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Reservoir models are generated by geostatistics using available static data. However, there is inherent uncertainty in the reservoir models due to limited information. A number of reservoir models with equivalent probabilities are created to quantitatively assess model uncertainty. The easiest way to evaluate the uncertainty is to perform a reservoir simulation for hundreds of reservoir models, but the simulation cost is too high. Recently, distance-based clustering (DBC) has been used as a means of efficient uncertainty assessment. DBC classifies similar reservoir models into the same group. Because models belonging to the same group have similar reservoir performances, simulating a representative model for each group will give a comparable uncertainty range from simulating all models. For DBC to be successful, the definition of distance, which represents non-similarity between models, is the key factor. In this research, after the main information from a reservoir model is extracted through a stacked autoencoder (SAE), which is one of deep learning algorithms, the 2-norm of feature vectors for two models is defined as the distance. First, the hyperparameters for SAE are analyzed by sensitivity analysis in order to optimize the feature vector from reservoir facies model. Similar to other artificial neural network algorithms, uncertainty results are sensitive to the number of neurons and the number of hidden layers but are stable for the number of clusters. After SAE-based clustering, only 20 representative models can realize the uncertainty range present in 800 individual initial models. If there are observed dynamic data, the best representative model can be determined by a misfit between the simulated production from the representative models and the observed data. The best model and its 9 closest models in feature space are selected as qualified models from among the entire 800 models. Additional reservoir simulations for the closest models can dramatically improve the uncertainty range of the prior models without inverse algorithms. The 10 qualified models can be utilized for generating pseudo-static data or can be used as initial models for inverse algorithms for further improvement of reservoir characterization. more...

History matching is a crucial procedure for predicting reservoir performances and making decisions. However, it is difficult due to uncertainties of initial reservoir models. Therefore, it is important to have reliable initial models for successful history matching of highly heterogeneous reservoirs such as channel reservoirs. In this paper, we proposed a novel scheme for sampling good geological models using support vector machine (SVM) and principal component analysis (PCA). First, we perform PCA for figuring out main geological characteristics of reservoir models. By the procedure, permeability values of each model are transformed to new parameters by principal components, which have eigenvalues of large magnitude. Secondly, the parameters are projected into two-dimensional plane by multi-dimensional scaling (MDS) based on Euclidean distances. Finally, we train a SVM classifier using 10% models which show the most similar or dissimilar well oil production rates (WOPR) with the true values (5% for each category). Then, the other 90% models are classified by the trained SVM. We select models on the side of lower WOPR errors. By repeating the classification process, we can select reliable models which have similar geological trend with the true reservoir model. The two channel fields are analyzed to demonstrate the superiority of the proposed sampling scheme. History matching results with 400 initial models cannot provide trustworthy results. It fails to find out correct geological features of the true model. In addition, since it uses all the models, it takes long computational time. However, history matching with the sampled ensemble offers reliable characterization results by figuring out proper channel trend and gives dependable prediction of future performances. Furthermore, it increases computational efficiency by using only selected geological models in history matching. more...

This study proposes a reliable evaluation method for three-phase saturation (water, gas hydrate (GH), and gas) evaluation during the GH dissociation core experiment using deep learning. A convolutional neural network (CNN) takes computed tomography (CT) images obtained during the GH core experiment as an input and provides three-phase saturation as an output. Although machine/deep learning methods have been applied to the saturation evaluation from CT images in previous research, they were not reliable due to the lack of adequate amount of training data where the model could not find appropriate parameters. Besides, non-zero gas hydrate saturation showed where it was supposed to be zero. This study improved the evaluation of three-phase saturation and solved the non-zero GH saturation problem by acquirement of extra data and application of data augmentation with CNN. The results of CNN and CNN with data augmentation presented 34% and 29% error compared to those of random forest. CNN with data augmentation brought 85% and 44% of error and its variance compared to those of CNN without data augmentation, respectively. Consequently, based on domain knowledge for GH, when it comes to the robustness of random data composition and consistency of performance, the evaluation of three-phase saturation can be boosted using CNN with data augmentation. more...

