SPE 141058 Numerical Simulation and Multiple Realizations for Sensitivity Study of Shale Gas Reservoir A.Kalantari-Dahaghi, SPE; S.D Mohaghegh, SPE, West Virginia University
Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Production and Operations Symposium held in Oklahoma City, Oklahoma, USA, 27–29 March 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract Shale gas in the United States went almost instantly from a practically invisible resource to massive reserves that challenge the largest conventional gas accumulations in the world. Shale gas success is directly the result of economically managed deployment of petroleum technology, namely horizontal wells .Horizontal drilling and multi-stage stimulation technologies are driving the successful development of shale plays. Modeling and simulation of shale gas reservoirs poses a unique problem. The geological complexity of shale gas reservoirs— containing both natural and hydraulic fractures—makes accurate modeling a significant challenge. To overcome these challenges and maximize recovery of a shale gas field requires specialized methods and state-of-the-art technology. In the first part of this paper an integrated workflow, which demonstrates a quantitative platform for shale gas production optimization through capturing the essential characteristics of shale gas reservoirs was discussed. A comprehensive sensitivity studies on key matrix, fracture system and all other shale related properties were performed and the results were presented. This study attempted to show how sensitivity analysis applied to this model can be used to aid in the design and history matching of a complex shale gas system. In the second part of this paper the state-of-the-art technology using Artificial Intelligence and Data Mining (AI&DM) techniques which is called single well shale surrogate reservoir model (S3) has been built. Shale surrogate reservoir model is new solution for fast track, comprehensive reservoir analysis (solving both direct and inverse problems) using existing shale gas reservoir simulation models. This model was defined as a replica of the shale gas reservoir simulation model that ran and provided accurate results in real-time very fast and can be used for automatic history matching, real-time optimization, realtime decision-making and quantification of uncertainties. The intelligent model was verified using several completely blind simulation runs. Introduction A vibrant and fast-growing literature exists related to various aspects of gas shales, including operational (e.g., drilling, completion, and production) and technological challenges. The latter mainly involves difficulties in formation evaluation/characterization, in modeling gas–matrix-fracture phenomena, and in developing reliable reservoir simulators. In times, these studies directly point to difficulties in accurately predict the ultimate gas recovery and to explain high variability in gas well productivity, which are common to nearly all shale gas reservoirs. Shale gas plays, which require maximum reservoir exposure to be economic, have been solved through the use of long horizontal wells that are fractured in multiple zones along their several-thousands feet length ; therefore horizontal completions are one of the key things that have led to all of the successes. Numerical simulation is a powerful tool that integrates core, log, and well-test data to help quantify well behavior by assessing the effects of variations in key reservoir parameters, incorporating unique components such as directional permeability and the contributions of free gas and sorbed gas, and evaluating the effects of various development strategies
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including well spacing, well pattern, and fracture-stimulation design. Once constructed, the model can be updated with production data, static reservoir pressures, and producing bottom-hole pressures obtained on a regular basis to better understand and predict future well performance. Modeling and simulation of shale gas reservoir is challenging due to complex nature, strong heterogeneous and anisotropic system, different reservoir behavior, multiple gas-storage mechanisms and unique attributes that control productivity, which is vastly different from conventional reservoirs. Therefore building a general workflow is critical in order to capture all aspects of shale characteristics and to obtain a clear understanding and an accurate description of the reservoir. In spite of tremendous effort and progress, the key factors that dominate reservoir production remain somewhat unclear, and a systematic approach is needed to integrate the variety of information and capture key elements. Methodology For this study, an integrated workflow which demonstrates a quantitative platform for shale gas production optimization through capturing the essential characteristics of shale gas reservoirs using conventional reservoir simulation techniques has been proposed .The well based surrogate reservoir model with high accuracy using artificial intelligence has been developed and the model was tested using several new simulation cases which were completely blind to neural network. The resulting intelligent model can be used for performing automated AI-Assisted history matching (Figure 1)
Figure 1.An Integrated for Shale Reservoir Modeling and Simulation
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Results and Discussions PART 1-Shale reservoir model development and Sensitivity study
The development of a discrete fracture network (DFN) for use in flow simulations is a multi-step process. Fracture network can be modeled deterministically using direct input or stochastically based on input statistics. The fracture sets are created deterministically either as a result of fault plane extraction from seismic cube or as previously defined fractures .Fracture types that can serve as an input are: fault patches (fault plane extraction from a seismic cube),fault surfaces/polygons(converted from the faults in the 3D grid ,fault points) and a previously defined discrete fracture network. In stochastic DFN approach, fracture set will be modeled for the whole 3D grid, per region or within zones. Such a model requires three basic inputs: Fracture distribution, geometry and orientation. Stochastic fracture network can typically be fractures where location, size and orientation is not directly known, but can be inferred from statistics. A DFN using typical shale properties was generated stochastically based on 80 acre spacing. Two fracture sets have been defined based on the available data. The complex DFNs were up-scaled using both Oda and flow-based methods in order to simulate fluid flow through the system. Figure 2 illustrates the fracture sets, aperture, and length and sigma, fracture porosity and fracture permeability which are the results of upscaled discrete fracture network. The Fracture network characteristics used for the base model are shown in Table1. Fracture aperture was less than 10 micrometer or even less than 5 micrometer based on core analysis.
