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

• Published in: Advances in water resources Vol. 144; p. 103696
• Main Authors: Ferreira, Leandro de Paulo, Oliveira, Thomas David Serafini de, Surmas, Rodrigo, da Silva, Mônica Antunes Pereira, Peçanha, Ricardo Pires
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2020
• Subjects: Brinkman equation; Carbonate dissolution; Darcy equation; Digital rock physics; Micro-CT; Reactive flow; Two-scale continuum model; Digital rock physics; Reactive flow; Two-scale continuum model; Micro-CT; Brinkman equation; Darcy equation; Carbonate dissolution
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2020.103696

•Consequences of opting for the Darcy or Brinkman equations in 3D reactive flow simulations of a vuggy carbonate.•Evaluation of individual terms from the Brinkman’s equation inside the wormhole path and at the sub-resolution porosity.•The carbonate heterogeneity was reproduced in porosity and permeability fields.•Simulations showed the Darcy equation tendency to predict smaller fluid injected volumes at the acid breakthrough.•Strong evidence against using Darcy equation for simulations at high injection velocities. 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.