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In the current business environment, oil and gas operators in unconventional plays are continually pushed to reduce risk and increase profitability. Recent advances in horizontal drilling, hydraulic fracturing, and completion design in shale wells have helped reduce costs. However, accurate reserve estimation and production forecasting remain the greatest unknowns impacting the bottom line. The use of advanced subsurface models is gaining momentum to address this challenge. Typical techniques currently used to build and history match these models are based on simplified assumptions and ignore uncertainty in the subsurface characterization. This paper presents a multi-disciplinary ensemble-based history matching approach for reliable forecast production from the shale reservoirs. It incorporates uncertainty from different modeling domains, leading to the generation of improved predictive shale models.

The proposed approach leverages micro-seismic data to create a more realistic representation of the Stimulated Reservoir Volume (SRV). Micro-seismic event locations, magnitude, and fracture plane characteristics are used to construct a Discrete Fracture Network (DFN) required for petrophysical modeling. A forward model comprising DFN modeling, an application to generate relative permeability curves, and a reservoir simulator is set up using a common platform integrator. These applications are run in tandem to generate an ensemble of history matched shale models that capture the range of uncertainties in fracture attributes, relative permeability, and other important dynamic parameters. Production data is assimilated into the shale model using Bayesian statistics and state-of-the-art supervised machine learning techniques.

Our approach is demonstrated using data acquired from three hydraulically fracked wells drilled in the Eagle Ford shale oil window. The use of Bayesian statistics and machine learning techniques led to the identification of multiple shale models calibrated to the production data. Fracture attributes, saturation endpoints, relative permeability curvature, matrix porosity, and initial water saturation were found to significantly affect the history match. A comparison of prior and posterior ensembles showed a significant reduction in uncertainty in predicted production.

The proposed technique ensures that important, previously neglected subsurface uncertainties and their dependencies are captured and used as input to the simulation model. Improved SRV delineation using micro-seismic data and property modeling using DFN, combined with the ability to capture uncertainty through an integrated multi-disciplinary approach, deliver predictive shale models that enable future decisions to be made with a high degree of confidence.

Artificial Intelligence, Bayesian Inference, complex reservoir, emulator, flow in porous media, Fluid Dynamics, Forward Model, fracture, history matching, machine learning, match point, micro-seismic data, Modeling & Simulation, oil shale, permeability, posterior distribution, Posterior Ensemble, relative permeability curve, Reservoir Characterization, reservoir simulation, shale gas, shale oil, shale well, simulation model, society of petroleum engineers, uncertainty parameter, Upstream Oil & Gas, urtec 1023

Oilfield Places:

- North America > United States > Texas > West Gulf Coast Tertiary Basin > Eagle Ford Shale (0.99)
- North America > United States > Texas > Sabinas - Rio Grande Basin > Eagle Ford Shale (0.99)
- North America > United States > Texas > Maverick Basin > Eagle Ford Shale (0.99)

SPE Disciplines:

Technology:

- Information Technology > Modeling & Simulation (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (1.00)

Ferreira, Carla Janaina (Durham University and University of Campinas) | Vernon, Ian (Durham University) | Caiado, Camila (Durham University) | Formentin, Helena Nandi (Durham University and University of Campinas) | Avansi, Guilherme Daniel (University of Campinas) | Goldstein, Michael (Durham University) | Schiozer, Denis José (University of Campinas)

