Two-Phase Relative Permeability Curves of Bingham Heavy Oil Under Different Types of Wettability: A Theoretical Model

As an important and universal petrophysics of heavy oil reservoirs, the two-phase flow ability inside porous medium is vital for heavy oil development. Utilizing the laminar flow theory and an ideal pore structure, especially cylinder model, the function of the relative permeability of heavy oil–water with water saturation is derived by incorporating the principles of momentum conservation and the characteristics of Bingham fluids, which was modified by validated experiment. Two-phase relative permeability, considering heavy oil as non-Newtonian fluid, is the function of water saturation, pore size, oil–water viscosity ratio, and yield stress. The results of the validated experiment show that the theoretical values calculated employing the modified equation exhibit better agreement with the experimental values, particularly when the viscosities of two-phase fluid are great. The results of the modified two-phase relative permeability show a decrease in water saturation interval corresponding to the two-phase flow area and a smaller value of permeability at equal two-phase relative permeability. The oil–water viscosity ratio in the hydrophobic pores affects the water-phase relative permeability, although the magnitude of its influence diminishes as the viscosity ratio increases. The behavior of relative permeability in hydrophilic pores is the opposite of that in hydrophobic pores. This work can afford good application prospects for mobility control in multilayered reservoirs through the heterogeneous-phase-composite fluid. The saturations of the remaining oil and irreducible water also play a vital role in the prediction of permeability. The work can afford good application prospects for the flow behavior of Bingham heavy oil in pores with different types of wettability.