The fractal analysis of the forced imbibition process in roughened porous media with slip length

Following the large-scale reconstruction of shale reservoirs, the microscale mechanisms and fluid distribution characteristics of multiscale media imbibition under pressure remain unclear. This ambiguity hinders the development of key technologies necessary for optimizing the design and implementation of volumetric fracturing in continental shale oil reservoirs. This study develops a fractal-based analytical model to quantify forced imbibition (FI) dynamics in shale reservoirs, integrating nanoscale slip effects and wall roughness. By coupling the porous medium layer method with fractal theory, we derive the flow resistance of rough capillaries and upscale it to heterogeneous porous media. The model explicitly links slip length to wettability and roughness parameters, revealing that: (1) Slip effects enhance FI capacity by up to 40% in hydrophobic organic nanopores, but only 10% in hydrophilic inorganic pores. (2) Wall roughness reduces FI rates by 15–50%, depending on pore size and roughness geometry, with roughness radius exhibiting triple stronger impact than height. (3) Fractal dimension dominates FI sensitivity, contributing 45% to rate variability, followed by wettability. These findings provide a predictive framework for optimizing fracturing fluid recovery in mixed-wettability shale reservoirs, emphasizing the interplay between nanoscale slip, roughness, and fractal heterogeneity.