Stochastic Simplex Approximate Gradient Research Articles

Efficient production optimization for naturally fractured reservoir using EDFM

Naturally fractured reservoirs make important contributions to global oil and gas reserves and production. The modeling and simulation of naturally fractured reservoirs are different from conventional reservoirs as the existence of natural fractures. To address the development optimization problem of naturally fractured reservoirs, we propose an optimization workflow by coupling the optimization methods with the embedded discrete fracture model (EDFM). Firstly, the effective and superior performance of the workflow is verified based on the conceptual model. The stochastic simplex approximate gradient (StoSAG) algorithm, the ensemble optimization (EnOpt) algorithm, and the particle swarm optimization (PSO) algorithm are implemented for the production optimization of naturally fractured reservoirs based on the improved versions of the Egg model and the PUNQ-S3 model. The results of the two cases demonstrate the effectiveness of this optimization workflow by finding the optimal well controls which yield the maximum net present value (NPV). Compared to the initial well control guess, the final NPV obtained from the production optimization of fractured reservoirs based on all three optimization algorithms is significantly enhanced. Compared with the optimization results of the PSO algorithm, StoSAG and EnOpt have significant advantages in terms of final NPV and computational efficiency. The results also show that fractures have a significant impact on reservoir production. The economic efficiency of fractured reservoir development can be significantly improved by the optimization workflow.

Life-Cycle Production Optimization of the CO2-Water-Alternating-Gas Injection Process Using Least-Squares Support-Vector Regression Proxy

SummaryIn this study, we present a framework for efficient estimation of the optimal carbon dioxide (CO2)-water-alternating-gas (WAG) parameters for robust production-optimization problems by replacing a high-fidelity model with a least-squares support-vector regression (LS-SVR) model. We provide insight and information on the proper selection of feature space and training samples of the LS-SVR proxy model for the CO2-WAG life cycle production optimization problem. Given a set of training points generated from high-fidelity model-based simulation results, an LS-SVR-based proxy model is built to approximate a reservoir-simulation model. The estimated optimal design parameters are then found by maximizing net present value (NPV) using the LS-SVR proxy as the forward model within an iterative-sampling-refinement (ISR) optimization algorithm that is designed specifically to promote the accuracy of the proxy model for robust production optimization. As an optimization tool, the sequential quadratic programming (SQP) method is used. CO2-WAG design variables are CO2 injection and water injection rates for each injection well at each cycle, production bottomhole pressure (BHP) for each production well at each WAG half-cycle, and inflow control valve (ICV) for each well at each WAG half-cycle and at each valve. We study different scenarios where we fix some of the design variables to investigate the importance of design variables on the life cycle production optimization of the CO2-WAG problem. We compare the performance of the proposed method using the LS-SVR runs with the popular stochastic simplex approximate gradient (StoSAG) and reservoir simulation runs for a synthetic example considering a three-layer, channelized reservoir with four injectors and nine producers. Results show that with the properly selected feature space and training points, the proposed LS-SVR-based ISR optimization framework is at least 1.5–8 times computationally more efficient, depending on the cases considered, than the StoSAG using a high-fidelity numerical simulator. However, we observe that the size and sampling of the training data, as well as the selection of well controls and their bound constraints for the well controls, seem to be influential on the performance of the LS-SVR-based optimization method. This is the first LS-SVR application to the CO2-WAG optimal well-control problem. The proposed LS-SVR-based ISR optimization framework has the potential to be used as an efficient tool for the CO2-WAG optimization problem.

Well Placement Optimization for Fractured Reservoirs: Coupling StoSAG and EDFM

Well placement optimization is a significant task in oil field development which aims to find the optimal well locations by maximizing the net present value (NPV) or other objective function. It is a highly nonlinear problem involving large number of variables. Despite lots of work has been done on conventional reservoirs, the optimization tool for naturally fractured reservoir (NFR) is still rare. Naturally fractured reservoirs represent significant amounts of oil reserves. The well placement optimization for NFR is challenging due to the high heterogeneity of matrix and fracture system. In this work, a computer-aided well placement optimization method is established for NFR based on the recent advances. The two phases flow discrete fracture numerical simulation model, i.e., the embedded discrete fracture method (EDFM) is used to model the natural fractures as its computational efficiency and flexibility to handle fracture. Then, stochastic simplex approximate gradient (StoSAG) is employed to obtain the approximate gradient by combing the EDFM. The steepest ascent algorithm is used to find the optimal well placement. A series of numerical case studies are set up to examine the performance of the proposed approach. The NPV for water flooding naturally fractured reservoir production optimization substantially increased by using StoSAG.

