Diffusive mass transport in the fluid–porous medium inter-region: Closure problem solution for the one-domain approach (original) (raw)
Related papers
On diffusion, dispersion and reaction in porous media
Chemical Engineering Science, 2011
The upscaling process of mass transport with chemical reaction in porous media is carried out using the method of volume averaging under diffusive and dispersive conditions. We study cases in which the (first-order) reaction takes place in the fluid that saturates the porous medium or when the reaction occurs at the solid-fluid interface. The upscaling process leads to average transport equations, which are expressed in terms of effective medium coefficients for (diffusive or dispersive) mass transport and reaction that are computed by solving the associated closure problems. Our analysis shows that these effective coefficients depend, in general, upon the nature and magnitude of the microscopic reaction rate as well as of the essential geometrical structure of the solid matrix and the flow rate. This study also shows that if the reaction rate at the microscale is arbitrarily large, the capabilities of the upscaled models are hindered, which is in agreement with the breakdown of the physical sense of the microscale formulation.
Transport in Porous Media, 2009
In this paper, mass transfer at the fluid-porous medium boundaries is studied. The problem considers both diffusive and convective transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., Pe 1), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a microporous medium.
Multiphase mass transport with partitioning and inter-phase transport in porous media
Chemical Engineering Science, 2006
We derive the effective mass-transfer coefficient between two fluid phases in a porous medium, one of which is flowing and the other is immobile. A passive tracer is advected by the flowing phase, becomes partitioned at the fluid-fluid interface and diffuses in the immobile phase. We use traditional volume-averaging methods to obtain a unit-cell boundary-value problem for the calculation of the effective mass-transfer coefficient. The problem is controlled by the Peclet number of the flowing phase, by a second dimensionless parameter that captures diffusion and partition in the two phases and by the geometrical properties of the porous medium.
Water Resources Research, 2013
Diffusive mass transfer into and out of intragranular micropores (''intragranular diffusion'') plays an important role in the transport of some groundwater contaminants. We are interested in understanding the combined effect of pore-scale advection and intragranular diffusion on solute transport at the effective porous medium scale. We have developed a 3-D pore-scale numerical model of fluid flow and solute transport that incorporates diffusion into and out of intragranular pore spaces. A series of numerical experiments allow us to draw comparisons between macroscopic measures computed from the pore-scale simulations (such as breakthrough curves) and those predicted by multirate mass transfer formulations that assume complete local mixing at the pore scale. In this paper we present results for two model systems, one with randomly packed uniform spherical grains and a second with randomly packed spheres drawn from a binary grain size distribution. Non-Fickian behavior was observed at all scales considered, and most cases were better represented by a multirate mass transfer model even when there was no distinct secondary porosity (i.e., no intragranular diffusion). This suggests that pore-scale diffusive mass transfer processes between preferential flow paths and relatively immobile zones within the primary porosity may have significant impact on transport, particular in low-concentration tails. The application of independently determined mass transfer rate parameters based on an assumption of well-mixed concentrations at the pore scale tends to overestimate the amount of mass transfer that occurs in heterogeneous pore geometries in which preferential flow leads to incomplete pore-scale lateral mixing.
Drying Technology, 2014
The scale-up and scale-down process is of great importance regarding modeling of mass transport phenomena in porous media. Three numerical simulations of porous media for three different scales were developed and validated in this study, analyzing the mass transport phenomena for each scale. More precisely, the first system is a spheres assemblage of various spatial distributions and sizes (mesoscopic), the second is a porous box (macroscopic), and the third is a sphere-in-cell model (microscopic). It was found that the porous structure-shape, size, and positioning-of the spheres at the mesoscopic scale have significant effects on the adsorption efficiency (up to 10%) of highly convective regimes. It was also concluded that a microscopic description at the pore scale is insufficient to adequately describe mass transport phenomena in porous media due to discontinuities of the structure and high local velocity. By comparing the results from the three scales, we obtained a method of matching all geometrical, flow, and transport parameters when a scale transition occurs. The qualitative description of transport phenomena through the three scales and their identical behavior demonstrates the method's effectiveness.
