spe-169507-ms artificial intelligence (ai) assisted...

SPE-169507-MS

Artificial Intelligence (AI) Assisted History Matching Alireza Shahkarami, Shahab D. Mohaghegh, Vida Gholami, Sayed Alireza Haghighat, West Virginia University

Copyright 2014, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Western North American and Rocky Mountain Joint Regional Meetingheld in Denver, Colorado, USA, 16–18April 2014. 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

History matching is the process of adjusting uncertain reservoir parameters until an acceptable match with the measured

production data is obtained. Complexity and insufficient knowledge of reservoir characteristics makes this process time-

consuming with high computational cost. In the recent years, many efforts mainly referred as assisted history matching have

attempted to make this process faster; nevertheless, the degree of success of these techniques continues to be a subject for

debate.

This study aims to examine the application of a unique pattern recognition technology to improve the time and efforts required

for completing a successful history matching project. The pattern recognition capabilities of Artificial Intelligence and Data

Mining (AI&DM) are used to develop Surrogate Reservoir Model (SRM) for utilization as the engine to drive the history

matching process. SRM is an intelligent prototype of the full-field reservoir simulation model that runs in fractions of a

second. SRM is built using a handful of geological realizations.

In this study, a synthetic reservoir model of a heterogeneous oilfield with 24 production wells and 30 years of production

history was used as the ground truth (the subject and the goal of the history match). An SRM was created to accurately

represent this reservoir model. The history matching process for this field was performed using the SRM and by tuning static

data (Permeability). The result of this study demonstrates the capabilities of SRM for fast track and accurate reproduction of

the numerical model results. Speed and accuracy make SRM a fast and effective tool for assisted history matching.

Keywords: History Matching, Artificial Intelligence, Surrogate Reservoir Model (SRM), AI Assisted History Matching

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1. Introduction

The purpose of reservoir management is to develop strategies to maximize recovery. Reservoir simulation is usually used as a

decision making tool in this procedure. The common concern of reservoir simulation and modeling is accuracy. It is generally

believed that models with higher resolution (in both time and space) are more accurate. Since increase in resolution (time and

space) translates to increase in computational time, a well-known dichotomy arises. On one hand the model must satisfy the

accuracy requirements (high resolution), and on the other hand, it needs to be fast enough to become practical.

The new advancements in reservoir data acquisition have raised the complexity of the reservoir model and therefore the time

required to run it. At the same time typical reservoir modeling tasks such as sensitivity analysis, history matching, field

development optimization, and uncertainty assessment require large number of simulation runs. The challenge now is to keep

the complexity of the reservoir model while shortening its run-time.

The main objective of history matching is to improve and validate the reservoir simulation model by incorporating the

observed data into the characterization process, in order to obtain reliable production forecast. A simulation model which has

been tuned to match the past performance of a reservoir offers a higher degree of confidence to predict the future. Having a

trustworthy prediction of field performance has direct impact on technical and financial performance of operators.

History matching, by nature, is an ill-posed inverse problem. Correspondingly, classical history matching where reservoir

parameters are adjusted manually by trial-and-error makes this scenario more tedious and time-consuming. Assisted

(automated) history matching was proposed to decrease the amount of labor required during the manual history matching.

During last two decades there have been efforts to improve assisted history matching in a way that could be applicable in the

real world. But despite all the attempts, due to increasing rate of complexity and resolution in the reservoir models, there is

still hesitation about the practicality and potential of these methods to handle highly complicated real reservoir models. This

makes assisted history matching still a challenging research topic.

The novelty of the idea in this study is to examine a new application of pattern recognition technologies to improve the time

and efforts required for completing a successful history matching project. The pattern recognition capabilities of Artificial

Intelligence and Data Mining (AI&DM) are used to develop a Surrogate Reservoir Model (SRM) and use it as the engine to

drive the history matching process. SRM is a prototype of the full-field reservoir simulation model that runs in fraction of a

second. SRM is built using a small number of geological realizations. The geological realizations are used to create a spatio-

temporal database. The AI&DM techniques are utilized to derive the complicated relationship between different parameters in

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the database. Clearly the relationship originates from the nonlinear behavior of fluid flow thorough the porous media. In this

study Artificial Neural Networks (ANNs) are the AI&DM tool in building the SRM. In order to develop the SRM, the spatio-

temporal database was used to build ANNs.

