Evolution of grain shapes by dissolution: Validation and upscaling of pore-scale simulations

We use numerical simulations to investigate the dissolution of model systems consisting of assemblies of soluble disks. Our goal is to develop an upscaling for transport limited dissolution, using pore-scale simulations for guidance. We have validated the fundamental physics of our pore-scale model by comparisons with microfluidic experiments (Dutka et al., Chem. Geol. 2020). In addition we have checked our numerical implementation by comparing with other simulation methods (Molins et al., Comput. Geo. 2020). A more detailed and quantitative check has been made by comparing with conformal mapping, which can produce nearly exact solutions for closely related models (Ladd et al., J. Fluid Mech., 2020).

In this talk I will summarize the most salient features of these studies and the key things that have been learned. Then I will describe ongoing work, which uses insights drawn from simulations of arrays of disks to suggest ways of upscaling in cases where dissolution is predominantly transport controlled. Traditional methods of upscaling, using homogenization or multiscale expansions, fail when the concentration gradients are large. Numerical simulations show that an additive decomposition of the concentration field into long and short scales, does not describe the concentration field in arrays of disks. Instead we introduce a multiplicative decomposition which is in much better agreement with simulations. The second key step is a distance-dependent rescaling of the time, which allows different REV's in the arrayto be mapped to the dissolution of a single REV.

Concentrstion field in a square (paeriodic) array of disks.