Penetration into porous media

P. G. Saffman and G. I. Taylor, The Penetration of Liquid into Porous Medium or Hele-Shaw Cell Containing a More Viscous Liquid , Proc. R. Soc. London, Ser. A 245, 312-329 (1958). 

In many cases, it has been found experimentally that for liquids penetrating a porous medium, the Washburn law is dimensionally applicable (h r ). Therefore, the simplest approach toward modelling and understanding the kinetics of penetration into a porous medium is to treat it as a capillary with an effective radius . However, the model of an effective radius may be insufficient, especially when a significant distribution of pore sizes exists. It was concluded that the effective pore radius of a network of interconnected capillaries of varying radius, calculated by using the Washburn equation, may be very different from the radius calculated by other measurements, such as mercury porosimetry (39). A more sophisticated approach is based on the idea to model a porous medium as a group of capillaries of various sizes (16). 

For fine suspended solids with particles that are too small to be separated from the liquid by gravitational or centrifugal methods, a barrier method such as a filter may be used. The liquid is passed through a filter medium (usually a cloth or screen) that provides a support for the solid particles removed from the slurry. In actuality, the pores in the filter medium are frequently larger than the particles, which penetrate some distance into the medium before being trapped. The layer of solids that builds up on the surface of the medium is called the cake, and it is the cake that provides the actual filtration. The pressure-flow characteristics of the porous cake primarily determine the performance of the filter. 

Deep electrophoretic penetration of spherical particles with infinitely thin double layer into an impermeable porous graphite substrate was examined by modeling the porous medium as a long slit with one closed end [44]. 

From Equation 2 it is possible to calculate the inner s,urface area of the porous medium, S. Hence, from the adsorption data of Figure 4 it is possible to calculate the volume of rock necessary to adsorb all of the surfactant and the total volume of rock attained by the fluid. Assuming a radial penetration, these two volumes may be transformed into the radius of penetration of the fluid as a whole, ri, and the radius necessary to consume the surfactant, r2 The ratio will be higher than one if the surfactant is... 

To determine the effect of a pressure field, resulting from cavitation bubbles compressing, on the penetration of a melt into a capillary channel of a filter, one should estimate the character of the pressure impulse propagation through the capillary. The mechanism of the flow is somewhat different under conditions of fine filtration of a melt through a porous medium (a filter from multilayer fiberglass with a cell of 0.6 x 0.6 or 0.4 x 0.4 mm in size) with rather short (about several mm) but complexly curved channels, but the main conditions remain. 

Saffman, P.G., and G.I. Taylor. 1958. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. London Ser. A 245 312-329. 

In the model, fresh air flows into the working face through the inlet, and flows out through the outlet. Since the two gobs and the gob-side coal pillar are assumed porous medium, the fresh air flows into the gob behind the working face and penetrates into the gob-side coal pillar and the adjacent gob. Energy equation is not considered in this model since the velocity field of the air leakage microcirculation is the main focus in the present study. 

Z)(r) is obtained from the slopes of a plot of V versus AP. An example is shown in Figure 2.2. Mercury porosimetry data, in terms of the rate of penetration into the porous medium, can also be evaluated with the aid of the Washburn equation (Equation 3.31). 

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... 

A very rough hydrophilic surface is somewhat similar to a thin porous medium. We can imagine that some liquid escapes from the drop and penetrates into the nooks and crannies of the solid. The volume of film captured in the recesses is generally negligible, and in the end the drop finds itself essentially on a wet substrate viewed as a patchwork of solid and liquid. 

K.L. Adams, et al.. Radial penetration of a viscous liquid into a planar anisotropic porous medium, Int J Multiph Flow 14 (2) (1988) 203-215. 

For practical applications, the kinetics of penetration of liquids into porous media is of major interest, in particular the interrelationship between the kinetics of penetration and the structure of a porous medium, as well as its surface energetic properties. 

The idea of in situ upgrading [4] (Fig. 16.2) is closely related to SAGD, but involves an additional underground refinery process. Instead of injecting steam, heavy oil is pre-injected into the oil sand reservoir through the injector well with ultra-dispersed (UD) catalysts and H2. The UD catalysts are usually on the nano-scale such that they could penetrate inside the porous medium in the reservoir... 

Filtration is more normally used as a post-treatment process, further to improve the water quality. However, oil-water separators are also designed on a filtration basis. When two non-miscible liquids of different densities flow by gravity through a porous medium, they wiU have different penetrability rates. In such a filter, the oil-water mixture first enters a sedimentation tank, where heavier particles settle out. The oil-water mixture then enters an inlet basket and flows into the porous medium, where the oil separates from the water. The water flows on down through a screen at the bottom, then up and over a water weir, which creates the water table supporting the oil longer. The oil travels horizontally on top of the water into the oil trap and then over an adjustable oil weir, which is set at a position slightly above the maximum water level. 

Many different types of filters are available commercially. They can be broadly classified into two types with, however, some overlap. Fibrous filters are composed of mats of fi bets that may be ntade of cellulose, quartz, glass, polymeric materials, or metals. Porous membrane filters are usually composed of thin films of polymeric materials 0.05 to 0.2 mm thick sufficiently porous for air to How through under pressure. Pore size is controlled in the manufacturing process and ranges from 0.02 to 10 /rm, A significant fraction of the panicles may be caught on the upstream surface of the filter, but some particles may also penetrate and be caught inside the pores of the medium as well. 

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