Analysis of Factors Influencing Mobility and Adsorption in the Flow of Polymer Solution Through Porous Media
Authors: Hirasaki G.J. , Pope G.A. 
Published: December 2007

Abstract
Displacement of oil by polymer solution has several unique characteristics that are not present in normal waterflooding. These include non-Newtonian effects, permeability reduction, and polymer adsorption. polymer adsorption. The rheological behavior of the flow of polymer solution through porous media could be Newtonian at low flow rates, pseudoplastic at intermediate flow rates, and dilatant at high flow rates. The pseudoplastic behavior is modeled with the pseudoplastic behavior is modeled with the Blake-Kozeny model for power-law model fluids. The dilatant behavior is modeled with the viscoelastic properties of the polymer solution. properties of the polymer solution. The reduction in permeability is postulated to be due to an adsorbed layer of polymer molecular coils that reduces the effective size of the pores. A dimensionless number has been formulated to correlate the permeability reduction factor with the polymer, brine, and rock properties. This polymer, brine, and rock properties. This dimensionless number represents the ratio of the size of the polymer molecular coil to an effective pore radius polymer molecular coil to an effective pore radius of the porous medium.A model has been developed to represent adsorption as a function of polymer, brine, and rock properties. The model assumes that the polymer is properties. The model assumes that the polymer is adsorbed on the surface of the porous medium as a monolayer of molecular coils that have a segment density greater than the molecular coil in dilute solution.

Introduction
Displacement of oil by polymer solutions has several unique characteristics that are not present in normal waterflooding. These include non-Newtonian effects, permeability reduction, and polymer adsorption. In principle, the effects could polymer adsorption. In principle, the effects could be measured experimentally for each fluid-rock system of interest over the entire range of flow conditions existing in the reservoir. However, there are seldom complete data on all systems of interest. A correlation that represents these effects as a function of the polymer, brine, rock properties, and flow conditions would result in a more accurate evaluation of systems that may not have been measured in the laboratory at the desired conditions. Moreover, if the dependence of these effects on the system properties were known, it would aid the search for an optimal system. A model is proposed for representing the effects as a function of the system properties. The model is consistent with a number of experimental observations but enough data have not yet been acquired to determine the extent of applicability of a correlation. It is hoped that the presentation of these models will encourage further research to verify or improve the models.

MODEL FOR PSEUDOPLASTIC FLOW THROUGH POROUS MEDIA
The Blake-Kozeny model represents the porous medium as a bundle of capillary tubes with a length that is greater than the length of the porous medium by a tortuosity factor, tau. The equivalent radius of the capillary tubes can be related to the particle diameter of a packed bed from the hydraulic radius concept or to the permeability and porosity by comparison with Darcy's law for Newtonian fluids.The modified Blake-Kozeny models represents the flow of a power-law fluid in the capillaries. The relationship between the pressure drop and flow rate can be expressed as a product of the friction factor and Reynolds number.(1)
This expression can be related to the apparent viscosity and the rock permeability and porosity through the following relationships:(2)
where(3)
SPEJ
P. 337