Parallel Workflow to Optimize Well Placement in Heterogeneous Reservoir using Covariance Matrix Adaptation Evolution Strategy

Adaptive scenario subset selection for worst-case optimization and its application to well placement optimization

“…First, simulations executed to evaluate f (x, s) are computationally demanding, as they require multicomponent and multiphase fluid simulators. For example, previous studies [16,22] have reported one simulation taking several hours to complete. Therefore, the number of f -calls is limited for the optimization.…”

“…That is, we require max i=1,2,3 f s (x i , s) < f (x, s) < 3 i=1 f s (x i , s). Our objective function (16) reflects this requirement, where the pressure interference is represented by i−1 j=1 (1 − exp(−d(x i:3 , x j:3 ))). 7 Figure 7 visualizes the injectable CO 2 volume at the worst case, max s=1,...,m f b ( x, s), when there is only one injection well and the support scenario at each location, x.…”

“…Third, they can be easily accelerated by running simulations for multiple solution candidates in parallel. Hence, although evolutionary approaches tend to require a relatively high number of function evaluations, the execution time of the optimization process can be easily reduced [16].…”

“…For this purpose, it would be preferable to run several trials for each approach and to compute the worst-case performance at each iteration of each trial. However, because CO 2 flow simulation requires high computational resources, such as supercomputers[22,16], running multiple trials for each approach was impossible. By contrast, Equation (16) is computationally inexpensive to evaluate and we expect that it reflects the characteristics of the reality.…”

Covariance Matrix Adaptation Evolutionary Strategy with Worst-Case Ranking Approximation for Min--Max Optimization and its Application to Berthing Control Tasks

“…Given a design vector 𝑥 ∈ X ⊆ R 𝑑 𝑥 , the objective function ℎ sim : X → R is evaluated via numerical simulation. Simulation-based optimization has been used in several real-world applications, such as berthing control [Maki et al 2020;Miyauchi et al 2022], well placement Miyagi et al 2018;Onwunalu and Durlofsky 2010], and topology design [Fujii et al 2018;Marsden et al 2004]. To perform simulation-based optimization, it is necessary to determine simulation conditions in advance so that the objective function values in the real-world, ℎ real (𝑥), are accurately computed.…”