Miscible Fluids Research Articles

Lattice Boltzmann method for diffusion-limited partial dissolution of fluids.

A lattice Boltzmann model for two partially miscible fluids is developed. By partially miscible we mean that, although there is a definite interfacial region separating the two fluids with a surface tension force acting at all points of the transition region, each fluid can nonetheless accept molecules from the other fluid up to a set solubility limit. We allow each fluid to diffuse into the other with the solubility and diffusivity in each fluid being input parameters. The approach is to define two regions within the fluid: one interfacial region having finite width, across which most of the concentration change occurs, and in which a surface tension force and color separation step are allowed for and one miscible fluid region where the concentration of the binary fluids follows an advection-diffusion equation and the mixture as a whole obeys the Navier-Stokes incompressible flow equations. Numerical examples are presented in which the algorithm produces results that are quantitatively compared to exact analytical results as well as qualitatively examined for their reasonableness. The model has the ability to simulate how bubbles of one fluid flow through another while dissolving their contents as well as to simulate a range of practical invasion problems such as injecting supercritical CO(2) into a porous material saturated with water for sequestration purposes.

Minimum miscibility pressure estimation for a CO2/n-decane system in porous media by X-ray CT

Accurate determination of gas–fluid miscibility conditions is important to optimize the displacement efficiency during CO2-enhanced oil recovery. This paper presents a new technique to investigate the phase behavior and to estimate the minimum miscibility pressure (MMP) of a CO2/n-decane system using an X-ray computerized tomography (CT) scanner. CT scans of the CO2/n-decane system are taken at various pressures during the experiments. The image intensity values taken from the CT images have a linear relationship with the densities of the measured objects; therefore, we can estimate the miscible point of CO2 and n-decane because the difference between the intensity values for each phase decays to zero as the pressure increases toward the MMP. This paper provides experimental evidence for the validity of the new CT method by comparing the results with previous studies and presents an application of the method to investigate the MMP of the CO2/n-decane system in porous media. Additionally, the influence of porous media on the equilibrium state when the CO2/n-decane system is close to miscibility is discussed.

Anisotropic Dispersion and Upscaling for Miscible Displacement

Summary Dispersion is the irreversible mixing that occurs during miscible displacements. Dispersion can reduce local displacement efficiency by lessening solvent peak concentration or increase volumetric sweep efficiency by spreading of the injected solvent to more of the reservoir. Dispersion is therefore an important parameter in predicting and simulating miscible displacements. The difficulty of simulating miscible displacement and understanding the effect of dispersion is also compounded by numerical dispersion, which increases the apparent dispersion in finite-difference simulation models. This paper presents an approach to estimate the total longitudinal and transverse dispersion in large-scale media by use of continuous solvent injection in a medium of finite thickness. The simulations are based on the experimental arrangement of Blackwell (1962) to estimate transverse dispersion, with experiments consisting of coinjecting two miscible fluids into different sections of the medium at similar rates. This model arrangement, coupled with analytical solutions for the 2D convection/dispersion equation for a continuously injected solvent, allows us to determine longitudinal and transverse dispersivity simultaneously for the flow medium. In this manner, we investigate the effects of stochastic permeability distributions and other scaling groups affecting first-contact-miscible simulations on dispersion. Sensitivity analysis of dispersion in stochastic permeability fields confirms that both longitudinal and transverse dispersion are scale dependent. Results also show that the effect of increasing autocorrelation of cell permeability in the longitudinal direction (parallel to flow) is to increase longitudinal dispersion, as solvent travels through more continuous layers, while reducing transverse dispersion. Increasing autocorrelation in the transverse direction reduces dispersion in both directions. This reduction is caused by equilibration of solvent concentrations in continuous sections of the reservoir, resulting in reduced solute fingering and channeling. Finally, we developed a simple procedure to use the estimated dispersivities to determine a priori the maximum gridblock size that will maintain an equivalent level of dispersion between fine-scale models and upscaled coarse models. Large gridblock sizes can be used for highly heterogeneous and layered reservoir models. Nonuniform coarsening (upscaling) methods were also recommended and validated for reservoir models with sets of sequential but different permeability distributions. The procedure was extended to multicontact miscible simulations. The sweep and recovery from upscaled multicontact miscible simulations were comparable with those of fine-scale models.

