Miscible Fluids Research Articles

Experimental investigation of nonlinear internal waves in deep water with miscible fluids

Laboratory experimental results are presented for nonlinear internal solitary waves (ISW) propagation in ‘deep water’ configuration with miscible fluids. The results are validated against direct numerical simulations and traveling wave exact solutions where the effect of the diffused interface is taken into account. The waves are generated by means of a dam break and their evolution is recorded with laser-induced fluorescence and particle image velocimetry. In particular, data collected in a frame moving with the waves are presented here for the first time. Our results are representative of geophysical applications in the deep ocean where weakly nonlinear theories fail to capture the characteristics of large amplitude ISWs from field observations.

Experimental and numerical research on the axial and radial concentration distribution feature of miscible fluid interfacial mixing process in products pipeline for industrial applications

During the process of sequential transportation of miscible but dissimilar fluid (MBDF) in pipelines, the adjacent of different kinds of MBDF will be mixed, leading to form a section of a liquid mixed segment in the pipeline which is an important aspect of mass transfer, especially in the multiproduct pipeline. This paper represents an experimental study of sequential transportation of MBDF in a single pipeline and thereby a set of experimental loop platform for sequential transportation has been designed. Several dimensionless indices including mixed segment length, axial tailing length, and radial difference have been proposed to measure the concentration distribution in the mixed segment (CDMS) in both axial and radial directions of a pipeline. A novel numerical model to simulate the CDMS of MBDF transported in a pipeline is also proposed and solved, where the turbulence effect, the difference in physical properties of the front and tail fluid, and the adsorption effect are taken into account to investigate the diffusion coefficient and concentration distribution. The complex flow and mass transfer in transportation process can be observed in the experiment and the results illustrate that the concentration profile is asymmetrical respect to the 50% concentration point at different time and distance, which is not revealed in the solutions of existing both numerical theory and empirical formula. The simulated results figure out the radial and axial feature of CDMS and achieve a good agreement with the experimental length of the mixed segment. Thus, the tailing phenomenon is found, analyzed and simulated. Those mentioned-above 3 kinds of effects are considered to form the tailing phenomenon in CDMS interactively. The overall uncertainty of the proposed dimensionless parameters has also been analyzed. The results reveal that the length of the tail of the mixed segment (LTMS) is 22% longer than that of the front (LFMS) when taking the 5% change of concentration as the judging criteria. The detection probe located at the center of the pipe earliest detects the CDMS while the probe near the pipe wall does latest. The corresponding detection time difference is up to 25.64%. Finally, the research results can provide guidance for delivering the refined oils sequentially and cutting the mixed segment in the industrial pipelines.

A two-layer model for buoyant displacement flows in a channel with wall slip

We study theoretically buoyant displacement flows of two generalized Newtonian fluids in a two-dimensional (2-D) channel with wall slip. We assume that a pseudo-interface separates two miscible (immiscible) fluids at the limit of negligible molecular diffusion (negligible surface tension). A heavy fluid displaces a light fluid at near-horizontal channel inclinations, implying that a stratified flow assumption is relevant. We develop a classical lubrication approximation model as a semi-analytical framework that includes a number of dimensionless parameters, such as a buoyancy number, the viscosity ratio, the non-Newtonian properties and the upper and lower wall slip coefficients. For specified interface heights and slopes, the reduced model can furnish the flux and velocity functions in displacing and displaced phases. We numerically solve the interface kinematic condition for four different wall slip cases: no slip (Case I), slip at the lower wall (Case II), slip at the upper wall (Case III) and slip at both walls (Case IV). The solutions for these cases deliver the interface propagation in time, for which leading and trailing displacement front heights, shapes and speeds and several key displacement features, such as front characteristic spreading lengths and short time behaviours, can be directly predicted by simplified analyses. The results reveal in detail how the presence of a channel wall slip may significantly affect the overall displacement flow and the interface evolution characteristics, for both Newtonian and non-Newtonian fluids. Regarding the latter, our analysis quantifies in particular the appearance and removal of static residual wall layers of the displaced phase, versus the wall slip cases.

