Chemical
Process
Design
Subject
6.
Material
and
Heat
Balances
Javier
R.
Viguri
Fuente
CHEMICAL
ENGINEERING
AND
INORGANIC
CHEMISTRY
DEPARTMENT
UNIVERSITY
OF
CANTABRIA
[email protected]
License:
CreaLve
Commons
BY‐NC‐SA
3.0
INDEX 1.- Analysis of the inputs effect on the outputs. 2.- Methodology for process analysis: Material and energy balances. 3.- Basic Ideas to develop LINEAR MASS BALANCES (LMB) models. 4.- Develop of LMBs. 5.- Case Study: Application of LMB algorithm and setting pressure and temperature levels in flowsheet. 6.- Heat Balances. 7.- Further Reading and References.
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1.- Analysis of the inputs effect on the outputs
Two categories of relationships 1.- Relationships independent of the equipment Independent of the equipment specifications BM / BE / Equilibrium / Kinetic 2.- Relationships dependent of the equipment Design equations with equipment specifications: - Heat transference equation (with Area value) - Frictional pressure relationships (with D, Le) 3
2.- Methodology for process analysis: Material and energy balances.
Analysis methodology to apply on the synthesized flowsheets - Simples - Fast - Useful to the preliminary design
Mass balances Energy balances
Systematic modeling with different degree of rigorousness
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2.- Methodology for process analysis: Material and energy balances.
Once we synthesize flowsheet, we must do mass and energy balances to analyze its PERFORMANCE and to SIZE equipment for economic evaluation 2.1.- Equation Oriented Write al equations that describe the process and solve them simultaneously. Equations: Material balances Equilibrium relations Kinetic expressions Enthalpy balances, etc. Need solve 100´s equations with Newton´s Software: gPROMS, GAMS, EXCEL, ASPEN equations
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2.2.- Sequential Modular
Solve for input streams in each unit at the flowsheet following the information flow. For each module, compute outlet from given inlet. 6
6´ 1
COMP
2
3 MX
RXN
4
FLASH 5
1.Calc. COMP 2 2.Guess stream 6’ 3.Calc. MIX 3 4.Cal. RXN 4 5.Cal. FLASH 5, 6 6.If stream 6 is similar 6’ STOP, otherwise return to step 2 More robust, but less flexible Software: ASPENPLUS, PRO-II, HYSYS, UniSIM
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3.- Linear Mass Balances (LMB) models Basic Ideas to develop LMB Fix levels at P, T in flowsheet to derive linear approximations at mass balances in each unit. 1.- Fix P and T levels in flowsheet. Specify recoveries, split fractions key components, conversion per pass, recycle ratios (Degrees Freedom-d.f.) 2.- Approximate each unit with (fracciones divididas) (Split Fractions) (e.g. ξ, in flash unit; β, γ in absorber) to relate linearly output molar flow with inputs 3.- Set up linear equations and solve for molar flows at each component 4.- Recalculate P, T in flowsheet with equilibrium equations * If there are not big changes go to the step 5. * If there are big changes go to step 2. * If process does not meet specifications (e.g. equil. of DEE), change the values of the d.f. or modify flowsheet structure returning to step 2.
