % reduction % amount of COD reduced, 1.9 gCOD/g VS and % mean value for reduced COD % calculation of protein content in feed
%values from Roediger et al.1967 from the book by VAV are used for the %methane fraction from different substrates. proCH4_fraction=0.68; fatCH4_fraction=0.7; suCH4_fraction=0.5; %calculation of fat content vfa=(-vaa*proCH4_fraction+suCH4_fraction*vaasuCH4_fraction+(pCH4/1))/(fatCH4_fraction-suCH4_fraction) vsu=1-vfa-vaa
III
IV
Appendix III Results from the sensitivity analysis Aalborg household waste Table III, 1 Results of SA, UA and variability on measured parameters for the Aalborg household waste simulation Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.23 0.17 0.18 0.07 0.18 0.11 7.4 10 160 48.7 34.3 55.3 1.33 1.02
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Variability
Sensitivity (Gas)
Sensitivity (VFAs)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank 12 2 14 9 3 10 8 13 1 11 4 4 13 6 6
rank 5 1 7 6 3 2 4 9 8
rank relative 1 0.74 8 0.98 10 1.00 6 0.95 4 0.88 7 0.97 9 0.99 14 1.00 11 1.00 13 1.00 15 1.00 12 1.00 5 0.90 3 0.87 2 0.78
rank relative 4 0.95 3 0.95 7 0.99 11 1.00 5 0.98 8 1.00 10 1.00 14 1.00 2 0.59 9 1.00 15 1.00 13 1.00 1 0.49 12 1.00 6 0.98
rank 1 3 2 6 7 9 11 14 4 5 13 15 12 8 10
rank relative 3 0.97 2 0.95 4 0.99 8 1.00 5 1.00 13 1.00 7 1.00 11 1.00 1 0.080 12 1.00 9 1.00 10 1.00 15 1.00 6 1.00 14 1.00
σ (%) 2.5S 20U 0.97J 3.5J 18J 3.4J 4.7J 2U 100 U 3L 10 U 10 U 2U 2U 2U
σ (%) 24.6B 59.7B 9.2H 12.0H 33.3H 50H 20.0H 1.4A 1.6A
relative 0.42 0.93 0.84 0.97 0.97 0.99 1.00 1.00 0.93 0.95 1.00 1.00 1.00 0.98 1.00
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Höjlund Christensen, et al., 2003), H (Hansen, et al., 2007)
Table III, 2 Results from SA on model parameters for the Aalborg household waste simulation
Parameter
Mean
Unit
µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.2
d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 1.00 14 1.00 16 0.99 2 1.00 24 1.00 7 1.00 5 1.00 17 1.00 18 1.00 4 1.00 13 1.00 23 1.00 11 1.00 15 1.00 21 0.99 3 1.00 22 1.00 6 1.00 8 1.00 25 1.00 10 1.00 12 1.00 19 1.00 9 1.00 27 1.00 26 1.00 20 0.019 1
Sensitivity (VFAs) rank relative 1.01 27 1.00 17 1.00 24 0.35 1 0.72 4 0.80 6 1.00 23 1.00 22 1.00 26 0.64 3 0.86 8 0.96 13 1.00 21 1.00 18 1.00 16 0.98 15 0.95 11 0.90 9 0.98 14 1.00 20 0.80 5 1.00 19 0.91 10 0.47 2 0.85 7 1.00 25 0.96 12
V
Sensitivity (NH4-N) rank relative 0.99 2 1.00 21 0.99 17 0.99 5 0.99 8 0.99 6 1.00 11 27 1.00 10 0.99 12 1.00 3 0.99 7 0.99 13 1.00 22 1.00 26 1.00 20 1.00 25 1.00 15 1.00 18 1.00 24 1.00 14 1.00 23 1.00 16 1.00 4 0.99 9 0.99 19 1.00 1 0.051
Sensitivity (HCO3) rank relative 1.00 19 1.00 22 1.00 16 0.80 3 0.75 2 0.93 8 1.00 20 1.00 25 1.00 27 0.88 7 0.88 6 0.99 13 1.00 18 1.00 23 1.00 17 0.99 15 0.96 10 0.97 12 0.99 14 1.00 21 0.94 9 1.00 24 0.96 11 0.85 4 0.86 5 1.00 26 0.57 1
Table III, 3 Results of SA of all parameters for the Aalborg household waste simulation
Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
0.05 0.23 0.17 0.18 0.07 0.18 0.11 7.4 10 160 48.7 34.3 55.3 1.33 1.02 4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.2
kg/kg g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 3 mgCOD/m 3 gCOD/m 3 mgCOD/m 3 mgCOD/m 3 mol/m mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 0.88 2 0.99 22 0.99 24 0.98 20 0.91 4 0.97 15 0.99 23 1.00 36 0.97 9 1.00 31 1.00 30 1.00 34 0.96 6 0.93 5 0.90 3 1.00 39 1.00 40 0.98 21 0.97 17 0.97 14 0.97 8 1.00 32 1.00 38 1.00 29 0.97 13 0.97 16 0.97 10 1.00 37 1.00 35 0.99 26 0.99 25 0.98 18 0.97 11 1.01 42 1.00 27 0.97 12 1.00 33 0.97 7 0.98 19 1.00 41 1.00 28 0.52 1
Sensitivity (VFAs) rank relative 0.97 15 1.01 40 0.99 20 1.00 29 0.95 14 0.98 18 1.00 25 1.00 31 0.82 7 1.00 27 1.00 28 1.00 30 0.99 23 42 1.02 17 0.98 41 1.01 35 1.00 19 0.98 1 0.33 4 0.69 5 0.78 39 1.00 36 1.00 38 1.00 3 0.66 8 0.83 12 0.91 37 1.00 34 1.00 21 0.99 16 0.97 13 0.92 11 0.88 26 1.00 22 0.99 6 0.80 32 1.00 10 0.88 2 0.43 9 0.85 24 0.99 33 1.00
VI
Sensitivity (NH4-N) rank relative 0.86 2 0.98 4 0.97 3 0.99 8 0.99 14 1.00 26 1.00 29 1.00 39 0.98 5 0.99 6 1.00 37 1.00 40 1.00 33 1.00 31 1.00 24 0.99 9 1.00 34 1.00 25 0.99 10 0.99 13 0.99 12 1.00 17 1.00 42 1.00 19 1.00 18 0.99 7 0.99 15 1.00 23 1.00 36 1.00 41 1.00 32 1.00 28 1.00 21 1.00 27 1.00 35 1.00 20 1.00 38 1.00 22 0.99 11 0.99 16 1.00 30 0.30 1
Sensitivity (HCO3) rank relative 9 0.98 3 0.96 18 0.99 32 1.00 17 0.99 20 1.00 26 1.00 35 1.00 1 0.24 34 1.00 30 1.00 33 1.00 24 1.00 41 1.00 22 1.00 27 1.00 38 1.00 19 1.00 5 0.97 4 0.96 8 0.98 31 1.00 40 1.00 42 1.00 6 0.97 7 0.98 14 0.99 1.00 39 1.00 37 1.00 21 1.00 29 0.99 16 0.99 13 1.00 25 1.00 23 0.98 10 1.00 36 0.99 12 0.98 11 0.99 15 1.00 28 0.93 2
