Permeability pressure solution

Here An = RT cosm, Lp = permeability for solute (cm s 1), AP = hydrostatic pressure difference, An = osmotic pressure, a = reflection coefficient, Acs = solute concentration difference, and cs = average solute concentration in upstream solution. Membranes with a reflection coefficient cj —> 0 are permeable to all components whereas a membrane with <7—> 1 rejects all solutes. 

It is unlikely, however, that the lithification of chalk will go on without consolidation, in which the volume of chalk material is reduced in response to a load on the chalk. Consolidation can lead to a reduction in porosity up to about 40%, and an increase in the effective stress (Jones et al., 1984). The increased effective stress is required to instigate the process of pressure solution. Pressure solution provides Ca2+ and HCO3 for early precipitation of calcite cement in the chalk. However, the inherently low permeability of chalk would inhibit the processes of consolidation and pressure solution/cementation unless some permeable pathways are opened up to permit the dissipation of excess pore pressure created by the filling of pore space by calcite cement. Pressure solution will cease if the permeable pathways are blocked by cement. Thus, it appears that the development of fractures, open stylolites and microstylolitic seams (Ekdale et al., 1988) is necessary to permit pressure solution to continue and lead to large rates of Ca2+ and HC03 mobilization. 

The influence of metal oxide derived membrane material with regard to permeability and solute rejection was first reported by Vernon Ballou et al. [42,43] in the early 70s concerning mesoporous glass membranes. Filtration of sodium chloride and urea was studied with porous glass membranes in close-end capillary form, to determine the effect of pressure, temperature and concentration variations on lifetime rejection and flux characteristics. In this work experiments were considered as hyperfiltration (reverse osmosis) due to the high pressure applied to the membranes, 40 to 120 atm. In fact, results reproduced in Table 12.3 show that these membranes do not behave as h)qjerfiltra-tion membranes but as membranes with intermediate performances between ultra- and nanofiltration in which surface charge effect of metal oxide material plays an important role in solute rejection. 

Radial compression uses radial pressure applied to a flexible-wall column to lessen wall effects. The mobile phase has a tendency to flow slightly faster near the wall of the column because of decreased permeability. The solute molecules that happen to be near the wall are carried along faster than the average of the solute band, and, consequently, band spreading results. Preparative scale radial compression chromatography columns have been found to possess efficiencies close to those of analytical-scale columns when an adequate radial compression level is used. Radial compression technology also helps lower the cost by substituting reusable column holders in place of expensive steel columns. 

These measurements provide unusual constraint on the evolving processes. Importantly, they allow the source of dissolved components to be determined we need to discriminate whether the source is from free-face dissolution of the fracture wall, or from stress-mediated dissolution at contacting asperities. This distinction is crucial since these two mechanisms impart opposite effects in the sense of permeability change, under net dissolution free-face dissolution increases permeability, and pressure solution reduces permeability. 

Yasuhara, H., Elsworth, D., and Polak, A. (2004a) The evolution of permeability in a natural fracture significant role of pressure solution. J. Geophys. Res., Vol. 109, B03204,... 

THE EVOLUTION OF PERMEABILITY IN NATURAL FRACTURES - THE COMPETING ROLES OF PRESSURE SOLUTION AND FREE>FACE DISSOLUTION... 

Two variable input parameters address the pressure solution creep and recrystaUization creep behaviour of plug and backfill and four variable input parameters address the porosity-permeability relation of the rock salt, including the imcertain evolution of permeability at very low porosities down to 0.0003. The parameters are derived from experimental data and their distribution is based partially on statistical analysis and partially on expert judgement As output parameters, the evolution of the porosity and permeability are computed as well as several risk-related parameters including the potential dose rate in biosphere and radiotoxicity fluxes in different compartments. 

Pressure solution. Next, consider the corresponding pressure field. We recall from Equations 12-2 and 12-4a that g(x,y,z) = p(x,y,z) Vk(x,y,z) satisfies 9 g/9 + g/9y + g/9z = 0. If we assume that both the permeabilities and pressures are known at all well positions and boundaries, it follows that g = pVk can be prescribed as known Dirichlet boundary conditions. Then, the numerical methods devised in Chapter 7 for elliptic equations can be applied directly on the other hand, analytical separation of variables methods can be employed for problems with idealized pressure boundary conditions. The general approach in this example is desirable for two reasons. First, the analytical constructions devised for the permeability function (see Equations 12-5b, 12-10, and 12-11) allow us to retain full control over the details of small-scale heterogeneity. Second, the equation for the modified pressure g(x,y,z) (see Equation 12-4a) does not contain variable, heterogeneity-dependent coefficients. It is, in fact, smooth thus, it can be solved with a coarser mesh distribution than is otherwise possible. 

The flux equations for membrane transport can now be developed by combining the effects of osmotic pressure, solute diffusion, and solvent transport. To do this, we consider the situation shown schematically in Fig. 18.3-3. In this situation, a concentrated solution at high pressure is being foreed across a membrane into a dilute solution at lower pressure. The membrane is more permeable to solvent than to solute, and so a concentration difference develops. This concentration difference in turn produces an osmotic pressure opposing the flow. 

First, we consider the experimental aspects of osmometry. The semiperme-able membrane is the basis for an osmotic pressure experiment and is probably its most troublesome feature in practice. The membrane material must display the required selectivity in permeability-passing solvent and retaining solute-but a membrane that works for one system may not work for another. A wide variety of materials have been used as membranes, with cellophane, poly (vinyl alcohol), polyurethanes, and various animal membranes as typical examples. The membrane must be thin enough for the solvent to pass at a reasonable rate, yet sturdy enough to withstand the pressure difference which can be... 

We consider this system in an osmotic pressure experiment based on a membrane which is permeable to all components except the polymeric ion P that is, solvent molecules, M" , and X can pass through the membrane freely to establish the osmotic equilibrium, and only the polymer is restrained. It does not matter whether pure solvent or a salt solution is introduced across the membrane from the polymer solution or whether the latter initially contains salt or not. At equilibrium both sides of the osmometer contain solvent, M , and X in such proportions as to satisfy the constaints imposed by electroneutrality and equilibrium conditions. 

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