modeling pressure and saturation distribution in a co2 … · 2017-02-03 · modeling and analysis...

289© 2014 Society of Chemical Industry and John Wiley & Sons, Ltd | Greenhouse Gas Sci Technol. 4:289–315 (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 CO 2 storage project using a Surrogate Reservoir Model (SRM) Alireza Shahkarami , Shahab D. Mohaghegh , Vida Gholami , Alireza Haghighat , and Daniel Moreno , West Virginia University , Morganstown, WV , USA

Abstract: Capturing carbon dioxide (CO 2 ) from large point sources and depositing it in a geological formation is an effi cient way of decreasing CO 2 concentration in the atmosphere. A comprehensive study is required to perform a safe and effi cient CO 2 capture and storage (CCS) project. The study includes different steps, such as selecting proper underground storage and keeping track of CO 2 behavior in the storage environment. Numerical reservoir simulators are the conventional tools used to implement such an analysis. The intricacy of simulating multiphase fl ow, having a large number of time steps required to study injection and post-injection periods of CO 2 sequestration, 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 CO 2 sequestration process requires multiple realizations of the reservoir model. Consequently, using a conventional numerical simulator 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-fi eld reservoir simulation models. It can generate outputs in a very short time with reasonable accuracy. These characteristics make SRM a unique tool in CO 2 sequestration modeling. This paper proposes developing an SRM for a CO 2 sequestration project ongoing in the SACROC unit to model pressure behavior and phase saturation distributions during different time steps of the CO 2 storage process.© 2014 Society of Chemical Industry and John Wiley & Sons, Ltd

COKeywords: 2 sequestration 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 (CO 2 ) is the primary greenhouse gas (GHG) that has been contributing to global warming and climate change since the beginning

of the Industrial Revolution. CO 2 comprises nearly 80% of global anthropogenic (produced by human activity) GHG emissions. 1 Th e atmospheric concentra-tion of CO 2 recently reached a considerable level of 400 ppm in May 2013 – an almost 100 ppm increase

A Shahkarami et al. Modeling and Analysis: Modeling pressure and saturation distribution in a CO2 storage project using a Surrogate Reservoir Model (SRM)

290 © 2014 Society of Chemical Industry and John Wiley & Sons, Ltd | Greenhouse Gas Sci Technol. 4:289–315 (2014); DOI: 10.1002/ghg

since 1960. 2 Fossil fuel use is considered the main source of CO 2 emission. Even with considering new policies of CO 2 emissions, 3 it is unlikely that there will be a signifi cant decrease over the next 25 years in the percentage of world energy produced by fossil fuels (81% in 2010). Th erefore, mitigating the amount of CO 2 coming from human activities is a major chal-lenge in reducing the anthropogenic eff ects on global warming and climate change.

Th e Intergovernmental Panel on Climate Change (IPCC) defi nes carbon capture and storage (CCS) as ‘a process consisting of the separation of CO 2 from industrial and energy-related sources, transport to a storage location and long-term isolation from the atmosphere’. 4 Th e geological storage of CO 2 is the injection of the captured CO 2 into appropriate deep geological formations. Th e geological sequestration of CO 2 is not a new technology. In the early 1970s, CO 2 was injected for the fi rst time into subsurface geologi-cal formations in Texas in order to enhance the oil recovery. 5–7 However, it was not until the 1990s when the geological storage of CO 2 gained enough credibil-ity to be applied in a large-scale project. 8,9 In 1991, the Norwegian government instituted a tax on CO 2 emission, which motivated Statoil to run the fi rst commercial CCS project in order to capture CO 2 from the Sleipner oil and gas fi eld in the North Sea and inject it into a thick layer saline aquifer in 1996. 10 In less than two decades, carbon storage in deep geologi-cal formations has emerged as one of the most impor-tant options for reducing CO 2 emissions. 4,11,12 CCS plays a critical role in the portfolio of technologies required to attain a considerable reduction of global GHG emissions in the most economically effi cient manner. Th is technology has the potential to decrease nearly one-fi ft h of the emissions required to cut GHG emissions from energy consumption in half by 2050. 13

CO 2 leakage is one of the major risks in a CCS project; therefore, keeping CO 2 in a safe and con-trolled environment for a long period of time is a main challenge. 14,15 Consequently, the following tasks must be thoroughly accomplished: quality control of candidate underground storage, keeping track of CO 2 plume conditions, and simulating the reservoir behavior (such as reservoir pressure, which is an appropriate indicator of potential leakage). Numerical reservoir simulators are the conventional tools used to perform the aforementioned tasks. 16–21

