Porous media compressible

Most authors who have studied the consohdation process of soflds in compression use the basic model of a porous medium having point contacts which yield a general equation of the mass-and-momentum balances. This must be supplemented by a model describing filtration and deformation properties. Probably the best model to date (ca 1996) uses two parameters to define characteristic behavior of suspensions (9). This model can be potentially appHed to sedimentation, thickening, cake filtration, and expression. 

Several alternative methods have been considered in order to increase the energy density of natural gas and facilitate its use as a road vehicle fuel. It can be dissolved in organic solvents, contained in a molecular cage (clathrate), and it may be adsorbed in a porous medium. The use of solvents has been tested experimentally but there has been little improvement so far over the methane density obtained by simple compression. Clathrates of methane and water, (methane hydrates) have been widely investigated but seem to offer little advantage over ANG [4]. Theoretical comparison of these storage techniques has been made by Dignam [5]. In practical terms, ANG has shown the most promise so far of these three alternatives to CNG and LNG. 

Very briefly, the Dave model considers a force balance on a porous medium (the fiber bed). The total force from the autoclave pressure acting on the medium is countered by both the force due to the spring-like behavior of the fiber network and the hydrostatic force due to the liquid resin pressure within the porous fiber bed. Borrowing from consolidation theories developed for the compaction of soils 22 23), the Dave model describes one-dimensional consolidation with three-dimensional Darcy s Law flow. Numerical solutions were in excellent agreement with closed-form solutions for one- and two-dimensional resin flow cases in which the fiber bed permeabilities and compressibility, as well as the autoclave pressure, are all held constant21). 

In the integration of equation 12 to give equation 13 it was assumed that Q was not a function of pressure. However, when a compressible fluid such as a gas is flowing this assumption is not valid. As the gas flows through the porous medium from a high pressure to a low pressure it expands as the pressure decreases. Consequently for a compressible fluid Q must be measured at the mean pressure of the system, that is, at a pressure equal to (Pi -f- P2) /2. If Boyle s Law applies to the gas it is evident that... 

In the original Buckley-Leverett theory, gravitational, compressibility and capillarity are ignored. Devereux (36) presents the solution for the case of constant pressure, and the constant-velocity case was derived by Soo and Radke 12). The model requires a knowledge of the capillary retarding force per unit volume of the porous medium, and the relative permeabilities of the oil droplets in the emulsion and the continuous water phase. These relative permeabilities are assumed to be functions of the oil saturation in the porous medium. These must be determined before the model can be used. 

The porous medium is compressible and behaves as a linear elastic solid ... 

Under the assumed conditions, the vertical compressibility of the porous medium, a, can be given by... 

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. 

Figure 2 shows the basic physical idea of the microstructure of the continuum rheologicS model we proposed earlier (2). The layers can be idealized as separated by porous slabs, which are connected by elastic springs. Liquid crystals may flow parallel to the planes in the usual Newtonian manner, as if the slabs were not there. In the direction normal to the layers, liquid crystals encounter resistance through the porous medium, proportional to the normal pressure gradient, which is known as permeation. The permeation is characterized by a body force which in turn causes elastic compression and splay of the layers. Applied strain from the compression causes dislocations to move into the sample from the side in order to relax the net force on the layers. When the compression stops and the applied stress is relaxed the permeation characteristic has no influence on stress strain field. 

Powdered metal is a porous medium. The physical characteristics, chemical composition, structure, porosity, strength, ductility, shape and size can be varied to meet special requirements. The porosity ranges up to 50% void by volume, tensile strength up to 10,000 psi, varying inversely with porosity, and ductility of 3-5% in tension, and higher in compression. 

We denote by s z,t) the porosity inside the porous medium. This varies with z. It is observed that pressing does not occur simultaneously in the entire layer. The porons medinm is gradually compressed from the top to the bottom of the layer. Conservation of the liquid mass links U(z,t) to s(z,t) ... 

