Surrogate Reservoir Model

8/12/2019 Surrogate Reservoir Model

1/271 2014 Society of Chemical Industry and John Wiley & Sons, Ltd | Greenhouse Gas Sci Technol.4:127 (2014); DOI: 10.1002/ghg

Received August 14, 2013; revised January 9, 2014; accepted January 10, 2014

10.1002/ghg.1414Published online at Wiley Online Library (wileyonlinelibrary.com). DOI:

Modeling and Analysis

Modeling pressure and saturation

distribution in a CO2storage projectusing a Surrogate Reservoir Model

(SRM)

AlirezaShahkarami, Shahab D. Mohaghegh, VidaGholami, AlirezaHaghighat,

and DanielMoreno, West Virginia University, Morganstown, WV, USA

Abstract: Capturing carbon dioxide (CO2) from large point sources and depositing it in a geological

formation is an efficient way of decreasing CO2concentration in the atmosphere. A comprehensive

study is required to perform a safe and efficient CO2capture and storage (CCS) project. The study

includes different steps, such as selecting proper underground storage and keeping track of CO2

behavior in the storage environment. Numerical reservoir simulators are the conventional tools used to

implement such an analysis.

The intricacy of simulating multiphase flow, having a large number of time steps required to study

injection and post-injection periods of CO2sequestration, a highly heterogeneous reservoir, a large

number of wells, etc., will lead to a complicated reservoir model. A single realization for such a reser-

voir takes hours to run. Additionally, a thorough understanding of the CO2sequestration process

requires multiple realizations of the reservoir model. Consequently, using a conventional numericalsimulator makes the computational cost of the analysis too high to be practical.

In this paper, we examine the application of a relatively new technology, the Surrogate Reservoir

Model (SRM), as an alternative tool to solve the aforementioned problems. SRM is a replica of full-field

reservoir simulation models. It can generate outputs in a very short time with reasonable accuracy.

These characteristics make SRM a unique tool in CO2sequestration modeling. This paper proposes

developing an SRM for a CO2sequestration project ongoing in the SACROC unit to model pressure

behavior and phase saturation distributions during different time steps of the CO2storage process.

2014 Society of Chemical Industry and John Wiley & Sons, Ltd

COKeywords: 2sequestration and storage; fast track modeling; pattern recognition; surrogate reservoir

models (SRMs)

Correspondence to: Department of Petroleum and Natural Gas Eng, Mineral Resources Building, Room 147, Evansdale Drive,

Morgantown, West Virginia, 26506, USA. E-mail: [email protected]

Introduction

Carbon dioxide (CO2) is the primary greenhousegas (GHG) that has been contributing to globalwarming and climate change since the beginning

of the Industrial Revolution. CO2comprises nearly80% of global anthropogenic (produced by humanactivity) GHG emissions.1Te atmospheric concentra-tion of CO2recently reached a considerable level of400 ppm in May 2013 an almost 100 ppm increase


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A Shahkarami et al. Modeling and Analysis: Modeling pressure and saturation distribution in a CO2storage project using a Surrogate Reservoir Model (SRM)

2 2014 Society of Chemical Industry and John Wiley & Sons, Ltd | Greenhouse Gas Sci Technol.4:127 (2014); DOI: 10.1002/ghg

since 1960.2Fossil fuel use is considered the mainsource of CO2emission. Even with considering newpolicies of CO2emissions,

3it is unlikely that there willbe a signicant decrease over the next 25 years in the

percentage of world energy produced by fossil fuels(81% in 2010). Terefore, mitigating the amount ofCO2coming from human activities is a major chal-lenge in reducing the anthropogenic effects on globalwarming and climate change.