In order to have a comprehensive study of a CCS project, hundreds to thousands of realizations with

diff erent reservoir characteristics and operational conditions are required. Although using a numerical reservoir simulator gives accurate results, it is very time-consuming and computationally expensive. Furthermore, due to the process of CO 2 sequestration, a compositional simulator should be utilized, which generally leads to an even higher computational time. 22

Th e reservoir simulation model in this work comes from the work done by Han. 23 Th e original geo-cellu-lar model in that work consisted of over nine million grid blocks. In order to simulate CO 2 trapping mecha-nisms, he had to upscale the model and decrease the number of grid blocks to 13 600. However, with the time 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. Th e reservoir simulation in this study was conducted using Computer Modeling Group (CMG) simulator called GEM-GHG TM . 24 GEM-GHG TM is specifi cally designed for simulating CO 2 sequestration processes.

Th e objective of this study is to examine the eff ect of the uncertainty involved in a reservoir parameter (permeability) and also the impact of operational constraints on the output of numerical reservoir simulators (pressure and phase saturations). Th e tool to accomplish the objectives of this study is a pattern-recognition-based technology known as Surrogate Reservoir Models (SRMs). SRMs have been intro-duced as a tool for addressing many time-consuming operations performed with reservoir simulation models. 25 SRMs attempt to reduce the dimensionality of the problem by using fuzzy pattern recognition techniques. Th e capability of SRMs to replicate full fi eld models that run in fractions of a second makes them an effi cient alternative tool to address many time-consuming operations performed with reservoir simulation models. 25 Th e engines of SRMs are based on Artifi cial Neural Networks (ANNs).

In order to develop the SRM, a few diff erent realiza-tions of the reservoir simulation model were created and run by numerical reservoir simulators. Th e inputs and outputs of these realizations generated a spatio-temporal database. Th e spatio-temporal database was used to train the SRMs (the pattern-recognition-based models, particularly ANNs). Th e SRM aims to repli-cate the results of traditional numerical reservoir simulators at the grid level in a matter of seconds. Th e SRM passed training, calibration, and validation steps to be qualifi ed as a reliable replica of the reservoir

Modeling and Analysis: Modeling pressure and saturation distribution in a CO2 storage project using a Surrogate Reservoir Model (SRM) A Shahkarami et al.


simulation model. Further validation process is applied to verify the effi ciency of the SRM on diff erent realizations of the reservoir simulation model. Th ese realizations were not seen during the training process; therefore they are referred to as ‘blind realizations’. At the end of this process the SRM is ready to reproduce the outputs (pressure and phase saturations) of numerical reservoir simulators at the grid block level. Th e time needed to accomplish each run and achieve the desired results using the SRM is in the order of seconds, whereas the time required to perform the process using a numerical reservoir simulator is in the order of hours and a day.

Potentials of pattern recognition techniques CO 2 sequestration in underground storage is one of the most viable methods for reducing GHGs. Th e petroleum industry has decades of experience inject-ing gas (CO 2 or hydrocarbons) into diff erent types of reservoirs. Th is leads to an overlap of issues in the petroleum industry and CCS, such as modeling, history matching, and uncertainty analysis and risk management. Th ese issues can be managed by the capabilities of pattern recognition techniques.

In pattern recognition concepts, the data analysis process deals with predictive modeling. By having a high dimensional database, the objective is to learn the underlying behavior in the data and forecast the performance of unforeseen validation database. Th e learning process refers to some form of algorithm to reduce the error on the set of training data. 26 Th e learning procedures could be distinguished into (i) supervised learning or (ii) unsupervised learning.* 27 Supervised learning generally represents a learning procedure which takes an available set of inputs and known outputs corresponding to these inputs. Eff orts will be made to build a predictive model by matching the available responses with the inputs. Th is predictive model is then able to generate reasonable predictions for the response to novel data. Th e most important characteristic of this learning technique is that the responses (outputs) are recognized or labeled in the training database. On the other hand, unsupervised learning involves only unlabeled data, which makes the process more challenging than the previous one.

In other words, unsupervised learning forms clusters or natural patterns underlying the structure of data.