Theoretical analysis on the onset of buoyancy-driven instability of horizontal interfaces between miscible fluids in a Hele–Shaw cell

The stability of the initially sharp interface between two miscible fluids saturated in a Hele–Shaw cell is analyzed. Based on the 2-dimensional Navier–Stokes–Brinkman (NSB) equation and its modification, new linear stability equations are derived in the similar (τ, ζ)-domain, and solved analytically and numerically with and without a quasi-steady state approximation (QSSA). Through the exact eigenanalysis without the QSSA, it is found that the system is unconditionally stable and the most unstable initial disturbance exists. The initial value problem analysis is conducted in the global (τ, z)-domain and also the similar (τ, ζ)-domain. It is interesting that for the present system, the linear stability characteristics obtained using the various methods support to each other. Using the linear stability results as a starting point, fully-nonlinear analysis is also carried out. The present linear and nonlinear studies suggest that the Brinkman's correction plays an important role in the onset and development of disturbance fields.

Pore-Scale Study of the Non-Linear Mixing of Fluids with Viscous Fingering in Anisotropic Porous Media

AbstractMixing processes of miscible viscous fluids in anisotropic porous media are studied through a lattice Boltzmann method in this paper. The results show that fluid mixing can be enhanced by the disorder and interfaces induced by viscous fingers. Meanwhile, the permeability anisotropy affects the developments of viscous fingers and the subsequent mixing behaviors significantly. Specifically, as the streamwise (longitudinal) permeability is larger than the spanwise (transverse) one, the mixing process is faster and stronger than that in the contrary case. Furthermore, the anisotropy can lead to different behaviors of the dissipation rates in streamwise and spanwise directions. Generally, the dissipation rate is dominated by the transverse concentration gradients when the longitudinal permeability is higher than the transverse one; on the contrary, as the transverse permeability is higher than the longitudinal one, the contributions to the dissipation rate from longitudinal and transverse concentration gradients are both significant.

On buoyancy driven mixing by volumetric microwave energy deposition

Investigation of buoyancy driven mixing by volumetric energy deposition is of particular interest to inertial confinement fusion research. This contribution describes a new microwave facility and an experiment to study buoyancy driven mixing of miscible fluids by volumetric energy deposition. A light weakly-polar fluid initially rested on top of a heavier and higher polarity fluid. As the fluid system was subjected to microwave radiation, less microwave energy was deposited into the weakly-polar fluid than the higher polarity fluid; thus, the bottom fluid was preferentially heated, and its density decreased due to thermal expansion. With continued microwave heating, the density of the bottom fluid dropped below the density of the upper fluid, creating a Rayleigh–Taylor unstable configuration, and, subsequently, buoyancy driven mixing. The miscible pair of toluene and tetrahydrofuran was chosen for the volumetric energy deposition experiments presented. Initially, single fluid microwave heating experiments, for which the source term in the heat equation was varied by variations in the fluid volume, were performed to provide calibration of a mathematical model. The model provided a prediction of the neutral stability point of the system, which facilitated experimental design and understanding. Measurements of the mixing layer width from this two-fluid mixing experiment are compared with results from a self-similar analysis of the governing equations.

Effect of Péclet number on miscible rectilinear displacement in a Hele-Shaw cell.

The influence of fluid dispersion on the Saffman-Taylor instability in miscible fluids has been investigated in both the linear and the nonlinear regimes. The convective characteristic scales are used for the dimensionless formulation that incorporates the Péclet number (Pe) into the governing equations as a measure for the fluid dispersion. A linear stability analysis (LSA) is performed in a similarity transformation domain using the quasi-steady-state approximation. LSA results confirm that a flow with a large Pe has a higher growth rate than a flow with a small Pe. The critical Péclet number (Pec) for the onset of instability for all possible wave numbers and also a power-law relation of the onset time and most unstable wave number with Pe are observed. Unlike the radial source flow, Pec is found to vary with t0. A Fourier spectral method is used for direct numerical simulations (DNS) of the fully nonlinear system. The power-law dependence of the onset of instability ton on Pe is obtained from the DNS and found to be inversely proportional to Pe and it is in good agreement with that obtained from the LSA. The influence of the anisotropic dispersion is analyzed in both the linear and the nonlinear regimes. The results obtained confirm that for a weak transverse dispersion merging happens slowly and hence the small wave perturbations become unstable. We also observ that the onset of instability sets in early when the transverse dispersion is weak and varies with the anisotropic dispersion coefficient, ε, as ∼√[ε], in compliance with the LSA. The combined effect of the Korteweg stress and Pe in the linear regime is pursued. It is observed that, depending on various flow parameters, a fluid system with a larger Pe exhibits a lower instantaneous growth rate than a system with a smaller Pe, which is contrary to the results when such stresses are absent.