2. Literature Review

2.1. History Matching

The advancement of computational power pushed reservoir simulation as the main tool to model the behavior of fluid flow in

reservoir (Watts 1997). Nowadays, feedbacks from reservoir simulation models are used in almost all reservoir development

decisions. Simulating reservoirs easily and realistically makes them a primary and reasonable choice for oil and gas companies

in the development of new (green) fields. Similarly, they are used in developed (brown or mature) fields where production

forecasts are required to help make future investment decisions.

In general, most of the required input data for building a numerical reservoir model comes from samples in wellbore or near

wellbore (Fanchi 2006). Compared to the size of a reservoir, these data are inadequate and their sources represent a very

limited section of reservoir. Furthermore, the methods applied for preparing these data are treating them in a very local aspect.

However, these data and the techniques to attain them are the only options that provide input data for the reservoir simulation

model of the field under study. The main point is that a huge part of the reservoir remains unknown to the engineers and

geologists working on the simulation model. As a result, the initial data in a simulation model should be adjusted in order to be

matched with the available historical data and predict the future performance of reservoir. This tuning procedure is performed

during history matching process. History matching is a calibration process that includes adjusting the uncertain parameters of

reservoir model until the model reproduces the historical field performance as closely as possible.

History matching is an ill-posed inverse problem. The inverse problem is the opposite of forward or direct problem which the

model parameters are used to predict the data. While in inverse problem the observed data is used to conclude (adjust) the

model parameters. On the other hand, a problem is ill-poised (not well-posed) when there are multiple non-unique solutions

for a certain problem. History matching is an ill-posed problem because many possible combinations of reservoir parameters

can result in almost the same behavior of reservoir (match the history data).

There is no doubt that history matching is a complicated procedure. Many criteria could be named which affect the degree of

success in this process: the quality and quantity of available data, the specific characteristics of the reservoir under study, the

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time and resources allocated to the study, and finally the experience and knowledge of the research group working on the

model. Consequently, each one of these criteria gives the history matching problem its most important characteristic which is

the non-uniqueness character of the results. There is no specific and unique method for history matching process. Each

reservoir has the particular specification and behavior.

Many efforts to improve manual history matching techniques have been made since the mid 1960’s to both speed up and

automate history match process (Kruger 1961) (Jacquard and Jain 1965) (Jahns 1966). Gradient optimization methods were

used for history matching in late 1960’s (Coats, Dempsey and Henderson 1968)(Slater and Durrer 1970). Chen et al. (1974)

tried to formulate history matching as an optimal control problem. Williams et al (1998) offered a structured approach to

perform history matching on a complex reservoir and based on their experience proposed multiple recommendations which

make the manual history matching easier. Bush and Carter (1996) showed that simple optimization techniques are not good

enough to address complex history matching problems. He and Chamber (1999) claimed that automatic history matching using

an object-based approach could provide acceptable results without the need to manually adjust the model. In the early 90’s,

using stochastic modeling to generate multiple realizations were started (Tyler, Svanes and Omdal 1993) (Palatnic, et al.

1993). Stochastic modeling, which provides many different geological realizations, increases the variation of the most

important input parameters, e.g. the geological properties influencing fluid flow. Sultan et al. (1994) and Ouenes et al. (1993)

used the Simulated Annealing Method (SAM) to automate history matching process. SAM was a non-gradient optimization

method capable of handling large number of parameters.

Gao et al. (2004) for the first time suggested the idea of combining the simultaneous perturbation stochastic approximation

(SPSA) method with a simulator to perform automatic history match of multiphase flow production data. Hajizadeh et al.