Centrifugally forced Rayleigh–Taylor instability

We consider the effect of high rotation rates on two liquid layers that initially form concentric cylinders, centred on the axis of rotation. The configuration may be thought of as a fluid–fluid centrifuge. There are two types of perturbation to the interface that may be considered, an azimuthal perturbation around the circumference of the interface and a varicose perturbation in the axial direction along the length of the interface. It is the first of these types of perturbation that we consider here, and so the flow may be considered essentially two-dimensional, taking place in a circular domain. A linear stability analysis is carried out on a perturbation to the hydrostatic background state and a fourth-order Orr–Sommerfeld-like equation that governs the system is derived. We consider the dynamics of systems of stable and unstable configurations, inviscid and viscous fluids, immiscible fluid layers with surface tension and miscible fluid layers that may have some initial diffusion of density. In the most simple case of two layers of inviscid fluid separated by a sharp interface with no surface tension acting, we show that the effects of the curvature of the interface and the confinement of the system may be characterised by a modified Atwood number. The classical Atwood number is recovered in the limit of high azimuthal wavenumber, or the outer fluid layer being unconfined. Theoretical predictions are compared with numerical experiments and the agreement is shown to be good. We do not restrict our analysis to equal volume fluid layers and so our results also have applications in coating and lubrication problems in rapidly rotating systems and machinery.

Viscous Wave Breaking and Ligament Formation in Microfluidic Systems.

Rapid layering of viscous materials in microsystems encompasses a range of hydrodynamic instabilities that facilitate mixing and emulsification processes of fluids having large differences in viscosity. We experimentally study the stability of high-viscosity stratifications made of miscible and immiscible fluid pairs in square microchannels and characterize the propagation dynamics of interfacial waves, including breaking and viscous ligament entrainment from wave crests at moderate Reynolds numbers. For large viscosity contrasts, parallel fluid streams adopt widely different velocities and provide a simple model system to probe the role of inflectional instabilities of stratified microflows in relation with classic inviscid-stability theory. We reveal novel viscous wave regimes and unravel dispersion relationships in the presence and absence of interfacial tension. Detailed examination of wave celerity shows the existence of optimal operation conditions for passively disturbing miscible fluid flows and continuously dispersing low-and high-viscosity fluids at the small scale.

How valid is Taylor dispersion formula in slugs?

How valid is Taylor dispersion formula in slugs?

Thermodynamic phase behaviour and miscibility of confined fluids in nanopores

In this paper, thermodynamic phase behaviour and miscibility of confined pure and mixing fluids in nanopores are studied. First, a semi-analytical equation of state (EOS) is developed, based on which two correlations are modified to predict the shifts of critical temperature and pressure. Second, the thermodynamic free energy of mixing and solubility parameter are derived, quantitatively calculated, and applied to study the conditions and characteristics of the fluid miscibility in nanopores. Third, an improved EOS model with the modified correlations is proposed and used to calculate the phase properties and miscibility-associated quantities of three mixing fluids. The critical temperature and pressure of confined fluids are always decreased by reducing the pore radius. The negative pressure state is validated for a confined liquid, whose upper temperature limit is quantitatively determined and found to be lowered with the reduction of pore radius. The liquid–gas miscibility is beneficial from the pore radius reduction and the intermediate hydrocarbons (e.g., C2, C3, i- and n-C4) perform more miscible with the liquid C8 in comparison with the lean gas (e.g., N2 and CH4). Moreover, the molecular diameter of single liquid molecule is determined to be the bottom limit, the pore radius above which is concluded as a necessary condition for the liquid–gas miscibility. The calculated phase behaviour and minimum miscibility pressures (MMPs) of the three mixing fluids agree well with the literature results, which reveals that the shifts of critical properties dominate the phase behaviour and miscibility changes of confined fluids from bulk phase to nanopores.

