The fate of continuous input of relatively heavy fluid at the base of a porous medium

We evaluate theoretically and confirm experimentally the shape of the fluid envelope resulting from the input of relatively heavy fluid at a constant rate from a point source at the base of a homogeneous porous medium. In three dimensions an initially expanding hemisphere transitions into a gravity current flowing over the assumed rigid, horizontal and impermeable bottom of the porous medium. A range of increasing transition times occurs if defined by extrapolation of the relationships in the two extreme regimes (hemispherical shape and thin-layer gravity current) so that they intersect, for: the ratio of buoyancy to fluid resistance; the horizontal extent of the fluid; the ratio of height at the centre to the radius; and just the height at the centre. Corresponding results are derived for two-dimensional geometries. In this case, we conduct a series of laboratory experiments demonstrating the transition between the radial and gravity current regimes both in terms of form and propagation rate. The results are extrapolated briefly to two-layer systems, in order to begin to understand effects due to vertically heterogeneous pore structures. We sketch, and verify by experiment, that an expanding hemisphere in a lower layer can reach a much more permeable upper layer and flow through it as a gravity current, thereby uniting the two regimes.

Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

The Rayleigh–Taylor instability in a porous medium

The classical Rayleigh–Taylor instability occurs when a heavy fluid overlies a lighter one, and the two fluids are separated by a horizontal interface. The configuration is unstable, and a small perturbation to the interface grows with time. Here, we consider such an arrangement for planar flow, but in a porous medium governed by Darcy’s law. First, the fully saturated situation is considered, where the two horizontal fluids are separated by a sharp interface. A classical linearized theory is reviewed, and the nonlinear model is solved numerically. It is shown that the solution is ultimately limited in time by the formation of a curvature singularity at the interface. A partially saturated Boussinesq theory is then presented, and its linearized approximation predicts a stable interface that merely diffuses. Nonlinear Boussinesq theory, however, allows the growth of drips and bubbles at the interface. These structures develop with no apparent overturning at their heads, unlike the corresponding flow for two free fluids.

Experiments on Fluid Placement in a Confined Pipe: Fluid Mechanics Analysis for Plug and Abandonment Applications

Plug and abandonment (P&A) of oil and gas wells is an essential process to prevent the oil and gas reservoir fluids migration over time and possibly contaminating other formations and also fresh water resources. In order to plug and abandon a well, a high quality cement plug placement is required. One of the most common methods of cement plug placement is the dump bailing method. In this method, a fixed volume of cement is dumped using a bailer on a mechanical plug in the wellbore. The cement slurry occupies the wellbore and also the annular region outside the dump bailer. In the processes of cement slurry placement, an extensive range of Newtonian or non-Newtonian fluids is used to remove the in-situ fluid (drilling fluid or water) in the wellbore. Based on the large number of parameters such as the density and viscosity differences between the fluids, the geometry type (pipe, annulus, etc.), the operation conditions (velocity, geometry inclination, dumping height), various kinds of placement and mixing flows can occur, and different flow regimes (e.g. inertial, viscous) can develop. In this paper, we experimentally study the placement of a heavy fluid to replace an in-situ light fluid in an inclined closed-end pipe (representative of the dump bailing method). The two fluids are Newtonian and miscible, and they have the same viscosity. We investigate the effects of some of the flow parameters such as the dumping height, the pipe inclination, and the inflow velocity of the heavy fluid on the degree of mixing and the placement quality and efficiency. Our results show that the the most efficient displacement happens with the shortest dumping height and at lower inclination from vertical. Also, a high inflow velocity displaces the light fluid promptly with more mixing in comparison with a low inflow rate. The results can help us to develop strategies for improving the dump bailing method in the P&A of the oil and gas wells.

Phase-Field-Based LBM Analysis of KHI and RTI in Wide Ranges of Density Ratio, Viscosity Ratio, and Reynolds Number

Numerous studies have elaborated the dominated roles of Kelvin-Helmholtz instability (KHI) and Rayleigh-Taylor instability (RTI) in the liquid sheet breakup and primary atomization. As for applications in aeronautics, the liquid-gas mixing generally occurs at the challenging conditions of a large density ratio and high Reynolds number. Hence, the evaluation of KHI and RTI under such challenging conditions will have great significance in better understanding the destabilizing mechanism of the liquid layer. To this end, a lattice Boltzmann multiple-relaxation-time (MRT) two-phase model, based on the conservative Allen-Cahn equation, is reconstructed for the present study. Preliminarily, the numerical stability and accuracy of this MRT model are tested by Laplace’s law under a large density ratio and high Reynolds number, including the sensitivity study to the values of mobility. Afterward, KHI and RTI are investigated in wide ranges of the Reynolds number, density ratio, and viscosity ratio. Numerical results indicate that the enhanced viscous force of light fluid with an increasing viscosity ratio notably suppresses the roll-ups of heavy fluid in KHI and RTI. As for the density ratio, it generally shows negative impacts on fluid-mixing in KHI and spike-spiraling in RTI. However, when the density ratio and the Reynolds number both arrive at high levels, the Kelvin-Helmholtz wavelets aroused by a dominated inertia force of heavy fluid trigger severe interface disintegration. The above results once more demonstrate the excellent ability of the present model in dealing with challenging conditions. Besides, the morphological characteristics of KHI and RTI at a high Reynolds number and large density ratio also greatly support the typical interface breakup mechanism observed in primary atomization.