Pore‐scale simulation of carbonate dissolution in micro‐CT images

Abstract

We present a particle‐based method to simulate carbonate dissolution at the pore scale directly on the voxels of three‐dimensional micro‐CT images. The flow field is computed on the images by solving the incompressible Navier‐Stokes equations. Rock‐fluid interaction is modeled using a three‐step approach: solute advection, diffusion, and reaction. Advection is simulated with a semianalytical pore‐scale streamline tracing algorithm, diffusion by random walk is superimposed, while the reaction rate is defined by the flux of particles through the pore‐solid interface. We derive a relationship between the local particle flux and the independently measured batch calcite dissolution rate. We validate our method against a dynamic imaging experiment where a Ketton oolite is imaged during CO2‐saturated brine injection at reservoir conditions. The image‐calculated increases in porosity and permeability are predicted accurately, and the spatial distribution of the dissolution front is correctly replicated. The experiments and simulations are performed at a high flow rate, in the uniform dissolution regime – Pe ≫ 1 and PeDa ≪ 1—thus extending the reaction throughout the sample. Transport is advection dominated, and dissolution is limited to regions with significant inflow of solute. We show that the sample‐averaged reaction rate is 1 order of magnitude lower than that measured in batch reactors. This decrease is the result of restrictions imposed on the flux of solute to the solid surface by the heterogeneous flow field, at the millimeter scale.

Pore‐space structure and average dissolution rates: A simulation study

“…[] and Pereira Nunes et al . [] discussed how sample‐scale transport limitations imposed by a heterogeneous flow field are responsible for a decrease of one order of magnitude in the average reaction rate when compared to the batch rate. It was shown that this flow and reaction regime, termed “uniform” in Darcy‐scale studies, is actually a regime where the average dissolution rate is severely constrained by pore‐scale heterogeneities.…”

“…Here we summarize the assumptions and implementation of the particle‐based dissolution method introduced by Pereira Nunes et al . [].…”

“…Pereira Nunes et al . [] introduced a model that describes the dissolution kinetics in terms of the concentration of a single kind of particle, which is, in turn, interpreted as the undersaturation, or the deviation from the equilibrium concentration, in the liquid phase. The fluid is in equilibrium with respect to the solid when C = 0; in this case, the flux of particles to the solids is zero and no dissolution occurs.…”

“…This was termed a channelled dissolution regime. In this paper, we will confirm this conceptual picture and we will use pore‐scale simulations, which in previous work were used to predict the results of pore‐scale imaging experiments [ Pereira Nunes et al ., ; Menke et al ., ], to obtain a quantitative estimate on the average dissolution rates of heterogeneous rocks (a bead pack, an oolite and a bioclastic limestone). We also provide estimates for the increase in the representative elementary volume (REV) after dissolution and show that changes in permeability are sample‐dependent.…”

“…We start by describing the flow, transport, and reaction model proposed by Pereira Nunes et al . []—section 2. Next, we discuss the characterization of transport and reaction in terms of the nondimensional Péclet and Damköhler numbers (section 3).…”