(2009) (2010) introduced a stochastic approach for automatic history matching based on a continuous Ant Colony

Optimization (ACO) algorithm. Other stochastic algorithms have been examined in this area. Evolutionary algorithms have

gained popularity as a standard optimization approach in history matching. These algorithms are generally inspired by the

evolution theory. There have been may examples of application of these algorithms in history matching (Schulze-Riegert et al.

2002) (Cheng et al. 2008)(Ferraro and Verga 2009) (Abdollahzadeh et al. 2012) (Christie et al. 2013).

However, high nonlinear behavior of the problem, large computational expenses and huge dimension of a real size field make

the history match process more difficult. Although significant computational and solver efficiencies have been gained over the

past four decades, ever-increasing size of geo-statistical earth models has continued to challenge the computational speed issue

(Kabir, Chien and Landa 2003).

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2.2. Artificial Neural Networks

Artificial neural network (ANN), usually called Neural Network (NN), is an algorithm that was originally motivated by the

goal of having machines that can mimic the brain. A neural network consists of an interconnected group of artificial neurons.

They are physical cellular systems capable of obtaining, storing information, and using experiential knowledge. Like human

brain, the ANN’s knowledge comes from examples that they encounter. In human neural system, learning process includes the

modifications to the synaptic connections between the neurons. In a similar way, ANNs adjust their structure based on output

and input information that flows through the network during the learning phase.

Data processing procedure in any typical neural network has two major steps: the learning and application step. At the first

step, a training database is needed to train the networks. This dataset includes an input vector and a known output vector. Each

one of the inputs and outputs are representing a node or neuron. In addition, there are one or more hidden layers. The objective

of the learning phase is to adjust the weights of the connections between different layers or nodes. After setting up the learning

samples, in an iterative approach a sample will be fed into the network and the resulting outputs will be compared with the

known outputs. If the result and the unknown output are not equal, changing the weights of the connections will be continued

until the difference is minimized. After acquiring the desired convergence for the networks in the learning process, the

validation dataset is applied to the network for the validating step (Hagan, Demuth and Beale 2002)(Haykin 1998). Figure 1

depicts the input, hidden and output layers and their connections. Since the advent of ANNs (McCulloch and Pitts 1943), they

have seen different stages of rise and fall; however nowadays ANNs enjoy huge popularity and interests in different fields.

Some applied applications of ANNs are listed in Table 1.

Shahab Mohaghegh is one of the pioneers in applying AI in petroleum engineering. He (Mohaghegh 1995) refers the main

advantage of ANN to the type of recognition ability and the difference of the mechanism that human brain processes

information compared to conventional digital computers. Computers are fast and accurate tools in performing prepared

instructions. On the other hand, human brain performance is tremendously slower but more efficient than computers at

computationally complicated jobs such as speech and other pattern recognition problems.

ANNs can be helpful tool to solve many conventional and unconventional problems in petroleum engineering. Although they

have a long history, their popularity in petroleum engineering started two decades ago (Ali 1994). Since this time, the

applications of ANNs in addressing conventional problems of petroleum industry have been widely studied. Table 2 concisely

lists different applications of ANNs in petroleum engineering.

http://en.wikipedia.org/wiki/Artificial_neuron

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Table 1- Application of ANNs in different fields. The popularity of ANNs has seen rise and fall since their advent.

Applications of ANNs in different fields Sales forecasting (Yip, Hines and Yu 1997)

Industrial process control (Devadhas, Pushpakumar and Mary 2012)

Customer research (Chattopadhyay, et al. 2012)

Risk management (Sarcià, Cantone and Basili 2007)

Credit evaluation (Baesens, et al. 2003)

Energy cost prediction (Yalcintas and Akkurt 2005)

Medical diagnosis (Amato, et al. 2013)(Lei and Xing-cheng 2010)

Business applications (Li 1994)

Financial applications (Tan 2004)

Stock market prediction (Adebiyi, et al. 2012)

Table 2- A brief list of ANN applications in petroleum engineering.