Te Intergovernmental Panel on Climate Change(IPCC) denes carbon capture and storage (CCS) as aprocess consisting o the separation o CO2romindustrial and energy-related sources, transport to astorage location and long-term isolation rom theatmosphere.4Te geological storage o CO2is the

injection o the captured CO2into appropriate deepgeological ormations. Te geological sequestration oCO2is not a new technology. In the early 1970s, CO2was injected or the rst time into subsurace geologi-cal ormations in exas in order to enhance the oilrecovery.57However, it was not until the 1990s whenthe geological storage o CO2gained enough credibil-ity to be applied in a large-scale project.8,9In 1991, theNorwegian government instituted a tax on CO2emission, which motivated Statoil to run the rstcommercial CCS project in order to capture CO2romthe Sleipner oil and gas eld in the North Sea andinject it into a thick layer saline aquier in 1996.10Inless than two decades, carbon storage in deep geologi-cal ormations has emerged as one o the most impor-tant options or reducing CO2emissions.

4,11,12CCSplays a critical role in the portolio o technologiesrequired to attain a considerable reduction o globalGHG emissions in the most economically effi cientmanner. Tis technology has the potential to decreasenearly one-fh o the emissions required to cut GHGemissions rom energy consumption in hal by 2050.13

CO2leakage is one o the major risks in a CCS

project; thereore, keeping CO2in a sae and con-trolled environment or a long period o time is amain challenge.14,15Consequently, the ollowing tasksmust be thoroughly accomplished: quality control ocandidate underground storage, keeping track o CO2plume conditions, and simulating the reservoirbehavior (such as reservoir pressure, which is anappropriate indicator o potential leakage). Numericalreservoir simulators are the conventional tools used toperorm the aorementioned tasks.1621

In order to have a comprehensive study o a CCSproject, hundreds to thousands o realizations with

different reservoir characteristics and operationalconditions are required. Although using a numericalreservoir simulator gives accurate results, it is verytime-consuming and computationally expensive.

Furthermore, due to the process o CO2sequestration,a compositional simulator should be utilized, whichgenerally leads to an even higher computationaltime.22

Te reservoir simulation model in this work comesrom the work done by Han.23Te original geo-cellu-lar model in that work consisted o over nine milliongrid blocks. In order to simulate CO2trapping mecha-nisms, he had to upscale the model and decrease thenumber o grid blocks to 13 600. However, with thetime lapse required to run this study (1000 years),

even this upscaled model requires a high computa-tional cost and takes hours to run a single realization.Te reservoir simulation in this study was conductedusing Computer Modeling Group (CMG) simulatorcalled GEM-GHGM.24GEM-GHGMis specicallydesigned or simulating CO2sequestration processes.

Te objective o this study is to examine the effect othe uncertainty involved in a reservoir parameter(permeability) and also the impact o operationalconstraints on the output o numerical reservoirsimulators (pressure and phase saturations). Te toolto accomplish the objectives o this study is a pattern-recognition-based technology known as SurrogateReservoir Models (SRMs). SRMs have been intro-duced as a tool or addressing many time-consumingoperations perormed with reservoir simulationmodels.25SRMs attempt to reduce the dimensionalityo the problem by using uzzy pattern recognitiontechniques. Te capability o SRMs to replicate ulleld models that run in ractions o a second makesthem an effi cient alternative tool to address manytime-consuming operations perormed with reservoirsimulation models.25Te engines o SRMs are based

on Articial Neural Networks (ANNs).In order to develop the SRM, a ew different realiza-

tions o the reservoir simulation model were createdand run by numerical reservoir simulators. Te inputsand outputs o these realizations generated a spatio-temporal database. Te spatio-temporal database wasused to train the SRMs (the pattern-recognition-basedmodels, particularly ANNs). Te SRM aims to repli-cate the results o traditional numerical reservoirsimulators at the grid level in a matter o seconds. TeSRM passed training, calibration, and validation stepsto be qualied as a reliable replica o the reservoir


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Modeling and Analysis: Modeling pressure and saturation distribution in a CO2storage project using a Surrogate Reservoir Model (SRM) A Shahkaramiet al.


simulation model. Further validation process isapplied to veriy the effi ciency o the SRM on differentrealizations o the reservoir simulation model. Teserealizations were not seen during the training process;

thereore they are reerred to as blind realizations. Atthe end o this process the SRM is ready to reproducethe outputs (pressure and phase saturations) onumerical reservoir simulators at the grid block level.Te time needed to accomplish each run and achievethe desired results using the SRM is in the order oseconds, whereas the time required to perorm theprocess using a numerical reservoir simulator is in theorder o hours and a day.