Onset of miscible and immiscible fluids’ invasion into a viscoplastic fluid

We simulate fluid invasion into a gelled cement slurry using a scaled laboratory experiment. This process is relevant to the construction of oil and gas wells, in which a tall column of cement suspension must resist fluid invasion through a combination of static pressure, yield stress, and interfacial tension. The sufficiently over-pressured fluids may enter from the surrounding rocks, leading to failure of the well integrity. Here, we model the cement suspension using a Carbopol solution (yield stress fluid) and apply different over-pressured invading fluids through a centrally positioned hole at the bottom of the circular column. We study water, glycerin, silicon oil, and air as invading fluids, in order to delineate the effects of yield stress, interfacial tension, and column height on fluid invasion. We find that the invasion is easiest for miscible fluids that penetrate locally at significantly lower invasion pressures than immiscible fluids. Viscosity affects this process by retarding the initial diffusive mixing of the fluids, which tends to weaken the gel locally. More viscous invading fluids require larger invasion pressures and result in larger invasion domes. The silicon oil penetrated in the form of a slowly expanding dome, resisted at the walls of the column – effectively by a Poiseuille flow above it in the Carbopol. Invasion pressures were significantly larger than those for the glycerin solutions. The largest invasion pressures were, however, found for air, which is influenced approximately equally by interfacial tension and yield stress.

Multi-phase Fluid Simulation Based on Narrow-Band FLIP Method

Euler method and Lagrangian method is applicable for fluid of different deformation respectively. The fluid implicit particle (FLIP) method is a combination of Euler method and Lagrangian method which embodies the advantages of both in fluid simulation. While narrow-band FLIP (NBFLIP) method is an improved FLIP method which limits the particles within the Narrow Band near the interface. NBFLIP method improves the computational efficiency by eliminating particle outside the Narrow Band without degrading the details. In this paper, the multi-phase volume of fraction (VOF) model based on NBFLIP (NBFLIP-VOF) method is proposed. This is the first combination of multi-phase VOF model with NBFLIP method. The method employees a unified framework to deal with miscible and immiscible fluid simulation, the simulation results are highly consistent with the results from previous literature. The results show that the NBFLIP-VOF method has a good performance in the simulation of multi-phase flow, it also proves the reliability of the method and the adaptability in multi-phase fluid simulation.

Radial Viscous Fingering in Case of Poorly Miscible Fluids

The displacement of a viscous fluid from an annular Hele-Shaw cell with a source of finite radius by a less viscous one is investigated. A special case of poorly miscible fluids is considered when corresponding dimensionless criteria—capillary and Peclet numbers—both tend to infinity. Brinkman model which additionally takes into account small viscous forces in a plane of the cell is used to describe the displacement process. Linear analysis shows a stabilizing effect of viscous forces and reveals a geometrical similarity criterion, namely the ratio of the interface’s radius to the gap between the cell’s plates. The displacement patterns, obtained numerically under Brinkman model, are very sensitive to the discovered criterion. The comparison with available experimental data is acceptable.

Two-layer displacement flow of miscible fluids with viscosity ratio: Experiments

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.

The effect of viscosity ratio on the dispersal of fracturing fluids into groundwater system

In the development of oil and gas reservoirs, the transport of miscible fluids in porous rocks is a key issue for oil and gas recovery. The simplified unidirectional flow model is employed to investigate the effects of the viscosity ratio on dispersion in semi-infinite homogenous media. The viscosity is supposed to be unsteady due to changing component concentration over time. In cases of both a viscosity ratio larger and less than 1, the pollutant concentration and flow velocity are computed at different initial conditions and viscosity ratios. The analytical solutions are then developed by introducing new variables and transforming the equation governing advection–diffusion equation in semi-infinite homogeneous media with a continuous source. A comparison of the numerical solution with the analytical solution revealed a similarity over 98%, highlighting the usability of the analytical solution. If the viscosity ratio is larger than 1, flow velocity declines exponentially and concentration attenuates with transporting time. In addition, the timescale plays a significant role and the effects become more prominent in long-term transport. In the case of a viscosity ratio less than 1, both the timescale and viscosity ratio variables have little influence on the changing speed of the concentration profile. This work helps to predict the position and the time required to reach the harmless pollutant concentration when monitoring fracturing fluids transportation into groundwater system and would be especially useful in designing and interpreting laboratory experiments studying the miscible flow.

T-mixer operating with water at different temperatures: Simulation and stability analysis

Flow patterns within a T-mixer are studied numerically when there is a temperature jump between the entering streams. The complex temperature distribution in the outlet channel affects the resulting mixing between the two miscible fluids as well as the bifurcation leading to the engulfment regime.

