Miscible Fluids Research Articles

Differences in miscible viscous fingering of finite width slices with positive or negative log-mobility ratio

When a sample of fluid of finite size is displaced in a porous medium by another miscible fluid, viscous fingering may occur when the two fluids have different viscosities. Depending whether the sample is more or less viscous than the carrier fluid, the log-mobility ratio R [defined as R=ln(mu_{2}mu_{1}) where mu_{2} and mu_{1} are the viscosities of the sample and of the carrier] is respectively positive or negative. In the case of a linear displacement of a finite slice of fluid, R>0 leads to fingering of the rear interface of the sample where the less viscous carrier invades the more viscous sample. If R<0 , it is on the contrary the frontal interface of the sample that develops fingers where the less viscous sample displaces the more viscous bulk solution. We investigate here numerically the differences in fingering dynamics between the positive and negative log-mobility ratio cases leading to the growth of fingers against or along the direction of the flow, respectively. To do so, we integrate Darcy's law coupled to a convection-diffusion equation for the concentration of a solute ruling the viscosity of the finite-size sample. The statistical moments of the solute's concentration distribution are analyzed as a function of dimensionless parameters of the problem such as the length of the slice l , the log-mobility ratio R , and the ratio between transverse and axial dispersion coefficients . We find that, on average, the mixing zones and the width of the sample broadening due to fingering are larger for negative R than for positive R . This is due to the fact that fingers travel quicker in the flow direction than against the flow. Relevance of our results are discussed for interpretation of experimental results obtained in chromatographic separation and for understanding conditions of enhanced spreading of contaminants in aquifers.

Motion of Miscible Magnetic Fluids in a Vertical Capillary Tube

AbstractAn experimental study of miscible magnetic fluid motion in a vertical capillary tube is presented. Transporting ferrofluids is dominated by a dimensionless magnetic number Ma, which characterizes the ratio of upward magnetic force to the downward gravity. Two distinct stages of motion, referred to as the sub-critical mode of finite lift and the effective transportation, are identified. These two modes are determined by the values of the sub-critical magnetic number Masub and critical magnetic number Macr respectively. For the cases of sub-critical mode (Masub &lt; Ma &lt; Macr), the ferrofluids are lifted to quasiequilibrium heights, which are nearly proportional to the magnetic number Ma. As for the situations of effective transportation (Ma &gt; Macr), a penetrating finger of ferrofluids is formed similar to the conventional miscible displacements. A dimensionless proportionality of fingertip velocity ν, magnetic number Ma and field distribution profile fz is obtained as ν ∼ Ma1/2fz by scaling arguments. This proportional correlation shows a good agreement with the experiments.

Formation of miscible fluid microstructures by hydrodynamic focusing in plane geometries

We experimentally investigate the flow structures formed when two miscible fluids that have large viscosity contrasts are injected and hydrodynamically focused in plane microchannels. Parallel viscous flows composed of a central stream surrounded by symmetric sheath streams are examined as a function of the flow rates, fluid viscosities, and rates of molecular diffusion. We study miscible interfacial morphologies and show a route for manipulating viscous flow-segregation processes in plane microsystems. The diffusion layer at the boundary of an ensheathed fluid grows as function of the distance downstream and depends on the Péclet number. In particular, we observe diffusion-enhanced viscous ensheathing processes. In the presence of a constriction, we investigate the formation of a lubricated viscous thread in the converging flow and also the buckling morphologies of the thread in the diverging flow. This study, relevant to multifluid flow between a "thick" material and a "thin" solvent, demonstrates the possibility to further control steady and oscillatory miscible fluid microstructures.

Decompaction and fluidization of a saturated and confined granular medium by injection of a viscous liquid or gas

We compare quantitatively two experimental situations concerning injection of a miscible fluid into an initially jammed granular medium saturated with the same fluid, confined in a Hele-Shaw cell. The two experiments are identical, apart from the interstitial and injected fluid, which is in one case air injected into a dry granular packing, and in the other case silicone oil injected into a dense suspension. In spite of the strong differences regarding the nature of the two fluids, strikingly similar dynamical and geometrical features are identified as functions of the control parameters: cell thickness and applied fluid injection pressure. In both cases an initial hydrodynamically driven decompaction process controls the unjamming and prepares the final displacement process characterized by fingerlike patterns empty of grains. The pattern shapes are comparable. In addition, the mobilities of the coupled fluid-grain flow, rescaled by the interstitial fluid viscosity and grain diameter squared, are of the same range and behave comparably. The mobility proves to depend on the initial solid fraction of the medium. Subtle differences are observed in geometrical aspects like the finger width with respect to the control parameters.