Västra Hamnen household waste Table III, 4 Results of SA, UA and variability on measured parameters for the Västra Hamnen household waste simulation Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.23 0.17 0.12 0.04 0.07 0.14 7.21 10 13.5 48.7 34.3 35.4 1.33 1.03
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Variability
Sensitivity (Gas)
Sensitivity (VFAs)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank σ (%) 12 2.5S 20U 2 0.97J 14 3.5J 9 18J 3 3.4J 10 4.7J 8 2U 13 100 U 1 3L 11 10 U 4 10 U 4 2U 13 2U 6 2U 6
rank 5 1 7 6 3 2 4 9 8
rank relative 1 0.69 5 0.93 10 1.00 7 0.95 4 0.90 9 0.99 6 0.95 12 1.00 15 1.00 13 1.00 14 1.00 11 1.00 8 0.99 3 0.87 2 0.79
rank relative 3 0.88 2 0.88 6 0.97 10 1.00 7 0.98 11 1.00 9 0.99 14 1.00 1 0.29 12 1.00 15 1.00 13 1.00 4 0.93 8 0.99 5 0.96
rank relative 1 0.46 2 0.76 3 0.86 6 0.98 7 0.98 9 1.00 8 0.99 13 1.00 15 1.00 10 1.00 12 1.00 14 1.00 4 0.97 5 0.97 11 1.00
rank relative 3 0.97 2 0.95 4 0.99 13 1.00 7 1.00 14 1.00 8 1.00 11 1.00 1 0.074 12 1.00 10 1.00 9 1.00 6 1.00 5 1.00 15 1.00
σ (%) 24.6B 59.7B 9.2H 12.0H 33.3H 50H 20.0H 1.4A 1.6A
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Höjlund Christensen, et al., 2003), H (Hansen, et al., 2007)
Table III, 5 Results of SA on model parameters for the Västra Hamnen household waste simulation
Parameter
Mean
Unit
µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.2
d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 1.00 12 1.00 19 1.02 26 0.98 7 0.78 2 1.01 23 1.01 24 1.00 21 0.98 6 0.99 10 0.91 5 1.00 22 1.00 18 1.00 16 0.99 9 0.99 15 1.00 20 1.00 11 1.02 27 1.00 13 1.00 8 1.01 25 0.86 4 1.00 14 0.78 3 1.00 17 0.21 1
Sensitivity (VFAs) rank relative 1.02 26 0.98 15 1.09 27 0.84 5 0.09 1 0.95 12 0.95 9 1.00 24 0.95 11 0.97 14 0.70 4 0.99 17 1.00 21 1.00 22 0.99 16 1.00 18 1.00 19 0.95 13 1.02 25 1.00 23 0.93 8 0.90 7 0.52 3 0.95 10 0.14 2 1.00 20 0.88 6
VII
Sensitivity (NH4-N) rank relative 6 1.00 26 1.00 7 1.00 8 1.00 2 0.98 13 1.00 9 1.00 27 1.00 10 1.00 12 1.00 4 0.99 21 1.00 16 1.00 19 1.00 23 1.00 20 1.00 25 1.00 22 1.00 15 1.00 17 1.00 14 1.00 18 1.00 5 0.99 11 1.00 3 0.98 24 1.00 0.024 1
Sensitivity (HCO3) rank relative 1.00 19 1.00 14 1.02 27 0.96 6 0.41 1 0.99 12 1.00 22 1.00 24 0.99 8 0.99 10 0.78 4 1.00 23 1.00 17 1.00 16 0.99 13 1.00 18 1.01 25 0.99 9 1.02 26 1.00 20 0.97 7 1.00 15 0.81 5 0.99 11 0.47 2 1.00 21 0.65 3
Table III, 6 Results of SA on all parameters for the Västra Hamnen household waste simulation
Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
0.05 0.23 0.17 0.12 0.04 0.07 0.14 7.21 10 13.5 48.7 34.3 35.4 1.33 1.03 4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.34
kg/kg g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 3 mgCOD/m 3 gCOD/m 3 mgCOD/m 3 mgCOD/m 3 mol/m mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 0.94 6 0.98 11 1.00 35 0.99 14 0.96 9 0.99 17 0.98 12 1.00 29 1.03 42 1.00 27 1.00 25 1.00 28 0.97 10 0.95 7 0.95 8 1.00 33 1.00 34 1.00 40 0.99 13 0.83 2 1.00 21 1.00 37 1.00 36 0.99 15 1.00 41 0.92 5 1.00 30 1.00 24 1.00 26 1.00 20 1.00 23 0.99 18 1.00 19 1.00 38 1.00 22 0.99 16 1.00 39 0.91 4 1.00 32 0.83 3 1.00 31 0.45 1
Sensitivity (VFAs) rank relative 1.01 39 0.99 20 1.00 27 1.00 25 0.98 15 1.00 33 0.99 23 1.00 31 1.01 40 1.00 28 1.00 32 1.00 30 0.91 7 14 0.97 24 1.00 37 1.01 19 0.98 42 1.10 5 0.81 1 0.10 11 0.95 18 0.98 29 1.00 13 0.96 16 0.98 4 0.69 22 0.99 36 1.00 34 1.00 17 0.98 26 1.00 21 0.99 12 0.96 41 1.04 38 1.01 9 0.94 8 0.94 3 0.58 10 0.95 2 0.16 35 1.00 6 0.87
VIII
Sensitivity (NH4-N) rank relative 0.92 2 0.96 3 0.98 4 1.00 9 1.00 17 1.00 40 1.00 27 1.00 34 1.00 13 1.00 22 1.00 33 1.00 35 1.00 11 1.00 24 1.00 31 1.00 10 1.00 39 1.00 12 1.00 16 0.98 5 1.00 15 1.00 28 1.00 42 1.00 20 1.00 21 0.99 7 1.00 38 1.00 26 1.00 29 1.00 37 1.00 32 1.00 41 1.00 25 1.00 19 1.00 30 1.00 23 1.00 14 0.99 8 1.00 18 0.98 6 1.00 36 0.19 1
Sensitivity (HCO3) rank relative 8 0.98 7 0.97 12 0.99 38 1.00 14 1.00 22 1.00 19 1.00 32 1.00 1 0.42 31 1.00 25 1.00 27 1.00 9 0.98 15 1.00 20 1.00 37 1.00 28 1.00 42 1.01 10 0.99 2 0.80 13 0.99 39 1.00 40 1.00 17 1.00 18 1.00 5 0.91 21 1.00 1.00 34 1.00 29 1.00 23 1.00 35 1.00 26 1.00 16 1.01 41 1.00 33 0.99 11 1.00 30 0.93 6 1.00 24 0.82 3 1.00 36 0.89 4
Sjölunda sludge Table III, 7 Results of SA, UA and variability on measured parameters for the sludge simulation Parameter
Mean
Unit
Uncertainty
Sensitivity (Gas)