Robust Optimization Technique Using Modified Net Present Value and Stochastic Simplex Approximate Gradient

Summary This article aims to combine, from previous works, a modified objective function and the stochastic simplex approximate gradient (StoSAG) to provide a robust technique that optimizes reservoir production on the basis of a sequence of short-term optimizations. Usually, in reservoir optimization, the main goal is to maximize the net present value (NPV); this work used a modified NPV (MNPV) function that introduces reservoir parameters into the objective function. This MNPV analyzes the relation between cash flow and the reduction of the produced oil fraction, which is an indicator of the reduction of the well production life. On the other hand, the StoSAG is a well-established algorithm for robust optimization, and it was used to perform a constructive optimization with the MNPV cost function. The proposed technique (MNPV), together with StoSAG, is compared with other techniques from the literature using a regular base of all reservoir life cycle and the same proposed short-term optimizations, but using the classical NPV. These comparisons were made based on two benchmarks, SPE9 and Egg reservoir models, with an ensemble of 5 and 100 realizations, respectively. As a result, the MNPV StoSAG presents strong cash flow at the beginning of the reservoir production, a competitive NPV along the entire life cycle, and fast simulation time.

Joint Optimization of Well Completions and Controls for CO2 Enhanced Oil Recovery and Storage

Summary Carbon dioxide (CO2) enhanced oil recovery (EOR) is considered one of the technologies to help promote larger scale deployment of geologic CO2 storage because of associated economic benefits through CO2 storage, associated benefits of oil recovery, and the 45Q tax credit (a tax incentive that would reduce CO2 emission in the United States) as well as potential for utilization of existing infrastructure. The objective of this study is to demonstrate how optimal operation strategies (including well completions and controls) can be used to optimize both CO2 storage and oil recovery. The optimization problem was focused on joint estimation of well completions (i.e., fraction of injection/production well perforations in each reservoir layer) and CO2 injection/oil production controls [i.e., rates or bottomhole pressures (BHPs)] that maximize the net present value (NPV) in a combined CO2-EOR and CO2 storage operation. We used the newly developed stochastic simplex approximate gradient (StoSAG), one of the most efficient optimization algorithms in the reservoir optimization community, to solve the optimization problem. The performance of the joint optimization approach was compared with the performance of the well-control-only optimization approach. The superiority of joint optimization was demonstrated with two examples. In addition, the performance of co-optimization of CO2 storage and oil recovery approach was compared with the performances of maximization of only CO2 storage and maximization of only oil recovery approaches.

