Porous media phase distributions

ENTROPY EFFECTS IN PHASE DISTRIBUTION POROUS MEDIA 31... 

Nonadsorptive retention of contaminants can also be beneficial. For example, oil droplets in the subsurface are effective in developing a reactive layer or decreasing the permeability of a sandy porous medium. Coulibaly and Borden (2004) describe laboratory and field studies where edible oils were successfully injected into the subsurface, as part of an in-situ permeable reactive barrier. The oil used in the experiment was injected in the subsurface either as a nonaqueous phase liquid (NAPL) or as an oil-in-water emulsion. The oil-in-water emulsion can be distributed through sands without excessive pressure buildup, contrary to NAPL injection, which requires introduction to the subsurface by high pressure. 

The distribution coefficient Kj (Equation 2) is defined as the volume fraction of pores, in a stationary phase, which is effectively permeated by a solute of a given size. V0 is the interstitial volume of the porous medium, measured by the elution volume of a high molar mass solute that is totally excluded from the matrix pores. Ve is the elution volume of the product of interest. Vs represents the total solvent volume within the pores, available for small solutes. 

Fig. 5. Distribution of covering radius rc. The solid phase of the porous medium is covered by circles of radius rc and the color of circles depends on circle radius. The integral distribution of covering radius G(rc) is then displayed.

The spatial distribution of matter in a porous medium can be typically represented by the phase function Z(x), defined as follows ... 

In SAXS, the amplitude function of the coherently-scattered monochromatic X-ray beam is proportional to the electron density distribution pe(r) integrated over the san le volume. In a two-phase porous medium such as the AAO membranes, the electron density is defined by two possible values, and we may write the spatial distribution as ... 

Effect of Porous Medium Characteristics. Several characteristics of the porous medium, including the average pore size, pore size distribution, and the wettability of the porous medium, can influence the flow of W/O emulsions. Very little information is available on these issues. The role of wettability is intuitively obvious. A water-wet medium would be more conducive to capture of the water droplets at pore walls. This capture facilitates formation of a free-water phase. An oil-wet medium, on the other... 

Pore-radius distributions and ab-/ desorption isotherms are important structural characteristics of generic porous media [80, 88]. The absorption isotherm provides a relation for the liquid uptake of a porous medium under controlled external conditions, viz., the pressure of an external fluid. Within a bounded system, such as a cylindrical tube, a discontinuity of the pressure field across the interface between two fluid phases exists. The corresponding pressure difference is called capillary pressure, Pc. In the case of contact between gas phase, Pg, and liquid water phase, P1, the capillary pressure is given by... 

A packed column as used in chromatography is a porous medium with a multimodal pore distribution. There are usually two modes in this distribution, but three-mode distributions may also be encormtered, as we see later. In a classical column made by packing the porous particles of an adsorbent, the first mode is made of the interparticle pores, the fraction of the column volume through which the mobile phase flows. The second one is made of the intrapartide pores, within... 

Other than the particle dimension d, the porous medium has a system dimension L, which is generally much larger than d. There are cases where L is of the order d such as thin porous layers coated on the heat transfer surfaces. These systems with Lid = 0(1) are treated by the examination of the fluid flow and heat transfer through a small number of particles, a treatment we call direct simulation of the transport. In these treatments, no assumption is made about the existence of the local thermal equilibrium between the finite volumes of the phases. On the other hand, when Lid 1 and when the variation of temperature (or concentration) across d is negligible compared to that across L for both the solid and fluid phases, then we can assume that within a distance d both phases are in thermal equilibrium (local thermal equilibrium). When the solid matrix structure cannot be fully described by the prescription of solid-phase distribution over a distance d, then a representative elementary volume with a linear dimension larger than d is needed. We also have to extend the requirement of a negligible temperature (or concentration) variation to that over the linear dimension of the representa-... 

This equation suggests that the capillary pressure in a porous medium is a function of the chemical composition of the rock and fluids, the pore size distribution, and the saturation of the fluids in the pores. Capillary pressures have also been found to be a function of the saturation history, although this dependence is not reflected in Eq. (1). Because of this, different values will be obtained dining the drainage process (i.e., displacing the wetting phase... 

