Media apparent shear rate

Thus, the above prescription represents the most common general approach to the problem of relating the bulk viscometric behaviour to that observed in porous media. It is applied by taking Equation 3.73 for the wall shear rate of a power law fluid and then replacing and R by Equations 6.3 and 6.9 respectively. This leads to an expression for the apparent shear rate in the porous medium, y, of the form ... 

A similar thing takes place when we consider flow curves obtained at different temperatures. As seen from Fig. 7, if we take a region of low shear rates, then due to the absence of the temperature dependence Y, the apparent activation energy vanishes. At sufficiently high shear rates, when a polymer dispersion medium flows, the activation energy becomes equal to the activation energy of the viscous flow of a polymer melt and the presence of the filler in this ratio is of little importance. 

The emulsion behaviour in porous media is discussed in [235]. O/w emulsions with volume fractions of up to 50% show Newtonian behaviour, whereas those with more than 50% are non-Newtonian liquids, the apparent viscosity of which depends on the shear rate. The viscosities of such emulsions are more than 20 times that of water and sometimes can be even comparable with that of oil. When the emulsion is moving, a temporary permeability reduction of the reservoir may occur due to the capture of small droplets by the surface of the porous medium. In this case, stable o/w emulsions may flow not as a continuous liquid, i.e. the emulsion flow largely depends on the nature of the porous medium. Therefore, it is necessary to know about the structure and physicochemical characteristics of the oil reservoir (porous medium) porosity, the mean pore diameter, the mean pore size and pore size distribution, chemical composition of the minerals ( acidic , basic , neutral ), the nature of the pore surface, first of all wettability, for a successful application of the emulsion flooding method. 

Cannella et al (1988) use the following expressions for the apparent porous medium shear rate, 7p, and apparent viscosity,... 

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).

Both phenomena can be understood if the local shear rate in the fluid around the particles is considered. Local rates increase more with concentration than the average shear rate does and thus reduce the apparent medium viscosity. The resulting shift in the curves can be partially compensated if the relative viscosities are calculated from medium and suspension viscosities at equal values of the shear stress, rather than at equal shear rates. 

---