A brief list of ANN application in petroleum engineering

Well log interpretation (Baldwin, Otte and Whealtley 1989)(Jong-Se and Jungwhan

2004)(Masoud 1998)

Well test data analysis (Al-Kaabi and Lee 1990)(Ershaghi, et al. 1993)(Athichanagorn and Horne

1995)(Sultanp and Al-Kaabi 2002)

Reservoir characterization (Mohaghegh., et al. 1995)(Ahmed, et al. 1997)(Singh, et al. 2008)

Seismic attributes calibration Seismic pattern recognition

Inversion of seismic waveforms

(David 1993)(Yang and Huang 1991) (Roth and Tarantoia 1992)

Prediction of PVT data (Briones, et al. 1994)(Gharbi and Elsharkawy 1997)(Osman, Abdel-

Wahhab and Al-Marhoun 2001)(Oloso, et al. 2009)

Identifying fractures and faults (Key, et al. 1997)(Sadiq and Nashawi 2000)(Aminzadeh and deGroot

2005)

Detecting hydrocarbons and

forecast formation damage (Cheng-Dang, et al. 1994)(Aminzadeh and deGroot 2005)(Nikravesh, et

al. 1996)(Kalam, Al-Alawi and Al-Mukheini 1996)

2.3. Artificial Intelligence (AI) Assisted History Matching

During the last decade, there have been attempts to find alternative methods to reduce the amount of CPU time needed to

execute a numerical full field model. AI methods are one of the most famous and efficient examples of these kinds of

techniques. Zangl et al. (2006) trained an ANN as a proxy model by using a limited number of simulation runs of a gas storage

model. Then they applied this proxy model to replace the numerical model in order to make hundreds and thousands of runs in

a very short time in an optimization loop. One of the objectives was to perform the history matching. The results were

acceptable and had considerably less computational expenses compared with numerical reservoir simulation outcomes. Cullick

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et al. (2006) compared the performance of proxy models based on ANNs with reservoir simulator to perform history matching.

Their results support using ANNs as a substitute for numerical simulator over the trained parameter space. They tried to

challenge the limitation of proxy model in their work by decreasing the number of training realizations and increasing the

uncertain parameters.

The objective of Rodriguez et al. (2007) work was accelerating the history matching process by applying singular value

decomposition method. This method helped them to save 75 % of total CPU time. At the same time, they used an ANN in

order to reduce number of simulation runs and help to increase the accuracy of solution. Silva et al. (2006)(2008) presented the

application of global optimizers combined with ANNs to address the history matching problem. Their results supported the

potential of ANNs to reduce the computational effort in history matching process. Sampaio et al. (2009) used feed-forward

neural networks as nonlinear proxies of reservoir simulation to speed up history matching. The focus of their work was to

discuss the technical criteria that will lead implementation of ANN to be a successful experience. The points that they have

mentioned in their paper are crucial for the researchers who are interested in applying ANN in petroleum engineering

problems.

The aforementioned cases are some examples of ANN application. However what is worth mentioning is the approach used in

these examples through development and implementation of AI models, which is the same as the statistical methods. The

degree of success of using AI models based on this approach is highly uncertain and it could be as successful or disappointing

as the statistical techniques (Cullick, Johnson and Shi 2006)(Zubarev 2009). Particularly addressing application of AI in

petroleum engineering problems (such as history matching), it requires a comprehensive knowledge in both areas of petroleum

engineering and AI and DM to achieve success. This knowledge plays an important role in keeping the physics to solve the

problem. The fact of using physics is something that has been neglected in statistical methods (or applying AI techniques using

the same approach).

2.4. Surrogate Reservoir Models

The main objective of this study is to speed up the history matching process. The focus of our work is based on a relatively

new technology known as Surrogate Reservoir Model (SRM). SRM has been introduced as a tool for addressing many time-

consuming operations performed with reservoir simulation models (Mohaghegh 2006). SRM is a replica of numerical

reservoir simulation model which is able to reproduce the results of simulation model with a high accuracy in real-time.

