SPE Eastern Regional Meeting 2016

SPE-184069-MS

Reservoir Simulation Using Smart Proxy in SACROC Unit - Case Study Qin He, Saint Francis University, Shahab D. Mohaghegh, Intelligent Solutions, Inc.& West Virginia University, Zhikun Liu, Xi'an Shiyou University

Copyright 2016, Society of Petroleum Engineers 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 In oil and gas industry, quick decisions on reservoir management have a huge impact on business

success. Reservoir simulation is used as a typical tool to predict field performance and analyze

uncertainties for assistance on decision making. Nevertheless, history matching, as a critical step of

reservoir simulation, typically requires running a numerical simulation model repeatedly with different

parameter settings, which is a huge computational cost, especially for complicated geological models

with numerous grid cells. For reservoir engineers, how to achieve efficient reservoir simulation by

taking full advantage of field data without compromise on the simulation time is a big concern.

In this work, Smart Proxy, as a relative new proxy model type, is proposed to investigate the feasibility

of fastening history matching process as an alternative. Smart Proxy is an ensemble of Artificial

Intelligence and Data Mining (AI&DM) technologies that are able to learn and replicate the behavior of

reservoir simulation model with high accuracy. It can be developed off line and put online for automatic

history matching at high speed such that a single run can be performed in a fraction of a second

(Mohaghegh 2006).

This paper presents the Smart Proxy generation and its implementation in a real oilfield simulation case

named SACROC Unit. It essentially involves detailing numerical reservoir simulation and Smart Proxy

generation for a naturally fractured carbonate numerical simulation model with highly complicated

development stages. The developed Smart Proxy is implemented to perform automatic history matching

in the designated study area of SACROC Unit. The efficient history matching has been proven to be

successfully accomplished using Smart Proxy simulation. Tremendous time and efforts have been saved

without any compromise on simulation accuracy compared with that of traditional numerical reservoir

simulation method.

Introduction Reservoir simulation has been a typical tool for reservoir management in terms of providing reservoir

performance prediction, uncertainty analysis and optimization design. History matching, as a

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fundamental step in reservoir simulation, should be performed as a calibration process with adjusting

various uncertain reservoir parameters over successive simulation runs aiming to minimize the

discrepancy between simulated and observed values (Rwechungura 2011). Typically, history matching

is carried out manually with the involvement of the engineers’ understanding on the study case, which

benifites the validity of simulation. On the other hand, to a great extend, manual history matching relies

on the experience of the engineers who carry out the simulation, which is considered very subjective.

Besides, while dealing with a reservoir model consisting of hundreds of thousands or even millions of

grid blocks, short-comings of manual history matching will be easily noted as process tedious, time

consuming and computational expensive.

In order to speed up history matching process, techniques of improving the optimization methodologies

applied in automatic or assisted history matching, such as Simulated Annealing, Evolutionary

Algorithms, Evolution Strategy, Ensemble Kalman filter et al. have been widely studied for the past

decades (Chen et al., 1974; Yang et al., 1988; Wang et al., 2000; Gomez, et al., 2001; Maschio et al.,

2002; Agarwal et al., 2003; Aziz et al., 2007). Although great contribution has been made in terms of

applications of optimization methods, they are found to function inefficiently in multi-dimensional, non-

linear reservoir conditions which have hindered them to become a standard in reservoir simulation cases

(Cancelliere et al., 2011).

Correspondingly, development of efficient proxy models has become another alternative of improving

simulation efficiency. Proxy model, also named surrogate model, is adopted as an inexpensive way to

resemble a numerical simulation model when full detailed reservoir simulation is not accessible. An

efficient proxy model enables replicating the reservoir behavior with high accuracy within short

computational time. Response Surface Methodology (RSM), Reduced order model (ROM) and Reduced

Physics Model (RPM), as different types of proxy model, have been widely studied and applied in

different simulation cases (Narayanan et al., 1999; Yeten et al., 2005; Pan et al., 2010; Wilson et al.,

2012; Shi et al., 2013; Azad et al., 2013; Yoon et al., 2014; Ghasemi et al., 2014;). Those proxy models

have been deemed as easy to estimate and apply, however, disadvantages of these proxy models such as

few enhancement on computational time, too much simplification on physics or mathematics, etc. stuck

their way on the applications of various simulation cases.

