Porous network Viscosity

Rebour et al. (1997) review the literature describing gas diffusion in a porous medium as a double porosity process. In this model, gas diffusion is affected by the increase in water viscosity when in the close vicinity of clay minerals. This produces an environment in which the gas diffusion rate is expected to be variable in the porous network depending on the local tortuosity and grain-size distribution. In modeling this type of system, diffusion is considered to occur along a direct pathway. These fast routes interconnect slow regions, into and out of which gas also diffuses. Experimental work by the same authors (Rebour et al. 1997) determines Rf = 200 for a clayey marl from Paris basin Callovo-Oxfordian sediments that have a porosity and permeability of 23% and 10 m, respectively. 

This is the viscosity that controls the rate of change of the volume of the porous network (with no liquid in the pores) when it is subject to a hydrostatic stress. As the porosity decreases, TV approaches 1/2 and the network becomes incompressible. Shear stresses and strains are related by the shear viscosity, >... 

See also Viscoelasticity, Viscosity of porous network, 396-398, 429-437 of silicate sol. 203-209 Rhodamine 6G, 665 Rigid rod polymer, 824 Rings, closed, 315, 318, 320 Ripening, 534. See also Coarsening,... 

Oil reservoirs are layers of porous sandstone or carbonate rock, usually sedimentary. Impermeable rock layers, usually shales, and faults trap the oil in the reservoir. The oil exists in microscopic pores in rock. Various gases and water also occupy rock pores and are often in contact with the oil. These pores are intercoimected with a compHcated network of microscopic flow channels. The weight of ovedaying rock layers places these duids under pressure. When a well penetrates the rock formation, this pressure drives the duids into the wellbore. The dow channel size, wettabiUty of dow channel rock surfaces, oil viscosity, and other properties of the cmde oil determine the rate of this primary oil production. 

In the past, various resin flow models have been proposed [2,15-19], Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al. [2], Loos and Springer [15], Williams et al. [16], and Gutowski [17] assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber network permeability is a function of fiber diameter, the porosity or void ratio of the porous medium, and the shape factor of the fibers. Viscosity of the resin is essentially a function of the extent of reaction and temperature. The second major approach is that of Lindt et al. [18] who use lubrication theory approximations to calculate the components of squeezing flow created by compaction of the plies. The first approach predicts consolidation of the plies from the top (bleeder surface) down, but the second assumes a plane of symmetry at the horizontal midplane of the laminate. Experimental evidence thus far [19] seems to support the Darcy s Law approach. 

In the past, various resin flow models have been proposed (2, 15-19). Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al.2), Loos and Springer15), Williams et al.16) and Gutowski17) assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber... 

After a significant amount of hydrolysis and condensation has taken place, a three-dimensional network of metal and oxygen forms within the sol (metal-oxygen colloids suspended in a liquid) and the viscosity of the sol increases. As condensation continues, the sol transforms into a nonfluid gel and an interconnected and fairly rigid 3-D network extends throughout the entire sample container. The resulting wet gel is an amorphous, porous metal oxide with water and alcohol in its mesoscopic pores. Typically, the solid phase is between 5 and 10% of the total volume. 

A point of terminology is repeated here to remind the reader. The term apparent viscosity , pp, is used to describe the observed macroscopic rheology of the polymeric fluid in a porous medium. The quantity effective viscosity ,, refers in a rather similar way to the observed effective viscosity in a single capillary. Each quantity is defined phenomenologically—from Darcy s law (Equation 6.4) and rj ff from Poiseuille s law (Equation 3.75). This distinction should be kept clear, especially when considering porous media models based on networks of capillaries, as discussed later in this chapter. The overall viscosity of the non-Newtonian fluid in the network as a whole is whereas the viscosity in each of the capillaries may be different and is In this latter case, will be in some sense an average value of the in the individual capillaries. 

Approach (iii) listed above refers to the use of effective medium theory (Kirkpatrick, 1973 Koplik, 1982 Levine and Cuthiell, 1986) for calculating certain average flow properties in idealised porous media models—usually simple networks. Cannella et al (1988) have recently applied this approach to the flow of power law fluids through networks of capillaries. They use this method to derive an expression for the apparent viscosity of the polymer in the porous medium which has the same overall form as the capillary bundle expression (e.g. Equation 6.18). They then adjusted the parameters in the effective medium formula in order to match their particular form of the capillary bundle formula with C = 6 (Equation 6.18). The values of the effective medium parameters are physically interpretable, and Cannella et al (1988) deduced from these that the effective radius for the flow of a power law fluid is larger than that for the flow of a Newtonian fluid. They also... 

Figure 6.15. Apparent viscosity versus corrected porous medium shear rate compared with the bulk fluid rj/y curve for the four networks with bond radius distributions shown inset (Sorbie et ai, 1989c).

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