Basically SRMs are a collection of (at least) one or multiple neuro-fuzzy systems that are trained and validated using the

information from numerical simulation models. The required information to train the SRM is assimilated in the form of a

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spatio-temporal database. Design of spatio-temporal database is a function of the objective of SRM.

The examples of Surrogate Reservoir Models in the industry to address time-consuming reservoir modeling are available in the

literature. Mohaghegh introduced this tool for the first time in 2006 to perform uncertainty analysis of a giant oilfield with 165

horizontal wells in the Middle East (Mohaghegh 2006). The efficiency of SRMs to reproduce the results of reservoir

simulators has been proved in several case studies (Mohaghegh et al. 2009)(Mohaghegh 2009)(Mohaghegh 2010)(Mohaghegh

et al. 2012b)(Mohaghegh et al. 2012)(Amini et al. 2012). In this study, SRM is being used, for the first time as a tool for

assisted history matching.

3. Methodology

SRMs are developed based on representative spatio-temporal databases. Building this database is the first step of developing

AI-based reservoir models. The main objective of the database is to teach the ANN model the whole process of fluid flow

phenomena in the reservoir. In general, this database should meticulously provide static and dynamic information of the

reservoir. The quality and quantity of this database determines degree of success to develop a successful AI-based reservoir

model including an SRM (Mohaghegh 2011). Compared to the other steps of SRM development, preparing the database is

relatively the most tedious part, which needs a lot of thought process. However a good database guarantees the success of the

modeling.

In order to build this SRM different steps were required. Followings are steps involved to develop the SRM:

1) Pre-processing step includes model development and dataset generation:

a. Development of a heterogeneous reservoir model using a commercial simulator. Starting with the base case

of reservoir model a small number of informative realizations were created. These informative realizations

represent the geological uncertainties involved in the reservoir model.

b. Depending on the objective of developing SRM, the reservoir could be divided into different segments and

tiers. Segmenting the reservoir helps to emphasize on the sections which are more important, such as well

block and the grid blocks around the well.

c. Extracting different static and dynamic data from the numerical simulation models in order to build the

spatio-temporal database.

2) SRM Development:

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a. Performing Key Performance Indicators (KPIs) to identify and rank the influence of different reservoir

characteristics on the reservoir performance. The ranked KPIs will be a guide to select ANN inputs.

b. Partitioning the spatio-temporal database into training, calibration and validation sets.

c. Designing Artificial Neural Network (ANN) architecture.

d. Training, calibrating and validating the ANNs.

e. Testing the created ANNs using a complete blind realization of the reservoir.

Figure 2 summarizes the steps to develop the SRM.

4. The Reservoir Model

The reservoir model used in this study is a synthetic replica of a highly heterogeneous oil field, with 24 production wells and

30 years of production history. The base simulation model is a single porosity oil reservoir, which was constructed in CMG-

IMEXTM1. The reservoir has been divided to 4800 Non-Orthogonal grid blocks, 80 in X direction and 60 in Y direction. The

reservoir has a single layer and thickness values are variable in different gird blocks. The field is producing oil at initial

pressure of 13,789.5 kilopascals (2,000 psi) and bubble point pressure of 2,068.4 kilopascals (300 psi), therefore it is expected

that the candidate reservoir will be producing oil for a long time in an under-saturated condition. The model is synthetic and

does not represent a real field. Figure 3 shows three and two dimensional views of the reservoir structure. Figure 4 and 5

illustrate three and two dimensional views of porosity and grid thickness distributions.

The given permeability range for the base model is from 10 to 75 md (Figure 6). In addition, the geological information from

the field identifies a high permeable zone. 24 production wells have been drilled in the field and they produce oil for 30 years.

Minimum bottom-hole pressure (BHP) is set as the production constraint which varies through time. The wells produce for 30

years, starting in 2000/01/01. The available historical data include oil rate production for all the wells.

