Mass transport in porous media

In order to calculate the concentration loss, according to Equation (3.77), a relationship between partial pressure of a gas species at the reaction zone and at the bulk is required. This relationship is provided by the equations regulating mass transport in porous media, as defined in Section 3.3.2. 

This tutorial paper begins with a short introduction to multicomponent mass transport in porous media. A theoretical development for application to single and multiple reaction systems is presented. Two example problems are solved. The first example is an effectiveness factor calculation for the water-gas shift reaction over a chromia-promoted iron oxide catalyst. The methods applicable to multiple reaction problems are illustrated by solving a steam reformer problem. The need to develop asymptotic methods for application to multiple reaction problems is apparent in this example. 

Quintard M, Bletzacker L, Chenu S, Whitaker S (2006) Nonlinear, multicomponent, mass transport in porous media. Chem Eng Sci 61 2643-2669 Ramkrishna D (2000) Population Balances. Academic Press, San Diego Randolph A (1964) A population balance for countable entities. Canadian J Chem Eng 42 280-281... 

Koptyug, I.V. 2011. MRI of mass transport in porous media Drying and sorption processes. Prog. Nucl. Magn. 

Carbonell, RG Whitaker, S, Heat and Mass Transfer in Porous Media. In Eundamentals of Transport Phenomena in Porous Media, Nato ASI Series, Series E Applied Sciences—No. 82 ed. Bear, J Corapcioplu, MY, eds. Marinus Nijhoff Dordrecht, The Netherlands, 1984 121. Carman, PC, Plow of Gases Through Porous Media Academic Press New York, 1956. Chae, KS Lenhoff, AM, Computation of the Electrophoretic Mobihty of Proteins, Biophysical Journal 68, 1120, 1995. 

Whitaker, S, Transport Processes with Heterogeneous Reaction. In Concepts and Design of Chemical Reactors Whitaker, S Cassano, AE, eds. Gordon and Breach Newark, NJ 1986 1. Whitaker, S, Mass Transport and Reaction in Catalyst Pellets, Transport in Porous Media 2, 269, 1987. 

Caebonelr R. G., Whitaker S., Heat and mass transfer in porous media, in Fundamentals of Transport Phenomena in Porous Media, Martinus Nijhoff, Dordrecht (1984) pp. 121-198. 

Bethke, C. M., M.-K. Lee and R. F. Wendlandt, 1992, Mass transport and chemical reaction in sedimentary basins, natural and artificial diagenesis. In M. Quintard and M. S. Todorovic (eds.), Heat and Mass Transfer in Porous Media. Elsevier, Amsterdam, pp. 421 —434. 

Berkowitz B, Emmanuel S, Scher H (2008) Non-Fickian transport and multiple rate mass transfer in porous media Water Resour Res 44, D01 10.1029/2007WR005906 Bijeljic B, Blunt MJ (2006) Pore-scale modeling and continuous time random walk analysis of dispersion in porous media. Water Resour Res 42, W01202, D01 10.1029/2005WR004578 Blunt MJ (2000) An empirical model for three-phase relative permeability. SPE Journal 5 435-445... 

Compared to rivers and lakes, transport in porous media is generally slow, three-dimensional, and spatially variable due to heterogeneities in the medium. The velocity of transport differs by orders of magnitude among the phases of air, water, colloids, and solids. Due to the small size of the pores, transport is seldom turbulent. Molecular diffusion and dispersion along the flow are the main producers of randomness in the mass flux of chemical compounds. 

The description of multicomponent gas transport in porous media at arbitrary Knudsen numbers is very complicated, especially in the transition region of Kn 0.1 -10. This problem has never been solved rigorously. The situation remains extremely complex, even if the porous medium is regarded as composed of long, straight, circular channels of equal diameter. In these circumstances a consideration of simplified and limiting situations, which are better understood, is very important. Moreover, the approximate relationship between mass fluxes of the species and concentrations can be found by an appropriate combination of the corresponding relationships for simpler situations. 

Whitaker S (1987) Mass Transport and Reaction in Catalyst Pellets. Transport in Porous Media 2 269-299... 

Based on the principle of mass conservation, the equation for non-conservative solute transport in porous media can be written (Bear 1972) ... 

Heat and mass transfers in porous media are coupled in a complicated way. On the one hand, heat is transported by conduction, convection, and radiation. On the other hand, water moves under the action of gravity and pressure gradient whilst the vapor phase moves by diffusion caused by a gradient of vapor density. Thus, the heat transfer process can be coupled with mass transfer processes with phase changes such as moisture sorption/desorption and evaporation/condensation. 

Whitaker, S. 1987, Mass transport and reaction in catalyst pellets. Transport in Porous Media, 2, 269-299. 

A total of 41 individual transport processes are listed in Table 4.1 as being the most significant ones of concern in this handbook. Seven in the hst are soil-side transport processes and the main focus of Part 2 of this chapter. Several of these processes including diffusion, advection, and fluid-to-solid mass transfer in porous media are also relevant to many other environmental compartments and are covered in more detail in other chapters of this book. Specifically the chapters are mass transport fundamentals from an environmental perspective (Chapter 2) molecular diffusion estimation methods (Chapter 5) advective porewater flux and chemical transport in bed-sediment (Chapter 11) diffusive chemical transport across water and sediment boundary layers (Chapter 12) bioturbation and other sorbed-phase transport processes in surface soils and sediments (Chapter 13), and dispersion and mass transfer in groundwater of the near-surface geologic formations (Chapter 15). 

Maraqa, M. 2001. Prediction of mass-transfer coefficients for solute transport in porous media. Journal of Contaminant Hydrology 53 153-171. 

The porosity or pore water volume fraction of total bed volume e (m m ) is obviously a key independent variable for assessing diffusive transport in porous media. The water that is contained in the bed is called the porewater or interstitial water because it fills the pores or interparticle spaces. It is the key phase for describing chemical mass transport interactions with the overlying water. Hence, all in-bed fluxes of dissolved constituents are transported in this fluid phase. 

The TDE solute module is formulated with one equation describing pollutant mass balance of the species in a representative soil volume dV = dxdydz. The solute module is frequently known as the dispersive, convective differential mass transport equation, in porous media, because of the wide employment of this equation, that may also contain an adsorptive, a decay and a source or sink term. The one dimensional formulation of the module is ... 

Lichtner PC (1988) The quasistationary state approximation to coupled mass transport and fluid-rock interaction in porous media. Geochim Cosmochim Acta 52 143-65. 

Transport of mass, energy, and momentum in porous media is a key aspect of a large number of fiber-reinforced plastic composite fabrication processes. In design and optimization of such processes, computer simulation plays an important role. Recent studies [1-14] have... 

It is extremely difficult to model macroscopic transport of mass, energy, and momentum in porous media commonly encountered in various fields of science and engineering based on microscopic transport models that account for variation of velocity and temperature as well as other quantities of interest past individual solid particles. The basic idea of porous media theory, therefore, is to volume average the quantities of interest and develop field equations based on these average quantities. 

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