The static modeling and dynamic simulation are essential and critical processes in petroleum exploration and development. In this study, lithofacies models for Wabiskaw Member in Athabasca, Canada are generated by multipoint statistics (MPS) and then compared with the models built by sequential indicator simulation (SIS). Three training images (TIs) are selected from modern depositional environments; the Orinoco River Delta estuary, Cobequid bay-Salmon River estuary, and Danube River delta environment. In order to validate lithofacies models, average and variance of similarity in lithofacies are calculated through random and zonal blind-well tests. In random six-blind-well test, similarity average of MPS models is higher than that of SIS model. The Salmon MPS model closely resembles facies pattern of Wabiskaw Member in subsurface. Zonal blind-well tests show that successful lithofacies modeling for transitional depositional setting requires additional or proper zonation information on horizontal variation, vertical proportion, and secondary data. As Wabiskaw Member is frontier oilsands lease, it is impossible to evaluate the economics from production data or dynamic simulation. In this study, a dynamic steam assisted gravity drainage (SAGD) performance indicator (SPIDER) on the basis of reservoir characteristics is calculated to build 3D reservoir model for the evaluation of the SAGD feasibility in Wabiskaw Member. SPIDER depends on reservoir properties, economic limit of steam-oil ratio, and bitumen price. Reservoir properties like porosity, permeability, and water saturation are measured from 13 cores and calculated from 201 well-logs. Three dimensional volumes of reservoir properties are constructed mostly based on relationships among properties. Finally, net present value (NPV) volume can be built by equation relating NPV and SPIDER. The economic area exceeding criterion of US$ 10,000 is identified, and the ranges of reservoir properties are estimated. NPV-volume-generation workflow from reservoir parameter to static model provides cost- and time- effective method to evaluate the oilsands SAGD project. more...

One objective of the field development plan (FDP) is to optimize well patterns, that is, the number and type of well (producers or injectors) and their locations, in order to maximize net present value (NPV). Optimization cost, including reservoir simulation, is strongly needed in terms of a global solution because of countless FDP scenarios, especially robust optimization for considering geological uncertainty. To solve this problem efficiently and reliably, this study introduces a convolutional neural network (CNN)-based proxy model into particle swarm optimization (PSO). For the proxy model, three map types having the same dimension as the reservoir model were fed into the input layer, giving an NPV for a given well-pattern scenario. The first map was a well configuration map, which consists of 1, -1, and 0 for producer, injector, and no well, respectively. The second and third maps were time-of-flight (TOF) maps from producers and injectors, respectively. Because the type of input data is an image, the CNN could extract features from 3500 scenarios while training the proxy model. When the predicted NPVs from the trained CNN-based proxy model were verified for 750 test data, the coefficients of determination for the true NPVs from reservoir simulation were higher than 0.94. In addition, the proxy model was flexibly applied to various well patterns, even for different numbers of wells because it utilizes TOF maps as input data. Three points are handled in PSO-Proxy to achieve a realistic well pattern: optimization of the number of wells, well spacing constraint, and operational condition for injection wells. The optimized well pattern maximizes NPV with the optimal number of producers and injectors under the predefined maximum number of wells. In the case of well spacing, two distances, that is, the distance between the wells and the distance between a production well and reservoir boundary, are used as criteria for the solution in terms of the filter method before evaluating the NPV. For injectors, water injection is controlled by bottomhole pressure instead of a constant injection rate, which gives meaningless injection wells placed at the edge of the reservoir. When the proposed method was tested using a 2-dimensional (D) synthetic field and 3-D Egg model, its well patterns showed approximately 1.2% lower NPV than the solution from a conventional method, PSO-ECL. This was relatively small when considering that there was approximately 7.8% NPV changes in each optimization run of the PSO-ECL. In addition, PSO-Proxy required only 21% and 8.6% of the optimization cost of the PSO-ECL for the 2-D and 3-D cases, respectively. Therefore, the proposed method was found to enable reliable and efficient decision-making for FDP; further, as the reservoir complexity increases, the CNN-based proxy model should be able to reduce the optimization time dramatically. more...

