Pore, capillary medium-sized

The phenomenon of capillary condensation provides a method for measuring pore-size distribution. Nitrogen vapor at the temperature of liquid nitrogen for which cos(0) = 1 is universally used. To determine the pore size distribution, the variation in the amount of nitrogen inside the porous particle is measured when the pressure is slightly increased or decreased. This variation is divided into two parts one part is due to true adsorption and the other to capillary condensation. The variation due to adsorption is known from adsorption experiments with nonporous substances of known surface area, so the variation due to condensation can be calculated. The volume of this amount of nitrogen is equal to the volume of pores with the size as determined by the Kelvin equation. Once a certain model has been selected for the complicated pore geometry, the size of the pores can be calculated. Usually it is assumed that an array of cylindrical capillaries of uniform but different radii, and randomly oriented represents the porous medium. So the Kelvin equation in the form of Equation 3.9 is used. Since condensation is combined with adsorption, the thickness of the adsorption layer... 

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... 

At the present time there exist no flux relations wich a completely sound cheoretical basis, capable of describing transport in porous media over the whole range of pressures or pore sizes. All involve empiricism to a greater or less degree, or are based on a physically unrealistic representation of the structure of the porous medium. Existing models fall into two main classes in the first the medium is modeled as a network of interconnected capillaries, while in the second it is represented by an assembly of stationary obstacles dispersed in the gas on a molecular scale. The first type of model is closely related to the physical structure of the medium, but its development is hampered by the lack of a solution to the problem of transport in a capillary whose diameter is comparable to mean free path lengths in the gas mixture. The second type of model is more tenuously related to the real medium but more tractable theoretically. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

The prime requirements for the separators in alkaline storage batteries are on the one hand to maintain durably the distance between the electrodes, and on the other to permit the ionic current flow in as unhindered a manner as possible. Since the electrolyte participates only indirectly in the electrochemical reactions, and serves mainly as ion-transport medium, no excess of electrolyte is required, i.e., the electrodes can be spaced closely together in order not to suffer unnecessary power loss through additional electrolyte resistance. The separator is generally flat, without ribs. It has to be sufficiently absorbent and it also has to retain the electrolyte by capillary forces. The porosity should be at a maximum to keep the electrical resistance low (see Sec. 9.1.2.3) the pore size is governed by the risk of electronic shorts. For systems where the electrode substance... 

The quantity of water that can be retrieved from a medium is related to size and shape of the connected pore spaces within that medium. The quantity of water that can be freely drained from a unit volume of porous medium is referred to as the specific yield. The volume of water retained in the medium by capillary and surface active forces is called the specific retention. The sum of specific retention and specific yield is equal to the effective porosity (see Table 3.4). Neither term has a time value attached. Drainage can occur over long periods (i.e., weeks or months). 

The cylindrical capillary model predicts that the size of the largest pore present in a membrane filter medium is inversely proportional to the pressure at which bulk flow of a test gas is not present. 

As shown in the studies commented below, the most important about the mechanism of foam in EOR applications are the connectivity and geometry of medium (a size distribution of pore bodies of the order of 100 pm in diameter and pore-throats of the order of 10 pm in diameter) the distribution of the two-phase systems (liquid-gas) in pores which depends on the wetting of pore walls and the volume ratio of the liquid and gas phases the regulating capillary pressure the mode of foam generation and foam microstructure. 

In actual use for mobility control studies, the network might first be filled with oil and surfactant solution to give a porous medium with well-defined distributions of the fluids in the medium. This step can be performed according to well-developed procedures from network and percolation theory for nondispersion flow. The novel feature in the model, however, would be the presence of equations from single-capillary theory to describe the formation of lamellae at nodes where tubes of different radii meet and their subsequent flow, splitting at other pore throats, and destruction by film drainage. The result should be equations that meaningfully describe the droplet size population and flow rates as a function of pressure (both absolute and differential across the medium). 

A novel flow cell has been developed to observe on a microscopic level the steady state, cocurrent flow of two pre-equilibrated phases in a porous medium. It consists of a rectangular capillary tube packed with a bilayer of monodisperse glass beads 109 microns in diameter. The pore sizes in the model are of the order of magnitude of those in petroleum reservoirs. An enhanced videomicroscopy and digital imaging system is used to record and analyze the flow data. 

The theoretical basis of the Hg-injection method is defined by Laplace law. By using a capillary model where the porous medium is assimilated to a bundle of cylindric capillary tubes the capillary pressure is Pc = y(l/Rci+l/Rc2) = 2y cos0 /Rc (3) where Pc is the capillary pressure Rd and Rc2 are mutually perpendiculcir radii of a surface segment R is the average pore-throat size (pm) 0is the angle between mercury menisc and pore wall (for mercury 0=140°) y is the interfacial tension (for mercury y = 0.480 N/m). 

Capillary Pressure. Because of the small size of pores, the fluid-fluid interfaces within the porous medium are highly curved, and the pressure difference across the interface can be substantial. This local pressure difference across the fluid-fluid interface is called capillary pressure. In general, one of the two fluids preferentially wets the solid and is called the... 

A) Pressure-controlled mercury porosimetry procedure. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+i-Pi >dP>0 where Pj+i, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters of porous medium such as total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson applied percolation theory to calculate permeability from mercury-injection data. 

In membrane filtration, water-filled pores are frequently encountered and consequently the liquid-solid transition of water is often used for membrane pore size analysis. Other condensates can however also be used such as benzene, hexane, decane or potassium nitrate [68]. Due to the marked curvature of the solid-liquid interface within pores, a freezing (or melting) point depression of the water (or ice) occurs. Figure 4.9a illustrates schematically the freezing of a liquid (water) in a porous medium as a fimction of the pore size. Solidification within a capillary pore can occur either by a mechanism of nucleation or by a progressive penetration of the liquid-solid meniscus formed at the entrance of the pore (Figure 4.9b). 

The primary reason for the minor capillary contribution to liquid-vapor interfacial area even in a medium with relatively large (triangular-shaped) pores and small surface area lies in the control exerted by the chemical potential on liquid-vapor menisci. For a given potential, meniscus curvature is constant throughout the porous medium irrespective of pore size. This means that after pore snap-off the capillary contribution to liquid-vapor interfacial area from small and large pores is equal if their shapes (polygon and angularity) are similar. 

The pore size distribution is usually measured based on straight capillaries having a uniform cross-section. Under this condition, the pore neck diameter can be assigned to serve as the diameter of the capillary. If a given pressure pc is applied to a fluid-filled porous medium, the saturation of the medium will be a function of the applied pressure. The relation between the saturation S and the capillary pressure pc can be found for a nonwetting fluid as... 

We observe here that in a capillary the volume flow rate due to a fixed pressure gradient is proportional to a Tra l8p. dpldx) for a circular capillary). The electroosmotic flow rate is proportional to U multiplied by the cross-sectional area TTa Therefore, the ratio of electroosmotic to hydraulic flow rate will be proportional to a. Thus, for example, if we employ a capillary model for a porous medium, it is evident that as the average pore size decreases electroosmosis will become increasingly effective in driving a flow through the medium, compared with pressure, provided... 

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