Figure 2.Discrete fracture network model-Fracture sets and aperture, length, sigma, fracture porosity and fracture permeability
Table1. Natural fracture network properties
Distribution
Geometry
Fracture
Fracture
Set
area/vol
1
0.1
2
0.05
Sides
4 4
Elongation Ratio
2 2
Length
Orientation Shape
Scale
Mean Dip
Mean Dip
Concentration
Azimuth Power Power
2.1 2.1
50 50
80
15
40
84
345
70
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Figure 3.Hydraulic fractures and logarithmic local grid refinement around them with global grid.
The modeled shale gas production well reaches a total depth of 2370 ft (driller’s depth) and has been completed with 4”production casing. The well was perforated and hydraulically fractured in eight stages. Figure 3 shows the logarithmic local grid refinement around the eight stages of hydraulic fractures of understudy shale gas well with associated global grids. The finest grid, which represents hydraulic fracture, has a permeability of 30 md and the rest of grid blocks have a fracture permeability value of 0.0004 md. As can be seen the finest grid, which is identified by red color, represents the hydraulic fracture. The well/field data Some basic well/reservoir data are listed as following: - Gas Composition: 85.1, 3.12, 0.25, 0.1, 0.2, 11.23 for (mol %) for C1, C2, C3, C4-6, CO2 ,and N2 respectively - Reservoir temperature:85(deg F) - Initial reservoir pressure:780 psi - Number of grid cells:139*42*5 (Corner point gridding method) - Grid size: 50*50 ft - Net pay thickness:100ft Because this well had no indication of water production, fracture and matrix have been assumed to be fully saturated with gas. The production rates along with known reservoir features have been imported to the model. Initial values for the adjusting parameters are chosen and the compositional simulation (dual porosity model) is run. Figure 4 illustrates the pressure distribution in reservoir after 15 years of production.
Figure 4. Shale matrix pressure distribution in the reservoir after 15 years of production
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Matrix Discretization Model-Traditional dual porosity models assume that the matrix to fracture flow is in steady state, and thus the matrix cell can be regarded as a single cell. In shale gas reservoirs, the flow is not instantaneous and requires matrix subdivision to capture transient nature of the matrix to fracture flow. Typically, shale gas reservoirs have multi porosity system (micro porosity, fractures and organic content) To model these systems a discretized matrix model can be used, which sub-divides each matrix cell into a series of nested sub-cells, allowing the simulator to predict the transient behavior in shale matrix otherwise the long production transients, characteristic of very low-permeability formations, are not captured properly. Sub-grids are logarithmic away from the fracture wall. The matrix cells are only connected to their corresponding fracture cell, but flow to the matrix surface is supplied from a 1-D grid system. The matrix subdivision can be set up by specifying the number of sub-cells that each matrix cell is going to be split into. In order to capture long transient flow through the shale matrix, matrix discretization model is used .As illustrated in Figure 5 the transient flow facilitated by matrix subdivision has a significant impact on early gas production and is a key factor during history matching process
Figure 5.Effect of transient flow because of matrix discretization on shale gas production rate and cumulative production
Comprehensive Sensitivity study After building the reservoir model, sensitivity analysis was applied to recognize the relative importance of each of the input parameters. If a small change in the input parameter or boundary condition causes a significant change in the output, the model is sensitive to that parameter or boundary condition. Sensitivity analysis was performed on seventeen parameters that have been used on shale simulation and listed on Table 2. Table 2.Shale gas simulation parameters
Matrix permeability
Fracture half length
Non-Darcy coefficient
Max. Gas content
Matrix porosity
Hydraulic frac. height
Rock compaction
Sorption type
Fracture permeability
Hydraulic frac. spacing
Diffusion coefficient
Fracture porosity Sigma
Hydraulic frac. conductivity Number of Matrix sub grids
Poisson ratio Young’s modulus
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Figure 6. Uncertainty analysis on hydraulic fracture length (ft), hydraulic fracture spacing (ft) and corresponding matrix pressure distribution correspondingly (From left to right)
Figure 6 illustrate the effect of fracture length and consequence of less hydraulic fracture spacing and number of stages on shale gas reservoir depletion and production. Optimizing the number of stages and creating optimum fracture length could guarantee efficient shale production. As illustrated in Figure7, which represents the comparison of the influence of most of shale properties on cumulative production based on the sensitivity analysis results, the key parameters that have substantial effect on production behavior are natural fracture permeability, sigma and hydraulic fracture parameters including fracture spacing, height, half-length and conductivity. Therefore, a successful hydraulic fracture design and modeling is a critical factor on unlocking most of shale plays.
