A fully coupled 3D transport model in SPH for multi-species reaction-diffusion systems

In this paper we present a fully generalized transport model for multiple species in complex two and three-dimensional geometries. Based on previous work [1] we have extended our interfacial reaction-diffusion model to handle arbitrary numbers of species allowing for coupled reaction models. Each species is tracked independently and we consider different physics of a species with respect to the bulk phases in contact. We use our SPH model to simulate the reaction-diffusion problem on a pore-scale level of a solid oxide fuel cell (SOFC) with special emphasize on the effect of surface diffusion

FLUID FLOW, SOLUTE MIXING AND PRECIPITATION IN POROUS MEDIA

Reactions that lead to the formation of mineral precipitates, colloids or growth of biofilms in porous media often depend on the molecular-level diffusive mixing. For example, for the formation of mineral phases, exceeding the saturation index for a mineral is a minimum requirement for precipitation to proceed. Solute mixing frequently occurs at the interface between two solutions each containing one or more soluble reactants, particularly in engineered systems where contaminant degradation or modification or fluid flow are objectives. Although many of the fundamental component processes involved in the deposition or solubilization of solid phases are reasonably well understood, including precipitation equilibrium and kinetics, fluid flow and solute transport, the deposition of chemical precipitates, biofilms and colloidal particles are all coupled to flow, and the science of such coupled processes is not well developed. How such precipitates (and conversely, dissolution of solids) are distributed in the subsurface along flow paths with chemical gradients is a complex and challenging problem. This is especially true in systems that undergo rapid change where equilibrium conditions cannot be assumed, particularly in subsurface systems where reactants are introduced rapidly, compared to most natural flow conditions, and where mixing fronts are generated. Although the concept of dispersion in porous media is frequently used to approximate mixing at macroscopic scales, dispersion does not necessarily describe pore-level or molecular level mixing that must occur for chemical and biological reactions to be possible. An example of coupling between flow, mixing and mineral precipitation, with practical applications to controlling fluid flow or contaminant remediation in subsurface environments is shown in the mixing zone between parallel flowing solutions. Two- and three-dimensional experiments in packed-sand media were conducted where solutions containing calcium and carbonate ions came into contact along a parallel flow boundary and mixed by dispersion and diffusion. The result is the propagation of calcium carbonate precipitates along the solution-solution boundary in the direction of flow. As carbonate precipitates fill the pore space mixing of the two solutions is restricted and therefore precipitation, flow, and transport are coupled. The distribution of carbonate phases is a complex interaction involving precipitation and dissolution kinetics, which are functions of pore-scale saturation indices and solute ratios, heterogeneous vs. homogeneous nucleation and growth mechanisms and changes in porosity and flow. Experimental and modeling results illustrate challenges in understanding the macroscopic and microscopic phenomena that depend on solute mixing, the relevance of molecular and pore-scale processes to the macroscopic behavior, and potential impact on metal mobility in porous media. Mineral precipitation and changes in porosity are simulated at the pore-scale using the Smooth Particle Hydrodynamics method. Macroscopic simulations were performed using discretized, continuum-scale modeling with parameterization representing macroscopic media properties. One of the modeling goals is to use pore-scale simulations to provide the basis for parameterization of macroscopic (more practical) model predictions

Unsaturated flow in heterogeneous soils with spatially distributed uncertain hydraulic parameters

Uncertain soil properties are often modeled as random fields. This renders the unsaturated flow equations stochastic. Determining statistics of pressure head is nontrivial, since the Richards equation is highly nonlinear. The prevalent approach is to linearize relative hydraulic conductivity around the ensemble mean pressure head, which often leads to significant errors. Recently, an approach has been proposed to avoid such a linearization for the Gardner model, with the soil parameter a being a random variable. We generalize this approach by allowing the latter to be a random field. This is achieved by means of a partial mean-field approximation. Using two-dimensional infiltration into a heterogeneous soil with uncertain hydraulic parameters as an example, we demonstrate that our predictions of the mean pressure head and its variance remain accurate for moderately variable systems. The robustness of our solutions increases with the correlation length of the Gardner parameter