It is assumed that the intrinsic permeability of the porous medium is small. Compression of the porous medium is controlled by the draining of liquid out of the porous medium, which is slow. The pressing of the granular medium therefore depends chiefly on the permeability k and the viscosity p of the liquid. The equilibrium of mechanical forces exerted on the solid is verified at all times. Since the presence of liquid inside the porous medium prevents the instantaneous compression of the cake, the force d, q/soi exerted by the liquid on the soUd through all solid-liquid surfaces within the slice of porous medium between z and z + dz planes contributes to the equilibrium of forces applied on the solid, which is written as follows for the component directed along ic ... 

Let us describe the mathematical model of a three-phase non-isothermal compressible flow in porous media taking into account capillary effects. It is assumed that the movement of phases obeys the generalized Darcy s law. We assume that the phases are in the local thermal equilibrium, so that in any elementary volume the fluids saturating the porous medium and the rock have the same temperature. Furthermore, oil is assumed to be homogeneous non-evaporable fluid and oil reservoir consists of one type of rock. In this case, three-phase non-isothermal flow in a bounded domain 2 c M (d = 1, 2, 3) taking into account capillary forces and the phase transitions between the phases of water and heat transfer is described by the following system of equations ... 

The porous medium (sorbent, membrane, gel particle) can be made of soft spherical particles that swell quite a bit when immersed in a solvent they are called gek. If they swell in water, they are called hydrogels however, the polymers are crosslinked so that they retain their overall structure. Of course, the polymers are soft and compress under pressure a typical example would be gels (which are crosslinked) based on agarose (Figure 3.3.5B). Such gel particles are widely used in a variety of separation techniques for separating macromolecules/proteins, etc. 

Studies on the effect of mobility ratio on areal sweep were made in models using compressed glass wool as the porous media with colored water solutions of glycol of different viscosities adjusted to represent mobility ratios. Although the polymer solutions exhibit resistance factor in this type of porous medium, the simpler solutions were used for experimental reasons. 

The models consist of a sandwichlike structure composed of a steel plate on the bottom, a thin rubbei sheet membrane, then a layer of Vi-in. fiberglass insulation mat which is sealed on the edges with latex. The organic binder is previously burned off in an annealing oven. A %-in. plexiglass sheet top is bolted through the steel which compresses the mat to about 1/16-in. thick. The porous medium has a uniform permeability in the order of 2 to 4 dafcies. Uniform compression of the mat is maintained by a 6-ft hydraulic head applied to the space between the steel and rubber membrane. 

Filter aids should have low bulk density to minimize settling and aid good distribution on a filter-medium surface that may not be horizontal. They should also be porous and capable of forming a porous cake to minimize flow resistance, and they must be chemically inert to the filtrate. These characteristics are all found in the two most popular commercial filter aids diatomaceous silica (also called diatomite, or diatomaceous earth), which is an almost pure silica prepared from deposits of diatom skeletons and expanded perhte, particles of puffed lava that are principally aluminum alkali siheate. Cellulosic fibers (ground wood pulp) are sometimes used when siliceous materials cannot be used but are much more compressible. The use of other less effective aids (e.g., carbon and gypsum) may be justified in special cases. Sometimes a combination or carbon and diatomaceous silica permits adsorption in addition to filter-aid performance. Various other materials, such as salt, fine sand, starch, and precipitated calcium carbonate, are employed in specific industries where they represent either waste material or inexpensive alternatives to conventional filter aids. 

Filter aids as well as flocculants are employed to improve the filtration characteristics of hard-to-filter suspensions. A filter aid is a finely divided solid material, consisting of hard, strong particles that are, en masse, incompressible. The most common filter aids are applied as an admix to the suspension. These include diatomaceous earth, expanded perlite, Solkafloc, fly ash, or carbon. Filter aids build up a porous, permeable, and rigid lattice structure that retains solid particles and allows the liquid to pass through. These materials are applied in small quantities in clarification or in cases where compressible solids have the potential to foul the filter medium. 

---