Upscaling multi-component two-phase flow in porous media with partitioning coefficient

This paper deals with the upscaling of multicomponents two-phase flow in porous media. In this paper, chemical potential equilibrium at the interface between both phases is assumed to be described by a linear partitioning relationship such as Raoult or Henry’s law. The resulting macro-scale dispersion model is a set of two equations related by a mass transfer coefficient and which involves several effective coefficients. These coefficients can be evaluated by solving closure problems over a representative unit-cell. The proposed model is successfully validated through direct analytical and numerical calculations

Equivalence between volume averaging and moments matching techniques for mass transport models in porous media.

This paper deals with local non-equilibrium models for mass transport in dual-phase and dual-region porous media. The first contribution of this study is to formally prove that the time-asymptotic moments matching method applied to two-equation models is equivalent to a fundamental deterministic perturbation decomposition proposed in Quintard et al. (2001) [1] for mass transport and in Moyne et al. (2000) [2] for heat transfer. Both theories lead to the same one-equation local non-equilibrium model. It has very broad practical and theoretical implications because (1) these models are widely employed in hydrology and chemical engineering and (2) it indicates that the concepts of volume averaging with closure and of matching spatial moments are equivalent in the one-equation non-equilibrium case. This work also aims to clarify the approximations that are made during the upscaling process by establishing the domains of validity of each model, for the mobile–immobile situation, using both a fundamental analysis and numerical simulations. In particular, it is demonstrated, once again, that the local mass equilibrium assumptions must be used very carefully

Direct numerical simulations for smouldering in horizontal channel

In the present study, direct numerical simulations for smouldering in a horizontal channel are performed for both compressible and incompressible flows. The reactant gas is passing through the char surface, where the chemical reaction is going to take place. For the sake of simplicity, the smouldering is treated to be a single step chemical reaction. In the incompressible flow, a set of governing parameters are discussed to elucidate their influences on the process of smouldering. Furthermore, the variations of density and dynamic viscosity of gaseous mixture are taken into account in the compressible flow. The comparison between the compressible and incompressible flows reveals that the effects of local compressibility and gaseous mixture on the propagation of smouldering wave are trivial

Numerical Simulations For Smouldering in a Horizontal Channel: Comparisons between variable density based formulation and incompressible one

In the present study, numerical simulations for smoldering in a horizontal channel are performed for both compressible and incompressible flows. The reactant gas is passing through the char surface, where the chemical reaction is going to take place. For the sake of simplicity, the smoldering is treated to be a single step chemical reaction. In the incompressible flow, a set of governing parameters are discussed to elucidate their influences on the process of smoldering. Furthermore, the variations of density and dynamic viscosity of gaseous mixture are taken into account in the compressible flow. The comparison between the compressible and incompressible flows reveals that the effects of local compressibility and gaseous mixture on the propagation of smoldering wave are striking

A diffuse interface model for solid-liquid-air dissolution problems based on a porous medium theory

The underground rock may be dissolved by the flows of groundwater where the dissolution mainly happens at the liquid-solid interface. In many practical cases, the underground cavities are not occupied only by the water, but also the gas phase, e.g., air, CO2. In this case, there are solid-liquid-gas three phases. Normally, the air does not participate the dissolution. However, it may influence the dissolution as the position of the solid-liquid interface may gradually change with the dissolution process. Simulating the dissolution problems with multi-moving interfaces is a difficult but rather interesting task. In this paper, we propose a diffuse interface model (DIM) to simulate the three-phase dissolution problem, based on a porous medium theory and a volume averaging theory. The interfaces are regarded as continuous layers where the phase indicator (for the solid-liquid interface) and the phase saturation (for the liquid-gas interface) vary rapidly but smoothly

Modeling non-equilibrium mass transport in biologically reactive porous media.

