Summary Horizontal well fracturing is widely regarded as the most effective technology for enhancing the recovery rate of shale-gas reservoirs. However, complex flow mechanisms and strong reservoir heterogeneity make the collaborative optimization of well-fracture pattern parameters challenging. In multiwell development optimization, the number of wells itself cannot be predetermined, and parameters of individual horizontal wells and their corresponding fractures vary. Thus, well-fracture pattern optimization is inherently a dynamic variable-dimensional optimization problem. Existing meta-heuristic algorithms typically fix the dimension of optimization variables and cannot address such variable-dimensional problems. To tackle this issue, we propose a variable-dimensional evolutionary transfer optimization (VDETO) framework, which incorporates a probability-controlled dimension adaptive adjustment mechanism. By minimizing the characteristics differences among population particles, it enables knowledge transfer across dimensions, allowing for the collaborative optimization of the number of wells, individual well parameters, and fracture parameters, thereby achieving an integrated design of well-fracture pattern. The VDETO framework was validated using benchmark functions and compared with methods such as particle swarm optimization (PSO), variable-length PSO (VPSO), and modified variable-length PSO (MVPSO). Furthermore, a collaborative optimization study of well-fracture pattern was conducted on a 2D shale-gas reservoir mechanistic model. The results demonstrate that VDETO outperforms commonly used variable-dimensional algorithms in both convergence speed and accuracy. Compared with traditional uniform well placement or concentrated well placement only in high-permeability zones, this method optimizes well locations across different sweet spots, creating high-permeability channels through fracturing to effectively connect multiple sweet spots, thereby significantly improving the net present value (NPV). This framework provides a novel approach for the collaborative optimization of well-fracture pattern parameters.
Zhao et al. (Wed,) studied this question.