Sensitivity (VFAs)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank rank relative relative 4 TS 0.039 8 0.99 kg/kg 2.5S 5 0.99 3 0.99 7 1.00 0.53J 10 VS 0.75 13 1.00 g/TS 8 1.00 5 1.00 12 1.00 U 20 8 Soluble TS 0.3 2 1.00 12 1.00 6 1.00 5 0.99 20 U 2 Protein 0.34 2 0.97 gCOD/gXS 1 0.46 1 0.43 2 0.78 gCOD/gXS 20 U 13 Fat 0.45 2 1.01 4 0.97 13 1.00 4 0.98 U gCOD/gXS 20 3 Sugar 0.16 2 0.98 6 0.99 12 1.00 6 1.00 gCOD/gXS 20 U 11 Inert 0.05 2 1.00 10 1.00 11 1.00 9 1.00 2U 5 pH 7.13 9 0.99 3 0.90 4 1.00 1 0.69 mol/m3 100 U 12 HCO3 12 1 1.00 9 1.00 8 1.00 10 1.00 3 L NH4-N gN/m 3 9 45 7 1.00 13 1.00 10 1.00 11 1.00 Temperature °C 2U 6 34 9 0.99 11 1.00 7 1.00 8 1.00 2U Flow l/d 7 1.5 9 0.99 7 1.00 9 1.00 13 1.00 U 2 Pressure bar 1 1.02 9 0.13 2 0.48 2 0.60 3 0.81 S (SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Höjlund Christensen, et al., 2003), H (Hansen, et al., 2007) rank σ (%)
rank relative
rank relative
Table III, 8 Results of SA on model parameters for the sludge simulation
Parameter
Mean
Unit
µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.2
d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 1.00 25 1.00 23 0.91 5 1.00 17 0.19 1 0.96 7 1.00 26 1.00 24 0.99 14 0.98 10 0.68 4 0.97 9 1.00 21 1.00 19 1.00 16 1.00 18 0.99 13 0.99 12 0.97 8 0.99 15 0.98 11 1.00 22 0.63 3 1.00 27 0.53 2 1.00 20 0.94 6
Sensitivity (VFAs) rank relative 1.01 24 0.96 12 1.03 27 0.85 5 0.25 1 0.91 6 0.98 13 1.02 25 0.99 15 0.96 11 0.79 4 0.95 9 1.00 23 1.00 20 1.00 17 1.00 18 0.99 14 1.00 21 0.96 10 1.00 22 0.95 8 0.99 16 0.74 3 0.94 7 0.54 2 1.00 19 1.03 26
IX
Sensitivity (NH4-N) rank relative 7 0.95 27 1.09 6 0.95 25 1.01 1 0.38 13 1.00 26 1.04 8 0.97 14 1.00 12 1.00 5 0.65 18 1.00 23 1.00 16 1.00 17 1.00 21 1.00 10 0.99 19 1.00 9 0.99 11 0.99 24 1.01 22 1.00 4 0.62 15 1.00 3 0.60 20 1.00 2 0.60
Sensitivity (HCO3) rank relative 1.00 22 1.00 18 1.01 26 0.96 5 0.24 1 0.97 6 1.01 25 1.00 16 1.00 21 0.99 10 0.80 4 0.99 8 1.00 20 1.00 23 1.00 19 1.00 24 0.99 11 1.00 13 0.99 12 1.00 17 0.98 7 1.00 15 0.80 3 0.99 9 0.51 2 1.00 14 1.03 27
Zero gasprod. 20 27 21 23 0 22 23 21 23 22 12 22 21 22 22 22 21 21 21 23 22 21 11 22 9 22 21 (23)
Table III, 9 Results of SA of all parameters for the sludge simulation
Parameter
Mean
Unit
TS VS Soluble TS Protein Fat Sugar Inert pH HCO3 NH4-N Temperature Flow Pressure µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
0.039 0.75 0.3 0.34 0.45 0.16 0.05 7.13 12 45 34 1.5 1.02 4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.34
kg/kg g/TS gCOD/gXS gCOD/gXS gCOD/gXS gCOD/gXS mol/m3 gN/m3 °C l/d bar d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 3 mgCOD/m 3 gCOD/m 3 mgCOD/m 3 mgCOD/m 3 mol/m mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 0.99 19 1.00 33 0.99 23 0.88 3 0.94 8 0.98 11 1.00 35 0.92 6 1.00 31 1.00 24 0.99 20 0.99 21 0.48 1 1.00 28 1.00 30 0.93 7 0.98 16 0.79 2 0.96 10 1.00 39 1.00 27 0.98 12 0.99 22 0.96 9 0.98 13 1.00 34 1.00 32 1.00 36 1.00 38 0.98 15 0.98 14 0.99 17 1.00 25 1.00 26 1.00 37 0.90 4 1.01 40 0.90 5 1.00 29 0.99 18
Sensitivity (VFAs) rank relative 1.00 24 1.00 34 0.99 14 0.67 2 0.98 9 0.99 13 1.00 27 0.90 6 1.00 28 1.00 26 1.00 22 1.00 23 0.66 1 1.00 33 0.99 17 1.01 39 0.98 10 3 0.72 15 0.99 32 1.00 37 1.00 12 0.98 25 1.00 7 0.96 31 1.00 18 0.99 30 1.00 36 1.00 29 1.00 38 1.00 19 1.00 21 1.00 20 1.00 16 0.99 11 0.98 5 0.89 8 0.97 4 0.82 35 1.00 40 1.01
X
Sensitivity (NH4-N) rank relative 0.99 12 1.00 33 1.00 34 0.46 1 1.00 14 1.00 29 1.00 32 0.98 6 1.00 35 1.00 23 1.00 24 1.00 37 0.60 2 1.00 17 1.00 40 0.99 11 0.99 10 0.96 3 0.99 8 1.00 39 1.00 18 1.00 26 1.00 20 0.99 7 0.99 13 1.00 38 1.00 30 1.00 31 1.00 36 1.00 15 1.00 22 1.00 16 1.00 25 1.00 21 1.00 19 0.98 5 1.00 27 0.98 4 1.00 28 0.99 9
Sensitivity (HCO3) rank relative 22 1.00 36 1.00 16 0.99 4 0.86 6 0.91 14 0.99 33 1.00 1 0.77 35 1.00 19 1.00 18 0.99 24 1.00 5 0.88 29 1.00 37 1.00 10 0.98 17 0.99 2 0.77 9 0.98 34 1.00 26 1.00 20 1.00 15 0.99 8 0.96 11 0.99 38 1.00 30 1.00 28 1.00 31 1.00 12 0.99 13 0.99 21 1.00 25 1.00 23 1.00 32 1.00 7 0.92 1.02 40 0.85 3 1.00 27 1.00 39
Aalborg household waste with general characterization Table III, 10 Results of SA, UA and variability on measured parameters for the general thermophilic household waste simulation Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.14 0.15 0.14 0.06 0.15 0.19 7.4 10 160 48.7 34.3 55.3 1.33 1.02
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Variability
Sensitivity (Gas)
Sensitivity (VFAs)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank 5 6 1 4 2 2 6 6 6
rank 5 1 7 6 3 2 4 9 8
rank 5 10 7 4 3 1 2 14 11 13 15 12 9 8 6
rank relative 8 0.98 5 0.95 1 0.60 10 1.00 6 0.96 4 0.88 7 0.96 14 1.00 3 0.77 11 1.00 15 1.00 13 1.00 2 0.66 12 1.00 9 0.99
rank relative 2 0.96 7 0.99 1 0.13 5 0.99 4 0.98 3 0.96 6 0.99 12 1.00 10 1.00 8 1.00 11 1.00 13 1.00 15 1.00 9 1.00 14 1.00
rank relative 4 0.98 3 0.94 2 0.70 8 1.00 6 0.99 5 0.99 7 0.99 11 1.00 1 0.39 13 1.00 12 1.00 10 1.00 15 1.00 9 1.00 14 1.00