One of the most famous pattern recognition tech-niques, one that has a long history in a variety of scientifi c fi elds, is ANNs, usually called Neural Networks (NNs). Th e learning procedure in ANNs is supervised learning. ANNs were originally motivated by the goal of having machines that are able to mimic the brain. In fact, the structure of ANNs is very similar to that of the human neural system, as it includes an interconnected group of artifi cial neurons. ANNs are cellular systems capable of obtaining and storing information and using experiential knowl-edge. An ANN is an adaptive system that adjusts its structure based on output and input information that fl ows through the network during the learning phase. 28

Although ANNs have been around for a long time, their popularity in petroleum engineering started only two decades ago. 29 Since this time, the applica-tions of ANNs in addressing the conventional prob-lems of the petroleum industry have been widely studied. Some applications of ANNs in petroleum engineering literature include well log inter-pretation, 30–32 well test data analysis, 33–36 reser-voir characterization, 37–39 calibration of seismic attributes, 40 seismic pattern recognition, 41 inversion of seismic waveforms, 42 prediction of PVT data, 43–46 fractures and faults identifi cation, 47–50 hydrocarbons detection, 50,51 and formation damage forecast. 52,53

Th at said, it should be noted that the eff ective use of pattern recognition techniques in the petroleum industry is not a trivial process. It requires insight in both the domain of reservoir engineering as well as a substantial application of pattern recognition tech-niques; otherwise, the results could be quite disappointing. 54

Surrogate reservoir models Surrogate Reservoir Models (SRMs) are approxima-tions of the full-fi eld 3-dimensional numerical reser-voir models that are capable of accurately mimicking the behavior of the full-fi eld models. Unlike statisti-cally based proxy models that require hundreds of simulation runs, 55–57 SRMs can be created in a few simulation runs. In 2006, SRM was presented for the fi rst time by Shahab D. Mohaghegh to solve the problem of time-consuming runs for an uncertainty analysis of a giant oil fi eld with 165 horizontal wells in

*Recently another set of learning was discussed in the literature which is referred as called semi-supervised.



recognition characteristics of SRMs help to develop these types of models by having a small number of simulation runs. However, there is no algorithm to fi nd the optimum number of simulation runs to build an SRM. Th e common practice when choosing the best number to train the SRM is to use rules of thumb based on the intricacy and heterogeneity of the reservoir model, which might change. Nevertheless, it is obvious that if the number of simulation runs is too small, the SRM will not be able to reproduce the simulator results properly. Otherwise, if the number of simulation runs is too big, there is no reason to develop an SRM since the solution is close to the original problem, which is a high number of simula-tion runs.

Aft er running the realizations, the static and dy-namic data are extracted in order to build the repre-sentative spatio-temporal database. Th e database includes diff erent types of data such as static and dynamic reservoir characteristics, operational con-straints, etc. Static data refer to properties of the reservoir that are not changing over time, such as permeability, porosity, top, and thickness. Dynamic refers to any data such as well constraints or pressure and phase saturation that change over time. 58

Th e training process of an SRM includes three diff erent steps: training (learning), calibration, and validation procedures. Based on that, the spatio-tem-poral database is divided into three sets: the training or learning set, calibration set, and validation or verifi cation set. Th e training set is part of the data shown to the ANNs during the training process. Th e 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. Th is set is utilized to assure that any increase in accuracy over the training data set will lead to an increase in accuracy over a data set that has not been seen by ANNs. Th is set of data is helpful in determin-ing when the training should be stopped. Finally, the verifi cation set is a part of the database used to verify the predictability of the trained ANN, and subse-quently, this data set is not used to train the ANNs. It is worth mentioning that the elapsed time to perform the training process (learning, calibration, and verifi cation) is negligible when compared to the reservoir simulation run-time. Another important point is an SRM may be a collection of several ANNs that are trained, matched and verifi ed in order to generate diff erent results.

the Middle East. Th e reservoir simulation model included about one million grid blocks and took 10 h to run using a cluster of 12, 3.2 GHz processors. In his study, SRM was used as an objective function for a Monte Carlo Simulation to build thousands of simula-tion runs in a very short time compared to numerical simulators. Mohaghegh describes SMRS as an ‘en-semble of multiple, interconnected neuro-fuzzy systems that are trained to adaptively learn the fl uid fl ow behavior from a multi-well, multilayer reservoir simulation model, such that they can reproduce results similar to those of the reservoir simulation model (with high accuracy) in real-time’. 58 Since 2006, applications of SRMs as an accurate and rapid replica of a numerical simulation model have been reviewed in diff erent studies. 58–63

