Construction of Semi-Analytical Flow Model and 3D Response Study for Staged Fracturing Horizontal Wells in Tight Reservoirs based on Multi-Physical Mechanism Coupling

Abstract

The flow behavior of fractured horizontal wells in tight reservoirs is governed by multiple coupled nonlinear mechanisms. Traditional models fail to simultaneously characterize threshold pressure gradient, stress sensitivity, adsorption storage, and fracture conductivity degradation, leading to reduced accuracy in productivity prediction. This study develops a semi-analytical flow model that integrates Forchheimer non-Darcy flow, Langmuir adsorption, and stress-dependent permeability within a unified framework, further extended to a three-dimensional dual-porosity system. The solution employs Laplace transformation and Stehfest inversion, combined with Duhamel’s principle, enabling efficient calculation under dynamic conductivity and multi-fracture boundary conditions. Based on dimensionless time, the pressure propagation process is divided into distinct control stages, supported by mechanism-specific response diagrams. Sensitivity analysis shows that threshold pressure controls early-time behavior, stress sensitivity governs mid-term trends, and conductivity degradation determines the duration of stabilized production. Adsorption and non-Darcy effects modulate late-time nonlinear responses. The proposed model offers both strong physical interpretability and engineering adaptability, providing theoretical support for well test analysis and production optimization.