Ensemble-based constrained optimization using an exterior penalty method

Oguntola, Micheal Babatunde; Lorentzen, Rolf Johan

doi:10.1016/j.petrol.2021.109165

Cited by 15 publications

(6 citation statements)

References 33 publications

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“…) for m = 1, … , N , we assume in Equation ( 10) that the mean of {u k,m } N m=1 is approximated by u k . By first-order Taylor series expansion of F about u k , it can easily be deduced that Equation ( 10) is an approximation of C k u G k at the k-th iteration, that is see [41,46] for a detailed proof. Therefore, we choose the search direction as (5).…”

Section: Optimization Algorithm For a General Objective Functionmentioning

confidence: 97%

Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

et al. 2022

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In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer flooding. The computational approach is based on an adaptive training procedure of a neural network that directly approximates an input-output map of the underlying PDE-constrained optimization problem. The training process thereby focuses on the construction of an accurate surrogate model solely related to the optimization path of an outer iterative optimization loop. True evaluations of the objective function are used to finally obtain certified results. Numerical experiments are given to evaluate the accuracy and efficiency of the approach for a heterogeneous five-spot benchmark problem.

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Section: Optimization Algorithm For a General Objective Functionmentioning

confidence: 97%

Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

et al. 2022

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“…The uncertainty are approximated by distributing the performance indicator into a finite number of possible outcome and then optimized over the production period of the reservoir [20]. Successful approaches have been reported for several problems including production optimization [21][22][23][24][25]. Upstream oil exploration are quite complex, hence utilization of conventional optimization strategy will not suffice because it only provide solutions of single uncertainty realization [26].…”

Section: Gradient Based Waterflood Optimizationmentioning

confidence: 99%

“…The adjoint equations are used to compute the system gradient [96]. waterflood optimal control is made up of [81], [97]: § Reservoir dynamic system of the form; 𝑔(𝑢 6 , 𝑥 651 , 𝑥 6 , 𝜑) = 0 (25) Where 𝑔 is a nonlinear function, 𝑢 is the input vector, 𝑘 is the system timesteps, 𝑥 651 and 𝑥 6 is the reservoir state, 𝜑 is a vector of parameters. § Initial conditions of the dynamic system [85];…”

Section: 𝐻(𝑥(𝑡) 𝑢(𝑡)⋋ (𝑡) = 𝐿(𝑥(𝑡) 𝑢(𝑡)) +⋋ $ (𝑡)[𝐴K𝑥(𝑡)n𝑥(𝑡) + 𝐵(𝑥(𝑡...mentioning

confidence: 99%

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2023

JESTR

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Waterflooding is the most common secondary recovery technique used in oil and gas industries today, owing to its cheap investment cost and easy implementation. However, major challenges are encountered in terms of oil sweep efficiency and breakthrough time which poses a risk to production and economic lifecycle of reservoirs. As a result, reservoir engineers are tasked with improvising optimal production strategies with the goal of maximizing profit. This review extensively describes some common optimization techniques reported in improving oil reservoir production. Also, their formulation, limitations and advantages with respect to production rates, oil well placement and control, inter-well connectivity and reservoir sweep efficiency were reviewed. While there are several optimization algorithms used in waterflooding, the emphasis in this work involves only the gradient and data driven optimizers since it is impossible to cover all optimization technique in a single review paper. Basically, no algorithm has been globally accepted as superior to the other since the sole aim is to improve productivity and economic profit, and each of these techniques has its unique practicability. However, when considering factors like design limitations, computational and economic cost, implementation timeframe, availability of data, some technique may suffice.

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“…For example, preference or net profit, or proximity to a desired, reference, outcome. The subject of constraints (Oguntola and Lorentzen, 2021, e.g.) is not considered, and the specifics of are not discussed herein.…”

Section: L(u)mentioning

confidence: 99%

Revising the Method of Ensemble Randomized Maximum Likelihood

Raanes¹,

Evensen²,

Stordal³

2019

Petroleum Geostatistics 2019

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In robust optimisation problems the objective function consists of an average over (an ensemble of) uncertain parameters. Ensemble optimisation (EnOpt) implements steepest descent by estimating the gradient using linear regression on Monte-Carlo simulations of (an ensemble of) control parameters. Applying EnOpt for robust optimisation is costly unless the evaluations over the two ensembles are combined, i.e. 'paired'. Here, we provide a new and more rigorous perspective on the stochastic simplex approximate gradient (StoSAG) used in EnOpt, explaining how it addresses detrimental cross-correlations arising from pairing by only capturing the variability due to the control vector, and not the vector of uncertain parameters. A few minor variants are derived from a generalized derivation, as well as a new approach using decorrelation. These variants are tested on linear and non-linear toy gradient estimation problems, where they achieve highly similar accuracy, but require a very large ensemble size to outperform the non-robust approach when accounting for variance and not just bias. Other original contributions include a discussion of the particular robust control objectives for which EnOpt is suited, illustrations, a variance reduction perspective, and a discussion on the centring in covariance and gradient estimation.

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Ensemble-based constrained optimization using an exterior penalty method

Cited by 15 publications

References 33 publications

Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

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Revising the Method of Ensemble Randomized Maximum Likelihood

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