Robust Multiobjective Nonlinear Constrained Optimization with Ensemble Stochastic Gradient Sequential Quadratic Programming-Filter Algorithm

SPE Journal ◽  
2021 ◽  
pp. 1-16
Author(s):  
Zhe Liu ◽  
Albert Reynolds
Keyword(s):  
Life Cycle ◽  
Sequential Quadratic Programming ◽  
State Constraints ◽  
Production Optimization ◽  
Pareto Optimal ◽  
Nonlinear Constraints ◽  
Water Production ◽  
Production Rates ◽  
Short Term ◽  
Lexicographic Method

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

Robust Constrained Optimization of Short- and Long-Term Net Present Value for Closed-Loop Reservoir Management

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 849-864 ◽  
Author(s):  
C.. Chen ◽  
G.. Li ◽  
A.C.. C. Reynolds
Keyword(s):  
Life Cycle ◽  
Net Present Value ◽  
Production Optimization ◽  
Nonlinear Constraints ◽  
Present Value ◽  
Short Term ◽  
Linear And Nonlinear Constraints ◽  
Linear And Nonlinear ◽  
Reservoir Description

Summary In this paper, we develop an efficient algorithm for production optimization under linear and nonlinear constraints and an uncertain reservoir description. The linear and nonlinear constraints are incorporated into the objective function using the augmented Lagrangian method, and the bound constraints are enforced using a gradient-projection trust-region method. Robust long-term optimization maximizes the expected life-cycle net present value (NPV) over a set of geological models, which represent the uncertainty in reservoir description. Because the life-cycle optimal controls may be in conflict with the operator's objective of maximizing short-time production, the method is adapted to maximize the expectation of short-term NPV over the next 1 or 2 years subject to the constraint that the life-cycle NPV will not be substantially decreased. The technique is applied to synthetic reservoir problems to demonstrate its efficiency and robustness. Experiments show that the field cannot always achieve the optimal NPV using the optimal well controls obtained on the basis of a single but uncertain reservoir model, whereas the application of robust optimization reduces this risk significantly. Experimental results also show that robust sequential optimization on each short-term period is not able to achieve an expected life-cycle NPV as high as that obtained with robust long-term optimization.

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

SPE Journal ◽  
2020 ◽  
Vol 25 (04) ◽  
pp. 1938-1963 ◽  
Author(s):  
Zhe Liu ◽  
Albert C. Reynolds
Keyword(s):  
Life Cycle ◽  
Quadratic Programming ◽  
Optimization Algorithm ◽  
Sequential Quadratic Programming ◽  
Optimization Problem ◽  
State Constraints ◽  
Optimization Problems ◽  
Filter Method ◽  
Reservoir Model ◽  
Nonlinear State

Summary Solving 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.

Gradient-Enhanced Support Vector Regression for Robust Life-Cycle Production Optimization with Nonlinear-State Constraints

SPE Journal ◽  
2020 ◽  
pp. 1-24
Author(s):  
Zhe Liu ◽  
Albert C. Reynolds
Keyword(s):  
Support Vector Regression ◽  
State Constraints ◽  
Production Optimization ◽  
Support Vector ◽  
Computationally Efficient ◽  
Production Rates ◽  
Order Of Magnitude ◽  
Reservoir Simulator ◽  
The Cost ◽  
Nonlinear State

