A continuous time random walk approach to predict dissolution in porous media based on validation of experimental NMR data

Abstract

We develop a reactive transport model for dissolution of porous materials using a Continuous Time Random Walk (CTRW) formulation with first-order kinetics. Our model is validated with a dataset for a Ketton carbonate rock sample undergoing dissolution on injection of an acid, monitored using Nuclear Magnetic Resonance (NMR). The experimental data includes the 3D porosity distribution at the beginning and end of the experiment, 1D porosity profiles along the direction of flow during dissolution, as well as the molecular fluid displacement probability distributions (propagators). With the calibration of only a single parameter, we successfully predict the porosity changes and the propagators as a signature of flow heterogeneity evolution in the dissolution experiment. We also demonstrate that heterogeneity in the flow field leads to an effective reaction rate, limited by transport of reactants, that is almost three orders of magnitude lower than measured under batch reaction conditions. The effective reaction rate predicted by the model is in good agreement with the experimentally measured rate. Furthermore, as dissolution proceeds, the formation of channels in the rock focused the flow in a few fast-flowing regions. The predicted dissolution patterns are similar to those observed experimentally. This study establishes a workflow to calibrate and validate the CTRW reactive transport model with NMR experiments.