σ (%) 2.5S 2U 100 U 3L 10 U 10 U 2U 2U 2U
σ (%) 24.6B 59.7B 9.2H 12.0H 33.3H 50H 20.0H 1.4A 1.6A
relative 0.96 1.00 0.98 0.92 0.85 0.55 0.83 1.00 1.00 1.00 1.00 1.00 0.99 0.98 0.97
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Höjlund Christensen, et al., 2003), H (Hansen, et al., 2007)
Table III, 11 Results of SA on model parameters for the general thermophilic household waste simulation
Parameter
Mean
Unit
µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.34
d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 1.00 19 1.00 25 0.98 2 0.98 4 0.98 8 0.98 3 1.00 21 1.00 23 0.99 15 0.98 5 0.99 13 0.98 6 1.00 20 1.00 24 0.99 12 1.00 18 0.99 14 0.99 10 1.03 27 1.00 16 0.98 9 1.00 22 0.98 7 0.99 11 1.00 26 1.00 17 0.04 1
Sensitivity (VFAs) rank relative 1.01 26 1.00 22 1.00 16 0.34 1 0.68 6 0.58 4 1.00 25 1.00 24 1.00 23 0.53 2 0.80 9 0.82 10 1.00 20 1.00 21 1.00 17 0.96 13 0.92 12 0.77 8 1.01 27 1.00 18 0.65 5 1.00 19 0.76 7 0.54 3 0.91 11 0.99 15 0.98 14
XI
Sensitivity (NH4-N) rank relative 2 0.98 23 1.00 17 1.00 9 0.99 12 1.00 4 0.99 6 0.99 27 1.00 7 0.99 10 0.99 3 0.99 5 0.99 8 0.99 24 1.00 26 1.00 19 1.00 20 1.00 13 1.00 21 1.00 22 1.00 14 1.00 25 1.00 15 1.00 11 0.99 16 1.00 18 1.00 0.08 1
Sensitivity (HCO3) rank relative 0.99 16 1.00 25 0.98 14 0.78 3 0.72 2 0.85 5 1.00 19 1.00 26 1.00 22 0.84 4 0.86 7 0.93 12 1.00 18 1.00 24 0.99 17 0.99 15 0.93 13 0.91 11 1.01 27 1.00 20 0.88 8 1.00 23 0.90 9 0.85 6 0.91 10 1.00 21 0.58 1
Table III, 12 Results of SA of all parameters for the general household waste simulation for thermophilic conditions
Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
0.05 0.14 0.15 0.14 0.06 0.15 0.19 7.4 10 160 48.7 34.3 55.3 1.33 1.02 4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.34
kg/kg g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 3 mgCOD/m 3 gCOD/m 3 mgCOD/m 3 mgCOD/m 3 mol/m mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 0.97 6 1.00 20 0.98 9 0.93 5 0.86 3 0.58 1 0.84 2 1.00 34 1.00 42 1.00 33 1.00 30 1.00 31 0.99 14 0.98 8 0.97 7 1.00 38 1.00 41 1.00 22 0.98 11 1.00 25 0.98 10 1.00 27 1.00 32 1.00 26 0.98 13 0.99 18 0.98 12 1.00 36 1.00 29 1.00 24 1.00 28 1.00 40 0.99 19 1.00 21 1.00 35 0.99 16 1.00 39 0.99 17 0.99 15 1.00 23 1.00 37 0.92 4
Sensitivity (VFAs) rank relative 0.93 17 0.97 20 0.80 11 0.99 22 1.00 27 0.75 9 0.83 13 1.00 34 0.93 16 1.00 29 1.00 28 1.00 33 1.00 23 41 1.01 21 0.98 26 1.00 18 0.96 39 1.01 1 0.26 12 0.83 4 0.51 31 1.00 40 1.01 36 1.00 3 0.47 7 0.73 5 0.63 32 1.00 30 1.00 38 1.00 19 0.97 25 1.00 10 0.76 14 0.85 35 1.00 6 0.69 24 0.99 8 0.73 2 0.46 15 0.90 37 1.00 42 1.04
XII
Sensitivity (NH4-N) rank relative 0.96 3 0.99 8 0.22 1 0.99 5 0.99 6 0.97 4 0.99 7 1.00 33 1.00 17 1.00 9 1.00 32 1.00 34 1.00 39 1.00 18 1.00 28 1.00 15 1.00 25 1.00 31 1.00 14 1.00 12 1.00 16 1.00 26 1.00 42 1.00 41 1.00 20 1.00 10 1.00 19 1.00 38 1.00 29 1.00 40 1.00 27 1.00 37 1.00 22 1.00 24 1.00 36 1.00 21 1.00 35 1.00 30 1.00 13 1.00 11 1.00 23 0.93 2
Sensitivity (HCO3) rank relative 9 0.99 3 0.95 2 0.73 19 1.00 14 0.99 7 0.99 13 0.99 29 1.00 1 0.43 34 1.00 31 1.00 27 1.00 33 1.00 22 1.00 37 1.00 23 1.00 32 1.00 20 1.00 8 0.99 16 0.99 6 0.98 35 1.00 36 1.00 38 1.00 5 0.98 15 0.99 10 0.99 1.00 39 1.00 28 1.00 21 1.00 40 1.00 18 1.00 17 1.00 25 1.00 26 0.99 12 1.00 30 0.99 11 1.00 41 1.01 42 1.00 24 0.98 4
Västra Hamnen household waste with general characterization Table III, 13 Results of SA, UA and variability on measured parameters for the general thermophilic household waste simulation Parameter
Mean
Unit
TS Soluble TS Protein Fat Sugar Starch Fibers pH HCO3 NH4-N Acetate Propionate Temperature Flow Pressure
0.05 0.14 0.15 0.14 0.06 0.15 0.11 7.2 10 13.5 48.7 34.3 35.4 1.33 1.03
kg/kg
S
g/TS g/TS g/TS g/TS g/TS mol/m3 gN/m3 gCOD/m3 gCOD/m3 °C l/d bar
Uncertainty
Variability
Sensitivity (Gas)
Sensitivity (VFAs)
Sensitivity (NH4-N)
Sensitivity (HCO3)
rank 5 6 1 4 2 2 6 6 6
rank 5 1 7 6 3 2 4 9 8
rank 5 9 7 4 3 1 2 14 11 13 15 12 10 8 6
rank relative 8 0.96 4 0.90 1 0.38 11 1.00 6 0.94 3 0.81 7 0.94 15 1.00 2 0.70 12 1.00 14 1.00 13 1.00 5 0.91 9 0.98 10 1.00
rank relative 3 0.96 5 0.98 1 0.17 7 0.98 4 0.98 2 0.94 6 0.98 12 1.00 15 1.00 10 1.00 11 1.00 13 1.00 9 1.00 8 1.00 14 1.00
rank relative 5 0.99 3 0.93 2 0.72 8 1.00 6 0.99 4 0.98 7 0.99 12 1.00 1 0.39 13 1.00 14 1.00 11 1.00 10 1.00 9 1.00 15 1.00
σ (%) 2.5S 2U 100 U 3L 10 U 10 U 2U 2U 2U
σ (%) 24.6B 59.7B 9.2H 12.0H 33.3H 50H 20.0H 1.4A 1.6A
relative 0.96 0.99 0.98 0.92 0.84 0.54 0.83 1.00 1.00 1.00 1.00 1.00 1.00 0.98 0.97
(SIS, 1981), U (Unknown), J (la Cour Jansen, et al., 2004), L(Dr Lange®), B (Höjlund Christensen, et al., 2003), H (Hansen, et al., 2007)
