Phase change in porous media

FIGURE 9.1 Aspects of treatment of transport, reaction, and phase change in porous media. 

Solid-Liquid Phase Change in Porous Media... 

Single-Component Systems. As an example of solid-liquid phase change in porous media, we consider melting of the solid matrix by flow of a superheated liquid through it. The analysis, based on local thermal nonequilibrium between solid and liquid phases, has been performed by Plumb [140] and is reviewed here. 

The two-phase flow in porous media (a three-phase system) is approached from the pore-level fluid mechanics The pertinent forces and their expected contributions are examined, and when available, empirical results are used. After arriving at a set of volume-averaged governing conservation and constitutive equations, some liquid-vapor phase change problems are examined. 

The definition of tortuosity factor in Eq. 3.5.b-2 includes both the effect of altered diffusion path length as well as changing cross-sectional areas in constrictions for some applications, especially with two-phase fluids in porous media, it may be better to keep the two separate (e.g., Van Brakel and Heertjes [39]). This tortuosity factor should have a value of approximately 3 for loose random pore structures, but measured values of 1.5 up to 10 or more have been reported. Satterfield [40] states that many common catalyst materials have a t 2 3 to 4 he also gives further data. 

Considerable effort has been dedicated to understand the changes on thermodynamical properties of gas and liquids due to their confinement in porous media [1-3]. The special case of water in porous silica (silica gels, zeolites, vycor. ..) [4-7] has grown interest due to large field of application, from geophysics (water and silica are the most represented on earth) to industry and environment (phase separation, catalysis...). 

Many numerical models make additional assumptions, valid if only some specific questions are being asked. For example, if one is not interested in the start-up phase or in changing the operation of a fuel cell, one may apply the steady state condition that time-independent solutions are requested. In certain problems, one may disregard temperature variations, and in the free gas ducts, laminar flow may be imposed. The diffusion in porous media is often approximated by an assumption of isotropy for the gas diffusion or membrane layer, and the coupling to chemical reactions is often simplified or omitted. Water evaporation and condensation, on the other hand, are often a key determinant for the behaviour of a fuel cell and thus have to be modelled at some level. 

Udell, K.S. Heat transfer in porous media considering phase change and capillarity... the heat pipe effect. J. Heat Mass Transfer 1985, 28 (2), 485-495. 

K. S. Udell, Heat Transfer in Porous Media Considering Phase Change and Capillarity—The Heat Pipe Effect, Int. J. Heat Mass Transfer, (28) 485-495,1985. 

Vilfan and Yuk " discussed the nuclear spin relaxation resulting from molecular translational dilfusion of a liquid crystal in the isotropic phase confined to spherical microcavities. Their analysis can be also applied to other fluids in porous media. Nilsson et used high-resolution NMR and high-resolution diffusion-ordered spectroscopy (DOSY) for the characterization of selected Port wine samples of different ages with the aim of identifying changes in composition. 

The salinity at which the middle phase microemulsion contains equal volumes of oil and brine is defined as the optimal salinity. The oil recovery is found to be maximum at or near the optimal salinity (8,10). At optimal salinity, the phase separation time or coalescence time of emulsions and the apparent viscosity of these emulsions in porous media are found to be minimum (11,12). Therefore, it appears that upon increasing the salinity, the surfactant migrates from the lower phase to middle phase to upper phase in an oil/brine/surfactant/alcohol system. The -> m u transition can be achieved by also changing any of the following variables Temperature, Alcohol Chain Length, Oil/Brine Ratio, Surfactant Solution/Oil Ratio, Surfactant Concentration and Molecular Weight of Surfactant. The present paper summarizes our extensive studies on the low and high surfactant concentration systems and related phenomena necessary to achieve ultralow interfacial tension in oil/brine/surfactant/alcohol systems. 

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. 

The problem of capillary equilibrium in porous media is complicated from both experimental and theoretical points of view. The mechanisms of saturation and depletion of the porous medium are essentially nonequilibriiun. Further equilibration is due to slow processes like diffusion. The process of equilibration may be unfinished, since no significant changes of fluid distribution may occur during the time of an experiment. This especially relates to the so-called discontinuous condensate existing in the form of separate drops. As a result, thermodynamic states, which are not fully equilibrated, are interpreted from the practical point of view as equilibrium [28]. To the best of our knowledge, a consistent theory of such quasiequihbrium states has not yet been developed. In the following, we discuss the possible states of the two-phase mixtures in a porous medium, assuming complete thermodynamic equihbrium. This serves as a first approximation to a more complicated picture of the realistic fluid distribution in porous media. 

In this chapter we define what is meant by a shock-wave equation of state, and how it is related to other types of equations of state. We also discuss the properties of shock-compressed matter on a microscopic scale, as well as discuss how shock-wave properties are measured. Shock data for standard materials are presented. The effects of phase changes are discussed, the measurements of shock temperatures, and sound velocities of shock materials are also described. We also describe the application of shock-compression data for porous media. 

A similar model has been applied to the modeling of porous media with condensation in the pores. Capillary condensation in the pores of the catalyst in hydroprocessing reactors operated close to the dew point leads to a decrease of conversion at the particle center owing to the loss of surface area available for vapor-phase reaction, and to the liquid-filled pores that contribute less to the flux of reactants (Wood et al., 2002b). Significant changes in catalyst performance thus occur when reactions are accompanied by capillary condensation. A pore-network model incorporates reaction-diffusion processes and the pore filling by capillary condensation. The multicomponent bulk and Knudsen diffusion of vapors in each pore is represented by the Maxwell-Stefan model. 

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