spe 125959 reservoir simulation and uncertainty analysis...

SPE 125959

Reservoir Simulation and Uncertainty Analysis of Enhanced CBM Production Using Artificial Neural Networks J. Jalali, SPE, and S.D. Mohaghegh, SPE, West Virginia University

Copyright 2009, Society of Petroleum Engineers This paper was prepared for presentation at the 2009 SPE Eastern Regional Meeting held in Charleston, West Virginia, USA, 23–25 September 2009. 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

Coalbed methane is becoming one of the major natural gas resources. CO2 injection into CBM reservoirs is used as

an effective method for CBM production enhancement (ECBM) and for long term sequestration of CO2 (CO2Seq). Reservoir

simulation is used regularly for building representative ECBM and CO2Seq models. Given the wide range of uncertainties

that are associated with the geological models (that forms the foundation of any reservoir simulation), comprehensive

analysis and uncertainty quantification of ECBM and CO2Seq models become very time consuming if not impossible.

This paper addresses the uncertainty quantification of a complex ECBM reservoir model. We use a new technique

by developing a Surrogate Reservoir Model (SRM) that can accurately mimic the behavior of the commercial reservoir

model.

Upon validation of SRM, we perform Monte Carlo Simulation (MCS) in order to quantify the uncertainties

associated with the geological (CBM) model. Performing MCS requires thousands of simulation runs that can be performed

easily once the SRM is developed. Key Performance Indicators (KPI) of the simulation model are identified to help reservoir

engineers concentrate on the most influential parameters on the model’s output when studying the reservoir and performing

uncertainty analysis. Unlike conventional geo-statistical techniques that require hundreds of runs to build a response surface

or a proxy model, building an SRM only requires a few simulation runs.

Introduction Reservoir simulation provides information on the behavior of the reservoir under various production and/or injection

scenarios. Reservoir engineers and managers use reservoir simulators to better understand the reservoir, perform future

performance predictions and uncertainty analysis. Because of non-uniqueness of simulation models and uncertainties

associated with the geo-cellular model (reservoir parameters), uncertainty analysis becomes an important task that is required

for making operational decisions, since such decision making process necessitates the quantification of model uncertainties.

Different techniques are used to quantify the uncertainties associated with reservoir parameters. MCS is a technique

that is widely used in the oil and gas industry for the purpose of uncertainty analysis. Since MCS uses a statistical

representation of parameters being studied, it requires thousands of reservoir realizations in order to provide a meaningful

(statistically representative) conclusion on the effect of uncertain parameters on the model’s performance. Generating

thousands of simulation models especially in case of large and complex models, which could take a long time to make a

single simulation run, is impractical. Attempts have been made to perform uncertainty analysis with as small number of

realizations as possible. Common techniques that have gained popularity in the oil and gas industry are the Experimental

Design technique and Reduced Models. Response Surface Models are generated in order to analyze the results obtained from

Experimental Design.

Experimental Design has been used in reservoir simulation since 1990s. It is used to get maximum information at

the lowest experimental cost, by changing all the uncertain parameters simultaneously. It is essentially an equation derived

from all the multiple regressions of all the main parameters that affect the reservoir’s response (1)

. Many studies have shown

that by using the Experimental Design the reservoir model still needs to be run hundreds of times.

Reduced Models are approximations of full three dimensional numerical simulation models that approach an

analytical model for tractability (2)

.

This paper presents the application of a recently developed technique for reservoir simulation and modeling, called

Surrogate Reservoir Modeling (SRM), to model and analyze an enhanced coalbed methane project. The CBM reservoir used

in this analysis is a synthetic reservoir with characteristics representative of a coal in the Appalachian Basin. All the reservoir

2 Modeling & Uncertainty Analysis of ECBM Using ANN SPE 125959

simulation is performed using a commercial reservoir simulator (3)

.

Methodology Surrogate Reservoir Models are essentially Artificial Neural Networks that behave like a reservoir simulation model.

The key to successful SRM development is design, preparation and compilation of reservoir simulation runs and results in a

manner that is most appropriate for use with Artificial Intelligence and Data Mining (AI&DM) techniques such as neural

networks and fuzzy systems. Once trained, the SRM can run thousands of simulation runs in a matter of seconds. Also, the

number of reservoir realizations required to develop the SRM is significantly small when compared to other techniques. The

reason SRMs can be developed with a small number of realizations is due to the way a single reservoir model is presented to

the SRM. Interested readers are encouraged to review other published papers by the authors to learn more about SRMs (4)(5)(6)(7)

.