Table III, 14 Results of SA on model parameters for the general thermophilic household waste simulation
Parameter
Mean
Unit
µmax3 µmax4 µmax5 µmax6 µmax7 µmax8 kd9 kd10 kd11 kd12 kd13 kd14 KSaa KSsu KSfa KSpro KSac KSH2 KIac56 KIH2,5 KIH2,6 KIH,34 KIH,58 KINH3,6 KINH3,7 kLaCO2 kH
4 4 0.6 0.6 0.37 2 0.8 0.8 0.06 0.06 0.05 0.3 50 50 1000 20 40 1 1500 3 1 0.01 5e-4 25 17 200 0.34
d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 d-1 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 gCOD/m3 mgCOD/m3 gCOD/m3 mgCOD/m3 mgCOD/m3 mol/m3 mol/m3 gN/m3 gN/m3 d-1 d-1
Sensitivity (Gas) rank relative 1.00 19 1.00 17 0.98 6 0.99 8 0.87 4 0.98 7 1.00 16 1.01 22 1.02 24 1.02 25 0.87 3 1.06 27 1.00 14 1.00 18 1.00 12 1.00 11 1.04 26 1.00 9 1.02 23 1.00 10 1.00 20 1.00 21 0.86 2 1.00 13 0.87 5 1.00 15 0.19 1
Sensitivity (VFAs) rank relative 0.98 15 1.02 22 0.99 17 0.53 5 0.44 1 0.56 6 1.03 24 0.95 11 1.02 23 0.93 10 0.52 4 1.10 25 0.99 18 1.00 21 1.00 19 0.98 14 1.23 27 0.82 8 0.98 16 0.96 12 0.70 7 0.98 13 0.45 2 0.92 9 0.52 3 1.00 20 1.12 26
XIII
Sensitivity (NH4-N) rank relative 0.99 7 1.00 26 1.00 10 1.00 14 0.98 3 1.00 11 9 1.00 8 1.00 6 0.99 23 1.00 2 0.97 13 1.00 15 1.00 18 1.00 25 1.00 20 1.00 19 1.00 17 1.00 27 1.00 24 1.00 12 1.00 22 1.00 5 0.98 16 1.00 4 0.98 21 1.00 1 0.06
Sensitivity (HCO3) rank relative 1.00 16 1.00 22 0.98 11 0.84 6 0.72 2 0.85 7 1.00 21 1.00 23 1.03 25 1.00 14 0.77 5 1.06 27 1.00 17 1.00 20 1.00 15 0.99 12 1.03 26 0.93 9 1.02 24 0.99 13 0.90 8 1.00 19 0.76 3 0.97 10 0.76 4 1.00 18 0.52 1
XIV
Application, uncertainty and sensitivity analysis of the anaerobic digestion model by Siegrist et al. (2002) on household waste digestion E. Ossiansson* and O. Lidholm** Water and Environmental Engineering, Department of Chemical Engineering E-mail: *
[email protected], **
[email protected] Abstract
In this paper the anaerobic digestion model published by Siegrist et al. (2002) is applied on household waste digestion. Data from two pilot scale experiments with measured characterizations were used, one with mesophilic and one with thermophilic temperature. Validation simulations with focus on the gas production rate, ammonium and VFA were first performed, using default values for model parameters. The steady state gas production could be predicted with acceptable accuracy, while the simulated ammonium and VFA concentrations were overestimated by the model. An uncertainty analysis was conducted to analyze the quality of the predictions with respect to measurements of input data. The measurement errors influenced the gas production the most, but that the VFA and ammonia predictions could not be improved with more accurate measurements. To find suitable parameters for calibration of model parameters, a Monte Carlo based sensitivity analysis was conducted, supplemented with scatter plots. The sensitivity analysis showed that the hydrolysis constant was the most important parameter to determine for both ammonium and gas production. This was problematic for the calibration, as the particulate organic matter is lumped and calibrating the ammonium from the hydrolysis constant therefore led to unrealistically low gas production. To model the protein degradation accurately, without changing the overall hydrolysis constant or the model structure, the protein content in the substrate was calibrated instead. The Siegrist model was hence not suitable for simulation of characterized household waste, unless a hydrolysis model with slower protein hydrolysis was introduced or the stoichiometry for the hydrolysis was calibrated. The VFA concentrations in the reactor were dependent on model parameters related to the aceticlastic methanogenesis and the propionate degradation. Calibration of half saturation constants for these processes was successful, but the values were increased considerably. A possible explanation for the considerable change in these parameter values could be that the mass transfer of substrate was more limiting than for the default Siegrist model. Keywords anaerobic digestion, model, household waste, uncertainty analysis, sensitivity analysis, calibration, Monte Carlo,
hydrolysis constant
ADM1 has been validated in the literature with varying success (Parker, 2005; Batstone, et al., 2003; Tartakovsky, et al., 2008). The Siegrist model is less utilized, but interesting because of the simpler structure with fewer input variables. The aim of the report is also to evaluate the required quality of input parameters, and to find the most important parameters to measure when modeling household waste digestion. Furthermore, the model parameters most suitable for calibration are evaluated and results with calibrated parameters are shown.