SRM development SRMs are developed using the data extracted from the realizations of simulation model. Th ese data are included in a spatio-temporal database. Building this database is the fi rst step in developing Artifi cial Intelligence (AI)-based reservoir models. Th e main objective of this database is to teach the model the whole process of fl uid fl ow phenomena in the reser-voir. Th erefore meticulous eff orts should be made in this part. Th e quality and quantity of this database determine the degree of success in developing a successful AI-based reservoir model including an SRM. Not dedicating enough attention to this part is the main reason behind unsuccessful attempts at applying AI-based models in the literature. 54 Mo-haghegh thoroughly discussed this step of SRM development in his paper. 64

In order to create the spatio-temporal database, the fi rst step is to identify the number of runs that are required to develop the SRM. Th e purpose of having diff erent realizations of a reservoir simulation model is to introduce the uncertainties involved in the model to the SRM. Th is is a common step in building SRMs and developing response surface methods; however, there is a key diff erence between these two methods: the functional forms behind these models. Response surface and other reduced models are developed using statistical approaches, which use predetermined functional forms. Th e output of reservoir simulation models are then fi tted to these predetermined forms. In order to match these functional forms, hundreds of runs are needed. On the other hand, the pattern



Reservoir simulation model We received the base reservoir model from a work performed by Han. 23 Th e original reservoir model was for a CO 2 enhanced oil recovery (EOR) project that lasted for 200 years, from 1972 to 2172. Th e model utilized in this study covers the period of January 1, 2172 to January 1, 3172 aft er the reservoir has been depleted from oil. Th erefore the simulation model is just considered for CO 2 storage and sequestration. Th e model contains 25 simulation layers of 16×34 grid blocks. Th ere are 45 injection wells planned to inject CO 2 at a constant rate (331801.9 m 3 /day) for 50 years starting in 2172. Each well is perforated in a single layer, although the perforated layers might be diff erent for diff erent wells. Th e perforations happen in layers 19 (one well), 20 (40 wells), 21 (one well), and 22 (three wells). It is assumed that there is no-fl ow boundary condition at the outer boundaries. Figure 1 shows a 3-dimensional view of the structure in this simulation model.

Th e objective of this reservoir model is to track the distribution of pressure and phase saturations at the target layer (layer 18) during and aft er injection of CO 2 . Th e total number of grid blocks in this layer is 544, of which only 422 are active. Th e initial proper-ties (pressure, water saturation and gas mole fraction [CO 2 ], respectively) at layer 18 are shown in Figs 2 , 3 , and 4 . Th e white grid blocks are ‘null’ or inactive because they have a negligible thickness value. Th e initial condition is the condition of the reservoir aft er 200 years of EOR process (from 1972 to 2172), which comes from the original model.

Uncertain properties and training realizations In order to introduce the uncertainties involved in the reservoir model to an SRM, a small number of geo-logical realizations were built and run using a com-mercial numerical reservoir simulator. Th e numbers of realizations used were 10 and 16 to train the SRM for predicting pressure and phase saturations, respec-tively. Moreover, three and two realizations were used at the end as the blind runs in order to validate the trained SRM for above-mentioned properties.

Th e variable properties in the realizations consist of permeability distributions at nine layers of the reser-voir (layers 1, 2, 19, 20, 21, 22, 23, 24, and 25) and fl owing bottom-hole pressure at 45 injection wells.

A further validation step in the SRM development is utilized to assure its robustness. Th is step is referred to as ‘blind verifi cation’ because it is a set of realiza-tions that has not been used during the training process. Th ese blind testing sets are complete realiza-tions of the reservoir, while the verifi cation set used in the training process is a randomly selected portion of spatio-temporal database.

Field background Th e Kelly-Snyder fi eld, discovered in 1948, is one of the major oil reservoirs in the USA, having approxi-mately 2.73 billion bbls of oil originally in place. Th e early performance history of the fi eld indicated its sole production mechanism as solution gas drive, which could result in an ultimate recovery of less than 20% of the original oil in place. Th e Scurry Area Canyon Reef Operations Committee Unit (SACROC Unit) was formed in 1953, and in September 1954 a massive pressure maintenance program was started. Water was injected into a center-line row of wells along the longitudinal axis of the reservoir. 65

