Flow of Polymer Solutions Through Porous Media

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. JPT P. 1065ˆ

Stress levels in rapid extensional flows of polymeric fluids

“…[5] gives : [7] Provided the radial momentum flux terms (in the cylindrical coordinate system) are properly negligible it may be shown that the pressure gradient term of eq. [7] is zero, on the basis of symmetry arguments alone, i. e. independently of any constitutive approximations. Under these conditions eqs.…”

“…Under these conditions eqs. [4] and [7] give: [8] o It was noted earlier that replacement of vz with V, the mean velocity through the orifice, would lead to an error of less than 4%, this error being primarily due to the actual velocities not coinciding perfectly with their axial projections. The same arguments apply to the second term within the square brackets of eq.…”

“…[3], with the cone angle q) being small, pressure gradient term (-~) and that the of eq. [7] may be dropped. Both of these approximations am in error by no more than a few percent under the experimental conditions studied by Uebler, and will be better yet in flows at high Weissenberg numbers -flows at higher velocities or of more highly elastic fluids.…”

“…Nevertheless such deformations are of widespread recurrence in practice (3, 8, 9, 12-15, 18, 19) and appear to be of singular importance in distinguishing between poor and adequate constitutive equations in view of wide divergences in the predicted stress levels (2,11,13,21,22). Experimentally, extensional flows are difficult to generate under well-defined conditions and the available studies are subject to important restrictions as to the deformation rate levels attained (5,6) or the duration of the deformation process (1), or are studies in which the analysis of the deformation process was only indirect or approximate (7,12,17). The present study was one of a series undertaken with a view to resolution of this problem; data of semi-quantitative value are reported and the problems which must be resolved to enable fully quantitative results to be obtained are defined.…”

Flow of a FENE Fluid in Packed Beds or Porous Media

“…The formulations describing the flow of viscous fluids do not apply to viscoelastic fluids as a consequence of the discovery (Sadowski and Bird, 1965;Marshall and Metzner, 1967;Dauben and Menzie, 1967;Savins, 1969) that in flows through packed beds or porous media viscoelastic fluids exhibit enhanced potential drops exceeding those predicted on the basis of the viscous flow behaviour. It may be noted that Christopher and Middleman (1965) developed an equation based on the Kozeny-Ergun bed model (Kozicki, 2001) that successfully predicts the flow of high shear-thinning fluids (Kozicki and Tiu, 1988) and provides an improved fit of the data of Sadowski and Bird (1965).…”