Introduction
Anaerobic digestion is a complex system of biochemical and physical processes. Due to the complexity of the process, it has traditionally been treated as a black box system, and optimization has been based on experience or trial and error methods. As experiments of anaerobic digestion processes are expensive and time consuming, modeling can provide a useful tool for process understanding and optimization. Models have potentials for revealing non-linear behaviors of the system and to quantify the performance of alternative operational setups. The aim of this report is to evaluate the applicability of a model for anaerobic digestion published by Siegrist, et al (2002), here referred to as the Siegrist model. The model was primarily developed for simulating the digestion of mixed sludge, but in this report the applicability for the model on household waste is studied. Compared to the more commonly used model by the International Water Association (IWA), called Anaerobic Digestion Model no 1 (ADM1), the Siegrist model is less complex, with a lumped hydrolysis constant and fewer Volatile Fatty Acids (VFA) included. The two models were constructed with different approaches, the Siegrist model parameters are based on experiments, whereas the ADM1 uses review consensus (Batstone, 2006).
Materials & Methods
The model was implemented in Matlab as a system of differential equations with 23 liquid phase state variables and 3 state variables describing gaseous compounds. The stiff ODE-solver ode15s was used for the numerical integration. The hydrolysis rate was described with first order kinetics with respect to the degradable particulate organic matter XS (process 1 in Figure 1). Monod kinetics, in combination with inhibition expressions with respect to ammonia, pH, acetate and dissolved hydrogen, were used to simulate the microbial processes (process 2-7 in Figure 1). The model also included stripping of the gases methane, carbon dioxide and hydrogen from the liquid with a pressure control loop (Siegrist, et al., 2002).
1
particulate degradable organic matter, XS. It was assumed that the hydrolysis step was rate limiting and that there were no inhibition effects on the microbial reactions. The hydrolysis constant, kH, was determined to 0.20 d-1 (Figure 2).
Gas production, [Nml/Day]
4 3.5
Triplicate 1
3
Triplicate 2 Triplicate 3 kh=0.2
2.5 2 1.5 1 0.5 0
Figure 1 Overview of the biochemical reactions in anaerobic digestion with flows expressed as percent of COD (from Siegrist et al 2002 based on Gujer et al 1983)
-0.5
0
10
20 30 Tim e, [Days]
40
50
Figure 2 Calibration of kH from batch experiment on household waste from the mesophilic digestion
Data from one mesophilic (35°C) and one thermophilic (55°C) pilot scale experiment was used for validation and model analysis (Davidsson, et al. 2007). The household waste used in the mesophilic experiment was collected in the city district of Västra Hamnen in Malmö, Sweden, and the thermophilic digester was fed with household waste from Aalborg, Denmark. Characterization data for fat, protein, fiber, sugar, starch, VFA and ammonium content as fractions of TS was found in Højlund Christensen, et al. (2003). The measurement errors of the characterization data were found in an evaluation of the analysis methods by la Cour Jansen, et al. (2004). Relative standard deviation for the ammonium measurements were provided by the analysis instrument manufacturer (3.5 %, Dr Lange®). The relative standard deviation for VFA was assumed to be 10 %, and 2.5 % for gas production measurements. The experiments were divided into three phases; startup, steady state and post digestion. As the inoculums were collected from digesters fed with sludge, the startup phase was needed for the microorganisms to get accustomed to the new type of feed. Post digestion data was not available for the mesophilic digestion experiment.
Except for the hydrolysis constant and the composition of the waste, default values for model parameters were used for the validation simulations. The results show that the steady state gas production rate could be predicted fairly well for both household wastes, while the correlation during the start-up phase was poorer (Figure a and 4a). The modeled gas production rate during the startup phase was higher than measured, indicating a slower degradation before adaptation to the substrate. The fit to data for steady state ammonium concentrations were unsatisfactory for both simulations, especially for the mesophilic case (Figure 3b and 4b). The good fit to data for the startup of the thermophilic experiment was mainly due to a washout effect. The VFA concentrations were underestimated in the model predictions, especially for the thermophilic household waste digestion (Figure 3c and 4c). Uncertainty analysis
The characterizations were based on measurements with inherent measurement errors. A Monte Carlo method with Latin Hypercube Sampling (LHS) was used to study the effects of these measurement errors on prediction uncertainty. The distributions of the measurement errors were assumed to be described by Gaussian functions, and the distributions of outputs from 5000 simulations were studied. In Figure 5 the uncertainty of simulated outputs presented as 95 % confidence intervals can be compared with measurement uncertainties of validation data (vertical intervals) for the thermophilic household waste simulation. When the confidence intervals overlap, the lack of fit could be explained by measurement error. Figure 5a shows that measurement errors can explain some of the discrepancy between simulations and data for the
Validation simulations
Before the pilot scale experiments could be simulated, some processing of data was needed, including unit conversions and calculation of stoichiometry and the rate constant for the hydrolysis process. The elemental compositions for protein, fat etc. were found in Davidsson, et al. (2007) and converted to the unit gCOD/gTS with the Buswell formula (Buswell, et al., 1930). The default stoichiometry of mixed sludge hydrolysis in Figure 1 was hence updated to apply for the household wastes. Data from batch experiments on the waste from Västra Hamnen was used to determine the first order hydrolysis constant for degradation of
2
0.05
3500
1600
Sim ulated dry biogas production
Sim ulated NH4 m odelled 3000
0.03
0.02
0.01
2500 2000 1500 1000 500
0
20
40 60 Tim e [days]
80
0.05
20
40 60 Tim e [days]
600 400
0
Measured biogas production Concentration [g N/m3]
0.03
0.02
0.01
0
10
20 30 Tim e [days]
40
800
600
400 Sim ulated NH4 m odelled 200
0
50
Figure 4a Modeled and measured biogas production for the mesophilic experiment
Measured NH4
0
10
20
30 40 Tim e [days]
50
20
40 60 Tim e [days]
80
Figure 3c Modeled and measured VFA for the thermophilic experiment 350 Sim ulated VFAs 300
Measured VFAs
250 200 150 100 50 0
60
Figure 4b Modeled and measured ammonia for the mesophilic experiment
0
10
20
30 40 Tim e [days]
50
60
Figure 4c Modeled and measured VFA for the mesophilic experiment
uncertainty analysis, e.g. Monte Carlo with LHS. This time, however, instead of varying all parameters, one parameter at a time was kept at a constant value. The relative decrease in output variance when keeping a parameter constant, compared to if all parameters varied, was used as a measure of the sensitivity for this parameter. This variance-based method needed to be supplemented with scatters plots to enable visual evaluation of the correlation between parameters and output. The analysis of measured input parameters was based on the same parameter distributions as in the uncertainty analysis. As no information of realistic distributions for model parameters was found, the model parameters were assumed to be uniformly distributed between ± 50 percent of the default values.