When performing classic uncertainty reduction according to dynamic data, a large number of reservoir simulations need to be evaluated at high computational cost. As an alternative, we construct Bayesian emulators that mimic the dominant behavior of the reservoir simulator, and which are several orders of magnitude faster to evaluate. We combine these emulators within an iterative procedure that involves substantial but appropriate dimensional reduction of the output space (which represents the reservoir physical behavior, such as production data), enabling a more effective and efficient uncertainty reduction on the input space (representing uncertain reservoir parameters) than traditional methods, and with a more comprehensive understanding of the associated uncertainties. This study uses the emulation-based Bayesian history-matching (BHM) uncertainty analysis for the uncertainty reduction of complex models, which is designed to address problems with a high number of both input and output parameters. We detail how to efficiently choose sets of outputs that are suitable for emulation and that are highly informative to reduce the input-parameter space and investigate different classes of outputs and objective functions. We use output emulators and implausibility analysis iteratively to perform uncertainty reduction in the input-parameter space, and we discuss the strengths and weaknesses of certain popular classes of objective functions in this context. We demonstrate our approach through an application to a benchmark synthetic model (built using public data from a Brazilian offshore field) in an early stage of development using 4 years of historical data and four producers. This study investigates traditional simulation outputs (e.g., production data) and also novel classes of outputs, such as misfit indices and summaries of outputs. We show that despite there being a large number (2,136) of possible outputs, only very few (16) were sufficient to represent the available information; these informative outputs were used using fast and efficient emulators at each iteration (or wave) of the history match to perform the uncertainty-reduction procedure successfully. Using this small set of outputs, we were able to substantially reduce the input space by removing 99.8% of the original volume. We found that a small set of physically meaningful individual production outputs were the most informative at early waves, which once emulated, resulted in the highest uncertainty reduction in the input-parameter space, while more complex but popular objective functions that combine several outputs were only modestly useful at later waves. The latter point is because objective functions such as misfit indices have complex surfaces that can lead to low-quality emulators and hence result in noninformative outputs. We present an iterative emulator-based Bayesian uncertainty-reduction process in which all possible input-parameter configurations that lead to statistically acceptable matches between the simulated and observed data are identified. This methodology presents four central characteristics: incorporation of a powerful dimension reduction on the output space, resulting in significantly increased efficiency; effective reduction of the input space; computational efficiency, and provision of a better understanding of the complex geometry of the input and output spaces.

Artificial Intelligence, Bayesian Inference, emulation, emulator, evaluation, Goldstein, history matching, informative output, input space, input-parameter space, machine learning, Modeling & Simulation, objective function, observational error, optimization problem, reservoir model, reservoir simulation, Scenario, space cutout, uncertainty analysis, uncertainty reduction, Upstream Oil & Gas, water rate, wave 1

Country:

- Europe (1.00)
- North America > United States (0.93)

Oilfield Places:

- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Not Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Ile Formation (0.99)
- (3 more...)

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Management (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)

Technology:

- Information Technology > Modeling & Simulation (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- (2 more...)

In this work, we evaluate different algorithms to account for model errors while estimating the model parameters, especially when the model discrepancy (used interchangeably with “model error”) is large. In addition, we introduce two new algorithms that are closely related to some of the published approaches under consideration. Considering all these algorithms, the first calibration approach (base case scenario) relies on Bayesian inversion using iterative ensemble smoothing with annealing schedules without any special treatment for the model error. In the second approach, the residual obtained after calibration is used to iteratively update the total error covariance combining the effects of both model errors and measurement errors. In the third approach, the principal component analysis (PCA)- based error model is used to represent the model discrepancy during history matching. This leads to a joint inverse problem in which both the model parameters and the parameters of a PCA-based error model are estimated. For the joint inversion within the Bayesian framework, prior distributions have to be defined for all the estimated parameters, and the prior distribution for the PCA-based error model parameters are generally hard to define. In this study, the prior statistics of the model discrepancy parameters are estimated using the outputs from pairs of high-fidelity and low-fidelity models generated from the prior realizations. The fourth approach is similar to the third approach; however, an additional covariance matrix of difference between a PCA-based error model and the corresponding actual realizations of prior error is added to the covariance matrix of the measurement error.

The first newly introduced algorithm (fifth approach) relies on building an orthonormal basis for the misfit component of the error model, which is obtained from a difference between the PCA-based error model and the corresponding actual realizations of the prior error. The misfit component of the error model is subtracted from the data residual (difference between observations and model outputs) to eliminate the incorrect relative contribution to the prediction from the physical model and the error model. In the second newly introduced algorithm (sixth approach), we use the PCA-based error model as a physically motivated bias correction term and an iterative update of the covariance matrix of the total error during history matching. All the algorithms are evaluated using three forecasting measures, and the results show that a good parameterization of the error model is needed to obtain a good estimate of physical model parameters and to provide better predictions. In this study, the last three approaches (i.e., fourth, fifth, sixth) outperform the other methods in terms of the quality of estimated model parameters and the prediction capability of the calibrated imperfect models.

algorithm, algorithm 1, algorithm 2, algorithm 3, algorithm 4, algorithm 5, Artificial Intelligence, Bayesian Inference, covariance matrix, ensemble, error model, history matching, machine learning, model discrepancy, model error, model parameter, oil production rate, pca-based error model, prediction, production rate, reservoir simulation, second-order error, Upstream Oil & Gas, water production rate

Country:

- North America > United States (0.46)
- Europe > United Kingdom > England (0.46)

Oilfield Places:

- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Not Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Ile Formation (0.99)
- (3 more...)

