Porous media polymer rheology

The correlations represented by Eqs. 5.26a through 5.26e can be extended to interpolate for polymer concentrations between 1,000 and 2,000 ppm by use of a correlation based on the modified Blake-Kozeny model for the flow of non-Newtonian fluids. 62 Eq. 5.27 is an expression for A bk derived from the Blake-Kozeny model. Note that all parameters are either properties of the porous medium or rheological measurements. Eq. 5.27 underestimates A/ by about 50%. However, Hejri et al. 6 were able to correlate pBK and A for the unconsolidated sandpack data with Eq. 5.28. Eqs. 5.27 and 5.28, along with Eq. 5.24, predict polymer mobility for polymer concentrations ranging from l.,000 to 2,000 ppm within about 7%. 

A hypothesis is developed to explain the formation mechanism of the ROS ring by the polymer rheology in high pH caustic media influenced by the microscopic heterogeneity of porous medium. 

It appears, then, that the mechanical degradation process is intimately connected with the molecular structure of the macromolecule and the resulting fluid rheology that arises from this structure. For a flexible coil macromolecule, such as HPAM or polyethylene oxide, the polymer solutions are known to display viscoelastic behaviour (see Chapter 3) and thus a liquid relaxation time, may be defined as the time for the fluid to respond to the changing flow field in the porous medium. It may be computed from several possible models (Rouse, 1953 Warner, 1972 Durst et al, 1982 Haas and Durst, 1982 Bird et al. 1987). The finite extendible non-linear elastic (FENE) (Warner, 1972 Bird et al, 1987a Haas and Durst, 1982 Durst et al, 1982) dumbbell model of the polymer molecule may be used to find the relaxation time, tg, as it is known that this model provides a good description of HPAM flow in porous media (Durst et al, 1982 Haas and Durst, 1982) the expression for fe is ... 

The various early approaches to the mathematical modelling of non-Newtonian rheology in porous media are reviewed by Savins (1969). One of these is via a capillary bundle view of the porous medium combined with a simple (usually power law) fluid model. From the discussion in Section 6.2, one might not expect this approach to be very fruitful. However, it has been used by a number of workers—in fact, virtually all studies of xanthan flow in porous media present a version (see below)—and results have been sufficiently simple and promising to deserve some further attention. The main objective in these studies is to relate the in-situ rheology of the polymer to... 

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