We consider the case of linear isotherm between the gas and solid phases. The mass transport into the particle is assumed to occur by two parallel mechanisms pore and surface diffusions. The mass balance equation describing the concentration distribution in a slab porous medium with these two parallel mechanisms is ... 

The distribution of the oil, gas and water in the porous medium was better understood when Botset and Wyckoff (9) carried out the first experiments on relative permeability. They showed that either oil or gas would flow only if a specific minimum saturation of the phase in question existed in the flow region of the porous material. Some of the early workers also recognized that either the oil or gas droplets could be discontinuous, and in this condition, would be hard to displace by flowing water because of the Jamin effect. In 1927, Uren and Fahmy (10) investigated a number of "factors which affect the recovery of petroleum from unconsolidated sands by waterflooding. Table 1 lists these factors and the general results observed by Uren and Fahmy. With one exception (rate), the results observed by Uren and Fahmy are similar to generalizations which most experts in this field claim today after work of more than 50 years. 

Capillary Pressure. At equilibrium, two immiscible fluid phases (water and oil) in contact with each other in a porous material will distribute themselves in such a manner to minimize the free energy of the total system. This distribution is a function of saturation history, surface wettability for each fluid, pore structure, interfacial tension, fluid densities, and fluid height. The pressures within the water and oil phases reflect the distribution of fluids in a porous medium and consequently the... 

Any chromatographic technique is based on the flow through a porous medium— the stationary phase. The flow in the pores is very slow and the transport of solutes and particles is mainly diffusive. Adsorption/desorption, hydrodynamic or steric effects specifically influence the residence time of the different species and, thus, facilitate their separation. In SEC, one employs stationary media with very hroad pore size distributions. Since the particles can only move into those pores that exceed their geometric dimensions, the penetrable pore volume decreases with increasing particle size. Coarse particles, therefore, pass the column more quickly than fine ones (Fedotov et al. 2011). SEC was originally developed for the separation of polymer... 

As mentioned in Sect. 5.5, in the classical diffusion theory for a porous medium, adsorption is described by a distribution coefficient Kd resulting from the transfer of the species from the fluid phase to the solid phase through the linearized equation of equilibrium adsorption isotherm (5.113). 

The spatial distribution of matter in a porous medium can be represented by the phase function, Z(x), which is equal to 1 if x belongs to the pore space, or 0 if x belongs to solid (x is the position vector fiom an arbitrary origin). A reliable 3D representatian of a porous medium should possess the same statistic properties as those determined in a single two-dimensional section, properly reflected by the various moments of Z(x) [6] and in most cases, the first two moments are considered sufficient. The one-point correlation function. Si, is the probability that any point lies in the pore space and is defined as 5i= (< > indicates spatial average, hence, Si is equal to the porosity, e). On the other hand, the two-point correlation function, -S2(u), is the probability that two points a specified distance u apart, both lie in the pore space and is defined as S 2(u)=. SiCa). is directly related to the autocorrelation function, RJyi) (ii (u)=[iS2(u)-fi ]/(E-0). For an isotropic m ium, iyu) is only a function of m=1u( [1] and thus degenerates to the one-dimensional autocorrelation function, Rz(u), of Eq. (1). 

Abstract. This article describes a hydrodynamic model of collaborative flnids (oil, water) flow in porons media for enhanced oil recovery, which takes into account the influence of temperature, polymer and surfactant concentration changes on water and oil viscosity. For the mathematical description of oil displacement process by polymer and surfactant injection in a porous medium, we used the balance equations for the oil and water phase, the transport equation of the polymer/surfactant/salt and heat transfer equation. Also, consider the change of permeabihty for an aqueous phase, depending on the polymer adsorption and residual resistance factor. Results of the numerical investigation on three-dimensional domain are presented in this article and distributions of pressure, saturation, concentrations of poly mer/surfactant/salt and temperature are determined. The results of polymer/surfactant flooding are verified by comparing with the results obtained from ECLIPSE 100 (Black Oil). The aim of this work is to study the mathematical model of non-isothermal oil displacement by polymer/surfactant flooding, and to show the efficiency of the combined method for oil-recovery. 

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. 

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