Joint Optimization of Well Completions and Controls for CO2 Use and Storage

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 200316, “Joint Optimization of Well Completions and Controls for CO2 Enhanced Oil Recovery and Storage,” by Bailian Chen, SPE, and Rajesh Pawar, Los Alamos National Laboratory, prepared for the 2020 SPE Improved Oil Recovery Conference, originally scheduled to be held in Tulsa 18–22 April. The paper has not been peer reviewed. Carbon dioxide (CO2) storage through CO2 enhanced oil recovery (EOR) has been considered an option for larger-scale deployment of CO2 storage because of the economic benefits of oil recovery, 45Q tax credits, and the use of existing infrastructure. The complete paper investigates how optimal reservoir management and operation strategies can be used to optimize both CO2 storage and oil recovery. Results of the authors’ study showed that joint optimization of well completions and well controls can achieve a higher final net present value (NPV) than that obtained from the optimization of well controls only. Introduction In CO2 EOR associated with storage processes, poorly designed well-operating conditions or completions can lead to low oil recovery factors and suboptimal CO2 storage. Co-optimization of oil production and CO2 storage has been recognized as a feasible technique to maximize benefit in terms of oil production and CO2 storage tax credit. To the best of the authors’ knowledge, settings for well completions have not been considered as optimization variables in a CO2 EOR and storage co-optimization process. The objective of this study is to conduct joint optimization of well completions and controls [well rates or bottomhole pressures (BHP)] that maximize life-cycle NPV in CO2 EOR and storage processes and demonstrate the superiority of joint optimization over well-control-only optimization. Optimization Problem In this study, the optimization problem considered is the joint optimization of well completions and well controls for a CO2 EOR and storage process. The mathematical process behind this determination is detailed in the complete paper. The optimization problem was focused on jointly estimating the well completions (i.e., fraction of injection/production well perforations in each reservoir layer) and CO2 injection and oil-production controls that maximize NPV in a CO2 EOR and storage operation. The authors used a newly developed stochastic simplex approximate gradient algorithm to solve the optimization problem. The performance of the joint optimization approach was compared with the performance of the well-control-only optimization approach. In addition, the performance of the co-optimization of CO2 storage and oil-recovery approach was compared with that of the maximization of only-CO2-storage and only-oil-recovery approaches.

Life-Cycle Optimization of the Carbon Dioxide Huff-n-Puff Process in an Unconventional Oil Reservoir Using Least-Squares Support Vector and Gaussian Process Regression Proxies

SummaryIn this work, we investigate the efficient estimation of the optimal design variables that maximize net present value (NPV) for the life-cycle production optimization during a single-well carbon dioxide (CO2) huff-n-puff (HnP) process in unconventional oil reservoirs. A synthetic unconventional reservoir model based on Bakken Formation oil composition is used. The model accounts for the natural fracture and geomechanical effects. Both the deterministic (based on a single reservoir model) and robust (based on an ensemble of reservoir models) production optimization strategies are considered. The injection rate of CO2, the production bottomhole pressure (BHP), the duration of injection and the production periods in each cycle of the HnP process, and the cycle lengths for a predetermined life-cycle time can be included in the set of optimum design (or well control) variables. During optimization, the NPV is calculated by a machine learning (ML) proxy model trained to accurately approximate the NPV that would be calculated from a reservoir simulator run. Similar to the ML algorithms, we use both least-squares (LS) support vector regression (SVR) and Gaussian process regression (GPR). Given a set of forward simulation runs with a commercial compositional simulator that simulates the miscible CO2 HnP process, a proxy is built based on the ML method chosen. Having the proxy model, we use it in an iterative-sampling-refinement optimization algorithm directly to optimize the design variables. As an optimization tool, the sequential quadratic programming (SQP) method is used inside this iterative-sampling-refinement optimization algorithm. Computational efficiencies of the ML proxy-based optimization methods are compared with those of the conventional stochastic simplex approximate gradient (StoSAG)-based methods. Our results show that the LS-SVR- and GPR-based proxy models are accurate and useful in approximating NPV in the optimization of the CO2 HnP process. The results also indicate that both the GPR and LS-SVR methods exhibit very similar convergence rates, but GPR requires 10 times more computational time than LS-SVR. However, GPR provides flexibility over LS-SVR to access uncertainty in our NPV predictions because it considers the covariance information of the GPR model. Both ML-based methods prove to be quite efficient in production optimization, saving significant computational times (at least 4 times more efficient) over a stochastic gradient computed from a high-fidelity compositional simulator directly in a gradient ascent algorithm. To our knowledge, this is the first study presenting a comprehensive review and comparison of two different ML-proxy-based optimization methods with traditional StoSAG-based optimization methods for the production optimization problem of a miscible CO2 HnP.

Optimization of Well Operations in a Carbonate Reservoir Using Stochastic Simplex Approximate Gradient

Optimization of Well Operations in a Carbonate Reservoir Using Stochastic Simplex Approximate Gradient

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimiza-tion method (EnOpt), the simplex gradient method (SG), and the stochastic simplex approximate gradient method (StoSAG), approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increas-ingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator, but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control vari-ables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control varia-bles using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the pro-posed gradients saved about 30–50% of the computational cost of the same optimiza-tion by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost signifi-cantly.

