Summary Trusting a machine-learning model is a critical factor that will speed the spread of the fourth industrial revolution. Trust can be achieved by understanding how a model is making decisions. For white-box models, it is easy to “see” the model and examine its prediction. For black-box models, the explanation of the decision process is not straightforward. In this work, we compare the performance of several white- and black-box models on two production data sets in an anomaly detection task. The presence of anomalies in production data can significantly influence business decisions and misrepresent the results of the analysis, if not identified. Therefore, identifying anomalies is a crucial and necessary step to maintain safety and ensure that the wells perform at full capacity. To achieve this, we compare the performance of K-nearest neighbor (KNN), logistic regression (Logit), support vector machines (SVMs), decision tree (DT), random forest (RF), and rule fit classifier (RFC). F1 and complexity are the two main metrics used to compare the prediction performance and interpretability of these models. In one data set, RFC outperformed the remaining models in both F1 and complexity, where F1 = 0.92, and complexity = 0.5. In the second data set, RF outperformed the rest in prediction performance with F1 = 0.84, yet it had the lowest complexity metric (0.04). We further analyzed the best performing models by explaining their predictions using local interpretable model-agnostic explanations, which provide justification for decisions made for each instance. Additionally, we evaluated the global rules learned from white-box models. Local and global analysis enable decision makers to understand how and why models are making certain decisions, which in turn allows trusting the models.

Summary Drilling sequence optimization is a common challenge faced in the oil and gas industry, and yet it cannot be solved efficiently by existing optimization methods due to its unique features and constraints. For many fields, the drilling queue is currently designed manually based on engineering heuristics. In this paper, we combined the heuristic priority functions (HPFs) with traditional optimizers to boost the optimization efficiency at a lower computational cost to speed up the decision-making process. The HPFs are constructed to map the individual well properties such as well index and interwell distance to the well priority values. As the name indicates, wells with higher priority values will be drilled earlier in the queue. The HPFs are a comprehensive metric of interwell communication and displacement efficiency. For example, injectors with fast support to producers, or producers with a better chance to drain the unswept region, tend to have high scores. They contain components that weigh the different properties of a well. These components are then optimized during the optimization process to generate the beneficial drilling sequences. Embedded with reservoir engineering heuristics, the priority function (PF) helps the optimizer focus on exploring scenarios with promising outcomes. The proposed HPFs, combined with the genetic algorithm (GA), have been tested through drilling sequence optimization problems for the Brugge Field and Olympus Field. Optimizations that are directly performed on the drilling sequence are used as reference cases. Different continuous/categorical parameterization schemes and various forms of HPFs are also investigated. Our exploration reveals that the HPF including well type, constraints, well index, distance to existing wells, and adjacent oil in place (OIP) yields the best outcome. The proposed approach achieved a better optimization starting point (∼5 to 18% improvement due to more reasonable drilling sequence rather than random guess), a faster convergence rate (results stabilized at 12 vs. 30 iterations), and a lower computational cost [150 to 250 vs. 1,300 runs to achieve the same net present value (NPV)] over the reference methods. Similar performance improvement was also observed in another application to a North Sea–type reservoir. This demonstrated the general applicability of the proposed method. The use of HPFs improves the efficiency and reliability of drilling sequence optimization compared with the traditional methods that directly optimize the sequence. They can be easily embedded in either commercial or research simulators as an independent module. In addition, they are also an automatic process that fits well with iterative optimization algorithms.

Summary With advancements in technology and computational capacity, the method of digital rock physics (DRP) for characterizing the storage and flow properties of a reservoir is gradually taking up the space that was once dominated by conventional methods such as routine core analysis (RCA) and special core analysis (SCAL). Unlike RCA and SCAL, the DRP method provides a nondestructive approach to deal with the core samples, which in a way is also more repeatable, economic, and is a clear improvement over the existing conventional methods in terms of its flexibility to experience the multiphysics of the rock and fluids. However, DRP still has some lacunae because the available algorithms have limitations in handling various challenges of complex lithology, such as grain/pore-boundary transition, soft/hard-matter transition, and imprints of intensity gradients of a 3D structure on 2D slices. Therefore, in this paper, we proposed a new approach to handle multiple issues by optimizing the segmentation algorithms and putting them together to standardize workflows (WFs) for reliable determination of the pore volume (PV), which could be verified with the field observation of porosity obtained using industry-standard laboratory methods and well logs. More emphasis was placed on the adaptability of the WF to deal with varying heterogeneity in the rocks. In this work, we proposed five WFs and compared them with the standard algorithms (including edge detections, watershed, and global thresholding) in terms of accuracy and computation time for a set of four homogeneous and four heterogeneous samples. We found that WF3 was the one that consistently performed better than all other WFs and some of the popular algorithms when compared one to one. We used a data-conditioning filter, contrast-limited adaptive histogram equalization (CLAHE)—a practice used in medical imagery—for local contrast enhancement in the heterogeneous carbonates to increase the signal/noise ratio of the rock-sample images. It successfully handled the contrast variability caused by the pockets of low illumination in the heterogeneous samples. Its limitation has also been detailed in the paper.