Analytical asymptotic solutions ofnA+mB→Creaction-diffusion equations in two-layer systems: A general study

Large time evolution of concentration profiles is studied analytically for reaction-diffusion systems where the reactants A and B are each initially separately contained in two immiscible solutions and react upon contact and transfer across the interface according to a general nA+mB-->C reaction scheme. This study generalizes to immiscible two-layer systems the large time analytical asymptotic limits of concentrations derived by Koza [J. Stat. Phys. 85, 179 (1996)] for miscible fluids and for reaction rates of the form A;{n}B;{m} with arbitrary diffusion coefficients and homogeneous initial concentrations. In addition to a dependence on the parameters already characterizing the miscible case, the asymptotic concentration profiles in immiscible systems depend now also on the partition coefficients of the chemical species between the two solution layers and on the ratio of diffusion coefficients of a given species in the two fluids. The miscible time scalings are found to remain valid for the immiscible fluids case. However, for immiscible systems, the reaction front speed is enhanced by increasing the stoichiometry of the invading species over that of the species being invaded. The direction of the front propagation is found to depend on the diffusion coefficient of the invading species in its initial fluid but not on its value in the invading fluid. Hence, a reaction front in immiscible fluids can travel in the opposite direction to the reaction front formed in miscible fluids for a range of parameter values. The value of the invading species partition coefficient affects the magnitude of the front speed but it cannot alter the direction of the front. For sufficiently large times, the total amount of product produced in time is independent of the rate of the reaction. The centre of mass of the product can move in the opposite direction to the center of mass of the reaction rate.

The circular internal hydraulic jump

Circular hydraulic jumps are familiar in single layers. Here we report the discovery of similar jumps in two-layer flows. A thin jet of fluid impinging vertically onto a rigid horizontal plane surface submerged in a deep layer of less-dense miscible fluid spreads radially, and a near-circular internal jump forms within a few centimetres from the point of impact with the plane surface. A jump is similarly formed as a jet of relatively less-dense fluid rises to the surface of a deep layer of fluid, but it appears less stable or permanent in form. Several experiments are made to examine the case of a downward jet onto a horizontal plate, the base of a square or circular container. The inlet Reynolds numbers, Re, of the jet range from 112 to 1790. Initially jumps have an undular, laminar form with typically 2–4 stationary waves on the interface between the dense and less-dense layers but, as the depth of the dense layer beyond the jump increases, the transitions become more abrupt and turbulent, resulting in mixing between the two layers. During the transition to a turbulent regime, single and sometimes moving multiple cusps are observed around the periphery of jumps. A semi-empirical model is devised that relates the parameters of the laboratory experiment, i.e. flow rate, inlet nozzle radius, kinematic viscosity and reduced gravity, to the layer depth beyond the jump and the radius at which an undular jump occurs. The experiments imply that surface tension is not an essential ingredient in the formation of circular hydraulic jumps and demonstrate that stationary jumps can exist in stratified shear flows which can be represented as two discrete layers. No stationary circular undular jumps are found, however, in the case of a downward jet of dense fluid when the overlying, less-dense, fluid is stratified, but a stationary turbulent transition is observed. This has implications for the existence of stationary jumps in continuously stratified geophysical flows: results based on two-layer models may be misleading. It is shown that the Froude number at which a transition of finite width occurs in a radially diverging flow may be less than unity.

Stochastic Langevin Model for Flow and Transport in Porous Media

We present a new model for fluid flow and solute transport in porous media, which employs smoothed particle hydrodynamics to solve a Langevin equation for flow and dispersion in porous media. This allows for effective separation of the advective and diffusive mixing mechanisms, which is absent in the classical dispersion theory that lumps both types of mixing into dispersion coefficient. The classical dispersion theory overestimates both mixing-induced effective reaction rates and the effective fractal dimension of the mixing fronts associated with miscible fluid Rayleigh-Taylor instabilities. We demonstrate that the stochastic (Langevin equation) model overcomes these deficiencies.