Smart Proxy, different from the abovementioned proxy models, is essentially data driven based proxy

model. Generally, Smart Proxy injects the idea of pattern recognition and machine learning technologies

that enables learning and mimicing the simulator’s behavior with high accuracy and speed, which can be

developed regularly off line and put online for automatic history matching and real time processing

(Mohaghegh et al. 2006). The objective of this paper is to utilize Smart Proxy to perform history

matching with the reproducuction of the monthly oil and water production rate in the study area of a full

field case (SACROC unit). The Smart Proxy development requires and is based on the numerical

simulaton model of SACROC Unit. The employed methodology in this paper to achieve the objective

can be summarized as:

(i) Generating the numerical simulation model

(ii) Developing a spatial-temporal database based on a handful numerical model simulation runs

(iii) Training a database with designated inputs and output from the spatial-temporal database

(iv) Validating the trained Neural Network, which can be the final Smart Proxy

(v) Performing automatic history matching by integrating the Smart Proxy with optimization

algorithm

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Smart Proxy Smart Proxy, previously named as Surrogate Reservoir Model (SRM), is fundamentally different from

any other proxy models, which is a new generation of proxy method classified as an artificial

intelligence based proxy model. It is firstly presented by Shahab Mohaghegh (2006) stating it as

“ensemble of multiple, interconnected neuro-fuzzy systems that are trained to adaptively learn the fluid

flow behavior from a multi-well, multi-layer reservoir simulation model, such that they can reproduce

results similar to those of the reservoir simulation model (with high accuracy) in real-time (Mohaghegh

2006). Since 2006, the applications of Smart Proxy have been widely performed as an accurate and rapid

replica of numerical simulation model in different cases (Kalantari-Dahaghi et al. 2011; Mohaghegh et

al. 2012; Shahkarami et al. 2014; Aminian et al. 2014; Haghighat et al. 2015).

The central of Smart Proxy modeling is the useful data extraction from numerical reservoir simulation

realizations. It all begins from a handful simulation scenarios’ design depending on the simulation

objectives. In this case, the purpose is to perform history matching, realizations with different porosity

and permeability distribution can be designed to cover as much heterogeneity as possible of the reservoir

static properties. If the objective is to perform field optimization, different scenarios of variable

operational constraints, such as injection pressure, bottom-hole pressure can be designed. The rule of

thumb regarding the number of simulation runs is to cover as much necessary information as possible

depending on the purposes in each case. It is possible that the proxy model can not capture the required

behaviors of the simulated reservoir without enough simulation runs; while too many simulations runs

result in reconsideration of the necessity of Smart Proxy generation.

Once the simulation runs are conducted, necessary static and dynamic data of the simulation realizations

need to be extracted in order to generate a representative spatio-temporal database, which commonly

contains hundreds of columns of parameters. Typically, static data refers to as the reservoir properties,

which keep constant over simulation time, such as reservoir depth, porosity, permeability, and thickness;

while dynamic data are the information that tend to vary, such as operational constraints, production

rate, phase saturation, etc. The spatial-temporal database is a basis for selection of necessary parameters

that are used for training process. Key performance indicator (KPI) that ranks the influence of different

properties is used for assisting inputs and output determination of the final dataset for the training, which

includes training, calibration and verification subsets. Specifically speaking, training set is the part

shown to the neural-network during the training process, which allows the ANNs to learn the

relationship between the inputs and output for finally matching the provided output; calibration set is

utilized to assure a corresponding increase in accuracy for the data set that has not been seen by the

ANNs as the accuracy of training data set increases, which is a reference for deciding whether the

training should be stopped or not, while verification step, which has not been learned by the ANNs

either, is used for verifying the predictability of the trained ANNs. Furthermore, a validation of the

ANNs robustness must be testified by a blind case run after the training process, which again has never

been used during the training process. As long as the training and verification results are satisfied, the

Proxy Model is officially ready for further analysis.

Compared with other proxy models, the beauty of Smart Proxy is its capability of replicating simulation

responses accurately as a function of changes of all the involved input parameters (reservoir

characteristics and operational constraints) in a fraction of a second by running only a handful

simulation scenario (Aminian et al. 2014). The debate of Smart Proxy is that this artificial intelligence

based model ignores the physics. Actually, all physical meanings of the system have been carried in the

generated database of Smart Proxy that includes both static and dynamic information of reservoirs.

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Although the physical functions in Smart Proxy are not directly perceived and pre-defined like some

other models, the neuron network has the ability to learn and mimic the physical process.

Numerical Simulation Model

The SACROC unit (Scurry Area Canyon Reef Operational Committee Unit), as the main part of the

Kelly-Snyder field, lies along a trend of fields described as the Horseshoe Atoll Play on the northeastern

fringe of the Permian Basin in Scurry County, West Texas (Han et al. 2008). It was discovered in 1948

and went through primary depletion with the main drive mechanism being solution gas expansion and a

water flood initiated with an injection rate of 132,000 barrels of water per day in 1954. Over 17 years of

water injection, continuous CO2 injection slug process begun in early 1972 as an alternative method for

improving recovery in the SACROC Unit, in which CO2 slug is injected followed with water until 2004

in the study area (Dicharry et al. 1973).

