A divide-and-conquer optimization paradigm for waterflooding production optimization

Production optimization technique, as a crucial step in the closed-loop reservoir management (CLRM), aims to achieve optimal development efficiency by adjusting development schemes (e.g., well-controls) with the aid of optimization methods. However, due to the unbearable computational burden brought by full-scale reservoir simulation, few optimizers can obtain satisfactory solution(s) within limited simulation calls, especially when the problem dimension is very high. This phenomenon is common in many real-world scenarios, which is also referred to as the “curse of dimensionality”. To address this issue, a novel divide-and-conquer (DAC) optimization paradigm is proposed for production optimization problems. Specifically, given a large-scale production optimization problem, it can be decomposed into a number of simpler subproblems with low dimensions. Then, to overcome the computationally expensive issue, multiple data-driven surrogates are built for the subproblems. Finally, all the subproblem surrogates are optimized cooperatively using a reuse strategy of subproblem samples. From the perspective of production optimization, the joint scheme optimization of the original problem is turned into cooperatively optimizing the schemes involved in multiple subproblems. Interestingly, the obtained subproblems always correspond to multiple flow units with weak flow interferences caused by some obstruction factors (e.g., low-permeability channel and vertical barrier layer). This indicates that the DAC method can not only serve as an optimization enhancement technique but also can be employed as an auxiliary means of connectivity analysis. In return, many connectivity analysis methods such as flow diagnostics that require fewer simulation calls can serve as the decomposition tool. More importantly, the superior flexibility of the proposed DAC-based expensive optimization framework allows it to incorporate a wide variety of state-of-the-art surrogate-assisted evolutionary solvers. In this paper, the differential evolution (DE) and two advanced surrogate-assisted evolutionary solvers are implemented under the proposed paradigm. The experimental results conducted on two 100-dimensional benchmark functions and two production optimization tasks verified the effectiveness of the proposed method.