In this study, an Enhanced Coalbed Methane (ECBM) reservoir is analyzed. An Artificial Neural Network (ANN) is

trained as the Surrogate Reservoir Model (SRM). The developed SRM can be considered a prototype of the full-field

reservoir model that was developed earlier using a commercial reservoir simulator.

Model Information

The synthetic reservoir used in this study is a single-layer coal with 13 Pinnate pattern wells (wells with branching

laterals also known as fishbone). Production from the reservoir starts at the beginning of year 2000 (start of the simulation)

from all the wells producing at a constant Bottom-Hole Pressure (BHP) of 50 psia. Primary production continues for 2 years.

Figure 1 is the structure of the CBM reservoir modeled in this study.

Figure 1: Structure of the CBM reservoir. Grid tops are shown in this figure.

After the completion of primary production from all thirteen wells, four wells at the bottom-left corner of the

reservoir (indicated as Group 1 in Figure 1) are converted into injectors. At the same time, as these four wells are converted

into injectors, the next four wells (indicated as Group 2 in Figure 1) are shut in for the rest of the simulation time, and the

remaining five wells (indicated as Group 3 in Figure 1) continue producing for the rest of the simulation time (the end of

2015).

The objective of this study was to develop an SRM that can predict CH4 and CO2 production of group 3 wells as a

function of CO2 injection rate of group 1 wells. Data from the first 5 years of production is introduced to the network and the

network will predict the wells’ production for the next 10 years. Also, using the developed SRM, uncertainty analysis is

performed on the reservoir parameters that were used in the model.

As part of the SRM development process, an elemental volume is defined in the reservoir that is a function of the

SPE 125959 Jalali and Mohaghegh 3

number of the wells. An Estimated Ultimate Drainage Area (EUDA) is identified for each well using Voronoi graph theory

(8). Then the EUDA is divided into four segments making a total of 52 segments for the entire reservoir. Static and dynamic

properties then are averaged for these segments. The segment properties are introduced to the SRM in order to provide a

picture of the reservoir’s characteristics.

SRM dataset is divided into cell-based and well-based data. Cell-based data are the reservoir properties, such as

depth, thickness, porosity, permeability, etc. Well-based data include well location, well configuration information, and well

production data. Tables 1 and 2 are the list of cell-based and well-based data used in this study, respectively. Note that

reference points mentioned in these tables refer to specific times that the reservoir properties are calculated. Reference points

1, 2, and 3 are years 2000, 2002, and 2005, respectively.

Table 1: Cell-based data used for SRM development.

Cell-Based Data used as input data to SRM CH4 adsorption @ reference points 2 and 3 CO2 adsorption @ reference point 3

Fracture CH4 mole fraction @ reference point 3 Fracture CO2 mole fraction @ reference point 3

Matrix CH4 mole fraction @ reference point 3 Matrix CO2 mole fraction @ reference point 3 Fracture Gas saturation @ reference points 2 and 3 Fracture pressure @ reference points 2 and 3

Water saturation @ reference points 2 and 3 Permeability

porosity Thickness

Table 2: Well-based data used for SRM development.

Well-Based Data used as input data to SRM Cumulative CH4 production of 3 offset wells from 2000 to 2005

Cumulative CO2 production of 3 offset wells from 2000 to 2005

Well location X Well location Y

Well’s main leg length Well’s first lateral length

Well’s second lateral length Well’s third lateral length

Well’s total length CO2 injection rate of 4 injectors @ 2002 and 2005

Date Distance from 3 offset wells

Cumulative CH4 Production of the 3 offset wells from 2000 to 2005

Cumulative CO2 Production of the 3 offset wells from 2000 to 2005

During the SRM development, input parameters are ranked based on their influence on the model’s output. This

process is important especially when the number of input parameters is high and the engineer has to choose a limited number

of parameters as input for the SRM. The parameters that have the highest impact on the model’s output are called Key

Performance Indicators (KPIs).

Figure 2 shows the schematic of the well pattern used for all the wells in the reservoir and SRM segments. Cell-

based properties are averaged for these segments and introduced to the SRM as input data.

Figure 2: Shows an schematic of well branches and SRM segments.

We assume to know the reservoir’s production for the first 5 years from 2000 to 2005. This usually is the case when

a history matched model is going to be used for field development strategies. We are assuming that the model has been

history matched with field production from 2000 to 2005. Therefore, some of the production data, such as cumulative CH4

and CO2 production from the three offset wells of each producing well, can be introduced to the network. Introduction of

offset wells is important in network training especially if well interference exists. Also, other cell-based properties, such as

pressure, gas and water saturation, etc. before or at 2005 can be introduced to the network.