Summary In the context of production optimization, we consider the general problem of finding the well controls that maximize the net present value (NPV) of life-cycle production, where the well controls are either the bottomhole pressure (BHP) or a rate (oil, gas, water, or total liquid) at each well on a set of specified control steps (time intervals), with the limitations on surface facility considered as nonlinear-state constraints [e.g., field-liquid-production rates (FLRs), field-water-production rates (FWRs), and/or field-gas-production rates]. If the reservoir simulation used for reservoir management has sufficient adjoint capability to compute gradients of the objective function and all state constraints, we show that one can develop a significantly more computationally efficient procedure by replacing the adjoint-enhanced reservoir simulator by a proxy model and optimizing the proxy. Our methodology achieves computational efficiency by generating a set of output values of the cost and constraint functions and their associated derivative values by running the reservoir simulator for a broad set of input design variables (well controls) and then using the set of input/output data to train a proxy model to replace the reservoir simulator when computing values of cost and constraint functions and their derivatives during iterations of sequential quadratic programming (SQP). The derivation of the equations for computing the proxy-based model that uses both function and gradient information is similar to that of least-squares support vector regression (LS-SVR). However, this method is referred to as gradient-enhanced support vector regression (GE-SVR) because, unlike LS-SVR, the method uses derivative information, not just function values, to train the proxy. Similar to LS-SVR, improved (higher) estimated optimal NPV values can be obtained by using iterative resampling (IR). With IR, after each proxy-based optimization, one evaluates the cost and constraint functions and their derivatives at the estimated optimal controls using reservoir-simulator output, and then adds this new input/output information to the training set to update the proxy models for predicting NPV and constraints. Using the updated proxies, one applies SQP optimization again. IR continues until the simulator and proxy evaluated at the latest estimate of the optimal well controls give the same value of NPV within a specified percentage tolerance and the constraints evaluated by reservoir simulator at the latest optimal well controls are such that the constraints are satisfied within some small specified tolerance. Our results indicate that proxy-based optimization with iterative resampling might require up to an order of magnitude less computational time than pure reservoir-simulator-based optimization. By comparing the results generated with an LS-SVR proxy with the GE-SVR results, we find that GE-SVR is roughly an order of magnitude more computationally efficient than LS-SVR but also provides a better approximation of a complex cost-function surface so that it is possible to locate multiple optima in cases where LS-SVR fails to identify the multiple optima.

Hierarchical Long-Term and Short-Term Production Optimization

SPE Journal ◽  
2010 ◽  
Vol 16 (01) ◽  
pp. 191-199 ◽  
Author(s):  
G.M.. M. van Essen ◽  
P.M.J.. M.J. Van den Hof ◽  
J.D.. D. Jansen
Keyword(s):  
Life Cycle ◽  
Optimization Problem ◽  
Primary Objective ◽  
Production Optimization ◽  
Cycle Performance ◽  
Short Term ◽  
Secondary Objective ◽  
Life Cycle Optimization ◽  
Term Performance

Summary Model-based dynamic optimization of oil production has a significant potential to improve economic life-cycle performance, as has been shown in various studies. However, within these studies, short-term operational objectives are generally neglected. As a result, the optimized injection and production rates often result in a considerable decrease in short-term production performance. In reality, however, it is often these short-term objectives that dictate the course of the operational strategy. Incorporating short-term goals into the life-cycle optimization problem, therefore, is an essential step in model-based life-cycle optimization. We propose a hierarchical optimization structure with multiple objectives. Within this framework, the life-cycle performance in terms of net present value (NPV) serves as the primary objective and shortterm operational performance is the secondary objective, such that optimality of the primary objective constrains the secondary optimization problem. This requires that optimality of the primary objective does not fix all degrees of freedom (DOF) of the decision variable space. Fortunately, the life-cycle optimization problem is generally ill-posed and contains many more decision variables than necessary. We present a method that identifies the redundant DOF in the life-cycle optimization problem, which can subsequently be used in the secondary optimization problem. In our study, we used a 3D reservoir in a fluvial depositional environment with a production life of 7 years. The primary objective is undiscounted NPV, while the secondary objective is aimed at maximizing shortterm production. The optimal life-cycle waterflooding strategy that includes short-term performance is compared to the optimal strategy that disregards short-term performance. The experiment shows a very large increase in short-term production, boosting first-year production by a factor of 2, without significantly compromising optimality of the primary objective, showing a slight drop in NPV of only -0.3%. Our method to determine the redundant DOF in the primary objective function relies on the computation of the Hessian matrix of the objective function with respect to the control variables. Although theoretically rigorous, this method is computationally infeasible for realistically sized problems. Therefore, we also developed a second, more pragmatic, method relying on an alternating sequence of optimizing the primary-and secondary-objective functions. Subsequently, we demonstrated that both methods lead to nearly identical results, which offers scope for application of hierarchical long-term and short-term production optimization to realistically sized flooding-optimization problems.

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.