Mixing Under Vibrations in Reduced Gravity

The aim of this study is to analyze the physical mechanism by which vibrations affect the mixing characteristic of two initially stratified miscible fluids. The translational periodic vibrations of a rigid cell filled with different mixtures (Sc = 7125) are considered. The vibrations with a constant frequency are imposed parallel to the initially planar interface. The ability of the applied vibrations to enhance the flow is examined. At the early stage after imposing the vibrations the Kelvin-Helmholtz instability is observed in absence and at low level of gravity. Later in time the system undergoes a transition to Rayleigh-Taylor instability. With increasing of gravity level the life-time of Kelvin-Helmholtz instability is decreased. We found the critical value of Gr above which this instability do not developed.

An Experimental Method for One Dimensional Permeability Characterization of Heterogeneous Porous Media at the Core Scale

Many reservoir simulator inputs are derived from laboratory experiments. Special core analysis techniques generally assume that core samples are homogeneous. This assumption does not hold for porous media with significant heterogeneities. This paper presents a new method to characterize core scale permeability heterogeneity. The method is validated by both numerical and experimental results. The leading idea consists in injecting a high viscosity miscible fluid into a core sample saturated with a low viscosity fluid. In such conditions, the fluid displacement is expected to be piston-like. We investigate the evolution of the pressure drop as a function of time. A continuous permeability profile is estimated along flow direction from the pressure drop assuming that the core sample is a stack of infinitely thin cross sections perpendicular to flow direction. Thus, we determine a permeability value for each cross section. Numerical and laboratory experiments are carried out to validate the method. Flow simulations are performed for numerical models representing core samples to estimate the pressure drop. The selected models are sequences of plugs with constant permeabilities. In addition, laboratory displacements are conducted for both low permeability and high permeability core samples. To investigate whether there is dispersion inside the porous medium, CT scan measurements are performed during fluid displacement: the location of the front is observed at successive time intervals. The results validate the methodology developed in this paper as long as heterogeneity is one dimensional.

Chaos, transport and mesh convergence for fluid mixing

Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids (as considered here), this interface is defined as a 50% mass concentration isosurface. For shock wave induced (Richtmyer-Meshkov) instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.

Effects of channel geometry on buoyancy-driven mixing

The evolution of the concentration and flow fields resulting from the gravitational mixing of two interpenetrating miscible fluids placed in a tilted tube or channel is studied by using direct numerical simulation. Three-dimensional (3D) geometries, including a cylindrical tube and a square channel, are considered as well as a purely two-dimensional (2D) channel. Striking differences between the 2D and 3D geometries are observed during the long-time evolution of the flow. We show that these differences are due to those existing between the 2D and 3D dynamics of the vorticity field. More precisely, in two dimensions, the strong coherence and long persistence of vortices enable them to periodically cut the channels of pure fluid that feed the front. In contrast, in 3D geometries, the weaker coherence of the vortical motions makes the segregational effect due to the transverse component of buoyancy strong enough to preserve a fluid channel near the front of each current. This results in three different regimes for the front velocity (depending on the tilt angle), which is in agreement with the results of a recent experimental investigation. The evolution of the front topology and the relation between the front velocity and the concentration jump across the front are investigated in planar and cylindrical geometries and highlight the differences between 2D and 3D mixing dynamics.

Fluid-fluid interaction during miscible and immiscible displacement under ultrasonic waves

This paper aims at identifying and analyzing the influence of high-frequency, high-intensity ultrasonic radiation at the interface between immiscible (different types of oils and aqueous solutions) and miscible (different types of oil and solvent) fluids. An extensive set of Hele-Shaw type experiments were performed for several viscosity ratios, and interfacial tension. Fractal analysis techniques were applied to quantify the degree of fingering and branching. This provided a rough assessment of the degree of perturbation generated at the interface when the capillary forces along with the viscous forces are effective. Miscible Hele-Shaw experiments were also presented to isolate the effect of viscous forces. We found that ultrasound acts to stabilize the interfacial front, and that such effect is most pronounced at low viscosity ratios.