A high-resolution geo-cellular model representing the northern platform of SACROC field was

constructed by Texas Bureau of Economic Geology with an approximate size of 4km wide and 10km

long. The reservoir model consists of 221 layers within five geological zones vertically and 149×287

cells spatially, which is a total of 9,450,623 grid blocks with more than 1,000 wells. Porosity data are

estimated from both wire-line logs and seismic survey. Permeability prediction is based on the rock-

fabric approach, which predicts permeability according to the relationship between the pore size and

rock-fabric (Han 2008). For the purpose of this study, part of the geological model has been selected as

our study area and the model is upscaled into 16 layers vertically and 39×52 cells spatially with a total

of 32,448 grid blocks.

Figure 1 demonstrated the 3-D view of the top, porosity and permeability distribution in the study area

of SACROC Unit reservoir model. Although up-scaling decreases the model resolution, the

heterogeneity is preserved as much as possible. No flow boundary condition is considered for reservoir

top, down and northern boundaries due to effective seal formations, while eastern, western, and northern

boundaries are open since there are lots of well operations going on beyond them. Initially, there are a

total of 27 production wells perforated in each single layer, and then 12 of them are converted into

injection wells either as water injector or WAG injector after a peorid of production time. Besides, in

order to imitate the effects of open boundaries on the reservoir simulation, a few pseudo production

wells are designed in the model to approach the average reservoir pressure change as much as possible.

The available information provided for SACROC Unit model is:

Geological description

Porosity, permeability and thickness distribution

Rock-fluid properties

Initial and boundary conditions

Production and injection history (1949~2004)

Considering well bottom-hole pressure data is unavailable in this study, the reservoir simulation process

was decided to be constrained by monthly liquid rate to reproduce historical monthly water and oil

production rate of each well.

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Figure 1: The 3-D view of grid top, porosity and permeability in study area of SACROC Unit model

Smart Proxy Modeling

The necessity of the Smart Proxy comes from its main characteristics of low development cost and

labor. In this study, SACROC unit is a carbonate reservoir with very heterogeneous reservoir

characteristics of totally 16 layers. The reservoir development is also very complicated with primary

depletion, water-flooding and Water-Alternating-Gas injection (WAG) of a total of 55 years.

Considering the situation, it may be a good idea to perform automatic history matching using Smart

Proxy rather than do it manually.

Simulation Scenario Design Essentially, Smart Proxy modeling is an objective directed process, which is highly dependent on the

objective of the study. In this case, the objective is to obtain satisfactory history matching through the

determination on proper values of all uncertain reservoir properties. In order to make the first

investigation simple, we decide to only consider porosity and permeability as the uncertain ones along

with the acceptance on all other given reservoir properties. Therefore, three geological realizations with

low, medium and high porosity (1%~8%, 1%~16%, 1%~25%) and high heterogeneous permeability

distributions (0~1,200 md) are designed to introduce sufficient reservoir heterogeneity range for the

further Smart Proxy modeling. Those distribution realizations are created by the utilization of Latin

Hypercube sampling method, which gurantees porosity and permeability values of all 32,448 grid cells

in the reservoir are evenly distributed in every designated range.

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Spatial-Temporal Database Development Once all simulation runs are finished, the static (well location, thickness, depth, porosity,

permeability…) and dynamic properties (liquid rate, oil rate, water rate…) of each grid block will be

extracted from the reservoir simulator. These data are initial candidates in the data pool for generation of

spatial-temporal database. In other words, rather than use all extracted data, only the necessary ones will

be selected and those selected data must process data summarization which are essentially reservoir

delineation and tier system for preparation of spatial-temporal database. All data processing is

performed on a well base for the purpose of history matching in this case.

Reservoir delineation, determined by Voronoi graph theory, aims art figuring out well drainage area

(Erwig, 2000). Consequently, each well drainage area is divided into four tier systems. The main

objective of data processing is to provide more information resolution of each well and its surrounding

areas. Figure 2 depicts the designated tier systems in a well base case. As it is demonstrated, tier 1(T1) is

the grid block where the well locates; tier 2(T2) is a combination of 8 grid blocks surrounding the well;

tier 3(T3) has 16 grid blocks adjacent to tier 2; tier 4(T4) includes all other grid block within the

boundary of the well drainage area.

