The industry has been developing numerical models to simulate the wormholing phenomenon in carbonate matrix acidizing, both to save cost and time with experiments and to scale up the laboratory results to field scale. The two-scale continuum model is a fundamental model that has been successfully used for this end. Previous studies with this model only simulated single-phase flow: injection of acid into a water-saturated rock. However, significantly different behavior is observed experimentally by injecting acid into oil- or gas-saturated cores. In this work, we present a fundamental multiphase model for wormhole formation using the two-scale continuum approach, allowing the simulation of wormholing for acid injection into oil- or gas-bearing rocks, with different saturations.
The two-scale continuum model represents the fluid flow and acid transport in the porous medium at the Darcy scale but calculates the acid-rock reaction with dissolution of the rock at the pore-scale. This model was implemented in transient 3D anisotropic form. Each phase occupies a volume fraction in each gridblock, defined by the porosity and fluid saturations. The fluid flow is calculated by solving the Darcy-Brinkman-Stokes equation, in which the relative permeabilities are functions of the saturations. The acid transport and reaction equations are solved, and as the acid injection proceeds and the rock is dissolved, the porosity increases in the gridblocks where dissolution occurs. The pore properties, such as permeability, pore radius, and specific surface area, are updated as porosity evolves, being scaled up from pore to Darcy scale. The simulation keeps track of the different fluid phases by calculating the saturations using the Implicit Pressure Explicit Saturation (IMPES) method.
The developed model was implemented in an open-source computational fluid dynamics package and validated against experimental data. For the validation, the adjustable parameters in the model were calibrated so that the simulation results represent the different dissolution patterns and correctly reproduce the acid efficiency curves obtained experimentally. The same calibrated model was used to simulate the coreflooding experiments with water- and oil-saturated cores. The dissolution patterns (face dissolution, conical wormhole, dominant wormhole, etc.) and acid efficiency curves predicted by the new model match the experimental data. Other simulations presented include the shift in the acid efficiency curves observed for different oil viscosities, residual oil saturations, and different water saturations.
To our knowledge, this is the first 3D two-scale continuum model to simulate wormhole propagation including multiphase flow. With adequate history match, it was shown to accurately predict the acidizing results for different fluid saturations, as observed in experiments.