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)

Technology:

- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (0.48)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.48)

Generating an estimate of uncertainty in production forecasts has become nearly standard in the oil industry, but is often performed with procedures that yield at best a highly approximate uncertainty quantification. Formally, the uncertainty quantification of a production forecast can be achieved by generating a correct characterization of the posterior probability-density function (PDF) of reservoir-model parameters conditional to dynamic data and then sampling this PDF correctly. Although Markov-chain Monte Carlo (MCMC) provides a theoretically rigorous method for sampling any target PDF that is known up to a normalizing constant, in reservoir-engineering applications, researchers have found that it might require extraordinarily long chains containing millions to hundreds of millions of states to obtain a correct characterization of the target PDF. When the target PDF has a single mode or has multiple modes concentrated in a small region, it might be possible to implement a proposal distribution dependent on a random walk so that the resulting MCMC algorithm derived from the Metropolis-Hastings acceptance probability can yield a good characterization of the posterior PDF with a computationally feasible chain length. However, for a high-dimensional multimodal PDF with modes separated by large regions of low or zero probability, characterizing the PDF with MCMC using a random walk is not computationally feasible. Although methods such as population MCMC exist for characterizing a multimodal PDF, their computational cost generally makes the application of these algorithms far too costly for field application. In this paper, we design a new proposal distribution using a Gaussian mixture PDF for use in MCMC where the posterior PDF can be multimodal with the modes spread far apart. Simply put, the method generates modes using a gradient-based optimization method and constructs a Gaussian mixture model (GMM) to use as the basic proposal distribution. Tests on three simple problems are presented to establish the validity of the method. The performance of the new MCMC algorithm is compared with that of random-walk MCMC and is also compared with that of population MCMC for a target PDF that is multimodal.

adaptation, algorithm, algorithm 3, algorithm 4, Artificial Intelligence, Bayesian Inference, Gaussian, GMM, history matching, machine learning, Markov chain, MCMC algorithm, McMC method, model parameter, oil-production rate, posterior distribution, posterior PDF, prediction, proposal distribution, reservoir simulation, target PDF, two-level mcmc method, Upstream Oil & Gas, water-injection rate, water-production rate

Country:

- Europe (1.00)
- North America > Canada (0.92)
- North America > United States > Texas (0.67)

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation > Evaluation of uncertainties (1.00)

Technology:

- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (0.92)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.92)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Undirected Networks > Markov Models (0.64)

analytical model, Artificial Intelligence, asset and portfolio management, big data, bubble point pressure, capacitance resistance model, classification, completion design, Completion Installation and Operations, Completion Monitoring Systems/Intelligent Wells, complex reservoir, computer based training, data mining, data quality, decision-making process, deep learning, downhole intervention, downhole sensor, drilling operation, Drillstem Testing, drillstem/well testing, educational software, educational technology, Energy Economics, enhanced oil recovery, enhanced recovery, equation of state, experimental design, expert system, field development optimization and planning, flow in porous media, flow metering, flow simulation, Fluid Dynamics, fluid modeling, gas injection method, geologic modeling, geological modeling, history matching, hydraulic fracturing, inflow performance, information management, integrated asset modeling, intervención de pozos petroleros, knowledge management, log analysis, machine learning, Modeling & Simulation, natural language, neural network, optimization problem, physics-based model, pressure transient analysis, pressure transient testing, production control, production enhancement, production forecasting, production logging, production monitoring, PVT measurement, real time system, reduced-order modeling, representation, reserves evaluation, Reservoir Characterization, Reservoir Management Decision, reservoir simulation model, Reservoir Surveillance, risk management, SAGD, scaling method, shale gas, steam-assisted gravity drainage, strategic planning and management, structural geology, Support Vector Machine, thermal method, uncertainty quantification, unconventional resource economics, unconventional resource s technology conference, san antonio, Upstream Oil & Gas, waterflooding, Well Intervention, well logging, well performance

Country:

- North America > United States > Texas (1.00)
- North America > United States > California (1.00)
- Asia > Middle East (1.00)
- (6 more...)

Industry:

- Energy > Oil & Gas > Upstream (1.00)
- Education > Educational Technology > Educational Software > Computer Based Training (0.45)

Oilfield Places:

- North America > United States > West Virginia > Appalachian Basin > Marcellus Shale (0.99)
- North America > United States > Virginia > Appalachian Basin > Marcellus Shale (0.99)
- North America > United States > Texas > Permian Basin > Wolfcamp Shale (0.99)
- (21 more...)