Sensitivity Study Instant sorption vs.Time dependent Natural fracture permeability
Shale-gas simulation parameters
Matrix-to-fracture coupling factor(Sigma) Hydraulic fracture spacing Hydraulic fracture height Hydraulic fracture half length Matrix Discretization Shale Gas content Hydraulic fracture conductivity Matrix permeability Matrix Porosity Natural fracture porosity Non-Darcy flow effect Rock compaction Shale matrix diffusion Coefficient Poisson ratio Young's modulus 0
10
20
30
40
50
60
Degree of influence% Figure7. Effect of all parameters on shale gas cumulative production
70
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90
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PART 2-Single wells Shale Surrogate reservoir Model development (S )
Surrogate Reservoir Model (SRM) is new solution for fast track, comprehensive reservoir analysis (solving both direct and inverse problems) using existing reservoir simulation models. SRM is defined as a replica of the full field reservoir simulation model that runs and provides accurate results in real-time (one simulation run takes only a fraction of a second). SRM mimics the capabilities of a full field model with high accuracy. SRM is developed using the state of the art in neural computing and fuzzy pattern recognition to address the ever growing need in the oil and gas industry to perform accurate, but high speed simulation and modeling. (Mohaghegh 2010) Single well shale surrogate reservoir model (S3) has been developed using 38 different simulation runs of 13 shale reservoir properties(design parameters) that are summarized in Table 2, in order to predict the cumulative production. Back propagation neural network with one hidden layer that includes 70 neurons has been built and used for training, calibration and verification (Figure 8).
Figure 8. Back propagation neural network architecture
Intelligent data partitioning has been performed and 70, 15 and 15 percent of data set have been used for training, calibration and verification respectively. 21 Cases have been defined and examined in order to get best training, calibration and verification results. In order to provide a more improved reservoir definition to the network cum. t-1, cum. t-2, hydraulic fracture height to net pay thickness ratio and fracture permeability to matrix permeability ratio have been used as input. It is worthwhile to note that while the contribution of matrix permeability in shale gas reservoir itself is not very significant, fracture/matrix permeability ratio is observed to be at a very high rank. This ratio defines the contrast between the two permeabilities. Fracture permeability provides the delivery of gas to the wellbore, while the matrix permeability contributes to the rate of diffusion from matrix to fracture. In order to take Ito account the sorption type, 0 and 1 were assigned to instant and time dependent sorption. It was observed that taking logarithm of input and output data to reduce the range of data improved the performance of network extensively. With the abovementioned change to the input data, the training, calibration, and verification results were improved noticeably. Figure 9 and Figure 10 are the cross-plots for cumulative methane production in training, calibration and verification. These graphs show a very nice correlation between the commercial simulation model and shale surrogate reservoir model results. The R2 obtained during training, calibration and verification are more than 0.9998. R2 is a statistical measure of how well the network’s outputs match the real data (in this study, data from the commercial simulator). An R2 value of 1 shows perfect match and a value of zero, no match.
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Figure 9. Actual vs. network cross-plot of cumulative CH4 production for all data points used in Back propagation neural network training and calibration. (Left to right)
Figure 10. Actual vs. network cross-plot of cumulative CH4 production for all data points used in BPNN verification and all the case together (training, calibration and verification). (Left to right)
Figure 11. Actual vs. neural network scatter-plot of cumulative gas production in verification process
As shown in Figure 11, the initial verification of neural network completed with very high accuracy (R2=0.99985) using 15 % of input data. It demonstrated the capability of SRM on performing prediction for future reservoir behavior. In the process of SRM design, Key Performance Indicators (KPI) can be identified, by using fuzzy pattern recognition technology. As seen in Figure 12, twelve parameters were ranked based on the degree of their influence on the model’s output. This technique can become very helpful when the number of input parameters to the system is relatively high and the engineer needs to identify, use only the most influential parameters, and discard the less influential parameters. It should be noted that the engineer’s expertise is very important since some parameters need to be included in model development even if they are ranked low in the KPI identification process.
