Kozeny theory

The present model development is based on a semi-heuristic model of flow through solid matrices using the concept of hydraulic diameter, which is also known as the Carman-Kozeny theory [7]. The theory assumes the porous medium to be equivalent to a series of parallel tortuous tubules. The characteristic diameter of the tubules is taken to be a hydraulic diameter or... 

In Kozeny theory, the porous medium is modeled as a system of parallel capillaries with different diameters, but constant length. Kozeny assumed no tangential flow at any cross section perpendicular to the direction of bulk flow. The permeability, derived directly from the equations of motion, is ... 

Models have been developed for this drainage process which are based upon theories of filtration. The Kozeny-Karmen equation is the most common rate expression used as a model for this filtration process. It can be expressed as ... 

The coefficient of proportionality K is called the permeability of the reinforcement. According to theory [5] K is only dependent on the geometry between the fibers in the reinforcement (the pore space ). Several models for the dependence of K on the fiber volume fraction Vf has been proposed. The most-cited model is the so-called Kozeny-Carman model [16,17], which predicts a quadratic dependence on the fiber radius R in addition to the dependence on Vf... 

Because the structure of a cake is highly dependent on operating conditions and its history, the Kozeny equation is only of qualitative value to filtration theory by giving directional effects. 

Although Ergun equation is widely accepted in predicting the pressure drop for flow-through porous media, it is a known fact that the Ergun equation or its modified forms overpredict the pressure drop by as much as 100% at high porosity and underpredict the pressure drop by as much as 300% for low porosity medium such as sandstones (31). A more accurate equation has been developed by Liu et al. (32) based on a revised Kozeny-Carman theory. 

As a comparison, the equation due to the Kozeny-Carman s theory is given by... 

In the permeability methods a known quantity of air is forced through a small bed of the fine solids under a constant pressure drop, and the flow time is recorded. The theory is based on the laminar flow of fluids through porous beds, and the specific surface area S (m g ) of the material is calculated from the Kozeny equation... 

Perturbation theory cannot be applied to describe the effect of the strong roughness. An approach based on Brinkman s equation has been used instead to describe the hydrodynamics in the interfacial region [82]. The flow of a liquid through a nonuniform surface layer has been treated as the flow of a liquid through a porous medium [83-85]. The morphology of the interfacial layer of thickness, L, has been characterized by a local permeability, that depends on the effective porosity of the layer, (j). A number of equations for the permeability have been suggested. For instance, the empirical Kozeny-Carman equation [83] yields a relationship... 

Thus, from the Kozeny-Carman theory, the relationship between porosity and permeability is given by the relation... 

The Navier-Stokes (NS) equations can be used to describe problems of fluid flow. Since these equations are scale-independent, flow in the microscale structure of a porous medium can also be described by a NS field. If the velocity on a solid surface is assumed to be null, the velocity field of a porous medium problem with a small pore size rapidly decreases (see Sect. 5.3.2). We describe this flow field by omitting the convective term v Vv, which gives rise to the classical Stokes equation We recall that Darcy s theory is usually applied to describe seepage in a porous medium, where the scale of the solid skeleton does not enter the formulation as an explicit parameter. The scale effect of a solid phase is implicitly included in the permeability coefficient, which is specified through experiments. It should be noted that Kozeny-Carman s formula (5.88) involves a parameter of the solid particle however, it is not applicable to a geometrical structure at the local pore scale. 

It was shown in Ref. 63 that Washburn s theory coincides with the approach exploiting the Darcy s law, if simply an appropriate relation is substituted for the permeability of the bundle of capillaries medium. Kozeny equation is suitable for this case. 

The capillaiy theories focus on the spaces or pores in the porous soUd, and an analogy is drawn between the tortuous pore system of the solid and the cy Undrical pores of an assembly of capillary tubes. The best-known equation of this type is the Kozeny-Carman equation, which gives an expression for the permeability coefficient as a function of the porous stracture ... 

Experimental results have shown that the Kozeny-Carman theory holds well when the porosity is less than 0.8 in porous media. For media with higher porosity, however, the Kozeny-Carman eqnation is not supported by experimental results. Denton s work indicated that, since the porosity of yam packages lies between 0.1 and 0.7, the Kozeny-Carman equation can be nsed in investigations of package dyeing processes. 

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