Improved sampling strategies for ensemble-based optimization

We are concerned with the efficiency of stochastic gradient estimation methods for large-scale nonlinear optimization in the presence of uncertainty. These methods aim to estimate an approximate gradient from a limited number of random input vector samples and corresponding objective function values. Ensemble methods usually employ Gaussian sampling to generate the input samples. It is known from the optimal design theory that the quality of sample-based approximations is affected by the distribution of the samples. We therefore evaluate six different sampling strategies to optimization of a high-dimensional analytical benchmark optimization problem, and, in a second example, to optimization of oil reservoir management strategies with and without geological uncertainty. The effectiveness of the sampling strategies is analyzed based on the quality of the estimated gradient, the final objective function value, the rate of the convergence, and the robustness of the gradient estimate. Based on the results, an improved version of the stochastic simplex approximate gradient method is proposed based on UE(s2) sampling designs for supersaturated cases that outperforms all alternative approaches. We additionally introduce two new strategies that outperform the UE(s2) designs previously suggested in the literature.

A Sequential-Quadratic-Programming-Filter Algorithm with a Modified Stochastic Gradient for Robust Life-Cycle Optimization Problems with Nonlinear State Constraints

SummarySolving a large-scale optimization problem with nonlinear state constraints is challenging when adjoint gradients are not available for computing the derivatives needed in the basic optimization algorithm used. Here, we present a methodology for the solution of an optimization problem with nonlinear and linear constraints, where the true gradients that cannot be computed analytically are approximated by ensemble-based stochastic gradients using an improved stochastic simplex approximate gradient (StoSAG). Our discussion is focused on the application of our procedure to waterflooding optimization where the optimization variables are the well controls and the cost function is the life-cycle net present value (NPV) of production. The optimization algorithm used for solving the constrained-optimization problem is sequential quadratic programming (SQP) with constraints enforced using the filter method. We introduce modifications to StoSAG that improve its fidelity [i.e., the improvements give a more accurate approximation to the true gradient (assumed here to equal the gradient computed with the adjoint method) than the approximation obtained using the original StoSAG algorithm]. The modifications to StoSAG vastly improve the performance of the optimization algorithm; in fact, we show that if the basic StoSAG is applied without the improvements, then the SQP might yield a highly suboptimal result for optimization problems with nonlinear state constraints. For robust optimization, each constraint should be satisfied for every reservoir model, which is highly computationally intensive. However, the computationally viable alternative of letting the reservoir simulation enforce the nonlinear state constraints using its internal heuristics yields significantly inferior results. Thus, we develop an alternative procedure for handling nonlinear state constraints, which avoids explicit enforcement of nonlinear constraints for each reservoir model yet yields results where any constraint violation for any model is extremely small.

Joint Optimization of Well Locations, Types, Drilling Order, and Controls Given a Set of Potential Drilling Paths

SummaryMuch work has been performed on the optimal well placement/control problem, including some investigations on optimizing well types (injector or producer) and/or drilling order. However, to the best of our knowledge, there are only a handful of papers dealing with the following problem that is sometimes given to reservoir-engineering groups: given a potential set of reasonable drilling paths and a drilling budget that is sufficient to drill only a few wells, find the optimal well paths, determine whether a well should be an injector or a producer, and determine the drilling order that maximizes the net present value (NPV) of production over the life of the reservoir.In this work, the optimal choices of drilling paths, types, and drilling order are found using the genetic algorithm (GA) with mixed encodings. A binary encoding for the optimization variables pertaining to well-location indices and well types is proposed to effectively handle a large amount of categorical variables, while the drilling sequence is parameterized with ordinal numbers. These two sets of variables are optimized both simultaneously and sequentially. Finally, control optimization using a stochastic simplex approximate gradient (StoSAG) is performed to further improve the NPV of life-cycle production.The proposed workflow is tested on two examples: a 3D channelized reservoir where the potential well paths are either vertical or horizontal, and the Brugge model where only vertical wells are drilled. Both numerical examples indicate that GA combined with StoSAG is a viable solution to the problem considered.

