Localization of Ensemble-Based Control-Setting Updates for Production Optimization

SPE Journal ◽  
2011 ◽  
Vol 17 (01) ◽  
pp. 122-136 ◽  
Author(s):  
Yan Chen ◽  
Dean S. Oliver
Keyword(s):  
Net Present Value ◽  
Production Optimization ◽  
Test Case ◽  
Ensemble Size ◽  
Control Variables ◽  
Loop Optimization ◽  
Localization Method ◽  
Steepest Ascent ◽  
Control Setting ◽  
Improved Performance

Summary In the ensemble-based approach to production optimization (EnOpt), a steepest-ascent direction is computed from an ensemble of controls to iteratively improve a set of control settings. The method was shown to work well in maximizing field net present value (NPV) with an ensemble size of 104 on the Brugge SPE comparative test case for closed-loop optimization that had 84 controllable completion intervals (and 3,360 control variables), but performance of the method with smaller ensemble size or on larger problems might be difficult. Without regularization, the crosscovariance between control variables and the objective function is often likely to be dominated by spurious correlations. Because the update to the control variables is proportional to the covariance, spurious correlations will result in poor control settings. We propose a localization method that updates the control setting to optimize the field production while reconciling information from each individual well. The proposed localization method reduces the effect of spurious correlations for improved performance. The Brugge test case is used as an example to show that with covariance localization, greater efficiency could be achieved through the use of a smaller ensemble, or that for a given ensemble size, the optimization results can be improved.

Ensemble-Based Closed-Loop Optimization Applied to Brugge Field

2010 ◽  
Vol 13 (01) ◽  
pp. 56-71 ◽  
Author(s):  
Yan Chen ◽  
Dean S. Oliver
Keyword(s):  
Relative Permeability ◽  
Large Scale ◽  
Closed Loop ◽  
Net Present Value ◽  
Real Field ◽  
Test Case ◽  
Management Scenarios ◽  
Water Contact ◽  
Loop Optimization ◽  
Benchmark Study

Summary In this paper, ensemble-based closed-loop optimization is applied to a large-scale SPE benchmark study. The Brugge field, a synthetic reservoir, is designed as a common platform to test different closed-loop reservoir management methods. The problem was designed to mimic real field management scenarios and, as a result, is by far the largest and most complex test case on closed-loop optimization. The Brugge field model consists of nine layers with a total of 44,550 active cells. It has one internal fault and seven rock regions with different relative permeability and capillary pressure functions. There are 20 producers and 10 injectors in the field. Noise corrupted production data are provided monthly. Each well has three different completions that can be controlled independently. The producing life of the reservoir is 30 years, and the objective of optimization is to maximize the net present value (NPV) at the end of 30 years. Because of the complexity of this test case, several advanced techniques are used in order to improve the solution of the ensemble-based closed-loop optimization. First, covariance localization was used to obtain good model updates with a relatively small ensemble of reservoir models. Localization alleviated the effect of spurious correlations and made it possible to incorporate large amounts of data. Second, covariance inflation was used to compensate for the tendency of small ensembles to lose variability too quickly. When covariance inflation was used together with localization, variability in the ensemble was maintained. Third, regularization was also used in the ensemble-based optimization to reduce the effect of spurious correlations and to smooth the optimized control parameters. Fourth, normalized saturations were used in the state vector because different rock regions had different relative permeability endpoint saturations. Finally, the addition of global parameters such as relative permeability curves and initial oil/water contact (IOWC) reduced the tendency for overshoot. The resulting combination of ensemble-based data assimilation and optimization performed very well on the benchmark study, achieving an NPV within 1% of the value obtained by the test organizers with known geology.

Production Optimization of Thin-Oil Rims: Evaluation of a Stochastic Steepest-Ascent Approach

2009 ◽  
Vol 42 (4) ◽  
pp. 1079-1084
Author(s):  
I.I. Ibragimov ◽  
R. Markovinović ◽  
A.I. Ermolaev ◽  
G. Naevdal
Keyword(s):  
Production Optimization ◽  
Steepest Ascent