Summary Short-term production optimization is an essential activity in the oil/gasfield-development process because it allows for the maximization of field production by finding the optimal operational point. In the fields that use gas lift as an artificial-lift method, the gas-lift optimization is a short-term problem. This paper presents a stochastic approach to include uncertainties from production parameters in gas-lift optimization, called the uncertain-gas-lift-optimization problem (UGLOP). Uncertainties from production variables are originated from the measurement process and the intrinsic stochastic phenomena of the production activity. The production variables usually obtained from production tests play an important role in the optimization process because they are used to update reservoir and well models. To include the uncertainties, the strategy involves representing the well-test data using nonlinear regression [support-vector regression (SVR)] and using the Latin-hypercube-sampling (LHS) method. The optimization gives a stochastic solution for the operational point. In the solved problem, this operational point is composed of the individual wells’ gas-lift-injection rate, choke opening, and well/separator routing. The value of the stochastic solution is computed to evaluate the benefit of solving the stochastic problem over the deterministic. The developed methodology is applied to wells of a Brazilian field considering uncertainty in water-cut (WC) values. As a result, an up-to-4.5% gain in oil production is observed using this approach.

Summary For any oil and gas company, well-testing and performance-monitoring programs are expensive because of the cost of equipment and personnel. In addition, it may not be possible to obtain all of the necessary data for a reservoir for a period of time because of production demand constraints or changes in surface process conditions. To overcome these challenges, there are many studies on the implementation and value of virtual flowmetering (VFM) for real-time well performance prediction without any need for a comprehensive well-testingprogram. This paper presents the VFM model using an adaptive neuro-fuzzy inference system (ANFIS) at Hai Thach-Moc Tinh (HT-MT) gas-condensate field, offshore Vietnam. The ANFIS prediction model can tune all its membership functions (MFs) and consequent parameters to formulate the given inputs to the desired output with minimum error. In addition, ANFIS is a successful technique used to process large amounts of complex time series data and multiple nonlinear inputs-outputs ( Salleh et al. 2017 ), thereby enhancing predictability. The authors have built ANFIS models combined with large data sets, data smoothing, and k -fold cross-validation methods based on the actual historical surface parameters such as choke valve opening, surface pressure, temperature, the inlet pressure of the gas processing system, etc. The prediction results indicate that the local regression “loess” data smoothing method reduces the processing time and gives both clustering algorithms the best results among the different data preprocessing techniques [highest value of R and lowest value of mean squared error (MSE), error mean, and error standard deviation]. The k -fold cross-validation technique demonstrates the capability to avoid the overfitting phenomenon and enhance prediction accuracy for the ANFIS subtractive clustering model. The fuzzy C-mean (FCM) model in the present study can predict the gas condensate production with the smallest root MSE (RMSE) of 0.0645 and 0.0733; the highest coefficient of determination ( R 2 ) of 0.9482 and 0.9337; and the highest variance account of 0.9482 and 0.9334 for training and testing data, respectively. Applied at the HT-MT field, the model allows the rate estimation of the gas and condensate production and facilitates the virtual flowmeter workflow using the ANFIS model.

