A proxy-assisted multi-layer cooperative optimization framework for economic shale gas field development

Shale gas development optimization faces significant challenges due to computational constraints when handling complex parameter interactions across different scales. Conventional optimization methods are limited by their inability to efficiently process high-dimensional parameter spaces, excessive computational demands that prevent field-scale application, and failure to simultaneously consider both technical performance and economic outcomes. The fundamental objective of this research is to maximize field-scale Net Present Value (NPV) through systematic optimization of engineering parameters under given geological constraints, transforming the complex field development decision-making process into a quantitative mathematical problem of maximizing the NPV objective function while determining the optimal corresponding engineering parameters. This paper introduces a novel proxy-assisted multi-layer cooperative optimization (PAMLCO) framework that systematically addresses these limitations through hierarchical problem decomposition and multi-scale parameter integration. The PAMLCO framework transforms the complex field optimization problem into three hierarchically connected subproblems: (1) an outer layer focuses on field-scale optimization, determining global parameters including fracture half-length (FHL), fracture conductivity (FC), cluster spacing (CS) and target A coordinate; (2) a middle layer optimizes well column parameters such as horizontal section length (HSL), well number and target B coordinate; and (3) an inner layer optimizes single well parameters such as the length from wellhead to target A and the drilling platforms connected to each well. Unlike conventional divide-and-conquer methods that often lead to locally optimal solutions, PAMLCO implements a bidirectional information exchange mechanism between adjacent optimization layers—higher-level optimization results provide constraint boundaries for lower-level optimization, while lower-level optimal solutions guide the evolution direction of higher-level parameters. The key innovation of the PAMLCO framework lies in its ability to efficiently handle the coupling effects between microscopic fracture parameters and macroscopic field development strategies while considering reservoir heterogeneity and surface constraints. At its core, a high-precision Gaussian Process Regression (GPR) proxy model (R 2 = 0.9999, RMSE = 0.0132) coupled with a genetic algorithm (GA) accelerates the optimization process over 2400 times compared to traditional numerical simulation methods while maintaining solution accuracy within 2 % of exhaustive approaches. This computational efficiency breakthrough makes comprehensive field-scale optimization practically feasible, enabling the integration of complex technical and economic factors in real-world decision-making processes. Applied to the Sichuan Basin, the PAMLCO framework achieved accumulated gas production of 68.58 × 10 8 m 3 , recovery efficiency of 15.8 %, and NPV of $3.07 × 10 8 , representing improvements of 201 %, 204 %, and 1235 % respectively over actual field schemes, and 11 %, 10 %, and 35 % respectively over traditional single-layer GA optimization. The optimized development scheme identified ideal field-level parameters including FHL (91 m), HSL (1000–3923 m), proppant volume per meter (2.67 m 3 /m), CS (22 m), well number and well location arrangement. This methodology represents a significant advancement in field development optimization by effectively bridging micro-scale fracture parameters and macro-scale deployment strategies while maintaining computational efficiency. The framework's versatility extends beyond the case study, offering potential applications for various unconventional reservoirs where economic optimization under complex geological and operational constraints is required. • First implementation of multilayer optimization resolving cross-scale parameter coupling in shale gas development. • Development of a comprehensive workflow that simultaneously optimizes well placement, completion parameters, and field development strategies under realistic constraints. • Achievement of 2400x faster optimization through innovative GPR-based proxy model while maintaining high accuracy. • Creation of a data model that integrates geological, engineering, and economic constraints in a unified computational framework.