Streamline Tracing and Applications in Dual Porosity Dual Permeability Models

2021 ◽  
Author(s):  
Tsubasa Onishi ◽  
Hongquan Chen ◽  
Jiang Xie ◽  
Shusei Tanaka ◽  
Dongjae Kam ◽  
...  
Keyword(s):  
History Matching ◽  
Net Present Value ◽  
Time Of Flight ◽  
Rate Allocation ◽  
Production Optimization ◽  
Dual Porosity ◽  
Computationally Efficient ◽  
Present Value ◽  
Sweep Efficiency ◽  
Streamline Tracing

Abstract Streamline-based methods have proven to be effective for various subsurface flow and transport modeling problems. However, the applications are limited in dual-porosity and dual-permeability (DPDK) system due to the difficulty in describing interactions between matrix and fracture during streamline tracing. In this work, we present a robust streamline tracing algorithm for DPDK models and apply the new algorithm to rate allocation optimization in a waterflood reservoir. In the proposed method, streamlines are traced in both fracture and matrix domains. The inter-fluxes between fracture and matrix are described by switching streamlines from one domain to another using a probability computed based on the inter-fluxes. The approach is fundamentally similar to the existing streamline tracing technique and can be utilized in streamline-assisted applications, such as flow diagnostics, history matching, and production optimization. The proposed method is benchmarked with a finite-volume based approach where grid-based time-of-flight was obtained by solving the stationary transport equation. We first validated our method using simple examples. Visual time-of-flight comparisons as well as tracer concentration and allocation factors at wells show good agreement. Next, we applied the proposed method to field scale models to demonstrate the robustness. The results show that our method offers reduced numerical artifacts and better represents reservoir heterogeneity and well connectivity with sub-grid resolutions. The proposed method is then used for rate allocation optimization in DPDK models. A streamline-based gradient free algorithm is used to optimize net present value by adjusting both injection and production well rates under operational constraints. The results show that the optimized schedule offers significant improvement in recovery factor, net present value, and sweep efficiency compared to the base scenario using equal rate injection and production. The optimization algorithm is computationally efficient as it requires only a few forward reservoir simulations.

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

SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2409-2427 ◽  
Author(s):  
Zhenyu Guo ◽  
Albert C. Reynolds
Keyword(s):  
Life Cycle ◽  
Simulation Model ◽  
Support Vector Regression ◽  
Reservoir Simulation ◽  
Production Optimization ◽  
Forward Model ◽  
Support Vector ◽  
Well Control ◽  
Steepest Ascent ◽  
Reservoir Simulation Model

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.

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

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 816 ◽  
Author(s):  
Daigang Wang ◽  
Yong Li ◽  
Jing Zhang ◽  
Chenji Wei ◽  
Yuwei Jiao ◽  
...  
Keyword(s):  
Time Delay ◽  
Net Present Value ◽  
Water Injection ◽  
Injection Rate ◽  
Production Optimization ◽  
Carbonate Reservoirs ◽  
Karst Reservoir ◽  
Control Step ◽  
Multi Phase Flow

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.

scholarly journals Improved performance of stellarator coil design optimization

2020 ◽  
Vol 86 (2) ◽  
Author(s):  
Jim-Felix Lobsien ◽  
Michael Drevlak ◽  
Thomas Kruger ◽  
Samuel Lazerson ◽  
Caoxiang Zhu ◽  
...  
Keyword(s):  
Stochastic Optimization ◽  
Design Optimization ◽  
Three Dimensional ◽  
Local Maximum ◽  
Average Field ◽  
Test Case ◽  
Coil Design ◽  
Applied Optimization ◽  
Improved Performance ◽  
Coil Shape

Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed.

Joint Optimization of Economic Project Life and Well Controls

SPE Journal ◽  
2017 ◽  
Vol 23 (02) ◽  
pp. 482-497 ◽  
Author(s):  
Mehrdad G. Shirangi ◽  
Oleg Volkov ◽  
Louis J. Durlofsky
Keyword(s):  
Production Optimization ◽  
Rate Of Return ◽  
Joint Optimization ◽  
Time Varying ◽  
Outer Loop ◽  
Loop Optimization ◽  
Contract Duration ◽  
Hurdle Rate ◽  
Project Life ◽  
The Impact

