Numerical simulation of fluid - mineral interaction and reactive transport in porous and fractured media

Porous media, ubiquitous to a number of environmental and engineering systems, exhibit heterogeneity on a continuity of scales. This, combined with nonlinear processes, complex topology and coupling between different physical processes (e.g. reaction, hydrodynamics and geometry evolution), significantly complicates numerical modeling efforts where a balance between computational efficiency and accuracy has to be stricken. While effective medium theories represent computationally convenient alternatives to pore-scale models, the true macroscopic behavior of the system often significantly deviates from mean field approximations: this is due to (i) strong coupling between processes occurring at different scales and (ii) localized invalidation of the macroscale approximation. Moreover, accurate modeling of flow and reactive transport at the pore-scale calls for high-fidelity numerical methods that have a high order of accuracy, are capable of handling complex geometry and physics of the porous media problems and require less computational resources. The reactive transport problem in porous media, typically involves moving boundaries (i.e. solid-fluid interfaces), which multiply the numerical challenges. Different mathematical and modeling approaches have been developed to describe, understand and predict the system behavior at different scales, ranging from the pore to the system-scale, although handling across-scale coupling in reactive porous media systems with evolving geometries still tests the limits of current computational models. In this study, we focus on the development of novel computational tools to model reactive transport in porous media, where lack of scale separation occurs and/or where reactions may alter pore-scale topology. Such models are able to handle (i) lack of scale separation, and (ii) the geometric evolution of the pore-structure due to localized reactions within an Immersed Boundary Method (IBM) framework, while retaining model predictivity and containing the computational costs, respectively. To this end, we developed a hybrid (multi-scale) model for reactive transport in porous and fractured media that employs finer scales (pore-scale models), whenever the macroscopic models break down, and uses the computationally cheaper Darcy-scale models when their fundamental assumptions are valid. Its accuracy and capabilities have been tested for several transport scenarios. To address the challenge of numerical implementation of governing equations within the complex geometries, a high-order Immersed Boundary Method is built that is able to handle various boundary conditions relevant to mass transport in reactive systems. We have extended this IBM for moving interface problems by developing a level-set IBM (LSIBM) that can track the interface separating fluid and solid accurately. This fully Cartesian grid based method is used to investigate the dissolution and precipitation of chemical species in fractures, and the role of surface roughness in altering the reaction rates is studied

Keywords: Energy Resources Engineering.
Advisor: Battiato Ilenia 
Kovscek Anthony R. (Anthony Robert)
Tchelepi Hamdi