Production optimization using a modified net present value

This paper aims to present the initial concept of modified net present value (MNPV) and its first results. The main goal of this study is to propose a production strategy aimed at maximizing the revenue of a reservoir using the best choice of reservoir inputs. The MNPV was tested with two widely used reservoir benchmarks in the oil industry: Egg Model and SAIGUP. This new strategy modifies the objective function in order to take into account not only the financial results of well’s production but also the well’s data. Thus, it is possible to compare different production strategies by just using medium-term reservoir simulations. This fact drastically reduces computational costs and increases optimization efficiency, anticipating production without significant degradation of the optimal NPV in comparison with similar approaches in the literature. The findings on this study indicate an equivalent undiscounted NPV to those found in literature, a reduction of 60% of the reservoir life-cycle time, and at least 95% of the reduction in computational costs. This number was obtained considering that each interaction of ss-StoSAG (singly-smoothed stochastic simplex approximate gradient) represents a computation cost of at least a dozen of complete reservoir simulations. Twenty iterations were needed to reach the final solution. MNPV only uses a small group of simulations with computation cost equivalent to one interaction ss-StoSAG. Thus, the 95% reduction does not take into account the sweep time of the reservoir for each optimization strategy. In other words, the obtained results show an average profit increase of 250% at the beginning of the reservoir production without sacrificing the total reservoir profit. Although the production strategy is still being developed for injector wells, its initial results for production wells are promising.

Optimization Framework Improves Mariner Field Development

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 193883, “Robust Multiobjective Field Development Optimization for the Mariner Asset,” by Remus Gabriel Hanea, SPE, Ole Petter Bjorlykke, Yastoor Hasmi, and Tao Feng, Equinor, and Rahul Mark Fonseca, TNO, prepared for the 2019 SPE Reservoir Simulation Conference, Galveston, Texas, USA, 10–11 April. The paper has not been peer reviewed. The growing popularity of model-based optimization work flows has resulted in an increase in their application to field cases. In the complete paper, the authors present the challenges, results, and learnings from a 2-year robust multiobjective optimization application at the Mariner heavy-oil asset in the UK sector of the North Sea. The authors used the efficient stochastic simplex approximate gradient technique (StoSAG) to achieve optimization incorporating geological and petrophysical uncertainty. Depending on the problems, significant increases of between 5 and 20% in the expected value of the objective function were achieved. For the multiobjective optimization cases, nontrivial optimal strategies reduced gas production by 40% with less than 1% loss in the economic objective. Introduction To date, most studies of single- and multiobjective optimization have focused on a single study with a specific purpose. Very few studies have used these work flows in an operational setting (i.e., during the field-development-planning stage at an asset tackling a variety of•problems). Including uncertainty is an important step in decision making during field-development planning, especially because uncertainty is so extensive at this stage in the life cycle of a field. Considering a range of potential development scenarios that will provide the necessary tools to enable robust decisions is imperative. These scenarios should also account for the fact that different objectives often conflict with one another. Thus, there is a need for multiobjective optimization under uncertainty, which can be applied in an operational setting. Adapting model-based optimization work flows requires computational efficiency. While the adjoint-based gradient method is computationally very efficient, it is not suitably flexible to incorporate different types of control variables and requires access to the simulation source code as well as a significant implementation effort. Thus, in this paper, the authors use the StoSAG technique. They chose to use an approximate gradient method for the optimization instead of a derivative-free technique because the computational costs for derivative-free methods are usually higher when uncertainty, in terms of different model realizations, is considered. StoSAG is an approximate-gradient-based approach that has proven practical for optimization under uncertainty. A user must decide on the ratio of geological model realizations to control perturbations. The authors used a ratio of 1:1 for all experiments unless otherwise specified, making the number of control perturbations equal to the number of geological realizations. This is computationally the most-efficient approach for large-scale optimization under uncertainty when using high-fidelity, full-physics-simulation models. The objective function is the usual expression for (simple) net present value as used in life-cycle-optimization studies.