The purpose of this study was to determine the three-phase saturation (water; gas hydrate, GH; and gas) in real time to gain insights into the GH depressurization process. Although X-ray computed tomography (CT) can be used to investigate the density changes in the GH core during the depressurization experiment, it is hard to distinguish between water and GH due to their similar densities and the limited resolution of the CT image. To address this issue, random forest (RF) was applied to quantitatively predict the three-phase saturation: CT images were used as input data and the three-phase saturation was the output. In the previous research, a RF model was developed based on training data that only involved the five preliminary stages before the depressurization step. However, the previous RF model failed to estimate the saturation values of the CT images during the depressurization. It could not properly estimate general GH dissociation trend and the GH equilibrium pressure, neither. In this study, CT data obtained in the early and late depressurization stage were used for the training of the RF model. The proposed method can be used to reliably estimate the GH dissociation behavior. The trained RF in this study can identify the GH equilibrium at which the dissociation starts (~16 MPa), which is consistent with the theoretical dissociation at a temperature and salinity of 16 °C and 3 wt%, respectively. The reliability of the proposed method was tested by checking if the estimated results approached zero GH saturation at the end of the GH dissociation (6 and 0 MPa). Therefore, the originality of this study is to improve RF model to reliably predict the three-phase saturation in real time during the GH depressurization by properly utilizing CT images in the depressurization stage for training RF. Based on further improvement, the proposed method could be utilized in the future to help finding adequate depressurization velocity by reliable saturation modeling and analysis of GH experiment because GH productivity depends on depressurization gradient. more...

Ensemble Kalman filter (EnKF) is one of the promising reservoir characterization schemes for history matching. It has been widely researched due to its excellence in recursive data processing and dependable uncertainty quantification. However, EnKF has critical limitations for applying to non-Gaussian distribution fields such as channel reservoirs. In this study, we propose a novel scheme to characterize channel reservoirs reliably. The scheme, recursive update of channel information (RUCI), updates key channel information such as facies ratio and permeabilities of each rock facies as components of the state vector. Since permeabilities assimilated by EnKF follow a Gaussian distribution, EnKF itself is not adequate to preserve channel structure. To overcome this limitation, we use cumulative distribution function mapping to maintain its bimodal distribution. In addition to RUCI, discrete cosine transform (DCT) is utilized to preserve clear channel continuities by figuring out essential channel trend. The proposed method, RUCI in EnKF with DCT, is applied to three different channel reservoir cases and is compared with typical three methods: EnKF, EnKF with DCT, and EnKF with normal score transform (NST). Both of conventional EnKF and EnKF with DCT show overshooting and fail to present channel details. Furthermore, their permeability distributions have a tendency to follow a Gaussian, not a typical bimodal distribution of sand and shale. Even if EnKF with NST maintains a bimodal distribution after updates, it cannot figure out overall channel trend. The proposed method not only prevents overshooting but also preserves a bimodal distribution of permeability. It can clearly characterize true channel trend even though initial reservoir models are poorly made. In addition, it gives better estimation of future oil and water productions than the other 3 methods by reducing uncertainties and matching true performances. more...

The Besa River Formation mainly comprises argillaceous sediments, and the upper shale bed of the Formation has been considered as a prospective shale gas reservoir. The maturity and quantity of organic matter found in source rock are considered as factors for evaluating resource value. Original hydrogen index (HIo) and total organic carbon (TOCo) are considered as properties to estimate generated gas volume in shale gas reservoirs. Generally, TOCo and HIo are determined via geochemical analysis of organic matter and calculated from well-log data like density, sonic data, and resistivity. In this study, these properties were measured or calculated by using geological analysis data and bulk-density log, and then the prospective area from the geochemical perspective in Liard Basin is defined by realizing a 3-dimensional static geochemical model. To validate the static model, the gas-in-place (GIP) (496 Bcf/section) of the production well in this study area was compared with GIP (262 Bcf/section) in the static model. Expulsion efficiency was considered as 0.6. The result implies that this model has a method of informative assessment with regard to undeveloped shale gas resources. The static model provides spatial information for generated and retained gas volume in the Besa River Formation, Liard Basin. more...

The shale gas potential of a Late Devonian shale sequence in the Liard Basin, an important unconventional gas reservoir, was assessed using the retained gas volume based on gas generation potential and hydrocarbon expulsion efficiency. Evaluation of gas generation potential in the Liard Basin depends on understanding the characteristics of the original organic matter. However, due to high thermal maturity, it is difficult to estimate the characteristics of the original organic matter from conventional methods. The type of original organic matter was inferred from inorganic geochemical proxies that reflect productivity (Ex-SiO2), terrestrial sediment input (Al2O3, Zr), and oxygen level in the bottom water (MoEF and UEF). By considering the present day TOC (TOCpd) and the type of original organic matter, the original hydrogen index (HIo) and original total organic carbon (TOCo) values were calculated to range from 200 to 700 mgHC/gTOC and from 0.3 to 29.0 wt%, respectively. The measured TOCpd values were similar to the TOCpd calculated from the 1-D petroleum system model using the original organic matter characteristics inferred in this study, which indicates that the TOCo values are reliable. Based on the evolution of the TOCo during its thermal history, the total gas generation potential in the Late Devonian shale sequence (550 ft) of the Liard Basin is estimated to be 1690 bcf/section. Considering the total gas in place (496 bcf/section), based on the estimated ultimate recovery, approximately 70% of the hydrocarbon might have been expelled. The retained gas volume fluctuates vertically in the Late Devonian shale sequence. The retained gas volume is higher in the 3946–3993 m (136 bcf/section) and 3993–4047 m (281 bcf/section) intervals than other intervals (less than 60 bcf/section), indicating that these intervals are the most prospective for shale gas exploration and development in the studied well. more...