Primary and Secondary Oil Recovery From Different-Wettability Rocks by Countercurrent Diffusion and Spontaneous Imbibition

Summary This study investigates optimum matrix-oil-recovery strategies in naturally fractured reservoirs (NFRs) for different wettabilities and rock types. We compare the recovery efficiencies of two cases: (a) primary countercurrent spontaneous imbibition followed by the diffusion of a miscible phase (secondary recovery) and (b) primary diffusion of miscible fluid without preflush of matrix by spontaneous imbibition. For these recovery strategies, the effects of the matrix shape factor, matrix wettability, and type of miscible displacing phase on the rate of recovery and development of residual-oil saturation were clarified experimentally. Cylindrical Berea-sandstone and Indiana-limestone samples with different shape factors were obtained by cutting the plugs 1, 2.5, and 5 cm in diameter and 2.5, 5, and 10 cm in length. The external surface except one end was coated with epoxy. Static imbibition experiments were conducted on vertically situated samples in which the fractures were at the bottom and matrix/fracture interaction took place in an upward direction. Mineral oil and crude oil were used as oleic phases. Brine was selected as aqueous phase for the primary spontaneous-imbibition recovery. For primary- and secondary-miscible-displacement experiments, n-heptane was used as solvent. Wettability of water-wet Berea-sandstone samples was altered by aging to observe its effects on the dynamics of spontaneous countercurrent imbibition and diffusion. Parametric analyses were performed for the appraisal of the secondary-and tertiary-recovery potential of NFRs by immiscible-and miscible-fluid injections. The optimal recovery strategies (recovery rate, recovery time, and ultimate recovery) for different rock properties were identified and classified. In water-wet cases, starting the recovery with capillary imbibition followed by diffusion was found to be the optimal way (i.e., both effective and efficient). For limestone or aged-sandstone samples, starting the recovery by diffusion yielded a faster recovery rate and higher ultimate recovery.

Heat transfer to sub-cooled binary solution in horizontal tube

Predicted heat transfer coefficients (HTC) are widely used for calculations of various heat and mass transfer processes. Various empirical and semi-empirical models of non-dimensional groups are used for calculating the heat transfer coefficients. These groups depend on the fluid and flow properties. The common accuracy of the predicted heat transfer coefficient is usually about ±25%; however, the accuracy is failing by the lack of mechanistic model for convective heat transfer and by the inaccurate predictions of the fluid properties. This work is aimed to improve the heat transfer coefficient prediction by reducing the deviations which associated with the fluid properties. When the fluid is a mixture of miscible fluids the predictions of the fluid properties are very rough and therefore the prediction of the heat transfer coefficient is more complicated. In the present study the heat transfer coefficient of sub-cooled organic mixture chlorodifluoromethane (R22)–dimethylacetamide (DMAC) was measured experimentally. In order to compare the experimental value with the predicted one, thermophysical properties of the solution, such as density, viscosity, heat capacity and thermal conductivity have to be known. Since the thermal conductivity of the solution (R22–DMAC) was the only unknown property, various correlations and mixing rules were tested, and the most appropriate was chosen. Based on this method for evaluating the solution’s properties the predicted HTC obtained with an error range of 15%.

A return toward equilibrium in a 2D Rayleigh–Taylor instability for compressible fluids with a multidomain adaptive Chebyshev method

We numerically simulate a single-mode Rayleigh–Taylor instability between compressible miscible fluids with a highly accurate self-adaptive pseudospectral Chebyshev multidomain method in two two-dimensional boxes at small aspect ratios. The simulations are started from rest and pursued until the return toward mechanical equilibrium of the mixing. Four regimes—linear and weakly nonlinear, nonlinear steady bubble rise, return toward equilibrium, and finally a system of acoustic waves—can be identified. We show that this one-dimensional system of stationary acoustic waves is damped by the physical viscosity. This provides a reference solution.

Pearl and mushroom instability patterns in two miscible fluids' core annular flows

We report on experiments with two miscible fluids of equal density but different viscosities. The fluids were injected co-currently and concentrically into a cylindrical pipe. The resulting base state is an axisymmetric parallel flow. The ratio of the two fluid flow rates determines the relative amount of the fluids, thus the radius of the inner core fluid. Depending on this radius and the total flow rate, two different and unstable axisymmetric patterns, denoted by mushrooms and pearls, were observed. We delineate the diagram of occurrence of the two patterns as a function of the various parameters.