In 1968, a technical committee investigating potential alternatives recommended that a water-driven slug of CO 2 be used to miscibly displace the oil in the non-water-invaded portion of the reservoir; they also recommended that a pattern injection program be developed in this area to implement the slug process and improve ultimate oil recovery. CO 2 injection began in early 1972. Investigations of alternative methods for improving recovery in the SACROC Unit showed that an inverted nine-spot miscible fl ood program consist-ing of injecting CO 2 driven by water would be the most eff ective and economical option. Under such a scheme, the predicted ultimate recovery would be about 230 million barrels more than what was expected from the original water injection program. 65

Th e SACROC Unit, within the Horseshoe Atoll, is the oldest continuously operated CO 2 enhanced oil recovery operation in the United States, having undergone CO 2 injection since 1972. Until 2005, about 93 million tonnes (93,673,236,443 kg) of CO 2 had been injected and about 38 million tonnes (38,040,501,080 kg) had been produced. As a result, a simple mass balance suggests that the site has accu-mulated about 55 million tonnes (55,632,735,360 kg) of CO 2 . 66 Currently SACROC continues to be oper-ated by the current owner/operator, Kinder Morgan CO 2 .



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.



An experimental design method was utilized over the properties range to construct combinations of the input parameter values such that the maximum information can be obtained from the minimum number of simulation runs. Latin hypercube sampling (LHS) is the experimental design method in this study. Latin hypercube sampling has enjoyed popular-ity as a widely used sampling technique for the propagation of uncertainty in analyses of complex systems. 67 Using the experimental design method, the range and average of permeability distribution is constrained to the base model. Th e distribution of permeability changes over diff erent realizations. It is

Th e reason behind varying the permeability distribu-tion maps for only nine layers goes back to the base model. In the base model, the permeability variation is only noticeable in the named layers while it is consistently low in the other layers. Figure 5 depicts the permeability distribution for the layers which were not altered during the SRM development. In this fi gure the low permeability range (less than a mili-Darcy) is notable. To generate the permeability distributions for other layers, the range of permeabil-ity in the base model was used. Additionally, the range for varying fl owing bottom-hole pressure is 60% to 100% of the litho-static pressure.

Figure 4. Initial gas (CO 2 ) 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.



BHP at injection wells). Th e permeability distributions at diff erent layers for training and validation realiza-tions are shown in Figs 8 and 9 . Each row in these fi gures represents a scenario; training and validation realizations have been marked. Also, each column shows the permeability distribution for a particular layer at diff erent realizations. Figure 10 displays the fl owing bottom-hole pressure at injection wells for training and validation realizations. Scenarios 1 to 10 are training realizations, and Scenarios 11 to 13 are validation realizations.

SRM development – training, calibration, and validation of neural networks In the path to develop the SRM, ANNs should be trained, calibrated and validated. In order to generate ANNs, IDEA TM † soft ware was used (Fig. 11 ). IDEA TM

assumed the permeability values at the well locations are available (in reality coming from the core data); therefore, using a geo-statistical method (Inverse Distance Estimation provided in CMG-Builder), a distribution of permeability can be generated. Figures 6 and 7 explain the process of generating new realizations (altering permeability distribution and

Figure 7. Flow chart to generate different realizations by altering fl owing bottom-hole pressure at injection wells.

Figure 6. Flow chart to generate different realizations by altering permeability distribution.

†Intelligent Data Evaluation & Analysis (IDEA TM ) software is built by Intelligent Solution Inc. (ISI). 68



Results and discussion Th e SRM was trained, calibrated and validated using a few simulation runs. In these realizations, the distributions of permeability (at nine layers) and fl owing bottom-hole pressure for injection wells are the variable properties. In order to validate the robustness of the SRM, it was deployed on blind realizations of the reservoir model. Th e blind cases of reservoir simulation models were not used during the training process of the SRM.

In this study, the SRM was trained and validated to reproduce the results of the reservoir simulation model (pressure, water saturation and CO 2 mole fraction) at the target layer (layer 18) for diff erent time steps during and aft er injection of CO 2 . Layer 18 is the fi rst layer above the injection layers, and it was chosen

is a soft ware application made for the development of general data driven, intelligent models. Figure 12 shows the inputs used to train the SRM. In addition, Fig. 13 demonstrates the outputs of the SRM in this study. IDEA TM provides a random data partitioning algorithm to set the training, calibration and verifi -cation shares of the dataset. As mentioned, the spatio-temporal database was built based on the information from ten simulation runs. Th e training, calibration and verifi cation included 80%, 10%, and 10% of the data in the database, respectively. Aft er training the SRM, its robustness was verifi ed using blind realizations. Th ese runs were not used at any step of training, calibration or verifi cation. Back-propagation was used as the training algorithm. More information on IDEA and building ANNs can be found in ISI. 68