Summary Optimally designed drilling campaigns are essential for improving oil recovery and value creation. They are required at different stages of the hydrocarbon-field life cycle, including exploration, appraisal, development, and infill. A significant fraction of the revenue risk comes from geological uncertainty, and for this reason, subsurface teams are frequently responsible for optimizing campaign parameters such as the number of wells, the corresponding locations, and the drilling sequence. Companies use the information and learning from drilled wells to adapt the remainder of the campaign, but classical optimization methods do not account for such learning and flexibility over time. Accounting for sequential geological information acquisition and decision making in the optimization of drilling campaigns adds value to the project. We propose a method to optimize drilling campaigns under geological uncertainty by using a sequential-decision model to obtain the optimal drilling policy and applying analytics over the policy to obtain the optimal number of wells and corresponding locations. The novel contribution of policy analytics provides better access to information within the complex data structure of the optimal policy, providing decision support for different decision criteria. The method is demonstrated in two different cases. The first case considers a set of eight candidate wells on predefined locations, mimicking the situation where the method is used after a prior subsurface optimization. The second case considers a set of 12 candidate wells regularly scattered in the same area and uses the method as the first optimization approach to filter out less-attractive regions. Exploiting the geological information on a well-by-well basis improved the expected campaign value by 65% in the first case and by 183% in the second case. The value of spatial geological information and value of flexibility from having more drilling candidates are two byproducts of the method application.

Summary A deep learning framework, called the theory-guided convolutional neural network (TgCNN), is developed for efficient uncertainty quantification and data assimilation of reservoir flow with uncertain model parameters. The performance of the proposed framework in terms of accuracy and computational efficiency is assessed by comparing it to classical approaches in reservoir simulation. The essence of the TgCNN is to take into consideration both the available data and underlying physical/engineering principles. The stochastic parameter fields and time matrix comprise the input of the convolutional neural network (CNN), whereas the output is the quantity of interest (e.g., pressure, saturation, etc.). The TgCNN is trained with available data while being simultaneously guided by theory (e.g., governing equations, other physical constraints, and engineering controls) of the underlying problem. The trained TgCNN serves as a surrogate that can predict the solutions of the reservoir flow problem with new stochastic parameter fields. Such approaches, including the Monte Carlo (MC) method and the iterative ensemble smoother (IES) method, can then be used to perform uncertainty quantification and data assimilation efficiently based on the TgCNN surrogate, respectively. The proposed paradigm is evaluated with dynamic reservoir flow problems. The results demonstrate that the TgCNN surrogate can be built with a relatively small number of training data and even in a label-free manner, which can approximate the relationship between model inputs and outputs with high accuracy. The TgCNN surrogate is then used for uncertainty quantification and data assimilation of reservoir flow problems, which achieves satisfactory accuracy and higher efficiency compared with state-of-the-art approaches. The novelty of the work lies in the ability to incorporate physical laws and domain knowledge into the deep learning process and achieve high accuracy with limited training data. The trained surrogate can significantly improve the efficiency of uncertainty quantification and data assimilation processes. NOTE: This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.

Summary X-ray imaging of porous media has revolutionized the interpretation of various microscale phenomena in subsurface systems. The volumetric images acquired from this technology, known as digital rocks (DR), make it a suitable candidate for machine learning and computer-vision applications. The current routine DR frameworks involving image processing and modeling are susceptible to user bias and expensive computation requirements, especially for large domains. In comparison, the inference with trained machine-learning models can be significantly cheaper and computationally faster. Here we apply two popular convolutional neural network (ConvNet) architectures [residual network (ResNet) and ResNext] to learn the geometry of the pore space in 3D porous media images in a supervised learning scheme for flow-based characterization. The virtual permeability of the images to train the models is computed through a numerical simulation solver. Multiple ResNet variants are then trained to predict the continuous permeability value (regression). Our findings demonstrate the suitability of such networks to characterize volume images without having to resort to further ad-hoc and complex model adjustments. We show that training with richer representation of pore space improves the overall performance. We also compare the performance of the models statistically based on multiple metrics to assess the accuracy of the regression. The model inference of permeability from an unseen sandstone sample is executed on a standard workstation in less than 120 ms/sample and shows a score of 0.87 using explained variance score (EVS) metric, a mean absolute error (MAE) of 0.040 darcies, and 18.9% relative error in predicting the value of permeability compared to values acquired through simulation. Similar metrics are obtained when training with carbonate rock images. The training wall time and hyperparameters setting of the model are discussed. The findings of this study demonstrate the significant potential of machine learning for accurate DR analysis and rock typing while leveraging automation and scalability.