gas production rate, but that further calibration was needed for ammonia and VFA (Figure 5b and 5c). The confidence intervals are broader for the gas production than the ammonia and VFA, indicating that the gas production is affected more by the quality of input data than the other two outputs. Sensitivity analysis
Sensitivity analysis was conducted with two main purposes; to determine the importance of measuring specific input parameters and to find model parameters suited for calibration. Sensitivity analyses of ADM1 found in the literature used sensitivity functions or other local analysis methods (Tartakovsky et al. 2008, Jeong et al. 2005, etc.). In this report, a global sensitivity analysis method was employed instead, to include the non-linear behavior of the system.The sensitivity analysis was carried out with the same methodology as in the 0.06
0
Figure 3b Modeled and measured ammonia for the thermophilic experiment
Sim ulated dry biogas production Production rate [m3/day]
800
80
1000
0.04
0
1000
200 0
Figure 3a Modeled and measured biogas production for the thermophilic experiment
Measured VFAs
1200
0
VFAs as acetate equivalents [g COD/m3]
0
Sim ulated VFAs
1400
Measured NH4
Concentration [g COD/m3]
Concentration [g N/m3]
Production rate [m3/day]
Measured biogas production 0.04
1500
1200 VFAs m odelled
0.04 0.03 Biogas production m odelled
0.02
95 % confidence interval 95 % confidence interval
0.01
1000
500
NH4 m odelled 95 % confidence interval 95 % confidence interval
Biogas production m easured 0 40
45
50
55 60 Tim e [days]
65
Concentration [g COD/m3]
Concentration [g N/m3]
Production rate [m3/day]
0.05
1000
95 % confidence interval 95 % confidence interval VFAs m easured
800 600 400 200
NH4 m easured 70
Figure 5a Confidence intervals of the gas production for the thermophilic experiment
0 40
45
50
55 60 Tim e [days]
65
70
0 40
45
50
55 60 Tim e [days]
65
70
Figure 5b Confidence intervals of the ammonium Figure 5c Confidence intervals of the VFA for the thermophilic experiment for the thermophilic experiment
3
Table 1 Results from sensitivity analysis of measured input parameters Parameter
TS Soluble TS Protein HCO3
Mean
0.05 0.23 0.17 10
Unit
kg/kg g/TS mol/m3
Sensitivity (Gas)
Sensitivity (VFA)
Thermophilic digestion
Mesophilic digestion
Thermophilic digestion
Mesophilic digestion
Thermophilic digestion
Mesophilic digestion
rank relative 1 0.69 5 0.93 10 1.00 15 1.00
rank relative 3 0.88 2 0.88 6 0.97 1 0.29
Rank 4 3 7 2
rank relative 3 0.88 2 0.88 6 0.97 1 0.29
rank relative 1 0.42 3 0.93 2 0.84 4 0.93
rank relative 1 0.46 2 0.76 3 0.86 15 1.00
The sensitivity analysis of measured input parameters showed that the variance for prediction of gas production rate decreased the most if the TS measurements were made without errors (Table 1). Reliable measurements for TS are thus important. The most significant sources of uncertainty for the ammonium predictions were the TS, solubilized TS and protein content of the feed (Table 1). For VFA, the uncertainty from distributed input parameters was not significant, but the HCO3 of the feed was most influential (Table 1). With the aid of scatter plots, the correlations between the measured input parameters and output could be visualized. From this analysis, the correlation between the degradable fraction of TS could be pointed out as more important for the gas production rate than the total measured TS (Figure 6 and 7). The linear correlation to the gas production is more pronounced for the degradable TS and the output values are less dispersed. This result is no surprise, however, since it is the degradable fraction of TS that is used for gas production. This result emphasizes the importance of measuring the degradability of the substrate.
Gas production rate [m 3/d]
relative 0.95 0.95 0.99 0.59
The results from the variance-based sensitivity analysis of model parameters showed that the hydrolysis constant kH is the most important parameter both for determining the gas production rate and the ammonium levels in the reactor (Table 2). This indicates that the hydrolysis step is rate limiting, and that the hydrolysis constant can be calibrated from either the gas production rate or the ammonia level in the reactors. Figure 8 shows the non-linear correlation between the hydrolysis constant and the gas production. 0.06
Gas production rate [m 3/d]
0.05
0.04
0.03
0.02
0.01
0 0.1
0.2
0.25
0.3
Figure 8 Gas production vs. kH for the thermophilic experiment
VFA levels in the reactor were sensitive to parameters related to the acetotrophic methanogenesis and the anaerobic degradation of propionate (Table 2). The scatter plot analysis of the correlations revealed that the high sensitivity to these parameters was partly due to that bacteria were washed out when these constants reached extreme values. Figure 9 shows an example of a frequent washout of bacteria for low maximum growth rates for the aceticlastic methanogens.
0.05 0.04 0.03 0.02 0.01 0 0.045
0.05 TS [kg/kg]
0.055
Figure 6 Gas production vs. total TS for the thermophilic experiment
0.03
0.05
0.025
Gas production rate [m 3/d]
0.06
0.04 0.03 0.02 0.01 0 0.03
0.15
k H [d-1]
0.06
Gas production rate [m 3/d]
Sensitivity (NH4-N)
0.02 0.015 0.01 0.005 0
0.032
0.034 0.036 TS [kg/kg]
0.038
0.04
0.2
0.3
0.4
0.5
0.6
µ max6
Figure 9 Gas production vs. maximum growth rate of aceticlastic methanogens
Figure 7 Gas production vs. degradable TS for the thermophilic experiment
4
Table 2 Results from sensitivity analysis of model parameters Parameter
Mean
0.6 0.37 0.2
µmax6 µmax7 kH
Unit
d-1 d-1 d-1
Sensitivity (Gas)
Sensitivity (VFA)
Sensitivity (NH4-N)
Thermophilic digestion
Mesophilic digestion
Thermophilic digestion
Mesophilic digestion
Thermophilic digestion
Mesophilic digestion
rank relative 24 1.00 7 1.00 1 0.019
rank relative 7 0.98 2 0.78 1 0.21
Rank 1 4 12
rank relative 5 0.84 1 0.09 6 0.88
rank relative 5 0.99 8 0.99 1 0.051
rank relative 2 0.98 8 1.00 1 0.024
relative 0.35 0.72 0.96
hydrolysis of particulate protein. The model structure was however not changed in this project, but is suggested for further studies. The problem was instead solved by decreasing the stoichiometric coefficient of protein in the degradation of XS. The result from this calibration is presented in Figure 10b. The sensitivity analysis showed that the maximum growth rate constants for the acetoclastic methanogenesis and the propionate degradation were most important for the VFA concentration. As discussed in the sensitivity analysis section, this result was partly due to the high rate of washout for extreme values of these parameters. This indicated that they may not be suited for calibration purposes. When calibrating with these values, the fit to data only improved slightly, and when changing the value further, the errors increased rapidly. An example when calibrating the maximum growth rate constant for the aceticlastic methanogens is presented in Figure 11.
