Previously, we developed a microscopic model for the bridging adsorption of flexible chains, during non-inertial flow of polymer solutions through granular porous media. Owing to its local character, that model does not take into account the filtration of the largest polymer molecules, while this filtration appears to be one of the essential features of bridging adsorption, from both fundamental and practical standpoints. During polymer placement for water control, for instance, polymer propagates over distances of several inches enabling filtration of polymer to take place.

In this paper, we develop a macroscopic model for layer and bridging adsorption during polymer flow through porous media. Our emphasis is on the filtration of the largest chains induced by bridging adsorption. In order to describe this effect, we introduce for the first time a space and time dependent probability (or fraction) of the largest chains. Our model condenses in a non-linear system of four partial differential equations describing polymer and the largest mass conservation and layer and bridging adsorption kinetics. The model appears to be relevant, beyond the description of bridging adsorption, to several in-depth filtration processes induced by flow and retention.

By physical arguments based upon previous experimental observations, we reduce the general equations to a simpler formulation for which we were able to derive an approximate analytical solution. We prove that, in one simple case, the concentration and the bridging adsorption probability profiles in the core decrease exponentially as a function of the distance from core inlet. The influence of the determinant parameters (velocity gradient, adsorption energy, etc.) is discussed. We show that the model is in good agreement with previous experiments conducted under well-controlled conditions.

You can access this article if you purchase or spend a download.