Summary As the crucial step in closed-loop reservoir management, robust life-cycle production optimization is defined as maximizing/minimizing the expected value of a predefined objective (cost) function over geological uncertainties (i.e., uncertainties in the reservoir permeability, porosity, endpoint relative permeability, etc.). However, with robust optimization, there is no control over downside risk defined as the minimum net present value (NPV) among the individual NPVs of the different reservoir models. Yet, field operators generally wish to keep this minimum NPV reasonably large to try to ensure that the reservoir is commercially viable. In addition, the field operator may desire to maximize the NPV of production over a much shorter time period than the life of the reservoir under the limitation of surface facilities (e.g., field liquid and water production rates). Thus, it is important to consider multiobjective robust production optimization with nonlinear constraints and when geological uncertainties are incorporated. The three objectives considered in this paper are; to maximize the average life-cycle NPV, to maximize the average short-term NPV, and to maximize the minimum NPV of the set of realizations. Generally, these objectives are in conflict; for example, the well controls that give a global maximum for robust life-cycle production optimization do not usually correspond to the controls that maximize the short-term average NPV of production. Moreover, handling the nonlinear state constraints (e.g., field liquid production rates and field water production rates for the bottom-hole pressure controlled producers in the robust production optimization) is also a challenge because those nonlinear constraints should be satisfied at each control steps for each geological realization. To provide potential solutions to the multiobjective robust optimization problem with state constraints, we developed a modified lexicographic method with a minimizing-maximum scheme to attempt to obtain a set of Pareto optimal solutions and to satisfy all nonlinear constraints. We apply the sequential quadratic programming filter with modified stochastic gradients to solve a sequence of optimization problems, where each solution is designed to generate a single point on the Pareto front. In the modified lexicographic method, the objective is always considered to be the primary objective, and the other objectives are considered by specifying bounds on them to convert them to state constraints. The temporal damping and truncation schemes are applied to improve the quality of the stochastic gradient on nonlinear constraints, and the minimizing–maximum procedure is applied to enforce constraints on the normal state constraints. The main advantage that the modified lexicographic method has over the standard lexicographic method is that it allows for the generation of potential Pareto optimal points, which are uniformly spaced in the values of the second and/or third objective that one wishes to improve by multiobjective optimization.

Summary We are interested in the development of surrogate models for the prediction of field saturations using a fully convolutional encoder/decoder network based on the dense convolutional network (DenseNet; Huang et al. 2017 ), similar to the approaches used for image/image-regression tasks in deep learning. In the surrogate model, the encoder network automatically extracts the multiscale features from the raw input data, and the decoder network then uses these data to recover the input image resolution at the output of the model. The input of multiple influencing factors is considered to make our surrogate model more consistent with the physical laws, which has achieved good results in the prediction of output fields in our experiments. Various reservoir parameters including the static reservoir properties (i.e., permeability field) and dynamic reservoir properties (i.e., well placement) are used as input features, and the water-saturation distributions in different periods are taken as the output. Compared with traditional numerical reservoir simulation, which has a high computational cost and is time consuming, not only does it present the same precision, but it costs less time. At the same time, it can also be used for production optimization and history matching.

Summary Accurately predicting wax deposits in a crude pipeline through empirical formulas or numerical modeling is unreliable because of the incomplete mechanism and the time-dependent unsteady actual operating conditions. With the help of the data collected by the supervisory control and data acquisition system of pipelines, wax deposit prediction is made possible by developing the time-dependent data mining method. In this article, the data from a typical long-distance crude pipeline in China operating over a 4-year time period was investigated. The inlet temperature prediction was first conducted by developing the long short-term memory (LSTM)-recurrent neural networks (RNNs) model, during which the feature sequencing, overfitting problems, and optimal hyperparameters were fully considered. Because of the time sequence cell, the accuracy of the LSTM-RNN model, as well as the time consumption, is much better than the RNN model when dealing with a great deal of data over a long period of time. Taking the inlet temperature prediction results as input features, the prediction model of average wax deposit thickness was established based on the backpropagation (BP) neural network and optimized by the particle swarm optimization (PSO), chaos particle swarm optimization (CPSO), and adaptive chaos particle swarm optimization (ACPSO) algorithms. The conclusions and associated algorithm from this article help to determine the reasonable pigging circle of long-distance pipelines practically. It could also be applied to guide the wax deposit prediction in the wellbore or oil-gathering pipes.