5. Training Realizations

In order to introduce the uncertainties involved in the reservoir simulation model to the SRM, a small number of simulation

runs should be made. In this study, ten different realizations of the base model were designed to develop the SRM. Using the

permeability map from base reservoir model, ten different permeability maps were generated. The range of permeability for

1 Computer Modeling Group

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the base model is from 10 to 70 md. Due to the uncertainty involved in reservoir properties, a range from 10 to 200 md was

considered to create the permeability distributions. Afterward, to create ten different cases of permeability values at well

location, an experimental method (Latin Hypercube) was used. Table 3 summarizes generated permeability values at the wells’

location.

Table 3- Permeability (md) values designed at well locations for generating permeability maps. The permeability values for each well have been ranged by color, which red and blue represent minimum and maximum value respectively.

6. Reservoir Segmentation- Tiering System and offset wells

In order to include the static data of adjacent grid blocks of a well in the spatio-temporal database, a tiering system was

generated. Another objective of this part is to summarize the information based on their influences on the wells’ production.

Obviously, if the Euclidian distance of grid blocks from the production well is considered, different grid blocks show different

behavior in terms of fluid flow. For example, the well grid block has the maximum influence on the production of a well.

Hence, this influence should be considered during developing the database. Furthermore, considering the impact of the

neighborhood wells’ production was interested (offset wells’ effects).

7. SRM Development

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10

Well-1 44.6 21.6 21.0 38.7 60.5 67.1 31.3 66.4 44.2 89.7

Well-10 40.3 29.8 51.5 140.8 49.7 142.8 146.9 87.5 113.6 107.3

Well-11 41.7 85.8 32.6 83.8 138.6 39.0 122.6 117.7 97.1 33.0

Well-12 33.4 18.0 44.7 51.9 40.1 21.2 89.8 73.9 75.5 34.9

Well-13 64.3 41.3 64.3 61.0 74.9 69.2 54.7 60.9 118.4 104.9

Well-14 17.6 42.8 30.0 31.0 38.1 28.4 43.1 56.1 35.2 62.9

Well-15 18.9 44.9 37.5 47.4 55.8 32.7 92.0 93.1 91.2 59.6

Well-16 21.7 40.0 29.9 32.5 41.1 33.9 43.0 57.8 38.8 66.8

Well-17 78.1 45.0 27.7 44.6 84.1 102.4 93.8 143.9 158.9 152.5

Well-18 34.6 24.6 40.2 56.8 29.5 44.1 75.7 74.9 54.6 81.3

Well-19 76.8 60.3 95.6 38.9 54.0 81.7 107.5 172.6 49.3 61.4

Well-2 58.8 42.9 52.6 92.2 78.0 105.4 93.7 81.6 107.2 119.5

Well-20 41.2 27.3 14.4 53.9 70.7 27.4 18.9 37.4 88.0 21.9

Well-21 19.5 22.4 39.5 27.4 19.6 47.5 50.5 63.4 60.7 89.6

Well-22 30.0 36.0 31.9 42.4 46.1 43.3 63.6 61.3 70.1 57.4

Well-23 58.6 67.8 60.4 117.6 109.0 59.6 82.4 55.8 47.6 73.2

Well-24 29.2 31.6 21.5 44.0 28.2 57.5 17.5 77.4 69.4 27.8

Well-25 29.5 88.8 46.1 68.4 31.7 109.8 159.9 112.4 182.8 153.0

Well-3 67.0 38.5 76.5 55.4 72.5 53.2 36.8 43.1 123.5 94.0

Well-4 26.5 37.5 32.9 71.0 66.7 42.0 31.6 29.8 22.8 19.0

Well-5 43.2 30.2 31.7 15.9 26.4 66.3 60.4 86.2 83.2 72.5

Well-6 24.5 38.1 34.9 40.3 46.5 38.5 62.3 63.4 56.7 61.7

Well-7 41.6 15.9 30.7 65.1 39.2 20.6 44.5 49.6 50.4 57.0

Well-8 54.1 79.0 73.4 112.9 101.4 71.8 193.9 161.8 140.1 131.8

Permeabilty @ Wells' Location for 10 Runs applied in Training partWell

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7.1. Input Selection

At this step, the inputs to develop the spatio-temporal database are selected. As it was mentioned, building this database is the

most important step of developing an SRM. In building of this database, the objective of the reservoir modeling should be

considered (Amini et al. 2012)(Mohaghegh et al. 2012a). For instance, the objective of this study is using the SRM to estimate

the well parameters such as oil production. Therefore, the reservoir properties, which are affecting the objective of study, have

higher degree of importance.

