Improved Lattice Boltzmann Models for Precipitation and Dissolution

A challenge when modeling mineral growth inside the pore space of a porous media is to minimize the effect of the computational grid on the shape of the minerals being formed. Pore surface area and volume are important quantities in estimating upscaled permeability and effective rate equations, which emphasize the importance of models that minimize or completely eliminate grid effects. In this paper, we study how the initial orientation of the solid structure on the numerical grid affects the growth pattern due to precipitation in a lattice Boltzmann model. We have implemented a volume of fluid method to represent the solid interface, and we introduce a surface tension term that extensively reduces the dependency on the underlying numerical grid. We study both diffusion-limited and reaction-limited precipitation. In the diffusion-limited case, instabilities will develop on small scales. The surface tension term effectively introduces a short wavelength cut off which limits the unstable precipitation and reduces grid effects. We argue that the surface tension term is needed to obtain a growth pattern independent of the initial orientation on the underlying grid in the diffusion-limited case, and that simpler models can be used in the reaction-limited case.     

Pore-Scale Level Set Simulations of Capillary-Controlled Displacement with Adaptive Mesh Refinement

Transport in Porous Media - Multiphase flow simulations on imaged porous rock structures require numerical methods that are accurate and robust when applied on complex geometries. A key element in...     

Stress-driven phase transformation and the roughening of solid-solid interfaces

The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials with different porosities under normal compression stresses. This instability is triggered by a finite jump in the free energy density across the interface, and it leads to the formation of fingerlike structures aligned with the principal direction of compaction. The model is proposed as an explanation for the roughening of stylolites-irregular interfaces associated with the compaction of sedimentary rocks that fluctuate about a plane perpendicular to the principal direction of compaction.