5.- Perform heat balances (heating + cooling utilities). Perform Heat integration at this stage. Idea Decouple mass and heat balances
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LMB algorithm P , T specify Specify split fractions of the key components Determine coefficients for linear models in each unit: αk/n, β, γ, ξ
Specifications and/or restrictions
Fenske, Kremser, Antoine equations
µ = Φ(µ ) out
in
Global mass balance P and T SIZING
Equilibrium equations (Bubble point, dew point)
T, P restrictions
COSTS 8
3.- Linear Mass Balances (LMB) models ASSUMPTIONS - L and V streams with ideal equilibrium relationships - Saturated streams - Linear equations simple to solve “tearing” - Convergence in few interactions (2) - Use basis at 100 gmol/s feed and calculate scale up factor to meet required production Approximations for following modules 1) Mixer Not real or physically equipments. Could be junctions. 2) Splitter 3) Reactor 4) Flash Linear in terms of split fractions 5) Distillation 6) Absorption and Stripper Associated (MEA Process) There are many other equipments as Adsorption, pervaporation, fermenters, etc. 9
4.- Develop of (LMB) models Simplifications and approximations Shortcut methods smaller problem MAIN CHARACTERISTICS: - Ideal solutions. Saturated streams. Ideal thermodynamic behaviour - Process units calculations Linear equations Linear coefficients k µ Mixer = ∑ µ ik , j
µ ik , j 1
Mixer
µ
1
µk
M
k i 2, j 2
l
k k µSplitter = ξ µ ,j j in k in
µ
Splitter
S
------
l
l
M
k µ S1
NS−1
Split fraction
k µSpitter ξj )µink ,NS=(1− ∑
µSk 2
j=1
Conversion
NR
Reactor
k µ IN
µ Rk
R
µ Fk 1
Flash
µ INk
µ
k Re actor
= µ + ∑ γ r ,kη r µ k in
r =1
Stoichiometric coefficients
µFk 1 = ξk µin
F
µFk 2 = (1 − ξk )µin µ Fk 2
l (r ) in
Split fractions 10
4.- Develop of LMB models
µ =ξ µ k
D
k
ξ 1− ξ N = ln / lnα ξ ξ α ξ ξ = 1 + ( α − 1 ) ξ Lk
k
Hk
m
in
Lk / Hk
Lk
Distillation
Hk
Nm
k / Hk
k
µ = (1 − ξ ) µ k
B
k
k
Nm
k / Hk
bub , c
≤T
β v = v + l β β
L0
V1
1
k
k
N +1
k
k
0
N +1
N
≤T
dew , R
n
n
n
0
E
n
n
E
N +1
n
n
E
n
N +1
N
1− (A ) β = 1− ( A )
N +1
k
ABS
Absorption
bub , R
l + (r − A ) v N = ln / ln(A ) l − A (1− r )v 0
1
≤T
dew , c
n
k
Hk
in
T
k
Hk
k
N
VN
E
k
E
LN
l = v +l −v k
k
k
k
N
N +1
0
1
1− ( A ) = 1− (A ) k
β
k N −1
N
E
k
E
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5.- CASE STUDY: Application of LMB algoritm and setting pressure and temperature levels in flowsheet OBTENTION OF ETHANOL • Establish levels of P, T in PFD Specify recoveries, splits key components. Fixed the recycle rate (specify d.g). • Determine coefficients linear models Calculate αk/n, ξk, AE, β, etc. Based on Antoine equation. • Set-up linear equations and solve for flowrates of each component. Solving equations of PFD by sequential approach • Calculate P, T through flowsheet If the guesses different step 1 return to step 2 • If process does not meet specifications either change recoveries (e.g. the recycle rate is too low) or modify flowsheet (e.g. need a 2nd flash unit to obtain the NH3 purity need) • Heat Balances (Heating – steam- and Cooling – water- utilities) Memo 2 is to calculate a mass and energy balance for a specified process flowsheet 12
6.- Heat Balances ENTLAPHIES: H (P,T ,zk) [J/gmol] - Reference state is necessary for the calculations. Ideal Gas, P0=1atm, T0=298 K - Assume elemental species - Assume ideal behaviour reflect effects of P and mixing (specially in the liquid phase) GAS MIXTURES
Cpk as function of T by heat capacity coefficients Ak,Bk,Ck, Dk
Constants for each k
T
H v (T , y ) = ∑ yk (∆H f k + ∫ C p0k dT ) 0
k
0
by Watson correlation in function of Tb, Tc, and ∆Hvap(Tb)
LIQUID MIXTURES T
H L (T , x) = ∑ xk [ ∆H 0 f k + ∫ C p0k dT − ∆H vk (T ) k
Handbook values (Perry,2008; Poling et al., 2000)
]
0
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7.- Further Reading and References • Biegler, L., Grossmann, I., Westerberg , A., 1997, Systematic Methods of Chemical Process Design, Prentice Hall. • Green, D., Perry, R., 2008, Perry's Chemical Engineers' Handbook. 8th edition. McGraw-Hill. • Kent, 1992, Riegel´s Handbook of Industrial Chemistry. • Lide, D., Ed., 1997, CRC Handbook of Chemistry and Physics. CRC Press. • McKetta, J., Ed. 1993, Chemical Processing Handbook. Marcel Dekker. • Poling, B., Prausnitz, J., O'connell, J., 2000, The properties of gases and liquids. 5th edition. McGraw-Hill. • Treybal, R., 1980, Mass Transfer Operations. 2nd Ed. McGraw Hill. • Woods, D., 1995, Data for Process Design and Engineering Practice. Prentice-Hall.
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