Nonlinear Pressure Evolution in Stress-Sensitive Porous Media by CO2 Injection

Abstract Predicting nonlinear flow in stress-sensitive porous media is critical for CO₂ displacement and storage performance. We develop a wavelet-based nonlinear partial differential equation (PDE) that explicitly captures localized pressure evolution and stress-permeability coupling beyond conventional Darcy flow. From this framework, three closure indicators are derived: the curvature \(\:κ\:(t)\), the scaling exponent \(\:n(t)\), and the inertial ratio \(\:R(t)\), which define a unified nonlinear criterion for regime transitions. Systematic displacement experiments reveal that these indicators robustly delineate three distinct flow regimes: nonlinear mixed-phase formation, quasi-Darcy displacement, and post-breakthrough inertial channelization. The measured transitions (\(\:{t}₁\),\(\:{t}₂\)) agree closely with theoretical predictions, confirming the robustness of the nonlinear PDE model. This integrated framework provides mechanistic insight into multi-phase transport under stress sensitivity and delivers quantitative tools for regime identification. The results offer direct guidance for optimizing injection strategies, predicting breakthrough, and mitigating channelization risks in CO₂-EOR and geological carbon storage.