Reservoir characterization is a key step to define the facies connectivity in channelized reservoirs. Recently, a new paradigm combining production data with geostatistics has been proposed. Pseudo-hard and -soft data are prepared from production-based techniques, such as ensemble-based methods. However, these methods contain inverse algorithms to integrate dynamic data and have limitations in their uncertainty quantifications on new production wells. In this study, a novel approach for re-static modeling scheme is proposed by history-matched facies-probability map without inverse modeling. Initial static models are realized and selectively simulated for center models, which are chosen by a distance-based method to reduce the number of forward simulation. The average of the selected models, which have a low level of mismatch with the observed data, is used for regeneration of facies models as facies-probability map. Regenerated channelized models are assessed again following the same procedure to select the final models. When the proposed method is applied to a 2D synthetic case, the final models successfully describe the true channel connectivities and facies ratios. Furthermore, the models preserve the bimodal distribution and given well data. Future productions for both the pre-existing production wells and a newly drilled well are properly predicted by the final models. In terms of the simulation time, the proposed method significantly decreases to 30 times from 800 times of the forward simulations over the ensemble smoother case. more...

For decision making, it is necessary to predict reservoir behaviors using reliable models. We can forecast future performances with less uncertainty after reservoir characterization, which is an essential step for integrating available static and dynamic data in history matching. Ensemble Kalman filter (EnKF) is one of the powerful methods for reservoir characterization. It uses recursive updates and provides uncertainty assessment. EnKF has been rarely applied to characterization of gas reservoirs in spite of its active research for oil reservoirs. Gas reservoirs show typically high recovery and are less sensitive to permeability uncertainty. However, the recovery of gas reservoirs is severely affected by an aquifer, which has considerable uncertainty. Therefore, aquifer characterization is crucial for production management and uncertainty assessment of gas reservoirs. This paper presents a method to characterize permeability distribution and aquifer sizes of gas reservoirs using static data and production data available. Covariance localization is applied for taking account of proper relationship between well production data and the properties of grid cells. The proposed method manages not only permeability overshooting but also successful assimilation of permeability distribution. Besides, the aquifer factors come closer to the reference values as compared with a standard EnKF. Therefore, it obviously improves future predictions of gas and water productions. more...

Reservoir characterization is necessary for making reliable models to have future reservoir performances. Since an aquifer typically has positive influences on oil production, its characterization has rarely been regarded as a critical issue. However, in channel oil reservoirs, an aquifer amplifies uncertainty of permeability estimations and has its own uncertainty due to limited information without any direct measurement. Although there have been some researches on channel oil reservoirs using discrete cosine transformation, we cannot characterize reliably an aquifer using discrete cosine transformation alone. Thus, we need additional schemes to manage increased uncertainty by an aquifer and to estimate the aquifer itself. In this study, ensemble Kalman filter with the combination of preservation of facies ratio and discrete cosine transformation is proposed for channel reservoirs with an aquifer. By the proposed method, we confirm that discrete cosine transformation and preservation of facies ratio contribute to preservation of overall channel properties and fine-tuning of the channel in the ensemble Kalman filter algorithm, respectively. Consequently, the proposed method gives us stable characterization performances on oil and water productions, permeability distribution, and aquifer strengths for a reasonable decision. more...

