Flow of Polymer Solutions Through Porous Media
Authors: Dauben D.L. , Menzie D.E. 
Published: December 2007

Abstract
This paper discusses the physical parameters involved in the slow flow of high molecular weight polymer solutions in porous media. The interacting erects of polymer properties and porous media properties on flow performance are considered. Experiments were conducted with the polyethylene oxides, with molecular weights ranging from 200,000 to over 5,000,000. Frontal advance velocities ranged from 1 to 30 ft/day. The porous matrix consisted of a flow cell packed with glass beads. Polymer solutions were characterized by viscosity and normal stress measurement. Under certain condition, unexpectedly high Row resistance was observed. This behavior was observed to be a function of flow rate, pore size, polymer molecular weight and concentration. The polymer solutions exhibit "dilatant" flow behavior in porous media in contrast with the pseudo plastic behavior in simple flow systems. A theoretical explanation of such behavior is presented.

Introduction
The use of polymers in the injected water of a waterflood increases oil displacement efficiency by reducing the mobility (kw/uw) of the driving phase. A reduced driving phase mobility results in improvements in the areal sweep efficiency and in the vertical coverage in stratified reservoirs. This mobility reduction may be achieved by a permeability reduction, a viscosity increase or by a combination of the two. Early attempts at increasing the injected water viscosity were not successful because of the poor economics involved. The use of such materials as glycerin, sugar or glycols to increase water viscosity was not economically feasible. Attempts in using certain naturally occurring polymers were not too successful because of the high polymer losses to the rock. A high molecular weight, partially hydrolyzed polyacrylamide was introduced 3 years ago as a waterflood additive. Initial work by Pye indicated that the presence of these polymers in dilute concentrations decreases the water mobility 5 to 20 times more than would be expected from measurements of the solution viscosity. Such an effect would be of obvious economic value since only a small polymer concentration would be required to accomplish a large reduction in water mobility. This research was designed to study the basic flow mechanisms of polymer solutions in porous media. The interacting effects of polymer properties and porous media properties on flow performance are considered. This study indicates some of the conditions under which these interactions can lead to significant mobility effects.

DEFINITION OF PROBLEM
The Darcy equation
........................................(1)
is valid only for Newtonian fluids. For polymer solutions and other non-Newtonian fluids the equation must be modified to consider that viscosity is a variable quantity.
Modification of the Darcy equation to include non-Newtonian effects has been the subject of several recent investigations. The modifications generally adopt a rheological model, such as an Ellis or power law model, to porous media by defining some characteristic channel radius. Most of these studies showed the porous media flow behavior to be predictable from viscometric data. Investigations involving the flow of high molecular weight polyacrylamide solutions through cores have generally encountered the high flow resistances reported previously by Pye. This high flow resistance has generally been attributed to an in-depth permeability reduction, as evidenced by a reduced permeability to water which has displaced polymer solution from the porous media. Marshall and Metzner report high flow resistances, which they attribute to viscoelastic effects. In this paper, the effects of polymer molecular weight. pore size, flow rate and concentration are considered. The polymers used are the polyethylene oxides known as Polyox. This class of polymers was used because of its availability in a wide range of molecular weights and because of its known ability to propagate well through porous media.

THEORY: PHYSICAL PROPERTIES OF POLYMER SOLUTIONS
The polymer molecule dissolves in water by means of hydrogen bonding, but retains some of its own structural identity while in solution. Nonionic polymers, such as polyethylene oxide, are generally considered to have a random coiling configuration. This type of molecule has the ability to "sequester" or hold a large volume of solvent within its coils in a manner similar to that of a sponge.