Optimum Hydrocarbon Fluid Composition for Use in CO2 Miscible Hydrocarbon Fracturing Fluids and Methods of Core Evaluation

Abstract Previous studies(1–4) described the theory and application of CO2 miscible hydrocarbon fracturing fluids for gas well stimulation. These fluids are ideally suited to gas reservoirs susceptible to phase trapping resulting from high capillary pressures when water-based fluids are used. Gas reservoirs particularly prone to phase trapping are those with in situ permeability less than 0.1 mD, those with initial water saturations less than what would be expected from normal capillary equilibrium (subnormally water saturated) and those that are under pressured. Such reservoirs represent a growing proportion of the market. This, combined with increased gas prices, creates a strong need for an optimized gas well fracturing fluid system. Hydrocarbon-based fracturing fluids present an ideal solution to phase trapping concerns associated with water-based fluids provided the hydrocarbon fluid can be effectively and quickly removed from the formation after the fracturing treatment. This paper investigates in more depth what constitutes an ideal hydrocarbon-base oil for this application. This involves consideration of many factors including cleanup mechanisms, safety, cost and capability to be gelled and broken. In order to meaningfully evaluate fluid clean up, regained core permeability evaluations must be conducted by accurately duplicating downhole conditions. This paper presents testing methodologies designed to achieve this goal. To illustrate the need for these methodologies, the applicable phase behaviour and fluid displacement mechanisms by which these fluid systems operate are discussed. Topics covered will include:Methane drive fluid recovery mechanism involving the use of CO2 with hydrocarbons and resulting effect on interfacial tension (IFT).Secondary recovery mechanism based on vapour pressure of light hydrocarbons resulting in their being produced back in the gas phase with methane.Application of these concepts to address phase trapping in low-permeability gas reservoirs and how these effects are accentuated in formations that may be subnormally water-saturated, have low reservoir pressure or have low permeability.The need to simulate downhole conditions accurately to properly represent the recovery mechanisms. This includes duplication of temperature, pressure and fluid-loss mechanisms. Duplicating leakoff is the key to representative duplication of phenomena at the fracture face.Compare nitrogen to methane for reference and fluid recoveries and discuss why it is necessary to use methane to obtain proper simulation and modelling of the actual field performance of the fracture fluids.To illustrate fluid performance and demonstrate test methodologies, results of a regain permeability evaluation conducted with the optimum fluid and test methodologies discussed will be presented. It will be shown that in a formation known to be highly sensitive to water-based fluid retention (phase trapping), 100% regain permeability can be achieved at a minimal 140 kPa of applied drawdown pressure. Introduction The use of water-based fracturing fluids in low-permeability reservoirs may result in the loss of effective fracturing half length due to phase trapping effects associated with the retention of a large portion of the introduced water-based fluid in the formation.

A unified handling of immiscible and miscible fluids

AbstractConventional level set‐based approaches have an inherent difficulty in tracking miscible fluids due to its discrete treatment for interface. This paper proposes a unified framework to efficiently handle both miscible and immiscible fluid simulations. Based on the chemical potential energy, our method describes the evolution of multiple fluids as time‐varying concentration fields. Handling of multiple fluids is straightforward and, unlike level set methods, ad hoc reinitialization or fictitious particle deployment is not necessary. For numerical computation of the Navier—Stokes equations, we adopt advanced lattice Boltzmann methods (LBMs) for computational efficiency. The experiments show that our approach works well with immiscible fluids, miscible fluids, and interaction with objects. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Magnetic instability between miscible fluids in a Hele--Shaw cell

We show experimentally the existence of a magnetic instability between two miscible fluids. The sample is an aqueous ferrofluid. At time t = 0, the ferrofluid and water are put into contact in a Hele–Shaw cell and then submitted to a homogeneous magnetic field perpendicular to the cell. Above a threshold value of the magnetic field a fingering instability is observed at the diffuse interface, with fingers growing with time. A wavelength can be defined as the mean distance between fingers. This wavelength in the linear regime is approximatively equal to the thickness of the cell.

Measurement of Translational Diffusivity by Microchannel Multiphase Flow

A method is proposed for the rapid measurement of translational diffusion coefficient by employing the unique multiphase flow of perfectly miscible incompressible fluids in microchannels. The molecule of interest is injected, as a bolus or continuously, into the middle phase of a three phase flow system. Subsequently, the phase or stream is depleted of molecule by diffusion into the adjacent streams through the common interface. By monitoring the elution profile of the molecule, one may obtain estimates of the diffusion coefficient under fixed experimental conditions. Transport of molecule in the microchannel is described by a transient convection-diffusion-dispersion model. Analytical and numerical solutions are provided to illustrate the change of elution profile with stream velocity and other design parameters. The diffusion coefficient is estimated from a graphical plot. It is shown that diffusion coefficient may be measured without prior knowledge of dispersion. Experimental data is presented for the proteins, fibrinogen and insulin. A number of advantages over the T-sensor and Taylor-Aris methods are highlighted.