Network modelling of non-Newtonian fluids in porous media

2 Network modelling of non-Newtonian fluids in porous media 

The main requirements for a network model of non-Newtonian flow are as follows  

In order to set up the flow problem, a constant pressure, AP, is set across the network. At each junction, flow is conserved for an incompressible fluid, and hence the flow must sum to zero when an appropriate sign convention is applied. A pseudo-Poiseuille equation can be applied in each of the network elements even for a non-Newtonian fluid, provided that an effective viscosity. 

The network calculations outlined here and expanded elsewhere (Sorbie et al, 1989c) have indicated why expressions of the type given in Equation 6.17 are useful for correlating in-situ rheological data for pseudoplastic fluids. The apparent viscosity, f/ pp, when plotted against the average in-situ effective 

As a final remark, note that it has been explained why the capillary bundle expressions give a reasonable correlative model for apparent shear rate in porous media. However, the physical basis of the capillary bundle model is not correct and it cannot be used to analyse subtle aspects of the detailed microscopic flows of non-Newtonian (or Newtonian) fluids in porous media. For example, the discussion of shear stress and tortuosity which is given in Teew and Hesselink (1980) in connection with the capillary bundle model must be treated with great caution, as must similar treatments in other works of this type (see, for example, other references in Section 6.3). 

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