Ensemble-based methods have been researched for reservoir characterization in petroleum engineering. Using observed data, ensemble members are assimilated to production data and then we can get reasonable uncertainty ranges for future performances from multiple models. However, these methods require hundreds of ensemble members for reliable future predictions. If a reservoir becomes heterogeneous, more ensemble members are needed for stable results. This paper proposes an improved sampling scheme for efficient simulation of Ensemble Smoother (ES). For principal components analysis using singular value decomposition (SVD), we select singular values preserving the original spectrum of the values. To verify the sampling scheme, we apply 2D fields. The qualities of ES results are compared for 3 cases with 400 ensembles, randomly chosen 100 ensembles, and 100 ensembles selected by the proposed method. The results are also checked with conventional sampling scheme of picking the largest singular values. By using randomly chosen 100 ensembles, it shows overshooting problem and provides poor future performances. For the conventional sampling scheme of adopting the largest singular values, it has a potential of biased results as the reference field is complex and heterogeneous. However, our proposed method using 100 ensembles represents as large spectrum as using all 400 ensembles. It also reduces overshooting problem and improves the quality of future reservoir performances. Through ES with the improved sampling scheme, it ensures efficient and reliable reservoir characterization for history matching. more...

This study develops ensemble smoother–neural network (ES-NN) that combines an ensemble smoother (ES) with a convolutional autoencoder (CAE) to yield comparable performance at a lower computational cost to that of an ensemble smoother–multiple data assimilation (ES-MDA). The ES-NN updates reservoir facies models using CAE trained by importing initial and updated ensembles of ES as input and output of the CAE, respectively, which aims to learn the principle of assimilation of the ES. The trained CAE is recurrently applied in reservoir model calibration without additional forward simulation. The ES-NN yields satisfactory history matching results in terms of production profiles and facies distributions compared to ES and ES-MDA in two case studies. This comparison highlights the efficacy of ES-NN as a prospective data assimilation tool for history matching. more...

The design of prior models has continued to receive research attention because of their importance for ensemble-based methods. There are two approaches to ensemble design: selection and regeneration. Both strategies try to utilize dynamic data in a qualified prior model. The regeneration approach has a higher degree of freedom than the selection approach because the latter is selected among given initial models. However, previous regeneration methods are still sensitive to prior models because these methods create new models based on the priors' statistics. In this study, a deep neural network (DNN) was implemented to build new prior models. If there is a data pair for a reservoir model and its production, the production data and model parameters become the input and output data, respectively, for training the DNN. The trained DNN can generate new prior models according to the observed production history. For the output layer of the DNN, the main information of the permeability field is extracted by a stacked autoencoder (SAE) to improve the DNN performance. New prior models from DNN with SAE become the qualified prior set for ensemble-based methods because they already reflect observed dynamic data. For validation, an ensemble smoother with multiple data assimilation (ES-MDA) was applied to an Egg model. The proposed method (i.e., prior models designed with DNN-SAE) gave reliable posterior permeability fields and future reservoir performances. Compared with the two control groups (i.e., prior models and prior models with DNN), the proposed method mitigated the overshooting problem and found channel connectivity in the reference field. In a comparison with reliable posterior models, the simulation results of the proposed method not only matched observed production data but also reliably predicted future production. This study is an example of the successful application of a machine learning algorithm to history matching. more...

Reservoir characterization is a process to make a model similar to a true reservoir by integrating available data. It is necessary for reliable estimation of future productions and making proper decisions. Ensemble Kalman filter is one of the most powerful reservoir characterization methods. Ensemble Kalman filter can update reservoir models in real time and assess uncertainty by multiple models. Characterization of a channelized reservoir is difficult because of irregular channel pattern and connectivity. In this paper, ensemble Kalman filter with preservation of facies ratio and discrete cosine transformation is proposed for solving overshooting problem and maintaining properties of channel. The proposed method gives us stable characterization performances on gas and water productions, channel pattern and connectivity, and aquifer strengths regardless of the existence of an aquifer and uncertainty of facies ratio. Although facies ratio has ± 10% uncertainty with the reference, updated models maintain channel properties properly. Discrete cosine transformation helps to preserve channel pattern and connectivity and, therefore, overall performances are enhanced. Consequently, the proposed method can provide reliable updated models and credible prediction of future reservoir performances for making a proper decision. more...

This paper presents a review of ensemble-based data assimilation for strongly nonlinear problems on the characterization of heterogeneous reservoirs with different production histories. It concentrates on ensemble Kalman filter (EnKF) and ensemble smoother (ES) as representative frameworks, discusses their pros and cons, and investigates recent progress to overcome their drawbacks. The typical weaknesses of ensemble-based methods are non-Gaussian parameters, improper prior ensembles and finite population size. Three categorized approaches, to mitigate these limitations, are reviewed with recent accomplishments; improvement of Kalman gains, add-on of transformation functions, and independent evaluation of observed data. The data assimilation in heterogeneous reservoirs, applying the improved ensemble methods, is discussed on predicting unknown dynamic data in reservoir characterization. more...