Calibration
In the sensitivity analysis, the most influential model parameters for each output were ranked. This result could then be used for calibration purposes, where the most influential parameters were chosen, and used to increase the fit to data. The calibration was conducted by varying parameters so that the sum of absolute errors for model predictions compared to data during the steady state phase could be minimized. Calibration of the hydrolysis constant to the gas production measurements resulted in an unchanged value for the mesophilic experiment, while the best fit to data for the thermophilic experiment was slightly decreased (from 0.2 to 0.15). This indicated a successful determination of kH from batch experiment for the household waste from Västra Hamnen. To enable calibration during the startup phase, the hydrolysis constant was iteratively increased until a good fit to data was achieved. The results from the calibration of the hydrolysis constant to the gas production errors are presented in Figure 10a. The hydrolysis constant was also the most influential parameter when it came to determining the ammonia levels in the reactor. When calibrating the hydrolysis constant with the ammonia measurements, the resulting hydrolysis constants were lower, indicating slower degradation of protein than other particulate constituents. The fact that the particulate organics were lumped into one state variable, XS, complicated the calibration process. As the hydrolysis constant determined both the protein degradation and the gas production rate, only one of the two processes could be calibrated at the same time. The model structure hence needed to be revised, to include a separate process of
7000
Sum of absolute errors
6000 5000 4000 3000 2000 1000 0
0
0.1
0.2
0.3
0.4
0.5
0.6
µ max7
Figure 10 Sum of absolute errors for VFA for the thermophilic simulation when varying maximum growth rate constant for the aceticlastic methanogenesis
0.06 3500
Biogas production m odelled
0.03 0.02 0.01 0
3000
NH4 m easured
2500 2000 1500 1000 500
0
20
40 60 Tim e [days]
80
Figure 11a Biogas production for the thermophilic experiment after calibration
0
0
20
40 60 Tim e [days]
80
VFAs m odelled 3000 Concentration [g COD/m3]
0.04
3500 NH4 m odelled
Biogas production m easured Concentration [g N/m3]
Production rate [m3/day]
0.05
VFAs m easured
2500 2000 1500 1000 500 0
0
20
40 60 Tim e [days]
80
Figure 11b Ammonium concentration for the Figure 11c VFA concentration for the thermophilic experiment after calibration thermophilic experiment after calibration
5
method for determining the hydrolysis constant could thus be used in this case. The ammonium concentration in the reactor was determined from the degradation of protein. As the particulate organics are lumped in the Siegrist model, the individual hydrolysis of particulate protein could not be modeled. This was problematic, since the protein degradation was much slower in the simulated experiments. It was therefore concluded that a hydrolysis model with separate hydrolysis rates as in ADM1 is preferable when modeling household waste degradation. This applies particularly when characterization measurements of the substrate are used; otherwise calibrations of the stoichiometric coefficients are needed.
Better calibration results were instead achieved when using half saturation constants. A better fit to data was obtained, and the process was stable for a wide range of values (Figure 12). The minimum error was acquired for a KS of 100 g COD/m3for propionate degradation and 260 g COD/m3 in the thermophilic digester (compare with the default values 20 and 40 g COD/m3 respectively). For mesophilic digestion, only KS for acetoclastic methanogenesis was calibrated, to 190 g COD/m3. The physical explanation for changing the half saturation constants could be that the mass transfer conditions was different than suggested in the implementation by Siegrist et al. The resulting simulation after calibration is showed in Figure 10c. 7000
References
Sum of absolute errors
6000
Batstone D J Mathematical modelling of anaerobic reactors treating domestic [Journal] // Reviews in Environmental Science and Bio/Technology. - 2006. - pp. 5, 57–71.
5000 4000 3000
Batstone D.J. and Keller J. Industrial applications of the IWA anaerobic digestion model No. 1 (ADM1) [Article] // Water science and technology. - 2003. - Vols. 47, 199-206.
2000 1000 0
0
50
100
150
200
Buswell E G and Neave S L Laboratory studies of sludge digestion [Article] // Illinois Division of State Water Survey. 1930. - Vol. Bulletin no. 30.
250
KSac
Figure 12 Sum of absolute errors for VFA for the thermophilic simulation when varying half saturation constant for the aceticlastic methanogenesis
Davidsson Åsa [et al.] Methane yield in source-sorted organic fraction of municipal solid waste [Article] // Waste Management. - 2007. - Vols. 27, p.406-414 .
Conclusions
Applying the Siegrist model on household waste experiments gave acceptable predictions of the steady state gas production. The simulation of the startup phase, i.e. before the inoculum was adapted to the substrate, was less successful. The correlation of ammonia and VFA predictions to data was not satisfying for simulations without calibrated values. The uncertainty analysis showed that measurement errors could explain some of the discrepancy for gas production predictions to data, but not to the same extent for ammonium and VFA. From the sensitivity analysis it could be concluded that the most important parameters to determine for predictions of gas production are the amount of degradable TS in the substrate, and the hydrolysis rate constant. The VFA concentrations of the reactor were mostly influenced by the availability of VFA as substrate in propionate degradation and acetoclastic methanogenesis. This implied that the mass transfer in the digester was more important for the VFA level than the input variables. The calibration showed that the hydrolysis rate constant determined from batch experiments gave the best fit to data for the gas production; this
Gujer W and Zehnder A J B Conversion processes in anaerobic digestion [Article] // Water Science and Technology. - 1983. Vols. 15 (8/9); 127-167. Højlund Christensen T, la Cour Jansen J and Jörgensen O Datarapport om sammensætning og biogaspotentiale i organisk dagrenovation [Report]. - [s.l.] : Danska Miljöstyrelsen, 2003. Jeong Hyeong-Seok [et al.] Analysis and application of ADM1 for anaerobic methane production [Article] // Bioprocess Biosyst Eng. - 2005. - Vols. 27; 81–89. la Cour Jansen J [et al.] Assessment of sampling and chemical analysis of source-separated organic household waste [Article] // Waste Management. - 2004. - Vols. 24; 541-549. Parker Wayne J. Application of the ADM1 model to advanced anaerobic digestion [Artikel] // Bioresource Technology. 2005. - Vol. 96, p.1832-1842. Siegrist H [et al.] Mathematical model for meso- and thermophilic anaerobic sewage sludge digestion [Journal] // Environmental Science and Technology. - 2002. - pp. 36, 11131123. Tartakovsky B [et al.] Anaerobic digestion model No 1- based distributed prameter model of an anaerobic reactor: II. Model validation [Article] // Bioresource technology. - 2008. - Vols. 99 3676-3684.
6
![A SENSITIVITY AND ERROR ANALYSIS FRAMEWORK FOR LAKE EUTROPHICATION MODELING]](https://kipdf.com/img/300x300/a-sensitivity-and-error-analysis-framework-for-lak_5b0d38a18ead0ec90c8b457f.jpg)