SPE Disciplines:

Technology:

Reliability of subsurface assessment for different field development scenarios depends on how effective the uncertainty in production forecast is quantified. Currently there is a body of work in the literature on different methods to quantify the uncertainty in production forecast. The objective of this paper is to revisit and compare these probabilistic uncertainty quantification techniques through their applications to assisted history matching of a deep-water offshore waterflood field. The paper will address the benefits, limitations, and the best criteria for applicability of each technique.

Three probabilistic history matching techniques commonly practiced in the industry are discussed. These are Design-of-Experiment (DoE) with rejection sampling from proxy, Ensemble Smoother (ES) and Genetic Algorithm (GA). The model used for this study is an offshore waterflood field in Gulf-of-Mexico. Posterior distributions of global subsurface uncertainties (e.g. regional pore volume and oil-water contact) were estimated using each technique conditioned to the injection and production data.

The three probabilistic history matching techniques were applied to a deep-water field with 13 years of production history. The first 8 years of production data was used for the history matching and estimate of the posterior distribution of uncertainty in geologic parameters. While the convergence behavior and shape of the posterior distributions were different, consistent posterior means were obtained from Bayesian workflows such as DoE or ES. In contrast, the application of GA showed differences in posterior distribution of geological uncertainty parameters, especially those that had small sensitivity to the production data. We then conducted production forecast by including infill wells and evaluated the production performance using sample means of posterior geologic uncertainty parameters. The robustness of the solution was examined by performing history matching multiple times using different initial sample points (e.g. random seed). This confirmed that heuristic optimization techniques such as GA were unstable since parameter setup for the optimizer had a large impact on uncertainty characterization and production performance.

This study shows the guideline to obtain the stable solution from the history matching techniques used for different conditions such as number of simulation model realizations and uncertainty parameters, and number of datapoints (e.g. maturity of the reservoir development). These guidelines will greatly help the decision-making process in selection of best development options.

application, Artificial Intelligence, Bayesian Inference, booth function, dummy parameter, ensemble smoother, evolutionary algorithm, Exhibition, forecast, genetic algorithm, History, history matching, iteration, machine learning, optimization problem, posterior distribution, probabilistic history, production forecast, rejection, reservoir simulation, risk management, simulation sample, uncertainty parameter, uncertainty quantification, Upstream Oil & Gas, workflow

Country:

- Asia (1.00)
- Europe (0.93)
- North America > United States > Texas (0.70)

Oilfield Places:

- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Tofte Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Not Formation (0.99)
- Europe > Norway > Norwegian Sea > Halten Terrace > Block 6608/10 > Norne Field > Ile Formation (0.99)
- (4 more...)

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Management > Risk Management and Decision-Making (1.00)

Technology:

- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- (2 more...)

Generating an estimate of uncertainty in production forecasts has become nearly standard in the oil industry, but is often performed with procedures that yield at best a highly approximate uncertainty quantification. Formally, the uncertainty quantification of a production forecast can be achieved by generating a correct characterization of the posterior probability-density function (PDF) of reservoir-model parameters conditional to dynamic data and then sampling this PDF correctly. Although Markov-chain Monte Carlo (MCMC) provides a theoretically rigorous method for sampling any target PDF that is known up to a normalizing constant, in reservoir-engineering applications, researchers have found that it might require extraordinarily long chains containing millions to hundreds of millions of states to obtain a correct characterization of the target PDF. When the target PDF has a single mode or has multiple modes concentrated in a small region, it might be possible to implement a proposal distribution dependent on a random walk so that the resulting MCMC algorithm derived from the Metropolis-Hastings acceptance probability can yield a good characterization of the posterior PDF with a computationally feasible chain length. However, for a high-dimensional multimodal PDF with modes separated by large regions of low or zero probability, characterizing the PDF with MCMC using a random walk is not computationally feasible. Although methods such as population MCMC exist for characterizing a multimodal PDF, their computational cost generally makes the application of these algorithms far too costly for field application. In this paper, we design a new proposal distribution using a Gaussian mixture PDF for use in MCMC where the posterior PDF can be multimodal with the modes spread far apart. Simply put, the method generates modes using a gradient-based optimization method and constructs a Gaussian mixture model (GMM) to use as the basic proposal distribution. Tests on three simple problems are presented to establish the validity of the method. The performance of the new MCMC algorithm is compared with that of random-walk MCMC and is also compared with that of population MCMC for a target PDF that is multimodal.