Summary The petroleum industry has long relied on predrilling geomechanics models to generate static representations of the allowable mud weight limits. These models rely on simplifying assumptions such as linear elasticity, a uniform wellbore shape, and generalized failure criteria to predict failure and determine a safe mud weight. These assumptions lead to inaccurate results, and they fail to reflect the effect of different routing drilling events. Thus, this paper’s main objective is to improve the process for predicting the wellbore rock failure while drilling. This work overcomes the limitations by using a new and integrated modeling scheme. Wellbore failure prediction is improved through the use of an integrated modeling scheme that involves an elasto-plastic finite element method (FEM) model, machine learning (ML) algorithms, and real-time drilling data, such as image logs from a logging while drilling (LWD) tool that accurately describes the current shape of the wellbore. Available offset well data are modeled in the FEM code and are then used to train the ML algorithms. The produced integrated model of FEM and ML is used to predict failure limits for new wells. This improved failure prediction can be updated with the occurrence of different drilling events such as induced fractures and wellbore enlargements. The values are captured from real-time data and reflected in the integrated model to produce a dynamic representation of the drilling window. The integrated modeling scheme was first applied to laboratory experimental results to provide a proof of concept and validation. This application showed improvement in rock-failure prediction when compared with conventional failure criteria such as Mohr-Coulomb. Also, offset-well data from wireline logging and drilling records are used to train and build a field-based integrated model, which is then used to show that the model output for a separate test well reasonably matches the drilling events from the test well. Application of this integrated model highlights how the allowable mud-weight limits can vary because drilling progresses in a manner that cannot be captured by the conventional predrilling models. As illustrated by a field case, the improvement in failure prediction through this modeling scheme can help avoid nonproductive time events such as wellbore enlargements, hole cleaning issues, pack-offs, stuck-pipe, and lost circulation. This efficiency is to be achieved by a real-time implementation of the model where it responds to drilling events as they occur. Also, this model enables engineers to take advantage of available data that are not routinely used by drilling.

Summary Gas kicks occur frequently in deepwater drilling because of the extremely narrow mud-weight window [minimum 0.01 specific gravity (sg)]. The traditional kick-detection method mainly relies on the driller's analysis of monitored compound comprehensive mud-logging data. However, the traditional method has significant time lag, including missed and false detection, and often leads to severe gas influxes during deepwater drilling. A novel machine-learning (ML) model is presented here using pilot-scale rig data combined with surface-riser-downhole monitoring for gas-kick early detection and risk classification. A series of pilot-scale test-well experiments (a total of 108 tests) are performed to simulate deepwater gas kicks and produce a multisource data set through fusion of comprehensive mud-logging data from surface monitoring, acoustic data from riser-monitoring technologies, and measurement-while-drilling data [e.g., bottomhole pressure (BHP)] from downhole monitoring technologies. During these experiments, the deepwater blowout preventer (BOP) is simulated using a variable cross section of crossover (X/O; equipped with booster-flow pipes); the Coriolis flowmeter is installed in the mud-return pipe to accurately measure flow out; the acoustic wave sensors are installed outside of the riser section (X/O) to monitor gas migration; and the downhole memory pressure gauges are installed to monitor BHP. Next, data preparation and data analysis are performed including raw-data exploration, data cleaning, signal/noise-ratio (SNR) analysis, feature scaling, outlier detection, and feature engineering. Further, a novel and improved data-labeling criterion for gas-kick alarms is proposed, with six levels (displayed using different colors) instead of two-state alarms (“kick” or “no kick”). The proposed gas-kick-alarm classification is in accordance with the actual field practices. Subsequently, four ML algorithms—decision tree (DT), k -nearest neighbors (KNN), support vector machine (SVM), and long short-term memory (LSTM)—are developed through the complete workflow, beginning with the data allocation and followed by building, evaluation, and optimization of each ML model. Because the LSTM recurrent neural network (RNN) algorithm showed the best performance, it is selected and deployed to early detect gas kicks and classify the corresponding kick alarms. The recall for gas-kick levels corresponding to Risk 0, Risk 1, Risk 2, Risk 3, Risk 4, and Risk 5 are 0.92, 0.93, 0.91, 0.91, 0.92 and 0.92, respectively. Because recall for each gas-kick-alarm level is greater than 0.9, it ensures rare false negatives (FNs) during kick detection. The accuracy, precision, recall, and f 1 score of the deployed LSTM model in the testing data set is 91.6%, 0.93, 0.92 and 0.92, respectively. Further, the detection time delay is approximately 2 to 7 seconds only, which provides an improved time margin to take appropriate safety measures, promptly deal with a gas kick through a well-control program, and prevent a potential blowout during deepwater drilling.