The spatio-temporal database includes different types of data such as static and dynamic reservoir characteristics, operational

constraints, etc. Static data refer to the properties of reservoir that are not changing through the time such as permeability,

porosity, top and thickness. Similarly, the dynamic data address variable parameters that are altering over the time, such as oil

production rate, bottom-hole pressure, and production time.

For the tiers which have more than one grid block, the average of the property was calculated. This calculation was done just

for static properties. Figure 7 summarizes different types of data in the spatio-temporal database.

7.2. Building the Artificial Neural Networks

After having the database ready, the next step is to create the ANNs. In order to generate ANNs, software called IDEATM2 was

used (Intelligent Solutions Inc. 2012). The inputs of ANNs are displayed in figure 7 and the output of the networks is annual

oil rate production. The training algorithm was Back Propagation (BP). BP is one of the most common training methods to

train the ANN and the time-based model development feature of this paradigm was appropriate for our study.

One novel pre-modeling analysis in SRM development is performing Key Performance Indicators (KPIs) analysis. This

feature provided in IDEATM identifies the most influential parameters in any given process prior to modeling. This feature

operates based on a pattern recognition and fuzzy logic engine. Figure 8 displays the results of KPI analysis in this study.

Training the ANNs is the following step. The training process includes three different processes: Training (learning),

Calibration and Validation (testing). Therefore, the database is partitioned into three categories: training or learning set,

calibration set and validation or verification set. The training set is part of data shown to the ANNs during the training process.

The ANNs are adapted to this set to match the provided outputs (reservoir simulation results). On the other hand, the

calibration set is not used to adjust the outputs. This set is utilized to assure that any increase in accuracy over the training data

2 IDEATM is a data-driving and AI modeling software developed by Intelligent Solutions Inc. (ISI).


set will lead to an increase in accuracy over a data set that has not been shown to the ANNs before. This set of data is helpful

to find out when the training should be stopped. If the error trend over the training data set has a decreasing trend, but the same

error for the calibration set has different trend, the ANN is over-fitting and it is time to stop the training process. Finally, the

verification set is a part of database to verify the validity of the trained ANN. Obviously this data set has not been used to train

the ANN. It is worth mentioning that the elapsed time to perform the training process (learning, calibration and verification) is

negligible compared to the reservoir simulation run-time. The training, calibration and verification included 80%, 10% and

10% of the data in the database.

7.3. Validation the SRM by a Blind Realization

The trained SRM is validated against a complete blind realization of the reservoir. Therefore, a new simulation run was made.

This realization has a permeability distribution which is completely different from the ten realizations used in training process.

However it should be noted that the permeability range should be in the range of values used in the training runs. Finally, the

trained SRM was applied to predict the oil rate from the blind realization inputs.

7.4. History Matching

The trained and validated SRM is ready to be used in the process of history matching. In order to accomplish the history

matching, permeability values at each defined tier have been adjusted. The oil rates predicted by the SRM are compared

against the real production rates. This procedure must be repeated until an acceptable match in each well is obtained.

The objective functions to compare the results are presented in Equation 1 and Equation 2. Equation 1 calculates the difference

between measured and actual data at the well level and Equation 2 includes the well level objective function in a global

objective function at the field level. In Equation 1, the subscripts and represent well and time respectively. is the

total number of measured data points (In this study is 30 corresponding to 30 years of annual oil rate existing for each

well). is the predicted production by SRM and is measured production data. is the scale calculated by

subtracting the maximum and minimum of measured production data for well . In the global objective function, is the

objective function for well , and is the total number of wells (24 wells in this study). In practice, it is also common to

consider that the quality and importance of measured data may be different for some specific wells. is the defined weight

for well . In this work, all the wells were considered equally important and the weight coefficient is one for all of them.


