PORE-SCALE MODELING OF FLOW AND REACTIVE TRANSPORT IN POROUS MEDIA

Flow and reactive transport of fluids in porous media are observed in a wide variety of fields and applications such as hydrology, contaminated site remediation and petroleum engineering. Concerning the environmental issues, fate and transport of dissolved contaminants in natural porous media is a fundamental aspect to understand pollutants migration in groundwater and to identify the most appropriate technologies to remove these compounds from subsurface (i.e. the vadose zone and the groundwater). The traditional approach used to study the motion of fluids (single or multi-phase) and transport of dissolved substances within porous media is based on a macroscopic representation, founded on the continuum hypothesis (Bear, 1972). At this scale, pore-scale effects are embedded into the model through a set of constitutive equations such as the phenomenological Darcy’s law for flow in saturated porous media (Hubbert, 1956; Bear, 1972), Richard’s equation in variable saturated media (Richards, 1931; Van Genuchten, 1980) and the advection-dispersion equation for solute transport (Bear, 1972). When the continuum description breaks down, the need to investigate a more detailed scale as the pore-scale brings to use the Navier-Stokes equations (NSE) and the advection-diffusion (and reaction) equation (ADE), able to capture microscopic-scale gradients in concentration resulting from transport and a non-uniform distribution of reactive material (Steefel et al., 2005; Blunt et al., 2013). Pore-scale modeling has developed rapidly over the last decades, thanks to the development of both direct 3D imaging of the pore space and faster and more efficiency computing tools. It can be used to predict macroscopic properties of porous media that are difficult to obtain experimentally and provides the opportunity to investigate phenomena impossible to be obtained by laboratory experiments for single and multi-phase fluids. In the framework of pore-scale modeling, the lattice Boltzmann method (LBM) is able to solve the NSE for incompressible fluids and ADE in porous media, which is emerged over the last decades as an alternative approach for computational fluid dynamics (CFD) (Chen and Doolen, 1998; Succi, 2001; Aidun and Clausen, 2010). Unlike the conventional CFD schemes based on discretization of macroscopic continuum equations, the LBM is based on microscopic models and mesoscopic kinetic equation. The main features are the relatively ease to code, versatility to model different process, handle complex boundary conditions and its efficiency for parallel platforms (Latt, 2009, Coon et al., 2014). For the above-mentioned reasons, the goal of my research is the study of pore-scale effects on different flow and transport processes, which have a close relationship with contaminant dynamics at a macroscopic scale (i.e. laboratory and field scale). Each of these processes is addressed in the following chapters of the thesis. The thesis consists of a collection of scientific papers, except for the first chapter, submitted to or already published in international journals and is organized as follows. In chapter I, the basics of the LB algorithm are introduced. The numerical schemes for the simulation of fluid flow and transport process of a concentration field are described. In chapter II, the effects of the pore spatial distribution on seepage velocity through numerical simulations of 3D fluid flow performed by the lattice Boltzmann method are investigated. The goal of this work is to evaluate the sensitivity of the flow, through the seepage velocity, inside a porous medium to the spatial distribution of the pores size and to address the uncertainty associated to the sample size and resolution. To this scope, we generate 3D porous media using a geostatistical method based on random spatially correlated fields applied at the pore-scale (typically from tens to hundreds μm). The use of 3D domains allows handling porous media with realistic porosity compared to 2D structures. Finally, a sensitivity analysis of the macroscopic velocity is carried out in relation to two semi-variograms models (or correlation functions) and different spatial resolutions. In Chapter III, the impact of heterogeneity through pore-scale flux and transport LBM simulations are carried out. One of the effects that heterogeneities produce in the framework of contaminated sites remediation is associated with the retention of pollutants in the finest (or less mobile for an effective transport) regions of the porous media, where contaminants are released by diffusion to more mobile zones after the concentration in the latter is significantly reduced because of efficient transport. Despite its microscopic nature, it may have important implications for macroscale pollutants transport. The process of mass transfer from low to high mobility regions at the back end of a contaminant plume has referred to back diffusion (also defined as matrix diffusion). The main question that we address in this study is the extent to which spatial heterogeneities in the structure (porosity and permeability) of the host porous medium influences the rate of migration of dissolved species (e.g. contaminants). Chapter IV is dedicated to reactive transport at the pore-scale. A lattice Boltzmann model is developed for surface reaction taking place at the interface between solid-fluids and multiphase fluids (Di Palma et al., 2015). The phase-field approach is used to identify the interface and its orientation, the concentration of reactant at the interface is then calculated iteratively to impose the correct reactive flux condition. The main advantages of the model is that interfaces are considered part of the bulk dynamics and the reactive scheme is introduced in the classical LBM algorithm; as a consequence, the model’s implementation and performance is independent of the interface geometry and orientation. Results obtained with the developed model are compared to analytical solution for three different benchmark tests.