Stochastic Simplex Approximate Gradient for Robust Life-Cycle Production Optimization: Applied to Brugge Field

In oil and gas industry, production optimization is a viable technique to maximize the recovery or the net present value (NPV). Robust optimization is one type of production optimization techniques where the geological uncertainty of reservoir is considered. When well operating conditions, e.g., well flow rates settings of inflow control valves and bottom-hole pressures, are the optimization variables, ensemble-based optimization (EnOpt) is the most popular ensemble-based algorithm for the robust life-cycle production optimization. Recently, a superior algorithm, stochastic simplex approximate gradient (StoSAG), was proposed. Fonseca and co-workers (2016, A Stochastic Simplex Approximate Gradient (StoSAG) for Optimization Under Uncertainty, Int. J. Numer. Methods Eng., 109(13), pp. 1756–1776) provided a theoretical argument on the superiority of StoSAG over EnOpt. However, it has not drawn significant attention in the reservoir optimization community. The purpose of this study is to provide a refined theoretical discussion on why StoSAG is generally superior to EnOpt and to provide a reasonable example (Brugge field) where StoSAG generates estimates of optimal well operating conditions that give a life-cycle NPV significantly higher than the NPV obtained from EnOpt.

Improved CRM Model for Inter-Well Connectivity Estimation and Production Optimization: Case Study for Karst Reservoirs

Due to the coexistence of multiple types of reservoir bodies and widely distributed aquifer support in karst carbonate reservoirs, it remains a great challenge to understand the reservoir flow dynamics based on traditional capacitance–resistance (CRM) models and Darcy’s percolation theory. To solve this issue, an improved injector–producer-pair-based CRM model coupling the effect of active aquifer support was first developed and combined with the newly-developed Stochastic Simplex Approximate Gradient (StoSAG) optimization algorithm for accurate inter-well connectivity estimation in a waterflood operation. The improved CRM–StoSAG workflow was further applied for real-time production optimization to find the optimal water injection rate at each control step by maximizing the net present value of production. The case study conducted for a typical karst reservoir indicated that the proposed workflow can provide good insight into complex multi-phase flow behaviors in karst carbonate reservoirs. Low connectivity coefficient and time delay constant most likely refer to active aquifer support through a high-permeable flow channel. Moreover, the injector–producer pair may be interconnected by complex fissure zones when both the connectivity coefficient and time delay constant are relatively large.

Robust Life-Cycle Production Optimization With a Support-Vector-Regression Proxy

Summary We design a new and general work flow for efficient estimation of the optimal well controls for the robust production-optimization problem using support-vector regression (SVR), where the cost function is the net present value (NPV). Given a set of simulation results, an SVR model is built as a proxy to approximate a reservoir-simulation model, and then the estimated optimal controls are found by maximizing NPV using the SVR proxy as the forward model. The gradient of the SVR model can be computed analytically so the steepest-ascent algorithm can easily and efficiently be applied to maximize NPV. Then, the well-control optimization is performed using an SVR model as the forward model with a steepest-ascent algorithm. To the best of our knowledge, this is the first SVR application to the optimal well-control problem. We provide insight and information on proper training of the SVR proxy for life-cycle production optimization. In particular, we develop and implement a new iterative-sampling-refinement algorithm that is designed specifically to promote the accuracy of the SVR model for robust production optimization. One key observation that is important for reservoir optimization is that SVR produces a high-fidelity model near an optimal point, but at points far away, we only need SVR to produce reasonable approximations of the predicting output from the reservoir-simulation model. Because running an SVR model is computationally more efficient than running a full-scale reservoir-simulation model, the large computational cost spent on multiple forward-reservoir-simulation runs for robust optimization is significantly reduced by applying the proposed method. We compare the performance of the proposed method using the SVR runs with the popular stochastic simplex approximate gradient (StoSAG) and reservoir-simulations runs for three synthetic examples, including one field-scale example. We also compare the optimization performance of our proposed method with that obtained from a linear-response-surface model and multiple SVR proxies that are built for each of the geological models.

