The modeling and numerical simulation of processes such as polymer placement for water control, fluid loss control during drilling, polymer based chemical flooding and the interpretation of the related laboratory studies need a correct quantification of the apparent viscosity of polymers in porous media.

Past experimental and theoretical studies have shown that, in the absence of adsorption, the viscosity of polymer solutions decreases in porous media due to polymer depletion near pore walls. The proposed models considered pores that are relatively large with respect to the thickness of the depletion zones and assumed Newtonian flow. The two fluid model, in particular, is based on a discontinuous concentration profile. These characteristics give rise to limitations in the estimation of the apparent viscosity in porous media with very small pores.

In this paper we provide new insights on the depletion effect and develop a new model for the apparent viscosity, taking into account an exact polymer depletion concentration profile and the Non-Newtonian character of the polymer solutions. In this way we are able to predict the lowering of the apparent viscosity in pores over entire ranges of pore radii. Using analytical and numerical hydrodynamic calculations, we investigate the influence of the parameters (polymer concentration, ratio between the thickness of the depletion layer and effective pore radius, velocity gradient, etc.). Model predictions are found to be in good agreement with experiments available in the literature.

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