adaptation, algorithm, algorithm 3, algorithm 4, Artificial Intelligence, Bayesian Inference, Gaussian, GMM, history matching, machine learning, Markov chain, mcmc, McMC method, model parameter, oil-production rate, posterior distribution, posterior PDF, prediction, prediction period, proposal distribution, reservoir simulation, target PDF, two-level mcmc, Upstream Oil & Gas, water-injection rate, water-production rate

Country:

- Europe (1.00)
- North America > Canada (0.92)
- North America > United States > Texas (0.67)

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Reservoir Description and Dynamics > Reservoir Simulation > Evaluation of uncertainties (1.00)

Technology:

- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (0.92)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.92)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Undirected Networks > Markov Models (0.64)

Gao, Guohua (Shell Global Solutions (US)) | Vink, Jeroen C. (Shell Global Solutions International) | Chen, Chaohui (Shell International Exploration and Production) | Araujo, Mariela (Shell Global Solutions (US)) | Ramirez, Benjamin A. (Shell International Exploration and Production) | Jennings, James W. (Shell International Exploration and Production) | El Khamra, Yaakoub (Shell Global Solutions (US)) | Ita, Joel (Shell Global Solutions (US))

Uncertainty quantification of production forecasts is crucially important for business planning of hydrocarbon-field developments. This is still a very challenging task, especially when subsurface uncertainties must be conditioned to production data. Many different approaches have been proposed, each with their strengths and weaknesses. In this work, we develop a robust uncertainty-quantification work flow by seamless integration of a distributed-Gauss-Newton (GN) (DGN) optimization method with a Gaussian mixture model (GMM) and parallelized sampling algorithms. Results are compared with those obtained from other approaches.

Multiple local maximum-a-posteriori (MAP) estimates are determined with the local-search DGN optimization method. A GMM is constructed to approximate the posterior probability-density function (PDF) by reusing simulation results generated during the DGN minimization process. The traditional acceptance/rejection (AR) algorithm is parallelized and applied to improve the quality of GMM samples by rejecting unqualified samples. AR-GMM samples are independent, identically distributed samples that can be directly used for uncertainty quantification of model parameters and production forecasts.

The proposed method is first validated with 1D nonlinear synthetic problems with multiple MAP points. The AR-GMM samples are better than the original GMM samples. The method is then tested with a synthetic history-matching problem using the SPE01 reservoir model (Odeh 1981; Islam and Sepehrnoori 2013) with eight uncertain parameters. The proposed method generates conditional samples that are better than or equivalent to those generated by other methods, such as Markov-chain Monte Carlo (MCMC) and global-search DGN combined with the randomized-maximum-likelihood (RML) approach, but have a much lower computational cost (by a factor of five to 100). Finally, it is applied to a real-field reservoir model with synthetic data, with 235 uncertain parameters. AGMM with 27 Gaussian components is constructed to approximate the actual posterior PDF. There are 105 AR-GMM samples accepted from the 1,000 original GMM samples, and they are used to quantify the uncertainty of production forecasts. The proposed method is further validated by the fact that production forecasts for all AR-GMM samples are quite consistent with the production data observed after the history-matching period.

The newly proposed approach for history matching and uncertainty quantification is quite efficient and robust. The DGN optimization method can efficiently identify multiple local MAP points in parallel. The GMM yields proposal candidates with sufficiently high acceptance ratios for the AR algorithm. Parallelization makes the AR algorithm much more efficient, which further enhances the efficiency of the integrated work flow.

algorithm, approximation, Artificial Intelligence, Bayesian Inference, conditional realization, covariance matrix, gaussian component, history matching, l-gmm approximation, l-gmm sample, local map point, machine learning, map point, objective function, optimization problem, optimizer, parallelized ar algorithm, posterior PDF, realization, reservoir model, reservoir simulation, rml sample, uncertainty quantification, Upstream Oil & Gas

Country:

- Europe (1.00)
- North America > United States > Texas (0.67)

SPE Disciplines:

Technology:

- Information Technology > Artificial Intelligence > Representation & Reasoning > Uncertainty > Bayesian Inference (1.00)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.66)

