We study characteristics of miscible displacement flows in inclined pipes with density-stable configuration, meaning the lighter fluid is pumped to displace the heavier fluid downward along the pipe. Experiments have been completed in a pipe covering a broad range of inclination angles, flow rates, and viscosity configurations. Viscosity contrast between the fluids is obtained by adding xanthan gum to water, while glycerol is used to achieve density difference. Novel instabilities appear in the case of shear-thinning displacements. Numerical simulations are performed using the finite volume package OpenFOAM. The unsteady three-dimensional Navier-Stokes equations are used with the volume of fluid method to capture the interface between the fluids. A number of numerical cases are compared against the experiments to benchmark the model favourably. The code allows us to examine in detail the 3D structure of the propagating front and other secondary flows.
We investigate the inertial flows found in buoyant miscible displacements using a two-layer model. From displacement flow experiments in inclined pipes, it has been observed that for significant ranges of Fr and Re cos β/Fr, a two-layer, stratified flow develops with the heavier fluid moving at the bottom of the pipe. Due to significant inertial effects, thin-film/lubrication models developed for laminar, viscous flows are not effective for predicting these flows. Here we develop a displacement model that addresses this shortcoming. The complete model for the displacement flow consists of mass and momentum equations for each fluid, resulting in a set of four non-linear equations. By integrating over each layer and eliminating the pressure gradient, we reduce the system to two equations for the area and mean velocity of the heavy fluid layer. The wall and interfacial stresses appear as source terms in the reduced system. The final system of equations is solved numerically using a robust, shock-capturing scheme. The equations are stabilized to remove non-physical instabilities. A linear stability analysis is able to predict the onset of instabilities at the interface and together with numerical solution, is used to study displacement effectiveness over different parametric regimes. Backflow and instability onset predictions are made for different viscosity ratios.
We investigate experimentally the density-unstable displacement flow of two miscible fluids along an inclined pipe. This means that the flow is from the top to bottom of the pipe (downwards), with the more dense fluid above the less dense. Whereas past studies have focused on iso-viscous displacements, here we consider viscosity ratios in the range 1/10–10. Our focus is on displacements where the degree of transverse mixing is low-moderate, and thus a two-layer, stratified flow is observed. A wide range of parameters is covered in order to observe the resulting flow regimes and to understand the effect of the viscosity contrast. The inclination of the pipe (β) is varied from near horizontal β = 85° to near vertical β = 10°. At each angle, the flow rate and viscosity ratio are varied at fixed density contrast. Flow regimes are mapped in the (Fr, Re cos β/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. Different instabilities develop at the interface and in the wall-layers.
We present a numerical investigation of laminar miscible displacement flows in narrow, vertical, eccentric annuli. This study is motivated by the primary cementing stage of oil and gas well production, where successful displacement of drilling mud is crucial for the well integrity and zonal isolation. The large number of characterizing parameters makes a complete description of such flows challenging. In turn, this means that the design of effective strategies for primary cementing is a difficult task. As a result the existing literature is mostly based on non-inertial Hele-Shaw models and experiments in narrow annuli, where the dimensionality of the problem is reduced. In this preliminary study, we run a series of three-dimensional numerical simulations, using a Volume of Fluid (VOF) method to capture the interface between the fluids. Both Newtonian and non-Newtonian fluids are considered, and a variety of different phenomena are observed, e.g. dispersive spikes, static layers, instabilities and secondary flows. The range of flow parameters used in the simulations are similar to existing experimental data to allow for a preliminary comparison. The results show qualitative agreement with the experiments and gap-averaged models.
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