Modeling Residual NAPL in Water-Wet Porous Media

A model is outlined that predicts NAPL which is held in pore wedges and as films or lenses on solid and water surfaces and contributes negligibly to NAPL advection. This is conceptually referred to as residual NAPL. Since residual NAPL is immobile, it remains in the vadose zone after all free NAPL has drained. Residual NAPL is very important because it is a long-term source for groundwater contamination. Recent laboratory experiments have demonstrated that current models for predicting subsurface NAPL behavior are inadequate because they do not correctly predict residual NAPL. The main reason for the failure is a deficiency in the current constitutive theories for multiphase flow that are used in numerical simulators. Multiphase constitutive theory governs the relations among relative permeability, saturation, and pressure for fluid systems (i.e., air, NAPL, water). In this paper, we outline a model describing relations between fluid saturations and pressures that can be combined with existing multiphase constitutive theory to predict residual NAPL. We test the revised constitutive theory by applying it to a scenario involving NAPL imbibition and drainage, as well as water imbibition and drainage. The results suggest that the revised constitutive theory is able to predict the distribution of residual NAPL in the vadose zone as a function of saturation-path history. The revised model describing relations between fluid saturation and pressures will help toward developing or improving numerical multiphase flow simulators

Modeling Residual NAPL in Water-Wet Porous Media

A model is outlined that predicts NAPL which is held in pore wedges and as films or lenses on solid and water surfaces and contributes negligibly to NAPL advection. This is conceptually referred to as residual NAPL. Since residual NAPL is immobile, it remains in the vadose zone after all free NAPL has drained. Residual NAPL is very important because it is a long-term source for groundwater contamination. Recent laboratory experiments have demonstrated that current models for predicting subsurface NAPL behavior are inadequate because they do not correctly predict residual NAPL. The main reason for the failure is a deficiency in the current constitutive theories for multiphase flow that are used in numerical simulators. Multiphase constitutive theory governs the relations among relative permeability, saturation, and pressure for fluid systems (i.e., air, NAPL, water). In this paper, we outline a model describing relations between fluid saturations and pressures that can be combined with existing multiphase constitutive theory to predict residual NAPL. We test the revised constitutive theory by applying it to a scenario involving NAPL imbibition and drainage, as well as water imbibition and drainage. The results suggest that the revised constitutive theory is able to predict the distribution of residual NAPL in the vadose zone as a function of saturation-path history. The revised model describing relations between fluid saturation and pressures will help toward developing or improving numerical multiphase flow simulators

A fully coupled 3D transport model in SPH for multi-species reaction-diffusion systems

In this paper we present a fully generalized transport model for multiple species in complex two and three-dimensional geometries. Based on previous work [1] we have extended our interfacial reaction-diffusion model to handle arbitrary numbers of species allowing for coupled reaction models. Each species is tracked independently and we consider different physics of a species with respect to the bulk phases in contact. We use our SPH model to simulate the reaction-diffusion problem on a pore-scale level of a solid oxide fuel cell (SOFC) with special emphasize on the effect of surface diffusion

Intermittent Properties of Flow in Porous Media

International audienceFrom numerical simulations of pore-scale flow in porous media, we demonstrate the existence of an intermittent-like behaviour of Lagrangian velocities similar to the one observed in turbulent flows. This phenomenon, characterized by non-Gaussian distributions of Lagrangian velocity increments and long-range correlation of Lagrangian accelerations, is at the origin at the breakdown of the classical upscaled models. For transport in porous media this is manifested by anomalous scaling of the temporal evolution of the characteristic dispersion length, called anomalous dispersion. Long range correlation is related to the existence of stagnation zones and localized high velocity channels. While for turbulence, intermittency of Lagrangian velocities can be represented by multifractal random walk, for porous media we show that the dynamical picture is different and that this process is well captured by a correlated continuous time random walk