Polymer Adsorption Effect on Relative Permeability and Capillary Pressure: Investigation of a Pore Scale Scenario
Authors: Barreau P. , Lasseux D. , Bertin H. , Glenat Ph. , Zaitoun A. 
Published: December 2007

Abstract
The present work deals with a numerical model where the porous medium is represented by a regular pore geometry, and aims at the evaluation in the change of two-phase flow properties induced by the introduction of an impenetrable polymer layer of constant thickness at the pore wall. The goal is to investigate the capability of this simple pore-scale scenario for polymer adsorption to account for phenomena observed experimentally at Darcy's scale.
Numerical experiments are performed to study the effect of an adsorbed polymer layer on two-phase flow properties in model pore geometries, with the wetting fluid (water) flowing near the walls, and the non-wetting one (oil) flowing through the central part of the pore channels. A two-dimensional, periodic convergent-divergent pore geometry is taken as a representative unit cell. The slow (Stokes) flow, resulting from the application of an external pressure gradient in the axial direction, is solved for both phases using a boundary integral element method. The polymer is considered to be solid but fully water saturated, resulting in a net pore size reduction. Relative permeabilities and capillary pressures are computed as a function of water saturation for a range of pore sizes, polymer layer thicknesses and flow rates.
Comparisons between the numerical results and previous experimental data indicate that this relatively simple polymer adsorption model, which involves just a wall effect, is successful in accounting for order of magnitude changes in relative permeabilities and capillary pressure.

Introduction
In some cases, direct injection of polymer or gels in production wells has proven to be an efficient method to prevent excessive water production. To understand the phenomenology, many experimental studies have investigated the resulting effect of a polymer injection on two-phase flow in porous media. All the studies indicate a selective action of the polymer with a significant reduction in the relative permeability to water with respect to the relative permeability to oil. The main physical phenomena that have been proposed to explain such a behavior are:
- partitioning of fluids leading to segregation of oil and water within the porous medium;
- lubrication effect of the polymer reducing pore wall roughness of the solid matrix;
- enhancement of water wettability due to adsorption of hydrophilic molecules.
Recent unsteady-state imbibition experiments confirmed the above result on relative permeabilities, and, in addition showed a strong increase in the capillary pressure after polymer injection. These results suggest that, in addition to the above mentioned mechanisms, the reduction of the pore diameter due to adsorption of polymer macromolecules, often referred to the "wall effect", is the dominant action of the polymer.
The objective of the present work is to qualitatively study the validity of this last hypothesis at the pore scale. It has to be emphasized that the goal is not to directly reproduce experimental situations with actual parameters, but rather to investigate the phenomenology of the problem for a test configuration. To do so, we perform numerical experiments of two-phase flow in a model pore 2D geometry using the boundary element technique. We compare numerical results obtained on relative permeabilities and capillary pressure as a function of water saturation, before and after polymer adsorption and for the same flow conditions.