The formation in this study has a fracture permeability of between 7 and 60 mD, fracture porosity between 5 and

14%, and an initial reservoir pressure of 1,400 psia.

Since the objective of the SRM was to predict cumulative CH4 and CO2 production due the CO2 injection rate from


the injector wells, 8 different reservoir simulation cases were generated, each with a different injection rate. Please note that

unlike Experimental Design technique used for the development of response surfaces that may require hundreds of runs,

development of this SRM only required 8 simulation runs. All four injector wells in a simulation case had the same initial

CO2 injection rate. However, in the case of higher injection rates, some injection wells reached the maximum allowable BHP

and their injection rate decreased. A maximum allowable BHP was imposed on the injection wells in order to avoid

fracturing the formation and possibly the cap rock and providing a leakage path for the injected CO2. Maximum allowable

BHP of 1,400 psia (initial reservoir pressure) was used as the well control. Table 3 shows the injection rates selected for

each simulation case ranging from 100 to 1,000 Mscf/day for each well. The range of injection rate used in training cases

should be selected based on the ECBM project plan.

Two separate cases of the model were built in order to test the SRM’s prediction. The injection rates selected for

these two cases were in the abovementioned range.

Table 3: Shows the CO2 injection rates in the simulation cases used for SRM development.

Case Number CO2 Injection Rate, Mscf/day 01 100 02 250

03 350

05 500

07 700

08 750

09 900 10 1,000

Figure 3 is an example of a CO2 injection profile for a well in simulation case 03. A total of about 7 BCF of CO2 is

injected at a rate of 350 Mscf/D per well through four injection wells during a period of 14 years (this is an equivalent of 80

tons of CO2 injection per day for the entire field). The entire injected CO2 will not be stored in the coal due to CO2

breakthrough and its production through the production wells (Group 3 wells in Figure 1).

0

50

100

150

200

250

300

350

400

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

Inje

ctio

n R

ate

, M

SC

F/

Da

y

Time, date

CO2 Injection Rate - Well 1

Start of CO2 Injection

Figure 3: Injection rate profile of injection well 1 in case 03 (350 Mscf/day).

Once the SRM is trained and validated, it can be applied to any scenario of the model. Uncertainty analysis can be

performed on any of the input parameters. An example of such analysis is provided in the results section.

Results

As mentioned earlier, 8 simulation cases were used to develop the SRM. In this study, a Back-Propagation Neural

Network (BPNN) (9)

was used as the neural network architecture for the SRM (Figure 4). The network has 84 input

parameters and one hidden layer with 100 neurons. The outputs of the network are Cumulative CH4 and CO2 production

between years 2005 and 2015.


Input Layer

Hidden Layer

Output Layer

Figure 4: Schematic of BPNN architecture.

Table 4 is a snapshot of the KPI calculations’ outcome that shows some of the input parameters in the dataset used

in this study. KPI calculation is performed on each output parameters and the top KPIs that are common in all KPI

calculations then can be used as input to train the SRM.

Table 4: KPIs ranked based on cumulative CH4 production (a) and CO2 production (b) as the output.

a b

Rank Feature % Degree of Influence

1 Pressure_Frac_Ref2_Seg4 100

2 Thickness_ft_Seg2 100

3 Gross Block Volume_ft3_Seg1 100


5 Total_Length 100

6 Ads_CH4_Ref2_Seg3 100

7 CH4_Prod_2005_W1 99



10 FirstLeg 99


12 Permeability_Seg1 99

13 D_W2 98

14 X-COORD 97

15 SW_Frac_Ref2_Seg4 97

16 SG_Frac_Ref2_Seg4 97








24 SecondLeg 91


Output: CH4

Rank Feature % Degree of Influence






6 Mole_Frac_CO2_Ref3_Seg1 75

7 Mole_Frac_CH4_Ref3_Seg1 75





12 CH4_Prod_2005_W2 69





17 Total_Length 66


19 D_W2 66


21 SecondLeg 65



24 FirstLeg 65

25 Permeability_Seg1 65

Output: CO2

Figure 5 shows the relative influence of the initial injection rate of well 1 on the cumulative CH4 production. As the

graph shows, cumulative CH4 production increases as the initial injection rate increases.


Figure 5: Influence of initial injection rate of well 1 on the cumulative CH4 Production.

Figures 6 and 7 are the cross-plots for cumulative CH4 and CO2 production, respectively. These graphs show good

correlation between the commercial simulation model and SRM results. The R2 obtained for both outputs is more than 0.99.

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.

Figure 6: Cross-plot of Cumulative CO2 production for all data points used in BPNN training.

R2 = 0.999


Figure 7: Cross-plot of Cumulative CH4 production for all data points used in BPNN training.

