Numerical Simulation Study on Waterflooding Heavy Oil Based on Variable Threshold Pressure Gradient

Abstract

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.

A Novel Threshold Pressure Gradient Model and Its Influence on Production Simulation for Shale Oil Reservoirs

“…In general, the water phase exerts resistance on the motion of the oil phase through the oil–water two-phase flow of shale oil, which results in the flow behavior of the whole fluid showing the characteristics of Bingham fluid. ,− Moreover, due to the adsorption of polar substances in shale oil on the rock surface, a boundary layer is formed, and there is interfacial molecular force η between boundary layer fluid, bulk phase fluid, and pores. , In physical terms, for Bingham fluid flow through an unsaturated porous media with the porosity of ϕ under a pressure drop of Δ P , the Bingham fluid will be subjected to the driving force (i.e., pressure drop Δ P ), capillary pressure, viscous force, and interfacial molecular force. Based on the assumption that the pressure drop and effective stress are uniformly distributed in the pore space, and the oil phase flows through the capillary with constant speed, according to the Newton’s second law, we have , true( normalΔ P − F γ nobreak0em0.25em⁡ normalcos nobreak0em.25em⁡ θ normald 2 r · 1 − ϕ ϕ true) π false( r − δ false) 2 − true( τ 0 + μ normald v normald r true) 2 π false( r − δ false) L t − η r 2 π false( r − δ false) L t = 0 where F is the shape factor, which is assigned as 4, γ is the oil–water interfacial tension, θ d denotes the dynamic contact angle, r is the effective pore radius, δ is the thickness of water film attached to the boundary layer, τ 0 is ultimate shear stress, μ is the viscosity of a fluid, v means the velocity, and L t denotes the actual capillary length.…”