Reversible and Irreversible Tracer Dispersion in an Oscillating Flow Inside a Model Rough Fracture

Fil: Roht, Yanina Lucrecia. Universidad de Buenos Aires. Facultad de Ingenieria. Departamento de Fisica. Grupo de Medios Porosos; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina

Phase separation during mixing of partially miscible fluids under near-critical and supercritical conditions, and the phenomenon of “uphill diffusion”

Partially miscible fluids often exhibit complex behavior. While previous studies have focused on the phase characteristics, the coupled phase equilibrium and transport processes under near-critical/supercritical conditions are not well studied. Here, the binary/ternary phase equilibria of light oil (maltenes)—heavy oil (asphaltenes)—water mixtures, are examined at 25 MPa and 640–660 K. Within this temperature range, three regimes exist in the ternary phase diagram. Next, the mixing of a two-component oil droplet under near-critical/supercritical water is studied numerically. In the simulations, the evolution and final distribution of the oils in the different phases depend on the temperature. The number of distinct zones in space and oil concentration in each zone are consistent with the phase diagram, while the separation process is driven by the heat and mass transfer from the bulk water phase to the oil droplet. The transport of the heavier oil exhibits the so-called “uphill diffusion”.

Gravitational Fingering Due to Density Increase by Mixing at a Vertical Displacing Front in Porous Media

CO2-improved oil recovery has been applied in petroleum production for many years. CO2 injection has attracted increasing attention because it represents a possible solution for the reduction of the CO2 concentration in the atmosphere to reduce greenhouse gas emissions and improve oil recovery. The density increase from CO2 dissolution in oil creates an unstable high-density layer and leads to gravitational fingers, which may have a significant effect on the mixing and flow path. In this work, we modeled gravitational fingering during injection by a miscible fluid pair with nonlinear density property and investigated the properties of the fingering resulting from the density increase by mixing in porous media using three-dimensional X-ray computer tomography. During the injection process, the mixing near the interface was enhanced, and slight fluctuations appeared at the interface, which grew into high-concentration fingers that interacted and merged with neighboring fingers and extended vertically downwa...

Three-dimensional structure of viscous fingering in miscible fluids

Three-dimensional structure of viscous fingering in miscible fluids

Dynamical behaviour of miscibles fluids in porous media

In this paper, we are interested in studying the dynamics of miscible fluids in porous media. The model describing this issue is a system of equations, coupling the standard Navier-Stokes equations with gravity g as external force and a convective diffusion equation for a dilute concentration in the carrier fluid. By assuming that the fluids are incompressible, we first derive a new system of equations, by taking into account additional terms, due to the concentration inhomogeneties and an interfacial tension between the fluids. Then we propose a numerical approach to solve our system in order to illustrate the effectiveness of the dynamics during the fluid miscibility process. At this stage, we start by showing a stability result for our numerical scheme and then present numerical results.

Effect of diffusing layer thickness on the density-driven natural convection of miscible fluids in porous media: Modeling of mass transport

Effect of diffusing layer thickness on the density-driven natural convection of miscible fluids in porous media: Modeling of mass transport

What is the final size of turbulent mixing zones driven by the Faraday instability?

Miscible fluids of different densities subjected to strong time-periodic accelerations normal to their interface can mix due to Faraday instability effects. Turbulent fluctuations generated by this mechanism lead to the emergence and the growth of a mixing layer. Its enlargement is gradually slowed down as the resonance conditions driving the instability cease to be fulfilled. The final state corresponds to a saturated mixing zone in which the turbulence intensity progressively decays. A new formalism based on second-order correlation spectra for the turbulent quantities is introduced for this problem. This method allows for the prediction of the final mixing zone size and extends results from classical stability analysis limited to weakly nonlinear regimes. We perform at various forcing frequencies and amplitudes a large set of homogeneous and inhomogeneous numerical simulations, extensively exploring the influence of initial conditions. The mixing zone widths, measured at the end of the simulations, are satisfactorily compared to the predictions, and bring a strong support to the proposed theory. The flow dynamics is also studied and reveals the presence of sub-harmonic as well as harmonic modes depending on the initial parameters in the Mathieu phase diagram. Important changes in the flow anisotropy, corresponding to the large scale structures of turbulence, occur. This phenomenon appears directly related to the orientation of the most amplified gravity waves excited in the system, evolving due to the enlargement of the mixing zone.