Figure 2: The defined tier system in well base of SACROC Unit reservoir model

The spatial-temporal database generation begins as soon as data processing is done. In SACROC Unit

case, considering the collection of static and dynamic properties in four tiers of 16 layers for a total of 49

study wells and three offset wells for each, there will be more than 1,400 inputs collected for Smart

Proxy modeling, which is not able to be handled efficiently. According to the geological

characterizations, all 16 layers belong to 5 geological layers; therefore, all static properties are re-

upscaled based on the lumping of layers for simulation efficiency improvement. Generally, the selected

parameters used for spatial-temporal database generation are shown below for all studied well and their

three offset wells (wells have the closed distance to the study well):

Well identifier : index, well name, simulation scenario

Well location: i,j,k,x,y,z

Reservoir properties: top, porosity, permeability, thickness (four tier systems of each layer)

Simulation time step: month t

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Operational constraint: monthly liquid rate (month t)

Production rate: water, oil, gas production (month t, t-1)

Injection rate: water, gas injection (month t, t-1)

Inputs and Output Selection SACROC Unit model has 5 geological layers after upscaling with a total of 27 well trajectories. As

aforementioned, only porosity and permeability are considered as uncertain parameters in this study.

Thus, there are 40 uncertain parameters (4 tiers × 5 layers × 2 properties) of each well, totally 1,080

static properties of all 27 wells, tending to be adjusted at each simulation time step (monthly basis)

during the history matching process. This calculation is very important, because it passes the

information to us that the generated Smart Proxy of SACROC Unit must be able to automatically find

1,080 proper values through a wide range of the uncertain properties with a repeat of totally 660 times

(55 years × 12 months/year) to fit the montly historical data until the history matching achieves.

The selected inputs and output generates the final database for neural network training, which is the last

step of Smart Proxy modeling. Iputs selction is a critical step. Appropriate inputs selection guarantees

high chance of Smart Proxy modeling success. It has been reported that many of artificial based models

fail in improper inputs selection (Mohaghegh, et al., 2012a). Except the abovementioned uncertain

properties, other parameters which have high effects on simulation process should also be included, such

as simulation constraint of monthly liquid rate. Table 1 shows the selected inputs and output for Neural

Network training in this study. Output is selected as monthly water production.

Table 1: Selected Inputs and Output for Neural Network Trainng

Output

Index Data Records

Well name Well 1 to 27

Simulation Scenario Scenario 1 to 3

Latitude (X)

Longitude (y)

Porosity at four tiers (T1 to T4) in five geological layes (L1 to L5)

Permeability at four tiers (T1 to T4) in five geological layes (L1 to L5)

Thickness at four tiers (T1 to T4) in five geological layes (L1 to L5)

Time (t) Months (1 to 660)

Monthly Liquid rate at time t, t-1

Monthly Water rate at timet-1

Monthly water rate at time t

Indexes

Static Inputs

Dynamic Inputs

Inputs

Well location

Neural Network Training (Smart Proxy Modeling) The neural network training is essentially the main part of Smart Proxy modeling, which is generally

divided into training, calibration and verification. Intelligent data partitioning was implemented in this

study as 80% of training (equivalent to 22,320 records), 10% of calibration (2,790 records), and 10% of

validation (2,790 records). Specifically speaking, the training set allows the ANNs to learn the

relationship between the inputs and output for the purpose of matching the provided output. The

calibration set helps assure a corresponding accuracy increase as the accuracy of training data set

increases and then decide whether the training should be stopped or not. At the same time, a verification

step is utilized for verifying the prediction ability of the trained ANNs. The elapsed time of training

process is much less compared with the numerical simulation time, which has much enhancement in

terms of computational cost.

Furthermore, a blind case run, which has never been used during the training process, must be used to

test the trained neural network robustness. Once both the training and blind case verification results are

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satisfied, the neural network model, which can be officially called Smart Proxy, is ready for further

analysis.

Figure 3 demonstrates part of the comparison results of monthly water production rate derived from

neural network training (Smart Proxy modeling, also named as SRM) and numerical simulation model.

Red color represents monthly water production rate from numerical simulation, blue color refers to

monthly water production rate from Smart Proxy training results.

Figure 3: Comparison of water production rate between Smart Proxy and numerical simulator in training

Figure 4 shows the comparison results of monthly water production rate derived from neural network

and numerical simulation model in the blind case. Again, red color represents monthly water production

rate from numerical simulation, blue color refers to monthly water production rate from Smart Proxy

training results.

According to the training and blind case validation results, the generated Smart Proxy is able to replicate

the simulation results derived from numerical simulator (CMG) and its robustness has been assured.

Therefore, we can state that Smart Proxy modeling is officially finished and it is now ready for the

implementation of automatic history matching in SACROC Unit.