Important decisions in the oil industry rely on reservoir simulation predictions. Unfortunately, most of the information available to build the necessary reservoir simulation models are uncertain, and one must quantify how this uncertainty propagates to the reservoir predictions. Recently, ensemble methods based on the Kalman filter have become very popular due to its relatively easy implementation and computational efficiency. However, ensemble methods based on the Kalman filter are developed based on an assumption of a linear relationship between reservoir parameters and reservoir simulation predictions as well as the assumption that the reservoir parameters follows a Gaussian distribution, and these assumptions do not hold for most practical applications. When these assumptions do not hold, ensemble methods only provide a rough approximation of the posterior probability density functions (pdf 's) for model parameters and predictions of future reservoir performance. However, in cases where the posterior pdf for the reservoir model parameters conditioned to dynamic observed data can be constructed from Bayes’ theorem, uncertainty quantification can be accomplished by sampling the posterior pdf. The Markov chain Monte Carlos (MCMC) method provides the means to sample the posterior pdf, although with an extremely high computational cost because, for each new state proposed in the Markov chain, the evaluation of the acceptance probability requires one reservoir simulation run. The primary objective of this work is to obtain a reliable least-squares support vector regression (LS-SVR) proxy to replace the reservoir simulator as the forward model when MCMC is used for sampling the posterior pdf of reservoir model parameters in order to characterize the uncertainty in reservoir parameters and future reservoir performance predictions using a practically feasible number of reservoir simulation runs. Application of LS-SVR to history-matching is also investigated.

algorithm, approximation, Artificial Intelligence, Bayesian Inference, covariance matrix, gmm approximation, history matching, ls-svr proxy model, machine learning, marginal distribution, Markov chain, minimization problem, posterior PDF, prediction, proposal distribution, reservoir simulation, reservoir simulation run, reservoir simulator, Reynolds, uncertainty quantification, Upstream Oil & Gas, vector

SPE Disciplines:

Technology:

- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning > Support Vector Machines (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Undirected Networks > Markov Models (0.82)

Araujo, Mariela (Shell International Exploration and Production Inc.) | Chen, Chaohui (Shell International Exploration and Production Inc.) | Gao, Guohua (Shell International Exploration and Production Inc.) | Jennings, Jim (Shell International Exploration and Production Inc.) | Ramirez, Benjamin (Shell International Exploration and Production Inc.) | Xu, Zhihua (ExxonMobil) | Yeh, Tzu-hao (Shell International Exploration and Production Inc.) | Alpak, Faruk Omer (Shell International Exploration and Production Inc.) | Gelderblom, Paul (Shell International Exploration and Production Inc.)

Increased access to computational resources has allowed reservoir engineers to include assisted history matching (AHM) and uncertainty quantification (UQ) techniques as standard steps of reservoir management workflows. Several advanced methods have become available and are being used in routine activities without a proper understanding of their performance and quality. This paper provides recommendations on the efficiency and quality of different methods for applications to production forecasting, supporting the reservoir-management decision-making process. Results from five advanced methods and two traditional methods were benchmarked in the study. The advanced methods include a nested sampling method MultiNest, the integrated global search Distributed Gauss-Newton (DGN) optimizer with Randomized Maximum Likelihood (RML), the integrated local search DGN optimizer with a Gaussian Mixture Model (GMM), and two advanced Bayesian inferencebased methods from commercial simulation packages. Two traditional methods were also included for some test problems: the Markov-Chain Monte Carlo method (MCMC) is known to produce accurate results although it is too expensive for most practical problems, and a DoE-proxy based method widely used and available in some form in most commercial simulation packages. The methods were tested on three different cases of increasing complexity: a 1D simple model based on an analytical function with one uncertain parameter, a simple injector-producer well pair in the SPE01 model with eight uncertain parameters, and an unconventional reservoir model with one well and 24 uncertain parameters. A collection of benchmark metrics was considered to compare the results, but the most useful included the total number of simulation runs, sample size, objective function distributions, cumulative oil production forecast distributions, and marginal posterior parameter distributions. MultiNest and MCMC were found to produce the most accurate results, but MCMC is too costly for practical problems.

algorithm, Artificial Intelligence, Bayesian Inference, chi-squared distribution, commercial simulator, history matching, information, machine learning, mcmc, mismatch, multinest, posterior distribution, posterior sample, probability density, reservoir simulation, risk management, test problem, uncertain parameter, uncertainty quantification, unconventional reservoir test problem, Upstream Oil & Gas

Oilfield Places: Asia > Middle East > Oman > Ad Dhahirah Governorate > Fahud Salt Basin > Fahud Field (0.99)

SPE Disciplines:

- Reservoir Description and Dynamics > Reservoir Simulation > History matching (1.00)
- Management > Risk Management and Decision-Making (1.00)
- Data Science & Engineering Analytics > Information Management and Systems (1.00)

Technology:

- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (1.00)

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