Xanthan in-situ rheology pseudoplastic behaviour

The general development of capillary bundle/non-Newtonian flow models usually takes the following pattern the Darcy velocity, u, for single-phase steady-state flow of fluid through a porous medium of length L is given by rearranging Equation 6.1 as follows  

Based on the capillary bundle model with equivalent radius given by Equation 6.9, several workers (Christopher and Middleman, 1965 Marshall and Mentzner, 1964 Teew and Hesselink, 1980 Greaves and Patel, 1985 Willhite and Uhl, 1986) have found that the equivalent wall shear rate for a power law fluid, 7p j, in a porous medium is given by Equation 6.10 above and that the Darcy velocity is given by the expression  

Hirasaki and Pope (1974) took a similar approach in which they described the apparent viscosity in the porous medium, as a power law function of the Darcy velocity, u, as follows  

For their approach, the equivalent shear rate in the porous medium is given 

Willhite and Uhl (1986, 1988) studied the flow of xanthan in Berea cores over the concentration range 500-1500 ppm and over a wide range of flow rates. Starting with equations 6.11 and 6.12 as theoretical models, they compared the experimentally measured in-core power law index and effective mobilities of the polymer solution with the bulk values of n and the viscosity prediction based on the power law equations. They found that the power law exponent for the flow of a xanthan biopolymer through Berea sandstone was larger than the bulk value for polymer concentrations above 500 ppm. Like Teew and Hesselink (1980), they found that the effective polymer viscosities are overestimated by the capillary bundle models. Similar results for the flow of xanthan through unconsolidated sandpacks have been found more recently by Hejri et al (1988). 

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POLYMER RHEOLOGY IN POROUS MEDIA 6.3.2 Xanthan in-situ rheology pseudoplastic behaviour... 

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