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Displacement flow of miscible fluids with density and viscosity contrast Etrati, Ali


We study downward displacement flow of buoyant miscible fluids with viscosity ratio in a pipe, using experimental, numerical and mathematical approaches. Investigation of this problem is mainly motivated by the primary cementing process in oil and gas well construction. Our focus is on displacements where the degree of transverse mixing is low-moderate and thus a two-layer, stratified flow is observed. An inertial two-layer model for stratified density-unstable displacement flows is developed. From experiments it has been observed that these flows develop for a significant range of parameters. Due to significant inertial effects, existing models are not effective for predicting these flows. The novelty of this model is that the inertia terms are retained, and the wall and interfacial stresses are modelled. With numerical solution of the model, back-flow, displacement efficiency and instability onset predictions are made for different viscosity ratios. The experiments are conducted in a long pipe, inclined at an angle which is varied from vertical to near-horizontal. Viscosity ratio is achieved by adding xanthan gum to the fluids. At each angle, flow rate and viscosity ratio are varied at fixed density contrast. Density-unstable flows regimes are mapped in the (Fr, Re cosß/Fr)-plane, delineated in terms of interfacial instability, front dynamics and front velocity. Amongst the many observations we find that viscosifying the less dense fluid tends to significantly destabilize the flow, for density-unstable configuration. Different instabilities develop at the interface and in the wall-layers. The results are compared to the inertial two-layer model. In density-stable experiments we mostly focus on the effects of viscosity ratio on displacement efficiency and stability of wall-layer. Unique instabilities appear in the case of shear-thinning displacements. Displacement efficiency decreases with increasing viscosity ratio, flow rate and inclination angle. Finally, a number of three-dimensional parallel numerical simulations are completed in the pipe geometry, covering both density-stable and unstable flows. Unsteady Navier-Stokes equations are solved and the Volume of Fluid (VOF) method is used to capture the interface between the fluids. The results give us great insight into several features of these flows that were not available from experiments or 2D simulations.

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