Potentials of pattern recognition

techniquesCO2sequestration in underground storage is one othe most viable methods or reducing GHGs. Tepetroleum industry has decades o experience inject-ing gas (CO2or hydrocarbons) into different types oreservoirs. Tis leads to an overlap o issues in thepetroleum industry and CCS, such as modeling,history matching, and uncertainty analysis and riskmanagement. Tese issues can be managed by thecapabilities o pattern recognition techniques.

In pattern recognition concepts, the data analysis

process deals with predictive modeling. By having ahigh dimensional database, the objective is to learnthe underlying behavior in the data and orecast theperormance o unoreseen validation database. Telearning process reers to some orm o algorithm toreduce the error on the set o training data.26Telearning procedures could be distinguished into (i)supervised learning or (ii) unsupervised learning.*27Supervised learning generally represents a learningprocedure which takes an available set o inputs andknown outputs corresponding to these inputs. Efforts

will be made to build a predictive model by matchingthe available responses with the inputs. Tis predictivemodel is then able to generate reasonable predictionsor the response to novel data. Te most importantcharacteristic o this learning technique is that theresponses (outputs) are recognized or labeled in thetraining database. On the other hand, unsupervisedlearning involves only unlabeled data, which makesthe process more challenging than the previous one.

In other words, unsupervised learning orms clustersor natural patterns underlying the structure o data.

One o the most amous pattern recognition tech-niques, one that has a long history in a variety o

scientic elds, is ANNs, usually called NeuralNetworks (NNs). Te learning procedure in ANNs issupervised learning. ANNs were originally motivatedby the goal o having machines that are able to mimicthe brain. In act, the structure o ANNs is verysimilar to that o the human neural system, as itincludes an interconnected group o articial neurons.ANNs are cellular systems capable o obtaining andstoring inormation and using experiential knowl-edge. An ANN is an adaptive system that adjusts itsstructure based on output and input inormation that

ows through the network during the learningphase.28Although ANNs have been around or a long time,

their popularity in petroleum engineering startedonly two decades ago.29Since this time, the applica-tions o ANNs in addressing the conventional prob-lems o the petroleum industry have been widelystudied. Some applications o ANNs in petroleumengineering literature include well log inter-pretation, 3032well test data analysis,3336reser-voir characterization,3739calibration o seismicattributes,40seismic pattern recognition,41inversion oseismic waveorms,42prediction o PV data,4346ractures and aults identication,4750hydrocarbonsdetection,50,51and ormation damage orecast.52,53

Tat said, it should be noted that the effective use opattern recognition techniques in the petroleumindustry is not a trivial process. It requires insight inboth the domain o reservoir engineering as well as asubstantial application o pattern recognition tech-niques; otherwise, the results could be quitedisappointing.54

Surrogate reservoir models

Surrogate Reservoir Models (SRMs) are approxima-tions o the ull-eld 3-dimensional numerical reser-voir models that are capable o accurately mimickingthe behavior o the ull-eld models. Unlike statisti-cally based proxy models that require hundreds osimulation runs,5557SRMs can be created in a ewsimulation runs. In 2006, SRM was presented or therst time by Shahab D. Mohaghegh to solve theproblem o time-consuming runs or an uncertaintyanalysis o a giant oil eld with 165 horizontal wells in

*Recently another set of learning was discussed in the literature

which is referred as called semi-supervised.


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recognition characteristics o SRMs help to developthese types o models by having a small number osimulation runs. However, there is no algorithm tond the optimum number o simulation runs to build

an SRM. Te common practice when choosing thebest number to train the SRM is to use rules o thumbbased on the intricacy and heterogeneity o thereservoir model, which might change. Nevertheless, itis obvious that i the number o simulation runs is toosmall, the SRM will not be able to reproduce thesimulator results properly. Otherwise, i the numbero simulation runs is too big, there is no reason todevelop an SRM since the solution is close to theoriginal problem, which is a high number o simula-tion runs.