Marangoni spreading due to a localized alcohol supply on a thin water film

Bringing two miscible fluids into contact naturally generates strong gradients in surface tension. Here, we investigate such a Marangoni-driven flow by continuously supplying isopropyl alcohol (IPA) on a film of water, using micron-sized droplets of IPA-water mixtures. These droplets create a localized depression in surface tension that leads to the opening of a circular, thin region in the water film. At the edge of the thin region, there is a growing rim that collects the water of the film, reminiscent of Marangoni spreading due to locally deposited surfactants. In contrast to the surfactant case, the driving by IPA-water drops gives rise to a dynamics of the thin zone that is independent of the initial layer thickness. The radius grows as r ∼ t1/2, which can be explained from a balance between Marangoni and viscous stresses. We derive a scaling law that accurately predicts the influence of the IPA flux as well as the thickness of the thin film at the interior of the spreading front.

FRACTAL ASPECTS OF MISCIBLE DISPLACEMENT IN ROUGH FRACTURES: AN EXPERIMENTAL APPROACH

Experiments were performed to study the effect of fracture surface roughness on fluid distribution during miscible displacement. The transparent replicas of single fractures obtained from seven different rocks were prepared and the surface roughness of each sample was described by fractal dimensions using the variogram, power spectral, and triangular prism (TP) techniques. Then, the effect of flow rate and viscosity on the geometry of the displacement front during miscible radial injection was investigated experimentally. The fractal dimensions of the fronts were obtained using box counting fractal analysis at different time lapses. The fractal values of invasion front varied from lithology to lithology, due to different surface roughnesses controlled by the lithology of the rocks. Although fluctuations of fractal values were observed during the growth of the front, fractal dimensions typically yielded an increasing trend. Fractal dimension became more stable with increasing flow rate and developed modestly with increasing viscosity. Finally, relationships between the fractal dimensions of displacement fronts and fracture surfaces were quantitatively analyzed and correlated in order to improve the prediction of fluid distribution within a single fracture during miscible displacement. Overall, correlations were observed between the surface characteristics and front fractal dimension values with some exceptions. In summary, to determine the probable distribution of miscible fluid and development of the front, all parameters except power spectral density (PSD) fractal dimension can be applied in the case of high viscosity ratios. In the case of low injection rates, TP could be applicable. No fractal behavior was present at extreme injection and low viscosity ratios, thus no correlation can be determined for the miscible displacement.

Observations of spontaneous oscillations in simple two-fluid networks.

We investigate the laminar flow of two-fluid mixtures inside a simple network of interconnected tubes. The fluid system is composed of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct phases. Downstream of a diverging network junction the two fluids do not necessarily split in equal fraction and thus heterogeneity is introduced into network. We find that in the simplest network, a single loop with one inlet and one outlet, under steady inlet conditions, the flow rates and distribution of the two fluids within the network loop can undergo persistent spontaneous oscillations. We develop a simple model which highlights the basic mechanism of the instability and we demonstrate that the model can predict the region of parameter space where oscillations exist. The model predictions are in good agreement with experimental observations.

Asymptotic analysis of Rayleigh–Taylor flow for Newtonian miscible fluids

Asymptotic analysis is used to derive anelastic, quasi-isobaric, and Boussinesq approximations for Rayleigh–Taylor induced flow between Newtonian fluids. The anelastic approximation appears to be valid for slightly stratified equilibrium states, but the analysis does not provide bounds on the Atwood number. The quasi-isobaric model is valid for unstratified equilibrium states without bounds on the Atwood number, while the Boussinesq approximation is a restriction of the quasi-isobaric model for vanishing Atwood numbers. These three models are consistently derived from first principles within the same framework, and they greatly facilitate investigations – including some compressibility effects – of Rayleigh–Taylor flow.

Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations.

We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.

A numerical study on radial Hele-Shaw flow: influence of fluid miscibility and injection scheme

Fingering instability triggered by injection of a less viscous fluid in a Hele-Shaw cell is numerically investigated. Simulations are based on a diffuse-interface method, and the formulation, capable of dealing with immiscible and miscible interfaces, is presented in details. Three miscibility conditions, including immiscible with surface tension, partially miscible with effective interfacial tension and fully miscible without interfacial stresses, are simulated to verify generality of an optimal linear injection scheme proposed by Dias et al. (Phys Rev Lett 109:144502, 2012) in the limit of infinite viscosity contrast. stabilizing effects of this linear injection scheme are universally confirmed for the interfaces with the presence of interfacial stresses, such as immiscible and partially miscible conditions. On the other hand, the linear injection scheme in a fully miscible interface leads to contradictory results. Even the fingering pattern appears qualitatively more stable without the secondary phenomenon of finger merging, relevant quantitative measurements, such as longer channeling zone and interfacial length, indicate enhancement of fingering prominence. The inconsistent behaviors suggest that the coupling effects with the interfacial stresses are crucial in the applications of the optimal linear injection scheme.

Regimes of miscible fluid thread formation in microfluidic focusing sections

We experimentally study the formation and stability of miscible fluid threads made of high-viscosity liquids using hydrodynamic focusing sections. Miscible core annular flows are useful for transporting viscous materials and can be destabilized for enhancing mass transfer. We delineate phase-diagrams of the generation of lubricated threads from low to large viscosity contrasts with various diffusion coefficients. Depending on fluid properties and flow rates of injection, stable microflows are classified into engulfment, thread, and tubing regimes. For low Péclet numbers, we examine thread dynamics when diffusive effects strongly alter basic flow structures and induce new flow configurations, including ultra-diffusive and diffusive instability regimes. Another unstable flow arrangement is investigated for moderate Reynolds numbers where small threads are rapidly destabilized in the inertial flow field of the sheath fluid near the fluid junction. This study provides an overview of stable and unstable flow regimes and their transitions during the formation of miscible viscous fluid filaments in square microchannels.

The influence of cell counts, cell size, EPS and microbial inclusions on the lubrication properties of microorganisms

Metalworking fluids (MWF) play an essential role in many machining applications and can be classified e.g. according to DIN 51385 in non-water miscible- and water miscible metalworking fluids. Most of the several billion liters of the worldwide and annually consumed MWF are water-based and thus exposed to a microbial contamination, which leads to a deterioration of MWF compounds and therefore to a loss of quality and technical performance. To maintain the MWF quality, biocides are used to reduce the microbial load, regardless of their potential risk for health and environment. A further limitation poses the high consumption of raw materials (mainly mineral oils) for the production of MWF, with approximately 50,000 t of raw materials consumed annually in Germany. To overcome these limitations, the paradigm shift of using microorganisms as a lubricant in a manufacturing process is investigated in this paper. Preliminary investigations on a Brugger-tribotester indicated the great potential of microorganisms as replacement for conventional metalworking fluid components. Against this background, the approach presented here intends to investigate the influence of cell counts, cell size, extracellular polymeric substances and microbial storage products on the lubrication properties of selected microorganisms. The results of the tribological tests show, that some microorganism exhibit superior lubrication properties (up to 68 % higher) compared to a highly concentrated conventional metalworking fluid. Therefore, the potential of microorganisms to substitute conventional MWF components can be derived.

Study of a Jacobian-free approach in the simulation of compressible fluid flows in porous media using a derivative-free spectral method

The development of Jacobian-free software for solving problems formulated by nonlinear partial differential equations is of increasing interest to simulate practical engineering processes. For the first time, this work uses the so-called derivative-free spectral algorithm for nonlinear equations in the simulation of flows in porous media. The model considered here is the one employed to describe the displacement of miscible compressible fluid in porous media with point sources and sinks, where the density of the fluid mixture varies exponentially with the pressure. This spectral algorithm is a modern method for solving large-scale nonlinear systems, which does not use any explicit information associated with the Jacobin matrix of the considered system, being a Jacobian-free approach. Two dimensional problems are presented, along with numerical results comparing the spectral algorithm to a well-developed Jacobian-free inexact Newton method. The results of this paper show that this modern spectral algorithm is a reliable and efficient method for simulation of compressible flows in porous media.

