Brinkman equation in reactive flow: Contribution of each term in carbonate acidification simulations

Abstract

This article studies the individual contribution of each term in the Navier-Stokes-Darcy (Brinkman) equation to the fluid linear momentum balance and the consequences of opting for the Darcy or Brinkman equations in 3D reactive flow simulations of a vuggy carbonate. A two-scale continuum model was used to simulate the acidification of a carbonate sample using the Darcy and Brinkman equations. Rock heterogeneity is considered in the initial porosity and permeability fields, which are calculated directly from micro-CT images. Simulations showed that the Darcy equation predicts the acid breakthrough earlier in most cases. The convective acceleration term in the Brinkman equation plays an important role in describing the fluid momentum balance at high injection velocities, and this is a clear evidence against the use of the Darcy equation to model reactive flow in such conditions.