Summary A new methodology for the joint optimization of optimal economic project life (EPL) and time-varying well controls is introduced. The procedure enables the maximization of net present value (NPV) subject to satisfaction of a specified modified internal rate of return (MIRR). Knowledge of the economic project life enables the operator to plan for infill drilling or some other type of field development in the case that the lease/contract duration is longer than the optimal project life. This will enable NPV to be maximized, and the hurdle rate to be honored, over the entire duration of the lease. The optimization is formulated as a nested procedure in which economic project life is optimized in the outer loop, and the associated well settings [time-varying bottomhole pressures (BHPs) in the cases considered] are optimized in the inner loop. The inner-loop optimization is accomplished by use of an adjoint-gradient-based approach, while the outer-loop optimization entails an interpolation technique. The successful application of this framework for production optimization for 2D and 3D reservoir models under waterflood is demonstrated. The tradeoff between maximized NPV and rate of return is assessed, as is the impact of discount rate on optimal operations. In the second example, we illustrate the advantages of initiating a new project (that satisfies the hurdle rate) once the EPL is reached. Taken in total, the results in this paper demonstrate the importance of explicitly incorporating both NPV and rate of return in production-optimization formulations.

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

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Bailian Chen ◽  
Jianchun Xu
Keyword(s):  
Life Cycle ◽  
Net Present Value ◽  
Oil And Gas ◽  
Oil And Gas Industry ◽  
Optimization Techniques ◽  
Production Optimization ◽  
Operating Conditions ◽  
Optimization Under Uncertainty ◽  
Theoretical Argument ◽  
Gas Industry

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.

Production optimization using a modified net present value

2020 ◽  
Vol 24 (3) ◽  
pp. 1087-1100
Author(s):  
Eugênio Libório Feitosa Fortaleza ◽  
Emanuel Pereira Barroso Neto ◽  
Marco Emílio Rodrigues Miranda
Keyword(s):  
Net Present Value ◽  
Production Optimization ◽  
Present Value

Optimization of Well Placement Under Time-Dependent Uncertainty

2006 ◽  
Vol 9 (02) ◽  
pp. 135-145 ◽  
Author(s):  
Umut Ozdogan ◽  
Roland N. Horne
Keyword(s):  
History Matching ◽  
Net Present Value ◽  
Optimization Technique ◽  
Production Optimization ◽  
Time Dependent ◽  
Hill Climbing ◽  
Process Data ◽  
Well Placement ◽  
Placement Decisions ◽  
Exploration And Development

Summary Well-placement decisions made during the early stages of exploration and development activities have the capability to improve later placement decisions by providing more information (greater certainty). Therefore, recovery and efficient use of information may add value beyond the amount of oil recovered. This study proposes an approach that emphasizes the value of time-dependent information to achieve better decisions in terms of reduced uncertainty and increased probable net present value (NPV). Unlike previous approaches, well-placement optimization is coupled with recursive probabilistic history-matching steps through the use of the pseudohistory concept. The pseudohistory is defined as the probable (future) response of the reservoir that is generated by a probabilistic forecasting model. To test the results of the proposed approach, an example reservoir was investigated with multiple realizations, all of which match the same production history. The results of this study showed that subsequent well-placement decisions can be improved when probabilistic production profiles obtained from the wells, as they are drilled, are incorporated in the optimization scheme.. Introduction Well placement is one of the important decisions made during the exploration and development phase of projects. Most of the time, the large number of possibilities, constraints on computational resources, and the size of the simulation models limit the number of possible scenarios that may be considered. In these cases, optimization algorithms become extremely valuable in searching for the optimum development scenario. Various approaches have been proposed for production optimization. Bittencourt (1994) optimized the scheduling of a field using the polytope algorithm. Beckner and Song (1995) applied the traveling salesman framework on a well-placement problem, using simulated annealing (SA) to find the optimum locations of the wells. Bittencourt and Horne (1997) hybridized genetic algorithms (GA) with the polytope algorithm and tabu search and referred to this hybrid optimization technique as HGA. HGA was observed to improve the economic forecasts and CPU effort during optimization. Pan and Horne (1998) used kriging as a proxy to the reservoir simulator to decrease the number of simulations. Guyaguler et al. (2000) showed that the number of simulations required to optimize the injector well locations decrease when an HGA was coupled with a kriging proxy. Yeten et al. (2002) coupled GA with hill-climbing methods and an artificial neural network (ANN) proxy to optimize the type, location, and trajectory of nonconventional wells. Guyaguler and Horne (2001) assessed the uncertainty of the well-placement results using utility theory together with multiple realizations of the reservoir. All these approaches considered only the information that was available at the beginning of the optimization process. Data that would become available as the reservoir developed in time was not taken into account.

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