Single-phase fluid flow shear factor

We then discussed the modeling for single-fluid phase flow in porous media. In particular, the shear factor and permeability model of Liu et al. (32) is discussed in detail. The bounding wall effects are presented. This section completed the modeling requirements for single-phase incompressible flow in porous media. We showed how to solve the governing equations for flow in porous media and an approximate solution of the pressure drop for an incompressible flow through a cylindrically bounded porous bed was constructed. 

The two key properties in single-phase flow are the fluid density and the viscosity. The density is quite straightforward it is the mass per unit volume. In turbulent flow, pressure drop is directly proportional to density, so that the accuracy of the density is the accuracy of the pressure drop prediction. It is easy to get better than 1% accuracy on such values. Viscosity, on the other hand, is a more complex measurement. Low viscosity systems usually run in turbulent flow, where the viscosity has little or no effect on mixing or pressure drop. For low viscosity material the prime use of the viscosity is in calculating a Reynolds number to determine if the flow is laminar or turbulent. If turbulent, little accuracy is needed. An error in viscosity of a factor of 2 will have negligible effect. In laminar flow, however, the viscosity becomes all important and pressure drop is directly proportional to it, so that an accuracy of 10% or less is often required. For laminar processing a complete relation of stress versus strain or shear rate versus shear stress is required. See Chapter 4 for the means and type of data required. 

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