Afer running the realizations, the static and dy-namic data are extracted in order to build the repre-sentative spatio-temporal database. Te databaseincludes different types o data such as static anddynamic reservoir characteristics, operational con-straints, etc. Static data reer to properties o thereservoir that are not changing over time, such aspermeability, porosity, top, and thickness. Dynamicreers to any data such as well constraints or pressureand phase saturation that change over time.58

Te training process o an SRM includes threedifferent steps: training (learning), calibration, andvalidation procedures. Based on that, the spatio-tem-poral database is divided into three sets: the trainingor learning set, calibration set, and validation orverication set. Te training set is part o the datashown to the ANNs during the training process. TeANNs are adapted to this set to match the providedoutputs (reservoir simulation results). On the otherhand, the calibration set is not used to adjust theoutputs. Tis set is utilized to assure that any increasein accuracy over the training data set will lead to anincrease in accuracy over a data set that has not been

seen by ANNs. Tis set o data is helpul in determin-ing when the training should be stopped. Finally, theverication set is a part o the database used to veriythe predictability o the trained ANN, and subse-quently, this data set is not used to train the ANNs. Itis worth mentioning that the elapsed time to perormthe training process (learning, calibration, andverication) is negligible when compared to thereservoir simulation run-time. Another importantpoint is an SRM may be a collection o several ANNsthat are trained, matched and veried in order togenerate different results.

the Middle East. Te reservoir simulation modelincluded about one million grid blocks and took 10 hto run using a cluster o 12, 3.2 GHz processors. In hisstudy, SRM was used as an objective unction or a

Monte Carlo Simulation to build thousands o simula-tion runs in a very short time compared to numericalsimulators. Mohaghegh describes SMRS as an en-semble o multiple, interconnected neuro-uzzysystems that are trained to adaptively learn the uidow behavior rom a multi-well, multilayer reservoirsimulation model, such that they can reproduceresults similar to those o the reservoir simulationmodel (with high accuracy) in real-time.58Since2006, applications o SRMs as an accurate and rapidreplica o a numerical simulation model have been

reviewed in different studies.5863

SRM development

SRMs are developed using the data extracted rom therealizations o simulation model. Tese data areincluded in a spatio-temporal database. Building thisdatabase is the rst step in developing ArticialIntelligence (AI)-based reservoir models. Te mainobjective o this database is to teach the model thewhole process o uid ow phenomena in the reser-voir. Tereore meticulous efforts should be made in

this part. Te quality and quantity o this databasedetermine the degree o success in developing asuccessul AI-based reservoir model including anSRM. Not dedicating enough attention to this part isthe main reason behind unsuccessul attempts atapplying AI-based models in the literature.54Mo-haghegh thoroughly discussed this step o SRMdevelopment in his paper.64

In order to create the spatio-temporal database, therst step is to identiy the number o runs that arerequired to develop the SRM. Te purpose o having

different realizations o a reservoir simulation modelis to introduce the uncertainties involved in the modelto the SRM. Tis is a common step in building SRMsand developing response surace methods; however,there is a key difference between these two methods:the unctional orms behind these models. Responsesurace and other reduced models are developed usingstatistical approaches, which use predeterminedunctional orms. Te output o reservoir simulationmodels are then tted to these predetermined orms.In order to match these unctional orms, hundreds oruns are needed. On the other hand, the pattern


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Reservoir simulation model

We received the base reservoir model rom a workperormed by Han.23Te original reservoir model was

or a CO2enhanced oil recovery (EOR) project thatlasted or 200 years, rom 1972 to 2172. Te modelutilized in this study covers the period o January 1,2172 to January 1, 3172 afer the reservoir has beendepleted rom oil. Tereore the simulation model isjust considered or CO2storage and sequestration. Temodel contains 25 simulation layers o 1634 gridblocks. Tere are 45 injection wells planned to injectCO2at a constant rate (331801.9 m

3/day) or 50 yearsstarting in 2172. Each well is perorated in a singlelayer, although the perorated layers might be differentor different wells. Te perorations happen in layers19 (one well), 20 (40 wells), 21 (one well), and 22 (threewells). It is assumed that there is no-ow boundarycondition at the outer boundaries. Figure 1 shows a3-dimensional view o the structure in this simulationmodel.