This paper develops a novel approach of deep neural network (DNN)-based inverse modeling with selecting more reliable supervised-learning datasets with distance-based maps allocated at individual well levels. To mitigate divergence and overshooting in multi-scaled data assimilation, the DNN-based inverse model introduces a stacked autoencoder (SAE) that reduces the dimension of the training data. The proposed workflow also implements k-medoids clustering by selecting geo-models that have dynamic performances close to the true responses of producers to obtain plausible supervised-learning datasets. History-matching accuracy and forecasting performance are investigated in comparison of typical ensemble Kalman filter (EnKF)-based data assimilation for a waterflooding problem of heterogeneous fluvial channel reservoirs. The proposed approach is capable of matching the oil production rates of all producers in the range of 1.1–11.3% mean absolute percentage error (MAPE) and can forecast the future performances within 15.5% errors, while the errors of the EnKF method are up to six times higher. The proposed workflow can estimate the water-breakthrough time and the water productions accurately by generating more reliable geo-models with geological realism. more...

Ensemble smoother (ES) assimilates all available dynamic data without iterations as global update. Therefore, ES is much faster than ensemble Kalman filter (EnKF), which uses recursive updates. Iterative concepts are introduced for ES to increase accuracy of history matching. However, they lose advantages of simulation time and cost over EnKF. We propose ES with selective use of observation data in assimilation to improve history matching results and to keep simulation time short. Three methods, EnKF with all data, ES with all data, and the proposed, are applied to 2D synthetic channelized reservoirs with a nine spot waterflooding. Ensemble-based methods interpret the reason of reduced oil production rate after water breakthrough as low permeability. In this research, we suggest selective measurement data to manage misinterpretable data for the ensemble-based methods. As a logical choice, oil production rate before water breakthrough and water cut after water breakthrough are used for assimilation. EnKF with all data cannot predict true performances of oil and water productions on each well. ES with all data shows severe overshooting and filter divergence problems, which are two typical problems in the ensemble-based methods. However, the proposed method overcomes the two problems and shows good history matching results. It provides reliable uncertainty quantification of reservoir performances for both each well production and field total productions. Simulation cost of the proposed method is about 2.2% of that of EnKF, which uses 45 times update. It has clear advantage over EnKF or iterative ES methods. more...

Ensemble Kalman filter (EnKF) has been researched for reservoir characterization in petroleum engineering. However, the repeated assimilation causes lots of simulation cost. Ensemble smoother (ES) assimilates all available data once. It has advantages over EnKF: efficiency and simplicity. The two ensemble methods are based on the same assumptions: Gaussian distribution and trust in the mean of all ensembles. Many researchers have pointed out that EnKF gives overshooting and filter divergence problems when the two key assumptions are not satisfied. This paper presents characterization of channel fields using ES with the concept of clustered covariance, especially improper ensemble design. The standard EnKF, ES, and the proposed method are applied to a 2D synthetic channel field with 200 ensembles. From distance-based clustering method, we separate initial ensembles into 10 groups based its on similarity. The proposed method uses 10 Kalman gains, since each cluster has own Kalman gain. They can represent ensembles properly by using similar ensembles instead of 200 different ensembles. For the channel fields, the standard EnKF and ES show overshooting and filter divergence problems. Updated permeability fields have extreme values and lose the continuity of channel stream. However, the proposed method manages those two problems and provides reasonable results. We can get future prediction with reliable uncertainty. The proposed method only requires about 5% of simulation time compared to EnKF, since it is based on ES. It can be applied to the characterization of channel fields, even though we have improper ensembles due to limited information. more...

Ensemble Kalman filter (EnKF) has the limitation of applications for multi-point geostatistics because it assumes Gaussian random field. It also uses all ensembles to get covariance matrix, even though they have different permeability field each other, resulting in filter divergence. The proposed method suggests the concept of clustered covariance by grouping initial ensembles using a distance-based method. Hausdorff distance is used for calculating similarity between permeability fields and they are separated by k-means clustering. When EnKF is applied to a 2D channel field, it shows overshooting problem and mismatches the true production data. The proposed method gives better history matching and future performance prediction without overshooting problems. Furthermore, it shows stable results for sensitivity analyses over the number of total ensembles. The more accurate covariance is calculated by clustering, the better results are obtained. more...