Application of Simultaneous Perturbation Stochastic Approximation to Well Placement Optimization under Uncertainty

Jesmani, Mansoureh; Jafarpour, Behnam; Bellout, Mathias; Hanea, R.G.; Foss, Bjarne A.

doi:10.3997/2214-4609.201601873

Cited by 10 publications

(8 citation statements)

References 12 publications

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“…Within the direct approach category, Bangerth et al [1] were the first to apply an integer variant of the Simultaneous Perturbation Stochastic Approximation (SPSA) method to well placement optimization, while in [11] and later [16], SPSA was used not only to derive well placement sensitivities but also to jointly optimize for well placement and control. Finally, Jesmani et al [12] optimized well trajectories (vertical, horizontal, and deviated) using a continuous variant of the SPSA algorithm.…”

Section: Direct Well Placement Gradient Approximationmentioning

confidence: 99%

Gradient-based constrained well placement optimization

Volkov

Bellout

2018

Journal of Petroleum Science and Engineering

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A novel well placement gradient approximation methodology is developed based on performing finite difference approximations of augmented Lagrangian derivatives within the adjoint formulation. The methodology is efficient because it requires only a pair of (forward and backward) simulations to yield a cost function sensitivity with respect to well placement coordinates. The approximated derivative is used within a Sequential Quadratic Programming (SQP) solver ensuring fast convergence and efficient constraint-handling. An extensive error analysis is performed to identify the gradient approximation errors associated with different perturbation ranges. This analysis provides information regarding the appropriate perturbation step size range needed to maintain a consistent gradient approximation while reducing errors associated with the simulation and the discretized nature of the reservoir. We validate the efficiency of the approach by solving for optimal well placement and comparing the results against two major gradient-based well placement approaches from the literature.

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Section: Direct Well Placement Gradient Approximationmentioning

confidence: 99%

Gradient-based constrained well placement optimization

Volkov

Bellout

2018

Journal of Petroleum Science and Engineering

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“…Gradient-based approaches involve the utilization of a gradient computed through either an adjoint system [17][18][19][20] or approximation techniques [21,22]. The adjoint method has been applied in several pieces of literature regarding vertical well placement optimization [19,20,23].…”

Section: Introductionmentioning

confidence: 99%

“…Li et al [26] applied the integer variant of SPSA to the joint optimization of well controls and well placement on three case studies, including the benchmark PUNQ-S3 model. Jesmani et al [22] applied continuous variants of SPSA to optimize the location of a single nonconventional well in the presence of four pre-existing injection wells. Simultaneous perturbation methods can provide an approximated gradient with only two function evaluations (if central), regardless of the number of decision variables.…”

Section: Introductionmentioning

confidence: 99%

An adaptive moment estimation framework for well placement optimization

Arouri

Sayyafzadeh

2022

Comput Geosci

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In this study, we propose the use of a first-order gradient framework, the adaptive moment estimation (Adam), in conjunction with a stochastic gradient approximation, to well location and trajectory optimization problems. The Adam framework allows the incorporation of additional information from previous gradients to calculate variable-specific progression steps. As a result, this assists the search progression to be adjusted further for each variable and allows a convergence speed-up in problems where the gradients need to be approximated. We argue that under computational budget constraints, local optimization algorithms provide suitable solutions from a heuristic initial guess. Nonlinear constraints are taken into account to ensure the proposed solutions are not in violation of practical field considerations. The performance of the proposed algorithm is compared against steepest descent and generalized pattern search, using two case studies — the placement of four vertical wells and placement of 20 nonconventional (deviated, horizontal and/or slanted) wells. The results indicate that the proposed algorithm consistently outperforms the tested methods in terms computational efficiency and final optimum value. Additional discussions regarding nonconventional parameterization provide insights into simultaneous perturbation gradient approximations.

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“…A simple approach to obtain the required gradients is by using Finite Difference Method (FDM) approximation, which is computationally expensive when a large number of optimization variables is involved [3]. An efficient alternative to FDM is stochastic gradient approximation, including ensemble-based approximation or simultaneous perturbation algorithms [3,24,26].…”

Section: Introductionmentioning

confidence: 99%

A reduced random sampling strategy for fast robust well placement optimization

Jesmani

Jafarpour

Bellout

et al. 2020

Journal of Petroleum Science and Engineering

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discrete, continuous, and adaptive) using several numerical experiments, followed by a discussion of the properties of the proposed reduced random sampling approach and comparison with global optimization techniques. The method is applied to several numerical experiments, including case studies involving vertical, horizontal, and lateral wells, to evaluate its performance. The results from these experiments indicate that the reduced random sampling approach can provide significant computational gain with minimal impact on the attained optimization performance.

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Application of Simultaneous Perturbation Stochastic Approximation to Well Placement Optimization under Uncertainty

Cited by 10 publications

References 12 publications

Gradient-based constrained well placement optimization

Gradient-based constrained well placement optimization

An adaptive moment estimation framework for well placement optimization

A reduced random sampling strategy for fast robust well placement optimization

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