Te objective o this reservoir model is to track thedistribution o pressure and phase saturations at thetarget layer (layer 18) during and afer injection oCO2. Te total number o grid blocks in this layer is544, o which only 422 are active. Te initial proper-ties (pressure, water saturation and gas mole raction

[CO2], respectively) at layer 18 are shown in Figs 2, 3,and 4. Te white grid blocks are null or inactivebecause they have a negligible thickness value. Teinitial condition is the condition o the reservoir afer200 years o EOR process (rom 1972 to 2172), whichcomes rom the original model.

Uncertain properties and trainingrealizations

In order to introduce the uncertainties involved in the

reservoir model to an SRM, a small number o geo-logical realizations were built and run using a com-mercial numerical reservoir simulator. Te numbers orealizations used were 10 and 16 to train the SRM orpredicting pressure and phase saturations, respec-tively. Moreover, three and two realizations were usedat the end as the blind runs in order to validate thetrained SRM or above-mentioned properties.

Te variable properties in the realizations consist opermeability distributions at nine layers o the reser-voir (layers 1, 2, 19, 20, 21, 22, 23, 24, and 25) andowing bottom-hole pressure at 45 injection wells.

A urther validation step in the SRM development isutilized to assure its robustness. Tis step is reerredto as blind verication because it is a set o realiza-tions that has not been used during the training

process. Tese blind testing sets are complete realiza-tions o the reservoir, while the verication set used inthe training process is a randomly selected portion ospatio-temporal database.

Field background

Te Kelly-Snyder eld, discovered in 1948, is one othe major oil reservoirs in the USA, having approxi-mately 2.73 billion bbls o oil originally in place. Teearly perormance history o the eld indicated its soleproduction mechanism as solution gas drive, whichcould result in an ultimate recovery o less than 20%o the original oil in place. Te Scurry Area CanyonRee Operations Committee Unit (SACROC Unit) wasormed in 1953, and in September 1954 a massivepressure maintenance program was started. Waterwas injected into a center-line row o wells along thelongitudinal axis o the reservoir.65

In 1968, a technical committee investigating potentialalternatives recommended that a water-driven slug oCO2be used to miscibly displace the oil in the non-water-invaded portion o the reservoir; they also

recommended that a pattern injection program bedeveloped in this area to implement the slug processand improve ultimate oil recovery. CO2injection beganin early 1972. Investigations o alternative methods orimproving recovery in the SACROC Unit showed thatan inverted nine-spot miscible ood program consist-ing o injecting CO2driven by water would be the mosteffective and economical option. Under such a scheme,the predicted ultimate recovery would be about 230million barrels more than what was expected rom theoriginal water injection program. 65

Te SACROC Unit, within the Horseshoe Atoll, isthe oldest continuously operated CO2enhanced oilrecovery operation in the United States, havingundergone CO2injection since 1972. Until 2005,about 93 million tonnes (93,673,236,443 kg) o CO2had been injected and about 38 million tonnes(38,040,501,080 kg) had been produced. As a result, asimple mass balance suggests that the site has accu-mulated about 55 million tonnes (55,632,735,360 kg)o CO2.

66Currently SACROC continues to be oper-ated by the current owner/operator, Kinder MorganCO2.


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Figure 3. Initial water saturation at the target layer (layer 18) for the base simulation

model.

Figure 2. Initial pressure (kPa) at the target layer (layer 18) for the base simulation

model.

Figure 1. A three dimensional view of simulation model.


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An experimental design method was utilized overthe properties range to construct combinations o theinput parameter values such that the maximuminormation can be obtained rom the minimumnumber o simulation runs. Latin hypercube sampling(LHS) is the experimental design method in thisstudy. Latin hypercube sampling has enjoyed popular-ity as a widely used sampling technique or thepropagation o uncertainty in analyses o complexsystems.67Using the experimental design method, therange and average o permeability distribution is

constrained to the base model. Te distribution opermeability changes over different realizations. It is

Te reason behind varying the permeability distribu-tion maps or only nine layers goes back to the basemodel. In the base model, the permeability variationis only noticeable in the named layers while it isconsistently low in the other layers. Figure 5 depictsthe permeability distribution or the layers which werenot altered during the SRM development. In thisgure the low permeability range (less than amili-Darcy) is notable. o generate the permeabilitydistributions or other layers, the range o permeabil-ity in the base model was used. Additionally, the

range or varying owing bottom-hole pressure is 60%to 100% o the litho-static pressure.