Drill and Learn: A Decision-Making Work Flow To Quantify Value of Learning

Summary The goal of reservoir management is to make decisions with the objective of maximizing the value creation from oil or gas production. To achieve this, models that preserve geological realism and have predictive capabilities are being developed and used. These models are commonly calibrated using assisted-history-matching (AHM) methods which, in general, will lead to reduced uncertainty in the predicted production. Although uncertainty assessment and reduction are often elements of high-quality decision making, they are not value-creating. Value can only be created through decisions, and any decision changes resulting from AHM should be modeled explicitly. Recently, there has been a surge in the application and understanding of value-of-information (VOI) work flows for reservoir management. In this text, we present a comparison of existing work flows and note the differences between them. After this, we introduce a practically driven approach, referred to as “drill and learn,” with elements and concepts from existing work flows to quantify the value of learning (VOL). VOL can be used as a metric to quantify the potential of such work flows and the strategies obtained. Ensemble methods [ensemble smoother with multiple data assimilation (ES-MDA) and stochastic simplex approximate gradient (StoSAG)] are used for the history matching and optimization. The results presented are obtained by applying the proposed drill-and-learn work flow on a realistic synthetic case. Sensitivities to the amount of information obtained before a closed-loop exercise is performed are also investigated. We show the benefit of performing the closed-loop approach to quantify the VOL to modify field-development decisions, which leads to a mature and robust decision-making framework.

An Efficient Robust Optimization Workflow using Multiscale Simulation and Stochastic Gradients

We present an efficient workflow that combines multiscale (MS) forward simulation and stochastic gradient computation - MS-StoSAG - for the optimization of well controls applied to waterflooding under geological uncertainty. A two-stage iterative Multiscale Finite Volume (i-MSFV), a mass conservative reservoir simulation strategy, is employed as the forward simulation strategy. MS methods provide the ability to accurately capture fine scale heterogeneities, and thus the fine-scale physics of the problem, while solving for the primary variables in a more computationally efficient coarse-scale simulation grid. In the workflow, the construction of the basis fuctions is performed at an offline stage and they are not reconstructed/updated throughout the optimization process. Instead, inaccuracies due to outdated basis functions are addressed by the i-MSFV smoothing stage. The Stochastic Simplex Approximate Gradient (StoSAG) method, a stochastic gradient technique is employed to compute the gradient of the objective function using forward simulation responses. Our experiments illustrate that i-MSFV simulations provide accurate forward simulation responses for the gradient computation, with the advantage of speeding up the workflow due to faster simulations. Speed-ups up to a factor of five on the forward simulation, the most computationally expensive step of the optimization workflow, were achieved for the examples considered in the paper. Additionally, we investigate the impact of MS parameters such as coarsening ratio and heterogeneity contrast on the optimization process. The combination of speed and accuracy of MS forward simulation with the flexibility of the StoSAG technique allows for a flexible and efficient optimization workflow suitable for large-scale problems.

A novel interwell connectivity evaluation method for waterflooding reservoir using oil-water production performance

To address the issues that the existing connectivity evaluation models can only predict liquid production rate and the widely-used fractional-flow equations are not efficient to represent the water-producing characteristics in the whole water-cut variation period accurately, a novel connectivity evaluation method for waterflooding reservoir is established by using injection and production data. This developed model discretizes the reservoir into a series of production-based reservoir control volume. By coupling the producer-based capacitance-resistance model (CRMP) with a segmented water fraction-flow equation to obtain liquid production rate and water-cut, oil-water production data of each well can be further determined. Finally, the estimated parameters including connectivity, time constant and drainage volume of each producer are determined by history matching the measured production data with the newly developed Stochastic Simplex Approximate Gradient (StoSAG) optimization algorithm. Case studies show that, compared with the EnKF algorithm and the traditional projected gradient algorithm, the robustness of the ensemble-based StoSAG optimization procedure is higher. Moreover, the segmented water fractional-flow equation can achieve better dynamic matching and prediction effect of the measured production data than that of the single Koval fractional-flow model, which fully validate the reliability of the proposed interwell connectivity evaluation method and provides the theoretical basis for the actual applications in strongly-heterogeneous waterflooding reservoirs.