Summary We studied the applicability of a gradient-boosting machine-learning (ML) algorithm for forecasting of oil and total liquid production after hydraulic fracturing (HF). A thorough raw data study with data preprocessing algorithms was provided. The data set included 10 oil fields with more than 2,000 HF events. Each event has been characterized by well coordinates, geology, transport and storage properties, depths, and oil/liquid rates before fracturing for target and neighboring wells. Each ML model has been trained to predict monthly production rates right after fracturing and when the flows are stabilized. The gradient-boosting method justified its choice with R 2 being approximately 0.7 to 0.8 on the test set for oil/total liquid production after HF. The developed ML prediction model does not require preliminary numerical simulations of a future HF design. The applied algorithm could be used as a new approach for HF candidate selection based on the real-time state of the field.

Summary The steam-assisted gravity drainage (SAGD) recovery process is strongly impacted by the spatial distributions of heterogeneous shale barriers. Though detailed compositional flow simulators are available for SAGD recovery performance evaluation, the simulation process is usually quite computationally demanding, rendering their use over a large number of reservoir models for assessing the impacts of heterogeneity (uncertainties) to be impractical. In recent years, data-driven proxies have been widely proposed to reduce the computational effort; nevertheless, the proxy must be trained using a large data set consisting of many flow simulation cases that are ideally spanning the model parameter spaces. The question remains: is there a more efficient way to screen a large number of heterogeneous SAGD models? Such techniques could help to construct a training data set with less redundancy; they can also be used to quickly identify a subset of heterogeneous models for detailed flow simulation. In this work, we formulated two particular distance measures, flow-based and static-based, to quantify the similarity among a set of 3D heterogeneous SAGD models. First, to formulate the flow-based distance measure, a physics-based particle-tracking model is used: Darcy’s law and energy balance are integrated to mimic the steam chamber expansion process; steam particles that are located at the edge of the chamber would release their energy to the surrounding cold bitumen, while detailed fluid displacements are not explicitly simulated. The steam chamber evolution is modeled, and a flow-based distance between two given reservoir models is defined as the difference in their chamber sizes over time. Second, to formulate the static-based distance, the Hausdorff distance (Hausdorff 1914) is used: it is often used in image processing to compare two images according to their corresponding spatial arrangement and shapes of various objects. A suite of 3D models is constructed using representative petrophysical properties and operating constraints extracted from several pads in Suncor Energy’s Firebag project. The computed distance measures are used to partition the models into different groups. To establish a baseline for comparison, flow simulations are performed on these models to predict the actual chamber evolution and production profiles. The grouping results according to the proposed flow- and static-based distance measures match reasonably well to those obtained from detailed flow simulations. Significant improvement in computational efficiency is achieved with the proposed techniques. They can be used to efficiently screen a large number of reservoir models and facilitate the clustering of these models into groups with distinct shale heterogeneity characteristics. It presents a significant potential to be integrated with other data-driven approaches for reducing the computational load typically associated with detailed flow simulations involving multiple heterogeneous reservoir realizations.

