Integrated Modeling of Time-Varying Permeability and Non-Darcy Flow in Heavy Oil Reservoirs: Numerical Simulator Development and Case Study

Studies have demonstrated that heavy oil flow exhibits threshold pressure gradient (TPG) which is closely related to the permeability and viscosity of the crude oil. Also, long-term water flooding continuously alters unconsolidated sandstone reservoir permeability through water flushing. These combined effects significantly influence water flooding performance. Therefore, in this paper, a comprehensive oil–water two phase mathematical model is developed for waterflooded heavy oil unconsolidated sandstone reservoirs based on the traditional black oil model, incorporating both time-varying permeability and threshold pressure gradient. The water-flooding-dependent threshold pressure gradient is firstly proposed, accounting for time-varying permeability. Subsequently, a simulator is developed with finite volume and Newton iteration method. Good agreement is obtained with the commercial simulator based on traditional black oil model. Afterward, the influence of permeability time variation and threshold pressure gradient is analyzed in detail. Results demonstrate that the threshold pressure gradient and time-varying permeability both decrease the oil recovery. The threshold pressure gradient (TPG) reduces the oil flow region and displacement efficiency since production. The increases in permeability after long term water flooding exacerbate reservoir heterogeneity and reduce sweep efficiency. The lowest oil recovery is observed when non-Darcy flow and permeability time variation are considered simultaneously. Furthermore, the time-varying threshold pressure gradient is observed with permeability time variation. Finally, a field data history matching was successfully performed, demonstrating the practical applicability of the proposed model. This new model better aligns with reservoir development characteristics. It can provide a theoretical guide for the development of heavy oil reservoirs.