Field development optimization using a sequence of surrogate treatments
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ORIGINAL PAPER
Field development optimization using a sequence of surrogate treatments Daniel U. de Brito1,2 · Louis J. Durlofsky1 Received: 23 July 2019 / Accepted: 15 June 2020 © Springer Nature Switzerland AG 2020
Abstract Field development optimization, in which well configuration, well types, and well controls are determined, represents a computationally demanding mixed integer nonlinear programming problem. Such problems may require very large numbers of function evaluations, and if each of these corresponds to a detailed flow simulation, the optimization can become intractable. In this paper, we incorporate a set of surrogate treatments (STs) into the field development optimization problem. The basic ST is a variant of a recently developed surrogate procedure for optimizing well rates. It entails the solution of two optimization problems that both involve simplified physics (unit-mobility ratio displacement) and can be solved very efficiently. In the first problem, we find optimal well-rate ratios (i.e., the fraction of total injection or production allocated to each well), while in the second problem we determine optimal overall field injection and production rates. This ST is incorporated into a particle swarm optimization (PSO) framework. Three treatments are considered for subsequent optimization steps. All of these approaches involve full-physics simulations, and two of the methods entail the use of mesh adaptive direct search (MADS). The ST-based procedures are evaluated for two different 3D problems involving waterflood (with mobility ratios of 2 and 5) and water-alternating-gas (WAG) injection. The surrogate treatments are compared with standard approaches involving PSO, MADS, and a PSO-MADS hybrid. Extensive optimization results demonstrate that the ST-based methods provide consistent improvement in optimizer performance. For example, in the WAG case, the ST-based approach gives an optimal net present value that is 3.2% higher than that achieved using standard PSO-MADS, while also providing a 2.4× computational speedup. Keywords Field development optimization · Joint optimization · Surrogate model · Reservoir simulation
1 Introduction Field development optimization entails the determination of well number, types, locations and controls (injection and production rates or bottom-hole pressures) such that a particular cost function is maximized or minimized. This optimization is a mixed integer nonlinear programming problem, and as such it is very challenging and requires large numbers of reservoir simulation runs to be performed. Daniel U. de Brito
[email protected]; [email protected] Louis J. Durlofsky [email protected] 1
Department of Energy Resources Engineering, Stanford University, Stanford, CA 94305, USA
2
Petr´oleo Brasileiro S.A., Petrobras, Brazil
For this reason, the use of efficient optimization techniques is essential. Approximate (surrogate or proxy) models are very useful in this context as they can provide the required function evaluations at much less computational c
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