The heavy-oil flow in porous media is characterized by non-Darcy law with variable threshold pressure gradient (TPG) due to the large fluid viscosity. However, available analytical and numerical models hardly consider this effect, which can lead to erroneous results. This paper is aimed at presenting an innovative approach and establishing a numerical simulator to analyze the heavy-oil flow behavior with waterflooding. The apparent viscosity of the oil phase and flow correction coefficient characterized by the TPG were applied to describe the viscosity anomaly of heavy oil. Considering the formation heterogeneity, the TPG was processed into a variable related to mobility and the directionality. The discretization and linearization of the mathematical model were conducted to establish a fully implicit numerical model; the TPG value on each grid node was obtained through oil phase mobility interpolation, and then, the Jacobi matrix was reassembled and calculated to solve pressure and saturation equations. The corresponding simulator was thus developed. The pre-/postprocessing module of the simulator is connected to ECLIPSE; then, an efficient algorithm is introduced to realize a fast solution. Results show that considering the TPG will not only reduce the waterflooding area but also reduce the oil displacement efficiency because of aggravating the nonpiston phenomenon and interlayer conflict. The numerical simulation study on the TPG of heavy oil provides theoretical and technical support for the rational development and adjustment of water-driven heavy oil.

In this paper, the characterization parameter ‘effective displacement flux’ is employed to describe the flushing intensity and a new numerical simulator in which the rock-fluid properties considered functions of the effective displacement flux is developed based on the black oil model. Additionally, a conceptual reservoir model is established to validate the effective characterization of the time-varying mechanisms: the time-varying oil viscosity can characterize the viscous fingering of the water phase the time-varying absolute permeability can present the aggravation of reservoir heterogeneity, the alteration of wettability is characterized with the time-varying relative permeability, and the ultimate recovery will increase with the combined effect of all three time-varying factors. Eventually, the new simulator is applied to the simulation of an actual waterflooding reservoir to illustrate the assistance in history matching. The simulation results of our simulator can readily match the history data, which proves that the consideration of comprehensive time-varying rock-fluid properties can significantly improve the accuracy during the numerical simulation of waterflooding reservoirs.