3-D numerical simulation of sandstone matrix acidizing by non-Newtonian fluid

Abstract

Matrix acidizing is a common technique to increase oil recovery in sandstone oil reservoirs. In the matrix acidizing process, reactive fluids are injected into the reservoir with the scope of dissolving and dispersing the rocks near the wellbore.In this study, the matrix acidizing of sandstone wells by a hydrochloric acid/hydrofluoric acid/additives mixture is described through mathematical modeling using the two-scale continuum model.The model developed in this study indicates the reactions and transport phenomena at pore and Darcy scales in 3-D radial flow. Due to using several additives during the acid injection process, the fluid phase has non-Newtonian behavior (shear-thinning). The effect of non-Newtonian fluid in porous media was investigated using a modified continuum model due to importance calculations in field scale. The Carreau-Yasuda constitutive equation has been used to modify the continuum model to consider the non-Newtonian fluid effects. In the proposed model, partial differential equations of reaction and diffusion at pore-scale, and simultaneously convection and dispersion phenomena at Darcy scale are solved using numerical methods. The finite volume and tri-diagonal matrix algorithm (TDMA) techniques were employed to gain a precise solution for the model and observe the dissolution pattern in different acidizing regimes and rheological properties. The effect of acid injection rate, dissolution rate constant and different reservoir properties, including permeability, porosity and heterogeneity on dissolution patterns, was investigated by considering non-Newtonian fluid effects, and concluded that acid having high shear-thinning behaviour (i. e., acid having low power-law index) seemed more promising for field operations because of deep penetration. The reservoir heterogeneity was defined by selecting a random local porosity distribution.It should be noted that the presented model can reproduce different types of acid/rock system (carbonate or sandstone reservoirs). Finally, the skin factor would be calculated to study the acidizing performance in the damaged zone. To solve the porosity evolution equation, couple pore and Darcy scales, and update the pore-scale parameters at each time step, the program was developed in FORTRAN by Parallel Processing and consisting of functions and routines. • Simultaneous numerical solution of Darcy, mass and pore equations in 3-dimension. • 3-D modeling of sandstone matrix acidizing by non-Newtonian fluid. • Pore volume to breakthrough and injection rate calculations in various conditions. • Consideration of power-law index (n) and viscosity effects in dissolution patterns. • Consideration of skin factor variation during the matrix acidizing.