Figure 4. Initial gas (CO2) mole fraction at the target layer (layer 18) for the base simula-

tion model.

Figure 5. The permeability distribution for the layers which permeability does not alter through different realizations.


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BHP at injection wells). Te permeability distributionsat different layers or training and validation realiza-tions are shown in Figs 8 and 9. Each row in thesegures represents a scenario; training and validationrealizations have been marked. Also, each columnshows the permeability distribution or a particularlayer at different realizations. Figure 10 displays theowing bottom-hole pressure at injection wells ortraining and validation realizations. Scenarios 1 to 10are training realizations, and Scenarios 11 to 13 are

validation realizations.

SRM development training,calibration, and validation of neuralnetworks

In the path to develop the SRM, ANNs should betrained, calibrated and validated. In order to generateANNs, IDEAMsofware was used (Fig. 11). IDEAM

assumed the permeability values at the well locationsare available (in reality coming rom the core data);thereore, using a geo-statistical method (InverseDistance Estimation provided in CMG-Builder), adistribution o permeability can be generated.Figures 6 and 7 explain the process o generating newrealizations (altering permeability distribution and

Figure 7. Flow chart to generate different realizations by

altering flowing bottom-hole pressure at injection wells.

Figure 6. Flow chart to generate different realizations by

altering permeability distribution.

Intelligent Data Evaluation & Analysis (IDEATM) software is built by

Intelligent Solution Inc. (ISI).68


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Results and discussion

Te SRM was trained, calibrated and validated usinga ew simulation runs. In these realizations, thedistributions o permeability (at nine layers) and

owing bottom-hole pressure or injection wells arethe variable properties. In order to validate therobustness o the SRM, it was deployed on blindrealizations o the reservoir model. Te blind cases oreservoir simulation models were not used during thetraining process o the SRM.

In this study, the SRM was trained and validated toreproduce the results o the reservoir simulationmodel (pressure, water saturation and CO2moleraction) at the target layer (layer 18) or different timesteps during and afer injection o CO2. Layer 18 is therst layer above the injection layers, and it was chosen

is a sofware application made or the development ogeneral data driven, intelligent models. Figure 12shows the inputs used to train the SRM. In addition,Fig. 13 demonstrates the outputs o the SRM in thisstudy. IDEAMprovides a random data partitioning

algorithm to set the training, calibration and veri-cation shares o the dataset. As mentioned, thespatio-temporal database was built based on theinormation rom ten simulation runs. Te training,calibration and verication included 80%, 10%, and10% o the data in the database, respectively. Afertraining the SRM, its robustness was veried usingblind realizations. Tese runs were not used at anystep o training, calibration or verication. Back-propagation was used as the training algorithm.More inormation on IDEA and building ANNs canbe ound in ISI.68

Figure 8. Permeability distributions at layers 1, 2, 19 and 20 for ten training and three blind realizations.


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Figure 10. Flowing bottom-hole pressure at 45 injection wells for ten training and three blind realizations.

Figure 9. Permeability distributions at layers 21, 22, 23, 24 and 25 for ten training and three blind

realizations.


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study originate rom the labor- and time-intensivecharacteristics o reservoir simulation models. Asingle realization o the reservoir simulation model inthis study runs in 424 h (depending on convergencetime) on a six processor computer with 24 GB RAM(random access memory). A typical analysis o a CO2sequestration problem requires hundreds o realiza-tions. On the other hand, a validated SRM (which wasprepared using less than 20 realizations) runs in theorder o seconds using the same computational power.

Figure 12. Inputs of SRM including static data, dynamic

data and operational constraints.

Figure 11. Structure of ANNs built in IDEA.