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Figure 4: Comparison of water production rate between Smart Proxy and numerical simulator in blind

case

Automatic History Matching Using Smart Proxy

In this study, the automatic history matching is performed well to well by coupling the Smart Proxy with

optimization algorithm, which is operated by an integrated code. Generally, an optimization problem is

to maximize or minimize a real function by systematically choosing inputs from within an allowed range

and computing the function value (Storn et al. 1996). In our case of history matching, the error between

the field data and simulated data will be the objective function that needs to be minimized, and the

minimization is conducted through optimization. Differential Evolution (DE) optimization method,

proposed by Storn and Price, is selected in this study due to its competitve advantages: first, is much

more simple and straightforward to implement. Main body of the algorithm only needs four to five lines

to code in any programming language, which is an important feature. Second, the number of control

parameters in DE is very few. Besides, the space complexity of DE is low as compared to some of the

most competitive real parameter optimizers (Karabo et al. 2004; Das et al. 2011).

The general procedure of the automatic history matching is:

For each individual well, the range of all 40 uncertain properties (porosity and permeability of 4

tier systems in 5 layers ) and the objective function are set up by engineers before the differential

evolution optimization starts;

Initialize the values of all uncertain parameters within the given range; run the code to call Smart

Proxy to run for simulating the model output (monthly water production rate);

The quantitative misfit between the predicted water rate and actual water rate is then calculated

using the designed objective function and all misfits and selected parameters in each simulation

run are saved in the computer.

If the misfit doesn’t meet the pre-defined criteria, the Smart Proxy will continuously perform

simulation using the re-selected values of uncertain parameters, and then evaluate the

discrepancy derived from objective function continuously until the overall misfit is satisfactory,

then the history matching of a well ends.

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Figure 5 presents part of the predicted monthly water production from Smart Proxy versus the historical

field water production data, which shows an excellent history match result for each well. Similarly, red

color represents predicted monthly water production rate from Smart Proxy (SRM), blue color refers to

historical field monthly water production rate.

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Figure 5: History matching results of monthly water production rate derived from Smart Proxy

Performance of Smart Proxy application on history matching, for 27 wells in a total of 55 years (660

months), has been a successful work in the case of SACROC unit. In terms of computational cost, it is

recorded that the whole history matching process has used 330,000 simulation runs by Smart Proxy.

Each single simulation run only takes a fraction of a second, which means that, for such a complicated

simulation case, the required time of only Smart Proxy execution just takes 4 days. If considering the

Smart Proxy coupled with optimization cycle for automatic history matching, the total simulation time is

three weeks in this case, which means the history matching of each month only requires an average of 5

mins, which has been such a tremendous enhancement on simulation time.

The history matching in SACROC Unit is performed at a monthly basis continuously by Smart Proxy;

accordingly, the uncertain parameters have been adjusted dynamically. Figure 6 and Figure 7 illustrate

the snapshots of dynamic porosity and permeability visualization of each layer to provide better

understanding of how the uncertain reservoir properties change as time in SACROC Unit model.

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Figure 6: Snapshots of dynamic porosity distribution visualization in layer 1 to layer 5

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Figure 6: Snapshots of dynamic permeability distribution visualization in layer 1 to layer 5

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Remarks and Conclusions Performance of history matching using Smart Proxy has been proven a successful work in SACROC

Unit case study. There has been several reported simulation work in SACROC Unit (Dicharry et al.

1973; Brummett et al. 1976; Schepers et al. 2007; Han 2008; Shahkarami et al. 2015), however, none

presents good work on history matching as Smart Proxy does.

In this paper, only three simulation runs are performed to create the Smart Proxy with the ability of

mimicking the SACROC Unit reservoir behavior, which is extremely less, but efficient. Also, the

developed Smart Proxy coupling with Differential Evolution optimization enables the automation of the

history matching process in which the optimal values of totally 40 uncertain reservoir parameters of

each well at each time step can be properly determined , which is very highlighted compared with other

simulation models.

As a state of art technology, Smart Proxy is able to not only obtain fast track replication of

numericalreservoir simulation results with high accuracy, but also achieve automatic, continuously

updated history matching at minimal computational cost, which can be highly considered as a new

opportunity in reservoir simulation field.

Acknowledgement The authors would like to thank Computer Modeling Group (CMG) and Intelligent Solution Inc. (ISI)

for supporting us with the software for reservoir simulation and development of Smart Proxy modeling,

respectively. The authors also want to express appreciation to Dr. Alireza Shahkarami in Saint Francis

Univerisity for his help on technical problems in the coding part.

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