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Modeling the rheological behavior of crude oil-water emulsions

During crude oil extraction, crude oil is often mixed with water, leading to the formation of water-in-oil (W/O) emulsions. Since these emulsions pose severe flow resistance, such as higher pressure drops, due to their complex fluid rheology, it is important to have in our arsenal a rheological constitutive model that accurately predicts their rheological response. In the present work, we propose such a model wherein the emulsions are modeled as deformable volume-preserving droplets via the use of a determinant-preserving contravariant second-rank tensor. We use the Generalized bracket formalism of non-equilibrium thermodynamics to make sure that the derived model is by construction thermodynamically admissible. An additional scalar structural variable is considered to allow for the prediction of a yielding point, following previous work. The predictions of the new model are shown to be in very good agreement with available experimental measurements.