Figure 13. Outputs of SRM.

to demonstrate the effect o changing the variableparameters on the pressure and phase saturationbehaviors in this layer. Te motivations behind this


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including injection and post injection periods wereselected as the representatives o the results. Tesetwo time steps consist o one injection and one postinjection period. Te injection time step is nine yearsafer injection starts; note that total years o injection

are 50 years. Te second selected time step is in post

In addition to the high pace o the SRM, this AImodel is able to accurately replicate the results o thereservoir simulation model. Te SRM was developedto predict the distribution o pressure, water satura-tion and gas (CO2) mole raction at layer 18 or 10

different time steps. In this paper, two time steps

Figure 15. Comparison between the results of simulation model (left) and SRM (right) for pressure distribution of a

training realization at layer 18, nine years after injection starts. The figure below represents the relative error.




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Figures 1416 demonstrate the pressure distribution atthe target layer (layer 18) during the injection (nineyears afer injection starts) or three different realiza-tions used to train the SRM. Tese images show theresults o the simulator (lef side) compared to the

injection period and shows the results or 100 yearsafer injection ends. For each time step three trainingrealizations and one blind realization were chosen.

Te accuracy o the SRM to reproduce the results othe simulation model is illustrated in Figs 1437.




blind (validation) realization at layer 18, nine years after injection starts. The figure below represents the relative error.


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the normal range due to numerical problems in thesimulation model, causing issues with the pressurebehavior. Although the SRM understands the generalbehavior at these blocks, it does not have a similar

perormance to the other blocks. Te reason goes back

SRM (middle). Te relative error distribution betweenthe simulator and the SRM is shown along the bottomo the images. Te SRM predicts the pressure distribu-tion very well, and the relative error distribution

conrms this. Tere are a ew blocks that are out o


training realization at layer 18, 100 years after injection ends. The figure below represents the relative error.




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obvious that the distribution o pressure is different indifferent realizations, although they are in a similarrange. Te main reason or such a behavior is alteringthe permeability distribution at the bottom layers(which are injection layers) or different realizations.

to pattern recognition characteristics o the SRM: itcannot learn a pattern that is out o the training range.Figure 17 is the results or the same property and timestep (pressure distribution or nine years afer injec-tion starts) or a blind (validation) scenario. It is




blind (validation) realization at layer 18, 100 years after injection ends. The figure below represents the relative error.


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relative errors or the pressure distribution are lessthan 10%.

Te results or the water saturation distribution areshown in Figs 2228. Figures 2224 display the results

Figures 1820 compare the pressure results ortraining realizations afer 100 years when theinjection plan ends, and Fig. 21 displays theresults or a blind realization. Te general

Figure 23. Comparison between the results of simulation model (left) and SRM (right) for water saturation distribution

of a training realization at layer 18, nine years after injection starts. The figure below represents the absolute error.




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and the SRM outputs. Figure 25 demonstrates thesame results and absolute error distributions or oneblind realization. Tese gures (Figs 2225) are theresults or nine years afer injection starts. Although

o the numerical simulator (lef) and the SRM (right)or three different realizations used in training,calibration and validation sets. Te bottom o thesegures shows the absolute error between the simulator




of a blind realization at layer 18, nine years after injection starts. The figure below represents the absolute error.


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results or the post injection time step (one hundredyears afer injection ends) as Figs 2225. Te generalabsolute error or this property is less than 3%.

Figures 3037 illustrate and compare the results o

the simulator and the SRM or the gas (CO2) mole

the changes in the water saturation are not as great asthe changes in the pressure (CO2is the injected uidand water does not tend to move due to low perme-ability values at this layer), the SRM perorms well in

these realizations. Figures 26 to 29 show the same


of a training realization at layer 18, 100 years after injection ends. The figure below represents the absolute error.




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injection period (nine years afer injection starts).Figures 3437 show the same property or a postinjection time step (100 afer injection). Although the

raction. Figures 3033 describe the results and theabsolute errors o training (three realizations) andblind realizations or a time step during the


of a blind (validation) realization at layer 18, 100 years after injection ends. The figure below represents the absolute

error.




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Figures 1437 prove the accuracy o the developedSRM in this study. Te number o simulation runsrequired to train the SRM was surprisingly low. When

general absolute error or the gas mole ractionincreases to 10%, the results o the SRM aresatisactory.