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Figure 12.KPIs identified for the SRM development
Figure 13 shows a perfect result of SRM prediction for one of the inputs as an example. Blue line represents the real data (conventional simulation result) while the red shows the SRM predication results for 15 years of production. Run # 9 350001
300001
Cumulative(mscf)
250001
200001
Real
150001
SRM
100001
50001
1
0
20
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60
80
100
120
140
160
180
200
Time(month)
Figure 13. Cumulative rate predication for 15 years of production
Once the SRM is developed and validated, it can be used to generate gas production profiles for the given shale reservoir characteristics. The SRM that was built to represent this reservoir simulation model was validated initially using 15% of total input cases (blind data) and had proven to be quite accurate with R2 of 0.99985.But, in order to examine the capability of network five data sets have been defined and production history for 15 years has been generated using Eclipse (completely new runs). Those five cases were completely blind and network did not see them before and the network predicts the cumulative production with very high accuracy. Figure 14 and Figure 15 shows the perfect result of SRM predication for four completely blind cases. Red dots represent the SRM prediction and blue shows the conventional simulation output.
Figure 14: Cumulative rate predication for 15 years of production (blind data set) (Km of 2e-5 and Φf of 0.5%)
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Figure 15: Cumulative rate predication for 15 years of production (blind data set) (Max. gas content of 0.09 and Φm of 3%)
Figure 16: Cumulative rate predication for 15 years of production (blind data set) (Changing 6 input parameters)
Figure 16 shows the comparison of simulation and SRM predication result with a good accuracy. In this case six input parameters including fracture and matrix porosity and permeability, sigma and maximum Langmuir volume have changed simultaneously (completely blind values to the network) to see the capability of SRM on prediction of cumulative production for 15 years in fraction of second. The results were used for important decision-making on the future of the field and optimum operation of the horizontal wells in a typical shale gas reservoir. The ultimate objective of this study is developing an AI-assisted history matching tool for shale formation with multiple stages of hydraulic fracture. Developing a Surrogate Reservoir Model that is capable of accurately representing the reservoir simulation model with all its details and complexity is a major step toward AI-assisted history matching. This study shows preliminary result on building a successful SRM for shale gas reservoir. Even though the SRM presented in this article has some limitations, it shows promising result. The limitations of the SRM that is presented here is that it needs some information from the simulation run (such as initial production) in order to be able to make good predictions. This is a limitation since the objective of the SRM is to be able to make complete prediction autonomously with no input from the simulator. This is a well known limitation that can be overcome. Such limitation has successfully been addressed and resolved on previous SRM development projects therefore we feel comfortable to solve this issues. Results of removing these limitations and the new SRM will be presented in future papers.
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Conclusion Comprehensive sensitivity study has been performed on all parameters, which play role in production from shale gas reservoirs. The results of this study showed that the fracture properties (both natural and hydraulic) could have a profound effect on the productivity of shale reservoirs therefore optimizing the multi-stage hydraulic fracture treatment design could guarantee the successful production from most of shale plays. In order to accurately model non-Darcy flow in hydraulic fractures, LGR grids have been used. Compositional simulator is used along with dual porosity model to simulate flow in shale gas reservoir. Matrix discretization technique was examined successfully to capture transient behavior of flow in shale. Shale surrogate reservoir model has been developed successfully and it has been validated by two steps verification process which in the final one, several parameters were changed individually and simultaneously which were completely blind to the network. The SRM could predict production profile for 15 years with high accuracy so quick (a fraction of second). Shale surrogate reservoir model provides instantaneous results and respond to change of shale properties that are used in the model construction and ease the history matching through AI-assisted history matching process. Acknowledgement Authors would like to acknowledge Intelligent Solutions Inc. for providing for supplying us with IDEA software package and also special thanks to Schlumberger for providing Eclipse and Petrel softwares. References Mohaghgeh, S.D., “Surrogate Reservoir Model” European Geological Union General Assembly, Vol. 12, EGU2010-234, 2010 Mohaghegh, S.D.;Hafez, H.; Gaskari, R.;Haajizadeh, M., and Kenawy, M.” Uncertainty Analysis of a Giant Oil Field in the Middle East Using Surrogate Reservoir Model” SPE 101474, Abu Dhabi, U.A.E. November 2006.
