A long-term fracture conductivity model for shale considering non-linear creep damage, proppant elastic-elastoplastic-plastic embedment, and hydration swelling effects

The prediction of long-term fracture conductivity in shale reservoirs remains challenging. Proppant embedment is exacerbated over time by the nonlinear creep damage behavior of shale, which reduces the effective fracture aperture. Simultaneously, the hydration swelling effect of clay minerals further constricts seepage channels, leading to a decline in conductivity. To achieve reliable prediction of long-term conductivity, this study aims to develop a novel analytical model that systematically integrates both creep damage and hydration swelling effects, providing an evaluation tool for fracturing design optimization. Compared to existing analytical models, the innovations and relative advantages of the proposed model are threefold: (1) It fully incorporates the elastic-elastoplastic-plastic stages of proppant embedment and the associated volume changes of the proppant pack; (2) It establishes a nonlinear creep damage model that considers the influence of the temperature field; (3) It couples the effects of hydration swelling, sparse proppant distribution, and proppant crushing in the fracture permeability calculation, thereby significantly enhancing the model’s predictive reliability. The results indicate that an increase in closure pressure triggers a transition in proppant embedment from the elastic to the plastic stage, reducing the normalized long-term conductivity while increasing the optimal proppant distance coefficient. For reservoirs with high closure pressure, it is recommended to employ higher proppant concentrations to maintain long-term fracture conductivity. Prolonged creep time aggravates proppant embedment and reduces conductivity. An increase in the damage factor and the thermal damage variable intensifies fracture wall deformation, leading to greater proppant embedment depth and a decrease in normalized long-term conductivity. Concurrently, increasing fracturing fluid viscosity within a certain range can effectively reduce shale hydration swelling volume and enhance fracture conductivity. For non-uniform placement at fixed areal concentrations, reducing proppant size or increasing layer count enhances conductivity while decreasing the optimal distance coefficient.