Porous media permeability predictions

Coimectivity is a term that describes the arrangement and number of pore coimections. For monosize pores, coimectivity is the average number of pores per junction. The term represents a macroscopic measure of the number of pores at a junction. Connectivity correlates with permeability, but caimot be used alone to predict permeability except in certain limiting cases. Difficulties in conceptual simplifications result from replacing the real porous medium with macroscopic parameters that are averages and that relate to some idealized model of the medium. Tortuosity and connectivity are different features of the pore structure and are useful to interpret macroscopic flow properties, such as permeability, capillary pressure and dispersion. 

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. 

The general form of the relationship to be expected between capillary pressure and permeability can be predicted. Capillary pressure (P ) is inversely proportional to a value of pore radius (r). Intrinsic permeability (k) is measured in units of (length), which may be taken to represent a radius (R) by reference to a capillary bundle representation of a porous medium. We do not know a priori whether r = / in a complex capillary network. Essentially,... 

The usage of the flow equations can be summarized as follows. For the case of a one-dimensional single fluid flow, either equation 106 or 108 can be used to predict the normalized pressure drop factor in a porous medium. The determined normalized pressure drop factor is related to the pressure drop by equation 11. For the simple case of packed spherical beads, ds and e are known a priori. The Reynolds number is evaluated using equation 93. For random packs of nonspherical particles, the particle s sphericity needs to be known. Equation 73 can be used to estimate ds. For the case of consolidated porous medium, one can estimate ds from the knowledge of the intrinsic permeability using equation 14. 

The gas relative permeability, Pr, is defined as the permeability of a fluid through a porous medium partially blocked by a second fluid, normalized by the permeability through the same porous solid, when the pore space is free of this second fluid. In most cases, the gas relative permeability diminishes at the percolation threshold , at which a significant portion of the pores are still conducting but they don t form a continuous path through the membrane along the direction of flow. The tortuous capillary model fails to predict this the percolation threshold arises only when all pores are blocked by capillary condensation. In comparison, the network model can provide a satisfactory analysis of the percolation threshold problem, without, as noted earlier, increasing the number of the model parameters. 

In the last expression, tortuosity t > 1 was added as a generalized factor to allow for a correction factor if the capillaries are not straight. Then, Th should be used instead of h [19]. Obviously, the other approach exploiting the permeability tensor offers better opportunity to account for the internal geometry of the porous medium because many theoretical predictions are... 

There exist many theoretical predictions of the permeability of fibrous porous media in the literatures [7] - [10], From early works on the theoretical predictions of the permeabihty of fibrous porous medium we can emphasize the works of John Happel (1959) [7] and Hasimoto (1959) [8]. John Happel [7] foimd the theoretical prediction of the permeability of fibrous porous media by solving the Stokes equation for a fluid flow in fibrous porous medium. The flow around a cylinder investigated in his work (see Fig. 2). His theoretical prediction of the permeabihty of fibrous porous medium ... 

In the work of Hasimoto [8] the exact solution of the Stokes equation for the fluid flow in fibrous porous medium in the form of the infinite series is used to predict the permeability of fibrous porous media. He found the theoretical prediction of the permeability of fibrous porous media using only the terms of lowest order of this series ... 

As can be seen from Fig. 6 and Table 1, the theoretical prediction of the permeability of the fibrous porous medium which given in the work of Tamayol and Bahrami (2008) [10] is the most accurate in comparison with other theoretical predictions. Also in Fig. 3, 4 and 5 showed that the error of the theoretical prediction of the velocity profile is not so large and allows to investigate in detail the fluid flow in pore scale or micro scale. 

Prediction of the permeability reduction from properties of the porous rock and the polymer is not possible at this time. Experimental measurement with the rock and polymer of interest is necessary. It is often possible, however, to correlate permeability reduction for the same polymer in the same type of porous medium and use the resulting correlation for interpolation and extrapolation. Gogarty37 correlated the permeability of consolidated porous rocks after contact with polyacrylamide by use of an empirical relationship. 

Shannon et al. developed a flow model which, using a finite difference method, predicts pressure and velocity profiles based on user-defined package geometry, permeability profile and fluid properties. The flow model was obtained by combining the continuity equation for fluid flow in a porous medium ... 

To predict a fiber-mafrix separation, the second force required to squeeze the resin through the bed of fibers at the rib entrance is now considered. The fiber bed has a permeability K which is expressed in terms of D Arcy s Law. Bakharev and Tucks- [5] used this law to describe flow through a porous medium. The flow of the resin through the fiber bed is modeled as one dimensional flow of a Non-Newtonian fluid through a porous matsial... 

Verleye et al. [60-61] had investigated the meso-scale permeability i.e. the permeability of a unit cell textile model of multi-scale porous technical textiles for which the macro-scale geometry was taken into account. They presented two methods to predict the permeability, namely the CFD based three-dimensional simulation and the Grid 2D [62] based simulation. The second method takes less time compared to CFD but less accmate. The aim of the work was to construct a network that represents the pore structure in which every pore of the medium is assigned certain conductivity and the overall permeability was computed using the laws of conservation. 

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