Equation 1: Individual well objective function

Equation 2: Global (Field) objective function

8. Results

This section intends to present the results for one of the wells (well # 20) for different steps of developing and applying the

SRM. The results for all wells can be found in somewhere else (Shahkarami 2012). Figure 9 displays the results after the

training process; the chart portrays the oil rate profile for 30 years of production comparing SRM results with the simulator

outputs. The blue squares represent the SRM and the red line with stars shows the numerical simulator results. It is evident that

SRM can reproduce the simulator results accurately. Figure 10 shows the results of blind verification realization. As was

mentioned earlier, a blind realization was used for testing the SRM. The blind set consists of a realization, which has not been

seen by SRM in the training process. Therefore, this graph validates the potential of SRM to predict a realization performance

out of the training dataset and displays the robustness of the technique. Finally figure 11 is a snapshot of the history matching

(HM) results for this well. This graph is the comparison of the SRM outcome with the measured production data.

The distribution of matched values of permeability is shown in figure 12. The right side of this figure pictures some shots of

the matched permeability map, while the left side shots are the actual permeability distribution. Figure 13 demonstrates the

error distribution of the results after history matching process. Figure 14 is an error frequency distribution of these results, as

well.

9. Summary and Concluding Remarks

An SRM was created for a synthetic but highly heterogeneous oil field, with 24 production wells and 30 years of production

history. The goal was achieving a match of the production history by tuning permeability distribution. SRM was trained using

ten heterogeneous realizations and then validated by a blind simulation run. Finally, the full field model was substituted by the

trained SRM to perform the history match process.


SRM was able to accurately match the results of training realizations. Robustness of SRM to predict the behavior of a

realization which has not been seen by SRM during learning process (blind case) was further verified. Matching the actual data

was perfect and comparison between the variable history matched property and actual distribution supports the claim. The

pattern recognition characteristics of SRM make it possible to achieve the results in a fraction of second. Although the running

time for the case study of reservoir model used in this study is not the concern, the number of simulation runs to attain a

desired match is time and power consuming. In numerical reservoir simulator, by increasing the size and complexity of the

components the run-time can increase in orders of magnitude. Nevertheless due to pattern recognition capability of SRM this

technology, it will not be an issue for SRM.

The results of this study could be counted as a proof of concept for showing the potential of this novel technology (SRM) to

assist history matching process. Increasing the uncertain variables and implementing the technology on a more sophisticated

(and real life) case study is the goal of the authors to achieve in future.


Figure 1- An artificial neural network is an interconnected group of nodes.

Figure 2- Steps to develop an SRM.


Figure 3-Three and two dimensional top views of simulation model.

Figure 4- Three and two dimensional views of porosity distribution.

Figure 5- Three and two dimensional views of thickness map.


Figure 6- Given permeability map for the base case.

Figure 7- Different types of data in the spatio-temporal database.

IndexWell Name

Run Number

i

j

k

X

Y

Z

Top

PorosityPermeability

Grid ThicknessTime

Operational Constraint Bottom-hole pressureOil Rate at t

Oil Rate at a time step behind (t-1)Production Rate

Dynamic Data

Well Location

Identifier

Static Reservoir Property (at 4 tiers and offset wells)

Stat

ic D

ata


Figure 8- The results of KPI analysis. Pre-modeling analysis of KPI is an appropriate guide to select the inputs of ANNs.

Figure 9- Training results for well # 20.


Figure 10- Blind run results for well # 20.

Figure 11- Comparison of the matched results coming from SRM with actual outputs (simulator) for well # 20.


Figure 12- Comparison of matched and actual Permeability distributions.

Figure 13- Error distribution for the history matched results.


Figure 14- Error frequency distribution for the history match results.


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