Mathematical model for the mass transport in multiple porous scales
Journal of Food Engineering, 2018
The transport of species in a vegetable matrix was modelled and studied based on a phenomenological model, in which a solid composed by the cells, pores and tissues was considered. The model is able to predict the multi-scale mass transport by defining only one effective diffusion coefficient, which made by proposing an inter-scale resistance constant. This parameter is a measure of the difficulty to the mass transport between two scales. The model was successfully validated with experimental data on the mass transport in both an organic and an inorganic matrix, which demonstrate the versatility of the model herein proposed.
Pore-scale modelling of transport phenomena in homogeneous porous media
1999
I wish to express my sincere gratitude to the people and organisations who inspired and assisted the development of this thesis. Many thanks to Prof Prieur du Plessis, my promoter, for his guidance, collaborative research approach and the interest he took in my work. He was supportive in many aspects concerning my dissertation and his motivation, friendly attitude and availability to discuss sections of this study at literally any time meant a lot to me. I, therefore, greatly acknowledge Prieur's judgement and leadership in the project. I would like to thank Prof J. LeGrand for inviting me to the Laboratoire de Genie de Procedes, IUT in Saint-Nazaire. He provided the opportunity to meet scientists in the same field and participate in laboratory experiments. I am also grateful to Dr Agnes Montillet for the numerous fruitful discussions we had during my visit to the IUT. She was very helpful in providing data obtained from her experiments and she generously shared her knowledge. Much of the credit for this dissertation must go to my wife, Lyndsey, who offered encouragement and support over the years. I would also like to thank Lyndsey for her perfectionistic approach in producing all of the figures in this dissertation. Finally, I would like to thank the FRD, the University of Stellenbosch and the Harry Crossley Fund for providing financial assistance. This enabled me to do three years full time research.
Modeling of flow and mass transport in granular porous media
Open Physics, 2011
The scope of this work is to estimate the effective mass-transfer coefficient in a two-phase system of oil and water fluid droplets, both being in a porous medium. To this end, a tracer is advected from the flowing aqueous phase to the immobile non-aqueous one. Partitioning at the fluid-fluid interface and surface diffusion are also taken into account. By using spatial/volume-averaging techniques, the appropriately simplified boundary-value problems are described and numerically solved for the flow velocity field and for the transport problem. The problem was found to be controlled by the Peclet number of the flowing phase, the dimensionless parameter Λ, containing both diffusion and partition in the two phases, as well as the geometrical properties of the porous structure. It is also verified that the usually involved unit cell-configurations underestimate the mass transport to the immobile phase.
A volume averaging approach for asymmetric diffusion in porous media
The Journal of Chemical Physics, 2011
Asymmetric diffusion has been observed in different contexts, from transport in stratified and fractured porous media to diffusion of ions and macromolecular solutes through channels in biological membranes. Experimental and numerical observations have shown that diffusion is facilitated in the direction of positive void fraction (i.e., porosity) gradients. This work uses the method of volume averaging in order to obtain effective medium equations for systems with void fraction gradients for passive and diffusive mass transport processes. The effective diffusivity is computed from the solution of an associated closure problem in representative unit cells that allow considering porosity gradients. In this way, the results in this work corroborate previous findings showing that the effective diffusivity exhibits important directional asymmetries for geometries with void fraction gradients. Numerical examples for simple geometries (a section with an obstacle and a channel with varying cross section) show that the diffusion asymmetry depends strongly on the system configuration. The magnitude of this dependence can be quantified from the results in this work.
Experimental studies of mass transport in porous media with local heterogeneities
Journal of Contaminant Hydrology, 1989
The effect of local heterogeneities in a porous medium, which are randomly distributed, upon longitudinal spreading in groundwater transport problems is described and related to the permeability ratio between the heterogeneities and the surrounding porous medium. Numerous experimental runs using simplified model aquifers provide a large data base. The measured breakthrough curves indicate the transport behavior of the system. They are compared with the solution of the classical Fickian advection-dispersion equation for the given boundary conditions as well as with a numerical approach of a modified transport formulation following the dual porosity concept of Coats and Smith. A significant difference in the transport behavior depending on the permeability of the heterogeneities is observed: while mass transport in the model aquifers with local heterogeneities of higher relative permeability remained Fickian, local heterogeneities of lower relative permeability caused a marked tailing and a significant spreading of the tracer. In the dual porosity formulation of transport the transfer coefficient had to be fitted, while the remaining transport parameter could be determined directly.