An Experimental and Simulation Study of Heavy Oil Recovery by the Liquid CO2 Huff and Puff Method

In this article a series of experiments were performed to demonstrate the effect of carbon dioxide injection pressure on a huff and puff process. The experimental data are used in a lab-scale model simulated with a commercial simulator to investigate the effect of soaking time, injection pore volume, and rate of injection on the heavy oil recovery. The result of experiments showed that a huff and puff process under miscible pressure conditions gives the most recovery. Simulation results illustrated that there is an optimum value for soaking time, which, for soaking times less than this value, recovery increases and for values greater than optimum the recovery decreases. The simulation study demonstrated that oil recovery increases with increasing volume of injected miscible fluid and recovery decreases with injection rate increase.

Miscible gravitational instability of initially stable horizontal interface in a porous medium: Non-monotonic density profiles

To simulate a CO2 sequestration process, some researchers employed a water/propylene glycol (PPG) system which shows a non-monotonic density profile. Motivated by this fact, the stability of the diffusion layer of two miscible fluids saturated in a porous medium is analyzed. For a non-monotonic density profile system, linear stability equations are derived in a global domain, and then transformed into a system of ordinary differential equations in an infinite domain. Initial growth rate analysis is conducted without the quasi-steady state approximation (QSSA) and shows that initially the system is unconditionally stable for the least stable disturbance. For the time evolving case, the ordinary differential equations are solved applying the eigen-analysis and numerical shooting scheme with and without the QSSA. To support these theoretical results, direct numerical simulations are conducted using the Fourier spectral method. The results of theoretical linear stability analyses and numerical simulations validate one another. The present linear and nonlinear analyses show that the water/PPG system is more unstable than the CO2/brine one, and the flow characteristics of these two systems are quite different from each other.

Fingering versus stability in the limit of zero interfacial tension.

The invasion of one fluid into another of higher viscosity in a quasi-two dimensional geometry typically produces complex fingering patterns. Because interfacial tension suppresses short-wavelength fluctuations, its elimination by using pairs of miscible fluids would suggest an instability producing highly ramified singular structures. Previous studies focused on wavelength selection at the instability onset and overlooked the striking features appearing more globally. Here we investigate the non-linear growth that occurs after the instability has been fully established. We find a rich variety of patterns that are characterized by the viscosity ratio between the inner and the outer fluid, η(in)/η(out), as distinct from the most-unstable wavelength, which determines the onset of the instability. As η(in)/η(out) increases, a regime dominated by long highly-branched fractal fingers gives way to one dominated by blunt stable structures characteristic of proportionate growth. Simultaneously, a central region of complete outer-fluid displacement grows until it encompasses the entire pattern at η(in)/η(out)≈0.3.

Nonlinear simulations of miscible viscous fingering with gradient stresses in porous media

Long-time behavior of the nonlinear simulations of miscible viscous fingering (VF), which arises during the displacement of a high viscous fluid by a lesser viscous one in a porous media, has been investigated in the presence of gradient stresses. Such non-conventional stresses appear in a miscible fluid system having steep concentration, density or temperature gradient. Experiments show that these gradient stresses, also called the Korteweg stresses, cause an effective interfacial tension (EIT) and act for the stabilization of the system against the growth of the fingers. Such fluid flow systems have been modeled by coupling the Darcy–Korteweg equation with the convection–diffusion equation for the evolution of the solute concentration. These equations are solved simultaneously using a highly accurate Fourier spectral method. Investigations have been carried out for classical single interface VF instability and it has been shown that the Korteweg stress stabilizes the downstream fingers more than the upstream fingers. The propagation of the non-zero axial velocity field, which is spread away from the fingertips, explains this effect. Korteweg stress seems to act against the broadening of the fingertip that resists the splitting of an isolated finger. The growth rate of the unstable modes at an early time of the nonlinear simulations is obtained for various flow parameters and the results obtained are found to be qualitatively in good agreement with the linear stability results available in the literature.