Quantifying Office Productivity: An Ergonomic Framework

1998 ◽  
Vol 42 (13) ◽  
pp. 974-978 ◽  
Author(s):  
Alan Hedge
Keyword(s):  
Life Cycle ◽  
Duty Cycle ◽  
Office Workers ◽  
Short Term ◽  
Task Time ◽  
Ergonomic Interventions ◽  
The Impact

An ergonomic framework for conceptualizing and measuring office productivity is described. This framework is based on the the analysis of task time, posture and sequence, and the subsequent the determination of the most appropriate pace, posture, and activities for any office job. The framework assesses various measures of pace, proficiency, and posture that currently can be readily assessed by ergonomists, and it uses these measures to quantify the short-term duty cycle productivity (DCP) and in the longer-term life-cycle productivity (LCP) of office workers. The approach that will be described allows companies to evaluate the impact of ergonomic interventions on the productivity of their workers. The benefits of this ergonomic approach to assessing productivity are discussed.

Production Optimization in Mature Field Through Scenario Prediction Using a Representative Network Model: A Rapid Solution Without Well Intervention

2021 ◽  
Author(s):  
Edwin Lawrence ◽  
Marie Bjoerdal Loevereide ◽  
Sanggeetha Kalidas ◽  
Ngoc Le Le ◽  
Sarjono Tasi Antoneus ◽  
...  
Keyword(s):  
Network Model ◽  
Test Data ◽  
Production Optimization ◽  
Operating Conditions ◽  
Fine Tuning ◽  
Well Test ◽  
Production Rates ◽  
Mature Field ◽  
Gas Lift ◽  
Field Production

Abstract As part of the production optimization exercise in J field, an initiative has been taken to enhance the field production target without well intervention. J field is a mature field; the wells are mostly gas lifted, and currently it is in production decline mode. As part of this optimization exercise, a network model with multiple platforms was updated with the surface systems (separator, compressors, pumps, FPSO) and pipelines in place to understand the actual pressure drop across the system. Modelling and calibration of the well and network model was done for the entire field, and the calibrated model was used for the production optimization exercise. A representative model updated with the current operating conditions is the key for the field production and asset management. In this exercise, a multiphase flow simulator for wells and pipelines has been utilized. A total of ∼50 wells (inclusive of idle wells) has been included in the network model. Basically, the exercise started by updating the single-well model using latest well test data. During the calibration at well level, several steps were taken, such as evaluation of historical production, reservoir pressure, and well intervention. This will provide a better idea on the fine-tuning parameters. Upon completion of calibrating well models, the next level was calibration of network model at the platform level by matching against the platform operating conditions (platform production rates, separator/pipeline pressure). The last stage was performing field network model calibration to match the overall field performance. During the platform stage calibration, some parameters such as pipeline ID, horizontal flow correlation, friction factor, and holdup factor were fine-tuned to match the platform level operating conditions. Most of the wells in J field have been calibrated by meeting the success criterion, which is within +/-5% for the production rates. However, there were some challenges in matching several wells due to well test data validity especially wells located on remote platform where there is no dedicated test separator as well as the impact of gas breakthrough, which may interfere to performance of wells. These wells were decided to be retested in the following month. As for the platform level matching, five platforms were matched within +/-10% against the reported production rates. During the evaluation, it was observed there were some uncertainties in the reported water and gas rates (platform level vs. well test data). This is something that can be looked into for a better measurement in the future. By this observation, it was suggested to select Platform 1 with the most reliable test data as well as the platform rate for the optimization process and qualifying for the field trial. Nevertheless, with the representative network model, two scenarios, reducing separator pressure at platform level and gas lift optimization by an optimal gas lift rate allocation, were performed. The model predicts that a separator pressure reduction of 30 psi in Platform 1 has a potential gain of ∼300 BOPD, which is aligned with the field results. Apart from that, there was also a potential savings in gas by utilizing the predicted allocated gas lift injection rate.

Short-Term Production Optimization Under Water-Cut Uncertainty

SPE Journal ◽  
2020 ◽  
pp. 1-21
Author(s):  
Gabriela Chaves ◽  
Danielle Monteiro ◽  
Maria Clara Duque ◽  
Virgílio Ferreira Filho ◽  
Juliana Baioco ◽  
...  
Keyword(s):  
Latin Hypercube Sampling ◽  
Stochastic Approach ◽  
Injection Rate ◽  
Production Optimization ◽  
Support Vector ◽  
Well Test ◽  
Short Term ◽  
Stochastic Solution ◽  
Water Cut ◽  
Gas Lift

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

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