We develop a one-equation non-equilibrium model to describe the Darcy-scale transport of a solute undergoing biodegradation in porous media. Most of the mathematical models that describe the macroscale transport in such systems have been developed intuitively on the basis of simple conceptual schemes. There are two problems with such a heuristic analysis. First, it is unclear how much information these models are able to capture; that is, it is not clear what the model's domain of validity is. Second, there is no obvious connection between the macroscale effective parameters and the microscopic processes and parameters. As an alternative, a number of upscaling techniques have been developed to derive the appropriate macroscale equations that are used to describe mass transport and reactions in multiphase media. These approaches have been adapted to the problem of biodegradation in porous media with biofilms, but most of the work has focused on systems that are restricted to small concentration gradients at the microscale. This assumption, referred to as the local mass equilibrium approximation, generally has constraints that are overly restrictive. In this article, we devise a model that does not require the assumption of local mass equilibrium to be valid. In this approach, one instead requires only that, at sufficiently long times, anomalous behaviors of the third and higher spatial moments can be neglected; this, in turn, implies that the macroscopic model is well represented by a convection–dispersion–reaction type equation. This strategy is very much in the spirit of the developments for Taylor dispersion presented by Aris (1956). On the basis of our numerical results, we carefully describe the domain of validity of the model and show that the time-asymptotic constraint may be adhered to even for systems that are not at local mass equilibrium

Upscaling for Adiabatic Solid–Fluid Reactions in Porous Medium Using a Volume Averaging Theory

In this paper, an upscaling study of solid–fluid combustion in porous medium with homogeneous and heterogeneous heat sources is carried out using a volume averaging theory. For the sake of simplicity, the reaction rate is assumed to be of first-order Arrhenius type and convection is not taken into account. Local thermal non-equilibrium is considered between the solid and fluid phases. During the resolution of closure problems, periodic boundary condition is utilized in order to determine the effective coefficients in the upscaled model. The obtained macroscale theory is validated against direct numerical simulation results for two typical porous medium geometries made of simple unit cells, namely unconsolidated and consolidated porous media. The comparisons between the present upscaled and microscale results are conducted for various Damköhler numbers for both homogeneous and heterogeneous reaction cases. It has been found that, for the low Damköhler number cases, the temperature profiles generated from the derived upscaled model are in accordance with that of the microscale model. For the high Damköhler number cases, however, the macroscale model fails to predict the combustion front and temperature profile, which evidently suggests that the effects of neglected terms during the upscaling process should be re-examined carefully in further investigations

The impact of compaction, moisture content, particle size and type of bulking agent on initial physical properties of sludge-bulking agent mixtures before composting

This study aimed to experimentally acquire evolution profiles between depth, bulk density, Free Air Space (FAS), air permeability and thermal conductivity in initial composting materials. The impact of two different moisture content, two particle size and two types of bulking agent on these four parameters was also evaluated. Bulk density and thermal conductivity both increased with depth while FAS and air permeability both decreased with it. Moreover, depth and moisture content had a significant impact on almost all the four physical parameters contrary to particle size and the type of bulking agent

Upscaling of mass and thermal transports in porous media with heterogeneous combustion reactions

The present paper aims at an upscaled description of coupled heat and mass processes during solid–fluid combustion in porous media using volume-averaging theory (VAT). The fluid flows through the pores in a porous medium where a heterogeneous chemical reaction occurs at the fluid–solid interface. The chemical model is simplified into a single reaction step with Arrhenius kinetic law, but no assumption of local thermal equilibrium is made. An array of horizontal channels is chosen for the microstructure. The corresponding effective properties are obtained by solving analytically the closure problems over a representative unit cell. For a range of Péclet and Δ numbers, the results of the upscaled model are compared with microscale computations found in the literature. The results show that, under the same circumstances, the upscaled model is capable of predicting the combustion front velocity within an acceptable discrepancy, smaller than 1% when compared to the analytical solution. Furthermore, it has been found that for the Péclet and Δ numbers considered in this study, the fluid concentration and temperature profiles that stem from the present upscaled model are in accordance with those obtained using a microscale model