As mentioned earlier, two new cases were built in order to test the SRM’s predictions. CO2 injection rate in the two

cases 04 and 06 are 400 and 600 Mscf/day, respectively. Figures 8 and 9 compare the results of the SRM and the

commercial simulator for cumulative CO2 production in case 04 between years 2005 and 2015. The SRM results show good

agreement with the commercial simulator results.

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

CO

2 P

rod

uct

ion

, M

SC

F

Time, year

Model 4 - Well 8 CO2

SRM

CMG

11% Error

PINN_INJ_001

PINN_INJ_002

PINN_INJ_003

PINN_INJ_004

PINN_PRO_001

PINN_PRO_002

PINN_PRO_003

PINN_PRO_004

PINN_PRO_005

PINN_PRO_006

PINN_PRO_007

PINN_PRO_008

PINN_PRO_009

PINN_PRO_010

PINN_PRO_011

PINN_PRO_012PINN_PRO_013

Figure 8: Results of SRM and CMG for cumulative CO2 production in well 8, model 4.

R2 = 0.999


0

50,000

100,000

150,000

200,000

250,000

300,000

2005 2006 2007 2009 2010 2012 2013 2014 2016

CO

2 P

rod

uct

ion

, M

SC

F

Time, date

Model 4 - Well 13 CO2

SRM

CMG

14% Error

PINN_INJ_001

PINN_INJ_002

PINN_INJ_003

PINN_INJ_004

PINN_PRO_001

PINN_PRO_002

PINN_PRO_003

PINN_PRO_004

PINN_PRO_005

PINN_PRO_006

PINN_PRO_007

PINN_PRO_008

PINN_PRO_009

PINN_PRO_010

PINN_PRO_011

PINN_PRO_012PINN_PRO_013

Figure 9: Results of SRM and CMG for cumulative CO2 production in well 13, model 4.

One of the main characteristics of an SRM is its capability to perform uncertainty analysis in a short time. The

simulation time for this reservoir (a 50x50x1 grid system) in the commercial simulator was about half an hour, where in the

developed SRM, this time was only a fraction of a second.

This capability becomes very helpful when a single simulation run could take hours or days due to its complexity

and the available computer power. Performing uncertainty analysis usually requires thousands of runs in order to provide a

meaningful conclusion on the effect of the reservoir parameter on its output.

As an example, let us consider permeability of well1-segment1 to be the uncertain parameter. Based on available

information about this parameter, one can choose different Probability Distribution Functions (PDF) to describe the

probability of having a permeability value for this segment. Different PDFs, such as uniform, Gaussian, Triangular, etc. can

be selected for this property. For example, we can choose a triangular distribution function for permeability with a minimum

value of 35, maximum value of 50, and a most likely value of 45 mD. The triangular PDF then generates random values of

permeability based on the minimum, maximum, and most likely values. For this parameter, the SRM was run 5,000 times

and the results of this analysis are shown on Figures 10 and 11. The 5000 SRM runs to perform this analysis took less than

10 seconds.

Figure 10: Result of MCS for cumulative CH4 production of well 13 with change in permeability of well1-segment1.


Figure 11: Result of MCS for cumulative CO2 production of well 13 with change in permeability of well1-segment1.

It can be seen that with a change of permeability in well1-segment1 between 35 and 50 mD, cumulative CH4

production ranges between 300 and 800 MMSCF with a most likely value of around 368 MMSCF. On the other hand,

cumulative CO2 production changes between 40 and 80 MMSCF with a most likely value of around 68 MMSCF.

Conclusions This paper presented the application of a recently developed reservoir simulation and modeling technique, called

Surrogate Reservoir Modeling (SRM), to model and analyze a synthetic enhanced coalbed methane project. Upon the

completion of the SRM training, calibration, and validation, uncertainty analysis of the input parameters is performed in a

short time (seconds), significantly shorter than the time required for this procedure using a numerical reservoir simulator.

Also, only 8 simulation runs were used to train, calibrate, and validate the SRM, which is a significantly smaller number of

simulation runs when compared to other techniques.

Acknowledgment

Authors would like to thank Computer Modeling Group (CMG) for providing the CMG reservoir simulator for

development of the reservoir models and Intelligent Solutions, Inc. (ISI) for providing the Intelligent Data Evaluation &

Analysis (IDEA) (10)

software for the development of the SRM.

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R., Haajizadeh, M., and Kenawy, M. Abu Dhabi, U.A.E. : SPE 101474, 2006.

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8. What is Voronoi Diagram in Rd. [Online] http://www.ifor.math.ethz.ch/~fukuda/polyfaq/node29.html.

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