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SummaryDecline–curve analysis (DCA) is an easy and fast empirical regression method for predicting future well production. However, applying DCA to shale–gas wells is limited by long transient flow, a unique completion design, and high–density drilling. Recently, a long short-term-memory (LSTM) algorithm has been widely applied to the prediction of time–series data. Because shale–gas–production data are time–series data, the LSTM algorithm can be applied to predict future shale–gas production. After information for 332 shale–gas wells in Alberta, Canada, is obtained from a commercial database, the data are preprocessed in seven steps, including cutoffs for well list, data cleaning, feature extraction, train and test sets split, normalization, and sorting for input into the LSTM model. The LSTM model is trained in 405 seconds by two features of production data and a shut–in (SI) period from 300 wells. The two–feature case shows a better prediction accuracy than both the one–feature case (i.e., production data only) and the hyperbolic DCA, where the three methods are tested on unseen data from 15 wells. The two–feature case can predict future production rates according to the SI period and provide a stable result for available time–series data.

Artificial intelligence is applied in various fields of human life and is being actively studied and applied in the oil fields. Especially, the digital oil field, which has recently been spotlighted, is required to simulate the reservoir using artificial intelligence. However, there is almost little research to date. Therefore, in this study, we applied TDRM using artificial intelligence technology to Zama field located on the land of Canada. The required static and dynamic data were obtained from Accumap, a Canadian well information S/W. As a result, the reservoir model was constructed successfully and the well location optimization could be performed in a short time using TDRM.

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.

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.

Natural fractures have a significant effect on fluid flow and heat transfer in naturally fractured geothermal reservoirs. However, most previous studies have assumed that reservoir systems are either a single continuum or dual continuum model, while some studies have just considered a pipeline model. In this study, we developed a discrete fracture network (DFN) geothermal reservoir simulator. The DFN model developed was validated for synthetic fracture systems using a Tetrad; a comparison of the results revealed good agreement between two models. However, developed model is only a fracture model and cannot simulate fluid flow and heat transfer in the matrix. A matrix flow model will be added in the future.

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.

Well operation optimization is vital in maximizing the net present value (NPV) of the field development plan (FDP). As well operation is a time-series scenario, this problem contains numerous parameters to be optimized and countless solutions. This results in huge optimization time to evaluate each scenario using the reservoir simulator, especially with robust optimization. In this study, particle swarm optimization is coupled with the deep learning-based proxy model to solve such problems in the 2D synthetic and 3D Egg cases. First, the long short-term memory (LSTM) proxy model is developed to estimate the reservoir response to the well operation scenario instead of reservoir simulation. When the drilling and bottomhole pressure (BHP) schedules are entered into the input layer for the proxy model, the average cumulative field oil and water productions and field water injection from the multiple reservoir models are obtained in the output layer. In case of well pattern, the optimized scenario of the location and type of wells in Kim et al. (2021a) was fixed in this study. After the LSTM proxy model fits with the training data pair of time-series BHP schedule and corresponding the responses obtained by ECLIPSE (ECL), it can predict the time-series field response for given BHP scenario. When the calculated NPV from the LSTM is compared with the true NPV from ECL, the coefficient of determination for the validation and test datasets is higher than 0.97, solving the overfitting problem of the simple neural network (NN) proxy model. It is critical to select a proper deep learning algorithm according to the characteristics of the input and output data. While the convolutional NN (CNN) is proper to make a proxy model for well pattern scenario, which consists of the static images with the same dimension in Kim et al. (2021a), the LSTM is suitable for well operation scenarios, which changes over time. Second, the drilling and BHP schedules are optimized under the constraint of the maximum available rig. Also, to reduce these high-dimensional optimization variables, we define the BHP schedule as a cosine function instead of the stepwise approach. It reduces the number of training data required for the proxy model. Third, optimization strategies are reviewed for both the well pattern and well operation optimizations. The sequential proxy, the CNN-LSTM, shows similar NPVs with the results of the sequential ECL-ECL. However, CNN-LSTM requires only 12% of optimization time compared to ECL-ECL for the 3D case. Therefore, CNN-LSTM is proposed as the reasonable solution for reliable decision-making for the FDP in a short time.

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.

Mineral quantification is essential to evaluate gas hydrate (GH) resources because the mineral composition is closely related to the origin of sediment, the reservoir properties, and even the existence of GH. However, it is difficult to analyze the mineral compositions of GH-rich unconsolidated layers because of complex compositional combinations. Thus far, mineral composition has relied on experts’ analysis. In this study, a machine learning model was developed that can efficiently probe the mineral composition from the X-ray diffraction (XRD) patterns of GH sediments in the Ulleung Basin, Korea, which has a complex composition including 12 minerals. It is the first time that machine learning algorithms have been applied to complex natural GH sediment with 12 minerals, including amorphous materials. To build a reliable data-driven analysis model, after data acquisition and preprocessing were conducted, various machine learning algorithms were employed, including convolutional neural network (CNN), recurrent neural network (RNN), multi-layer perceptron (MLP), and random forest (RF). For data acquisition, 488 sediment samples were analyzed by XRD experiment, and the intensity profiles were manually analyzed by an expert to obtain their mineral compositions. In particular, the intensity profile according to the XRD angle of incidence serves as the input data, and the corresponding 12 mineral composition provides label data for supervised learning. The RF approach yields the best prediction result with an average mean absolute error (MAE) of 2.56%, and the other algorithms also exhibits reasonable performance with average MAEs of less than 3%. If XRD is newly performed for GH sediment, the intensity profile can be automatically analyzed by the trained machine learning model in seconds. This approach will enable experts to analyze mineral compositions efficiently and reliably.

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.

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.

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.

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.

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.

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.

Accurate predictions of the intensity and variability of ground motions are essential in simulation-based seismic hazard assessment. Advanced simulation-based ground motion prediction methods have been proposed to complement the empirical approach, which suffers from the lack of observed ground motion data, especially in the near-source region for large events. It is important to quantify the variability of the earthquake rupture process for future events and to produce a number of rupture scenario models to capture the variability in simulation-based ground motion predictions. In this study, we improved the previously developed stochastic earthquake rupture modeling method by applying the nonparametric co-regionalization, which was proposed in geostatistics, to the correlation models estimated from dynamically derived earthquake rupture models. The nonparametric approach adopted in this study is computationally efficient and, therefore, enables us to simulate numerous rupture scenarios, including large events (M>7.0). It also gives us an opportunity to check the shape of true input correlation models in stochastic modeling after being deformed for permissibility. We expect that this type of modeling will improve our ability to simulate a wide range of rupture scenario models and thereby predict ground motions and perform seismic hazard assessment more accurately.

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.

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.

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.

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.

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.

Summary Shale resources are developed with high-density drilling and differ to predict future production rate with conventional methods such as decline curve analysis (DCA). We developed a prediction model for shale production using machine learning (ML) algorithm. Long short-term memory algorithm, which is suitable for training time-series data, is applied to more than 300 shale gas wells at Duvernay formation in Alberta. To increase performance of the prediction model, an additional feature, shut-in (SI) period, is introduced for input layer. SI information is easily extracted from production history and it is highly correlated with production rate. The trained model can give reliable and stable prediction of shale gas production rates. Especially, the two-feature model (production and SI period) shows better performance than the one-feature model (production only). Therefore, a domain knowledge for petroleum industry has an important role to build reliable ML model. The developed model can dramatically reduce analysis cost comparing with DCA, which requires expert's judgement for each shale well. Also, this concept can be extended to other conventional and unconventional production wells.

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.

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.