Numerical analysis of two-phase flow in heterogeneous porous media during pre-flush stage of matrix acidizing: Optimization by response surface methodology

Oil trapping behavior during the pre-flush stage is critically important to evaluate the effectiveness of matrix acidizing for the oil well stimulation. In this study, the visco-capillary behavior of the two-phase flow in the pore-scale is analyzed to investigate the influence of wetting properties for a natural rock sample. A two-dimensional model, based on Cahn-Hilliard phase-field and Navier-Stokes equations, was established and solved using the finite element method. A stability phase diagram for log capillary number (Ca)-log viscosity ratio (M) was constructed and then compared with the reported experimental works. The maximum and minimum ranges of capillary number and viscosity ratio to identify both viscous and capillary fingering regions were found to be Log M ≈ −2.5, Log Ca ≈ −5, and Log M ≈ −0.5, Log Ca ≈ −5, respectively. However, the most stable displacement region was found to be located at Log M ≈ 0.5 and Log Ca ≈ −2. Furthermore, the impact of four independent variables, including pore volume of injection (1 < PV < 5), capillary number (−6 < Log Ca < 0), viscosity ratio (−5 < Log M < 2), and contact angle (π/6&amp;lt;θ&amp;lt;5π/6), on recovery factor (RF) was investigated using central composite design of response surface methodology. For the chosen range of independent variables, the optimum conditions for the immiscible two-phase flow (e.g., RF > 0.95) occurred at Log M > 0, −4.5 < Log Ca < −2, PV > 1, θ > π/6 condition. It is worth mentioning that for Log M< 0, the optimum condition occurred at Log M ≈ 0, Log Ca ≈ −3.5, PV ≈ 4, and θ ≈ π/6.