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



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.



study originate from the labor- and time-intensive characteristics of reservoir simulation models. A single realization of the reservoir simulation model in this study runs in 4–24 h (depending on convergence time) on a six processor computer with 24 GB RAM (random access memory). A typical analysis of a CO 2 sequestration problem requires hundreds of realiza-tions. On the other hand, a validated SRM (which was prepared using less than 20 realizations) runs in the order of 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 eff ect of changing the variable parameters on the pressure and phase saturation behaviors in this layer. Th e motivations behind this



including injection and post injection periods were selected as the representatives of the results. Th ese two time steps consist of one injection and one post injection period. Th e injection time step is nine years aft er injection starts; note that total years of injection are 50 years. Th e second selected time step is in post

In addition to the high pace of the SRM, this AI model is able to accurately replicate the results of the reservoir simulation model. Th e SRM was developed to predict the distribution of pressure, water satura-tion and gas (CO 2 ) mole fraction at layer 18 for 10 diff erent 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 fi gure below represents the relative error.




Figures 14–16 demonstrate the pressure distribution at the target layer (layer 18) during the injection (nine years aft er injection starts) for three diff erent realiza-tions used to train the SRM. Th ese images show the results of the simulator (left side) compared to the

injection period and shows the results for 100 years aft er injection ends. For each time step three training realizations and one blind realization were chosen.

Th e accuracy of the SRM to reproduce the results of the simulation model is illustrated in Figs 14–37 .


Figure 17. Comparison between the results of simulation model (left) and SRM (right) for pressure distribution of a blind (validation) realization at layer 18, nine years after injection starts. The fi gure below represents the relative error.



the normal range due to numerical problems in the simulation model, causing issues with the pressure behavior. Although the SRM understands the general behavior at these blocks, it does not have a similar performance to the other blocks. Th e reason goes back

SRM (middle). Th e relative error distribution between the simulator and the SRM is shown along the bottom of the images. Th e SRM predicts the pressure distribu-tion very well, and the relative error distribution confi rms this. Th ere are a few blocks that are out of

Figure 19. Comparison between the results of simulation model (left) and SRM (right) for pressure distribution of a training realization at layer 18, 100 years after injection ends. The fi gure below represents the relative error.




obvious that the distribution of pressure is diff erent in diff erent realizations, although they are in a similar range. Th e main reason for such a behavior is altering the permeability distribution at the bottom layers (which are injection layers) for diff erent realizations.

to pattern recognition characteristics of the SRM: it cannot learn a pattern that is out of the training range. Figure 17 is the results for the same property and time step (pressure distribution for nine years aft er injec-tion starts) for a blind (validation) scenario. It is


Figure 21. Comparison between the results of simulation model (left) and SRM (right) for pressure distribution of a blind (validation) realization at layer 18, 100 years after injection ends. The fi gure below represents the relative error.



relative errors for the pressure distribution are less than 10%.

Th e results for the water saturation distribution are shown in Figs 22–28 . Figures 22–24 display the results

Figures 18–20 compare the pressure results for training realizations aft er 100 years when the injection plan ends, and Fig. 21 displays the results for a blind realization. Th e 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 fi gure below represents the absolute error.




and the SRM outputs. Figure 25 demonstrates the same results and absolute error distributions for one blind realization. Th ese fi gures (Figs 22–25 ) are the results for nine years aft er injection starts. Although

of the numerical simulator (left ) and the SRM (right) for three diff erent realizations used in training, calibration and validation sets. Th e bottom of these fi gures shows the absolute error between the simulator


Figure 25. Comparison between the results of simulation model (left) and SRM (right) for water saturation distribution of a blind realization at layer 18, nine years after injection starts. The fi gure below represents the absolute error.



results for the post injection time step (one hundred years aft er injection ends) as Figs 22–25 . Th e general absolute error for this property is less than 3%.