Summary Minimum miscibility pressure (MMP) is one of the key design parameters for gas injection projects. It is a physical parameter that is a measure of local displacement efficiency while subject to some constraints due to its definition. Also, the MMP value is used to tune compositional models along with proper fluid description constrained with other available basic phase behavior data, such as bubble point pressure and volumetric properties. In general, carbon dioxide (CO 2 ) and hydrocarbon gases are the most common gases used for (or screened for) gas injection processes, and because of recent focus, they are used to screen for the coupling of CO 2 -sequestration and CO 2 -enhanced oil recovery (EOR) projects. Because the CO 2 /oil phase behavior is quite different than the hydrocarbon gas/oil phase behavior, researchers developed specialized correlations for CO 2 or CO 2 -rich streams. Therefore, there is a need for a tool with expanded range capabilities for the estimation of MMP for CO 2 gas streams. The only known and widely accepted measurement technique for MMP that is coherent with its formal definition is the use of a slimtube apparatus. However, the use of slimtube restricts the amount of data available, even though there are other alternative techniques presented over the last three decades, which all have various limitations (Dindoruk et al. 2021). Due to some of the complexities highlighted in Dindoruk et al. (2021) and time and resource requirements, there have been a number of correlations developed in the literature using mostly classical regression techniques with relatively sparse data using various combinations of limited input data ( Cronquist 1978 ; Lee 1979 ; Yellig and Metcalfe 1980 ; Alston et al. 1985 ; Glaso 1985 ; Jaubert et al. 1998 ; Emera and Sarma 2005 ; Yuan et al. 2005 ; Ahmadi et al. 2010 ; Ahmadi and Johns 2011 ). In this paper, we present two separate approaches for the calculation of the MMP of an oil for CO 2 injection: analytical correlation in which the correlation coefficients were tuned using linear support vector machines (SVMs) ( Press et al. 2007 ; MathWorks 2020 ; RDocumentation 2020 b; Cortes and Vapnik 1995) and using a hybrid method (i.e., superlearner model), which consists of the combination of random forest (RF) regression ( Breiman 2001 ) and the proposed analytical correlation. Both models take the compositional analysis of oils up to heptane plus fraction, molecular weight of oil, and the reservoir temperature as input parameters. Based on statistical and data analysis techniques in combination with the help of corresponding crossplots, we showed that the performance of the final proposed method (hybrid method) is superior to all the leading correlations ( Cronquist 1978 ; Lee 1979 ; Yellig and Metcalfe 1980 ; Alston et al. 1985 ; Glaso 1985 ; Emera and Sarma 2005 ; Yuan et al. 2005 ) and supervised machine-learning ( Metcalfe 1982 ) methods considered in the literature ( Altman 1992 ; Chambers and Hastie 1992 ; Chapelle and Vapnik 2000 ; Breiman 2001 ; Press et al. 2007 ; MathWorks 2020 ). The proposed model works for the widest spectrum of MMPs from 1,000 to 4,900 psia, which covers the entire range of oils within the scope of CO 2 EOR based on the widely used screening criteria ( Taber et al. 1997a , 1997b). NOTE: A correction notice has been issued for this paper and is available under the Supplementary Data section.

Summary Although researchers have applied many methods to history matching, such as Monte Carlo methods, ensemble-based methods, and optimization algorithms, history matching fractured reservoirs is still challenging. The key challenges are effectively representing the fracture network and coping with large amounts of reservoir-model parameters. With increasing numbers of fractures, the dimension becomes larger, resulting in heavy computational work in the inversion of fractures. This paper proposes a new characterization method for the multiscale fracture network, and a powerful dimensionality-reduction method by means of an autoencoder for model parameters. The characterization method of the fracture network is dependent on the length, orientation, and position of fractures, including large-scale and small-scale fractures. To significantly reduce the dimension of parameters, the deep sparse autoencoder (DSAE) transforms the input to the low-dimensional latent variables through encoding and decoding. Integrated with the greedy layer-wise algorithm, we set up a DSAE and then take the latent variables as optimization variables. The performance of the DSAE with fewer activating nodes is excellent because it reduces the redundant information of the input and avoids overfitting. Then, we adopt the ensemble smoother (ES) with multiple data assimilation (ES-MDA) to solve this minimization problem. We test our proposed method in three synthetic reservoir history-matching problems, compared with the no-dimensionality-reduction method and the principal-component analysis (PCA). The numerical results show that the characterization method integrated with the DSAE could simplify the fracture network, preserve the distribution of fractures during the update, and improve the quality of history matching naturally fractured reservoirs.

Summary Stimulated reservoir volume (SRV) is a prime factor controlling well performance in unconventional shale plays. In general, SRV describes the extent of connected conductive fracture networks within the formation. Being a pre-existing weak interface, natural fractures (NFs) are the preferred failure paths. Therefore, the interaction of hydraulic fractures (HFs) and NFs is fundamental to fracture growth in a formation. Field observations of induced fracture systems have suggested complex failure zones occurring in the vicinity of HFs, which makes characterizing the SRV a significant challenge. Thus, this work uses a broad range of subsurface conditions to investigate the near-tip processes and to rank their influences on HF-NF interaction. In this study, a 2D analytical workflow is presented that delineates the potential slip zone (PSZ) induced by a HF. The explicit description of failure modes in the near-tip region explains possible mechanisms of fracture complexity observed in the field. The parametric analysis shows varying influences of HF-NF relative angle, stress state, net pressure, frictional coefficient, and HF length to the NF slip. This work analytically proves that an NF at a 30 ± 5° relative angle to an HF has the highest potential to be reactivated, which dominantly depends on the frictional coefficient of the interface. The spatial extension of the PSZ normal to the HF converges as the fracture propagates away and exhibits asymmetry depending on the relative angle. Then a machine-learning (ML) model [random forest (RF) regression] is built to replicate the physics-based model and statistically investigate parametric influences on NF slips. The ML model finds statistical significance of the predicting features in the order of relative angle between HF and NF, fracture gradient, frictional coefficient of the NF, overpressure index, stress differential, formation depth, and net pressure. The ML result is compared with sensitivity analysis and provides a new perspective on HF-NF interaction using statistical measures. The importance of formation depth on HF-NF interaction is stressed in both the physics-based and data-driven models, thus providing insight for field development of stacked resource plays. The proposed concept of PSZ can be used to measure and compare the intensity of HF-NF interactions at various geological settings.

