A theoretical model of nonlinear percolation in heavy oil reservoirs under multi-factor influences

Heavy oil reservoirs, due to their high viscosity, exhibit percolation behavior that follows the non-Darcy percolation regime, which consists of a non-flow region, a nonlinear percolation region, and a linear percolation region. Most existing models overlook the impact of the nonlinear percolation region, failing to accurately capture the percolation characteristics and threshold pressure behavior of heavy oil. This study develops a continuous nonlinear percolation theoretical model, considering the effects of the adsorption boundary layer and yield stress, based on the physicochemical properties and percolation behavior of heavy oil reservoirs. The model is validated through core percolation tests and threshold pressure gradient experiments. The results show that this model is applicable to heavy oils with various rheological behaviors, with the theoretical results closely matching the experimental data. The average deviation between the theoretical model and the experimental data for the nonlinear percolation behavior of heavy oil reservoirs is 7.45%, confirming the model's accuracy. This model provides valuable insight for the development planning of reservoirs, particularly for ultra-viscous oils and low-permeability reservoirs under complex conditions.