Figures 30–37 illustrate and compare the results of the simulator and the SRM for the gas (CO 2 ) mole

the changes in the water saturation are not as great as the changes in the pressure (CO 2 is the injected fl uid and water does not tend to move due to low perme-ability values at this layer), the SRM performs well in these realizations. Figures 26 to 29 show the same

Figure 27. Comparison between the results of simulation model (left) and SRM (right) for water saturation distribution of a training realization at layer 18, 100 years after injection ends. The fi gure below represents the absolute error.




injection period (nine years aft er injection starts). Figures 34–37 show the same property for a post injection time step (100 aft er injection). Although the

fraction. Figures 30–33 describe the results and the absolute errors of training (three realizations) and blind realizations for a time step during the

Figure 29. Comparison between the results of simulation model (left) and SRM (right) for water saturation distribution of a blind (validation) realization at layer 18, 100 years after injection ends. The fi gure below represents the absolute error.




Figures 14–37 prove the accuracy of the developed SRM in this study. Th e number of simulation runs required to train the SRM was surprisingly low. When

general absolute error for the gas mole fraction increases to 10%, the results of the SRM are satisfactory.

Figure 31. Comparison between the results of simulation model (left) and SRM (right) for gas (CO 2 ) mole fraction distribution of a training realization at layer 18, nine years after injection starts. The fi gure below represents the absolute error.




Figure 33. Comparison between the results of simulation model (left) and SRM (right) for gas (CO 2 ) mole fraction distribution of a blind (validation) realization at layer 18, nine years after injection starts. The fi gure below represents the absolute error.




Figure 35. Comparison between the results of simulation model (left) and SRM (right) for gas (CO 2 ) mole fraction distribution of a training realization at layer 18, 100 years after injection ends. The fi gure below represents the abso-lute error.




Figure 37. Comparison between the results of simulation model (left) and SRM (right) for gas (CO 2 ) mole fraction distribution of a blind (validation) realization at layer 18, 100 years after injection ends. The fi gure below represents the absolute error.




Th e Midwest Geological Sequestration Consortium is funded by the U.S. Department of Energy through the National Energy Technology Laboratory (NETL) via the Regional Carbon Sequestration Partnership Program (contract number DE-FC26-05NT42588) and by a cost share agreement with the Illinois Department of Commerce and Economic Opportu-nity, Offi ce of Coal Development through the Illinois Clean Coal Institute.

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it is compared to the computational power and the time needed for running the simulation model, the SRM shows its effi ciency.

Concluding remarks Th e consequences of the daily increasing CO 2 con-centration in the atmosphere have been shown as a real threat to life on this planet. CCS has showed the potential as a practical method to reduce the amount of CO 2 coming from human activities. In order to secure the stability of a CCS project, a comprehensive study of fl uid fl ow through porous media is required. Th e conventional tools used to perform such an analysis are numerical reservoir simulation models. Although numerical reservoir simulators are able to perform detailed analysis, they are highly time-con-suming and computationally expensive. Th e pattern recognition based reservoir models are effi cient alternative tools to address the aforementioned issues.

Th e technology developed and utilized in this study is known as Surrogate Reservoir Models (SRMs). Th e capabilities of SRMs to be a fast and accurate replica of a reservoir simulation model make them an effi -cient tool to perform the conventional analyses in the petroleum industry.

In this study, ten diff erent realizations of the base model were designed to develop the SRM to predict pressure behavior in the reservoir. Sixteen realizations were considered in order to simulate the phase saturation behavior. Th e comprehensive spatio-tempo-ral database was developed based on the data ex-tracted from these realizations. Th e SRM was trained, calibrated and validated using a data driven and intelligent model developer soft ware. Th e robustness of the SRM was further validated using blind realizations.

Acknowledgements Th e authors wish to acknowledge the US Department of Energy (DOE) National Energy Technology Labo-ratory (NETL) for their support of this project and for providing the base simulation model. Th ey also extend their appreciation to Computer Modeling Group (CMG) and Intelligent Solution Inc. (ISI) for providing the soft ware applications for reservoir simulation and for development of the SRM, respectively.



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Alireza Shahkarami

Alireza Shahkarami is a PhD candidate in Petroleum Engineering at West Virginia University (WVU). Alireza’s research mainly focuses on the implementation of artifi cial 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 artifi cial intelligence and data mining in the exploration and production industry, he holds BSc,

MSc, and PhD degrees in Petroleum and Natural Gas Engineering.

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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 artifi cial intelligence and data mining (AI&DM) in the petroleum industry.

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. Alireza’s research focuses on application of AI and smart fi eld technology in CO 2 sequestration.

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 Bakersfi eld, CA.

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