Summary The modern focused ion beam-scanning electron microscopy (FIB-SEM) allows imaging of nanoporous tight reservoir-rock samples in 3D at a resolution up to 3 nm/voxel. Correct porosity determination from FIB-SEM images requires fast and robust segmentation. However, the quality and efficient segmentation of FIB-SEM images is still a complicated and challenging task. Typically, a trained operator spends days or weeks in subjective and semimanual labeling of a single FIB-SEM data set. The presence of FIB-SEM artifacts, such as porebacks, requires developing a new methodology for efficient image segmentation. We have developed a method for simplification of multimodal segmentation of FIB-SEM data sets using machine-learning (ML)-based techniques. We study a collection of rock samples formed according to the petrophysical interpretation of well logs from a complex tight gas reservoir rock of the Berezov Formation (West Siberia, Russia). The core samples were passed through a multiscale imaging workflow for pore-space-structure upscaling from nanometer to log scale. FIB-SEM imaging resolved the finest scale using a dual-beam analytical system. Image segmentation used an architecture derived from a convolutional neural network (CNN) in the DeepUNet (Ronneberger et al. 2015) configuration. We implemented the solution in the Pytorch® (Facebook, Inc., Menlo Park, California, USA) framework in a Linux environment. Computation exploited a high-performance computing system. The acquired data included three 3D FIB-SEM data sets with a physical size of approximately 20 × 15 × 25 µm with a voxel size of 5 nm. A professional geologist manually segmented (labeled) a fraction of slices. We split the labeled slices into training, validation, and test data. We then augmented the training data to increase its size. The developed CNN delivered promising results. The model performed automatic segmentation with the following average quality indicators according to test data: accuracy of 86.66%, precision of 54.93%, recall of 83.76%, and F 1 score of 55.10%. We achieved a significant boost in segmentation speed of 14.5 megapixel (MP)/min. Compared with 0.18 to 1.45 MP/min for manual labeling, this yielded an efficiency increase of at least 10 times. The presented research work improves the quality of quantitative petrophysical characterization of complex reservoir rocks using digital rock imaging. The development allows the multiphase segmentation of 3D FIB-SEM data complicated with artifacts. It delivers correct and precise pore-space segmentation, resulting in little turn-around-time saving and increased porosity-data quality. Although image segmentation using CNNs is mainstream in the modern ML world, it is an emerging novel approach for reservoir-characterization tasks.

Summary Decline curve analysis (DCA) has been widely applied in production forecasting of wells in unconventional hydrocarbon reservoirs. However, traditional curve-fit-based methods fall short of forecast accuracy due to three weaknesses: first, they cannot capture the reservoir signals not modeled by the underlying DCA model formulas; second, when predicting the production of a target well, the production history of other wells in the geologic formation (which is valuable information) is not considered; third, the wells’ geographic, geologic, wellbore, well spacing, and completion properties, which are highly relevant to production capability, are not used. More recent approaches have begun replacing traditional DCA with machine-learning methods [e.g., random forest (RF), support vector regression (SVR), etc.] for production forecast. Nevertheless, these methods are still suboptimal in detecting similar production trends in different wells, leading to large forecast error. A new and simple method called dynamic production rescaling (DPR) is developed to improve the accuracy of machine-learning DCA (ML-DCA). By combining DPR with common ML-DCA methods, we observe that the error mean, deviation, and skewness can be significantly reduced by 15 to 35% compared with ML-DCA without DPR. The error reduction is 30 to 60% compared with automatic curve fit of the traditional modified Arps DCA model. DPR has been tested successfully on monthly production data of over 20,000 unconventional horizontal wells in the Permian and Appalachian basins for both long- and short-term forecasts. The significant error reduction is consistent across different basins and formations. DPR is computationally efficient, so a large number of wells can be analyzed automatically and quickly. Moreover, the effectiveness and efficiency of DPR is independent of the underlying machine-learning algorithm, further demonstrating its robustness.