Figure 31. Comparison between the results of simulation model (left) and SRM (right) for gas (CO2) mole fraction

distribution of a training realization at layer 18, nine years after injection starts. The figure below represents the

absolute error.



absolute error.


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distribution of a blind (validation) realization at layer 18, nine years after injection starts. The figure below represents

the absolute error.



absolute error.


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distribution of a training realization at layer 18, 100 years after injection ends. The figure below represents the abso-

lute error.



lute error.


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distribution of a blind (validation) realization at layer 18, 100 years after injection ends. The figure below represents the

absolute error.



lute error.


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it is compared to the computational power and thetime needed or running the simulation model, theSRM shows its effi ciency.

Concluding remarks

Te consequences o the daily increasing CO2con-centration in the atmosphere have been shown as areal threat to lie on this planet. CCS has showed thepotential as a practical method to reduce the amounto CO2coming rom human activities. In order tosecure the stability o a CCS project, a comprehensivestudy o uid ow through porous media is required.Te conventional tools used to perorm such ananalysis are numerical reservoir simulation models.

Although numerical reservoir simulators are able toperorm detailed analysis, they are highly time-con-suming and computationally expensive. Te patternrecognition based reservoir models are effi cientalternative tools to address the aorementionedissues.

Te technology developed and utilized in this studyis known as Surrogate Reservoir Models (SRMs). Tecapabilities o SRMs to be a ast and accurate replicao a reservoir simulation model make them an effi -cient tool to perorm the conventional analyses in thepetroleum industry.

In this study, ten different realizations o the basemodel were designed to develop the SRM to predictpressure behavior in the reservoir. Sixteen realizationswere considered in order to simulate the phasesaturation behavior. Te comprehensive spatio-tempo-ral database was developed based on the data ex-tracted rom these realizations. Te SRM was trained,calibrated and validated using a data driven andintelligent model developer sofware. Te robustnesso the SRM was urther validated using blindrealizations.

Acknowledgements

Te authors wish to acknowledge the US Departmento Energy (DOE) National Energy echnology Labo-ratory (NEL) or their support o this project and orproviding the base simulation model. Tey alsoextend their appreciation to Computer ModelingGroup (CMG) and Intelligent Solution Inc. (ISI) orproviding the sofware applications or reservoirsimulation and or development o the SRM,respectively.


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Alireza Shahkarami

Alireza Shahkarami is a PhD candidate

in Petroleum Engineering at West

Virginia University (WVU). Alirezas

research mainly focuses on the

implementation of artificial intelligence

and data mining techniques to

address conventional and unconven-

tional problems in petroleum

engineering.

Shahab D. Mohaghegh

Shahab D. Mohaghegh is the presi-

dent and CEO of Intelligent Solutions,

Inc. (ISI) and Professor of Petroleum

and Natural Gas Engineering at West

Virginia University. A pioneer in the

application of artificial intelligence and

data mining in the exploration and

production industry, he holds BSc,

MSc, and PhD degrees in Petroleum and Natural Gas

Engineering.

Vida Gholami

Vida Gholami is a Research Associate

in the PEARL (Petroleum Engineering

and Analytics Research Laboratory) at

West Virginia University (WVU). For

the past six years she had been

working on the application of artificial

intelligence and data mining (AI&DM)

in the petroleum industry.

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Propagation of Uncertainty in Analyses of Complex Systems,

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NM, USA (2002).

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www.intelligentsolutionsinc.com/ [May 2013].


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Alireza Haghighat

Alireza Haghighat earned his MSc in

Petroleum Engineering from Delft

University of Technology in Nether-lands. He is currently pursuing his PhD

in Petroleum Engineering at West

Virginia University. Alirezas research

focuses on application of AI and smart

field technology in CO2sequestration.

Daniel Moreno

Daniel Moreno earned his BSc in

Mechanical Engineering from the

Metropolitan University in Caracas,Venezuela in 2004. He holds an MSc in

Petroleum and Natural Gas Engineer-

ing from West Virginia University.

Presently, he works as a Production

Engineer at Chevron in Bakersfield, CA.

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