Flow of polymer solutions through porous media: link between the pore-scale physics and the macroscale behaviour

When a complex fluid is flowing through a porous medium, in addition to the fluid intrinsic physics, the multi-scale properties of the porous structure play a significant role. From the interaction between these features arise a great number of complex physical phenomena. The understanding and the modelling of the variety of these phenomena involved at the small scales and their impact on the large scales is the subject of intense work. In this thesis, the fluids we consider are polymer solutions and the porous media are typical sandstones met in petroleum applications. In petroleum engineering, the injection of a polymer slug into the oil-bearing reservoir is indeed a method commonly used in enhanced oil recovery. This method allows to increase the sweep efficiency, hence to improve the oil production of the reservoir. Due to the non-Newtonian rheology induced by the polymer molecules as well as specific mechanisms occurring at the liquid/solid interface, a polymer solution may be qualified as a complex fluid. The goal of this thesis is to investigate the non-Newtonian rheology and the behavior of the polymer molecules near the liquid/solid interface. These phenomena are related to macro-scale effective properties. To thoroughly address this goal, we perform numerical simulations of flows through porous media. The goal is to obtain a better understanding of the underlying physics and, furthermore, we wish to propose possible improvements of the models that are currently used in reservoir simulators. Primarily, we are interested in the macro-scale transition from a Newtonian to a non-Newtonian flow (Chapter 3). This transition is induced by the non-Newtonian rheology. By simulating flows through a wide panel of porous media, we study the macro-scale transition. An analysis of the fluid mechanics involved allows us to propose a simple model for the critical average velocity at which the transition occurs. In addition, we study the apparent slip induced by a repulsive mechanism of the polymer chains from the liquid/solid interface (Chapter 4). We propose a pore-scale model to this mechanism. By performing comparisons with experimental datasets, we show that the model allows for a good description of the observed macro-scale behavior. Finally, with direct simulations over periodic media, we link the phenomenology at the micro and macro-scale for the flow of non-Newtonian fluids (Chapter 5). On a fundamental level, we study the competition that emerges between the nonlinearity induced by the rheology and the disorder inherent to the porous structure. The results are related to models commonly used in reservoir simulators. (author)