Flow Of Immiscible Fluids Research Articles

Phase distribution and intrapore salt exchange during drilling mud invasion of an oil- and gas-bearing formation

As a result of drilling mud filtrate invasion of a formation saturated with oil, gas and natural water, the distribution of the immiscible phases and the electrophysical characteristics of the near-well zone change as compared with its initial state. Taking this change into account is necessary for successful interpretation of electrical well logging data. In this paper, on the basis of the equations of immiscible fluid flow through a porous medium and the system of transfer equations with account for instantaneous salt exchange between the filtrate and the natural water inside the pores, the regions of initial formation fluid saturations for which in the invasion zone the displacement fronts retain their relative position are determined.

A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

AbstractWe have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix‐free implicit cell‐centered FV method. The pressure Poisson equation is solved by the node‐based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered‐mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix‐free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid. Copyright © 2009 John Wiley & Sons, Ltd.

Amyloid Peptide Aggregation In Plugs Formed By Microfluidics

We present a novel microfluidic device for amyloid peptide aggregation research. The device relies on the control of interfacial chemistry, which allows miniaturizing of aggregation measurements to nanoliter volumes. In traditional in vitro aggregation experiments, adsorption of amyloid peptides to various interfaces has been shown to nucleate and to enhance peptide aggregation. The problem of adsorption is even more pronounced upon miniaturization of aggregation experiments. Miniaturization leads to an increase of the surface-to-volume ratio, and concomitantly to an increase of amyloid peptide aggregation if the surface is not controlled. Nevertheless, miniaturization of aggregation experiments is desirable for samples available only in small volumes, as for example cerebrospinal fluid (CSF) from mice. CSF has recently gained interest in Alzheimer research, however CSF analytics has been hampered to due the small available volume.In order to miniaturize and control the interfacial chemistry of aggregation experiments we used a plug based microfluidic approach. Plugs are nanoliter sized aqueous droplets formed in the flow of immiscible fluids inside microfluidic channels. Upon peptide encapsulation into plugs, the unfavorable interfaces are exchanged for an adjustable liquid/liquid interface. We show for one prominent amyloid peptide, the Alzheimer's peptide Aβ(1-40), that aggregation in plugs has kinetics of orders of magnitude slower than under standard conditions. Further we show the applicability of this miniaturized system to aggregation experiments by testing the inhibitory potency of CSF from wild type and ceAPPswePS1ΔE9/TTR-/- mice on Aβ aggregation. Using the plug-based approach, we were able to perform over 750 experiments with a single mouse CSF sample of 5 μl in volume. The plug system offers many new opportunities to investigate in vitro aggregation studies, as for example time controlled aging of amyloid peptides, nucleation in a confined environment, and screening of drug components.

Shear-Based Droplet Production for Biomaterial Printing

The highly uniform shear forces at millimeter and smaller dimensions can produce monodisperse particles spontaneously during continuous flow of immiscible fluids. Microfluidic techniques have also recently been used to generate and organize arrays of solid monodisperse microparticles with various material properties. Combining these developments with a well-engineered “chip-to-world” interface will provide a new high-resolution 3-D printing technology for rapid prototyping and biotechnology.We produced hydrogel droplets at rates of 10-200 Hz in PDMS microreactors. Droplets were monodisperse, with 50-200 micron diameter dependent on flow rate, channel shape and the presence of surfactants. Droplets may be dispensed from the chip in their liquid state, or solidified by one of three mechanisms. Ultraviolet (UV) light was used to solidify photosensitized hydrogels. We also discuss other hydrogel systems that are solidified by a chemical reaction (sodium alginate and CaCl2) or by thermal gelation (Pluronic F-127), methods to vary the droplets' chemical composition and mechanical properties, and methods for closed-loop electrical feedback on particle position for precision fabrication. Biocompatible hydrogels are of great interest for biomaterial applications such as drug delivery and tissue engineering.

Numerical model for tsunami generation by subaerial landslides

AbstractA discretization method based on stabilized space–time finite elements is presented for the numerical analysis of three–fluid flows of immiscible and incompressible fluids. Signed distance functions are used to assign the material properties to each spatial point in the domain. The motion and the change in topology of fluid–fluid interfaces are implicitly described by the level–set method. Strong and weak discontinuities in the fields of the physical state variables are captured by locally enriched approximations based on the partition–of–unity concept. An interior penalty method enforces interfacial conservation of mass and momentum. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Droplets and jets in microfluidic devices

Abstract When immiscible fluids flow in microchannels, monodisperse droplets or jet are obtained depending upon the flow rate of the aqueous phase and the oil phase. In this work, we present experimental data showing that the confinement and the shape of the geometry play a fundamental role. We analyze the stability of the jet in the framework of the lubrication at low Reynolds number. In cylindrical geometry, we relate the transition between the droplets regime and the jet regime to the absolute/convective transition of the Rayleigh Plateau instability and reach a remarkable agreement with the data. In rectangular geometry, we follow the same analysis and point out the existence of an absolutely stable bidimensional jet.

Drop-size effects on coalescence of two equal-sized drops in a head-on collision

When two equal-sized drops collide in a two-dimensional extensional flow of a second immiscible fluid, the time required to drain the thin film between the drops prior to coalescence is referred to as the drainage time. In a previously proposed scaling theory [H. Yang et al., Phys. Fluids 13, 1087–1106 (2001)] we found that in the low Ca regime, the dimensionless product of the film drainage time (td) and the applied shear rate (G) should scale as Ca1∕2. Yet, recent numerical simulations contradict this result and show that the dimensionless drainage time (tdG) in this regime scales as Ca. Furthermore, the existing experiments suggest that the drainage time may become independent of Ca in the limit Ca⪡1. In this paper, we attempt to address these apparent contradictions. First, we carry out coalescence experiments in a four-roll mill for significantly smaller drops than have heretofore been studied. Our results show that as R is decreased for a fixed Ca range, the scaling exponent m in the correlation tdG∼Cam falls in the range 1⩽m⩽4∕3, but never exhibits a value smaller than 1. Thus, we corroborate the numerically predicted scaling of tdG with Ca in the low Ca regime. We then reexamine the scaling theory. We find that the disagreement between scaling theories and the numerical simulations (as well as the present experiments) ultimately emanates from a fundamental limitation in the definition of the drainage time. Finally, our experiments show that the scaling exponent unexpectedly increases when the viscosity ratio is increased from λ=0.19 to λ=6.8 for a drop radius smaller than 27μm. We show that one must evidently account for interfacial “slip” between the drops and the surrounding film to account for this observed increase in m. We define a slip parameter that gives an a priori estimate of the importance of slip in the experimental data.

Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries

We adress the question of the stability of a confined coflowing jet at low Reynolds number in various geometries. Our study is motivated by recent experiments in microfluidic devices. When immiscible fluids flow in microchannels, either monodisperse droplets or parallel flows are obtained depending upon the flow rate of the aqueous phase and the oil phase. In these experiments, the confining and the shape of the geometry play a fundamental role. In a previous paper [Guillot, Phys. Rev. Lett 99, 104502 (2007)], we analyzed the stability of the jet in the framework of the lubrication approximation at low Reynolds number in a cylindrical geometry, and we related the transition between the droplets regime and the jet regime to the absolute-convective transition of the Rayleigh plateau instability. In this work, the effect of the channel geometry and the jet position within the microfluidic device are discussed. New flow patterns are pointed out. Bidimensional jets are encountered in square and rectangular geometry. Contrary to jets occuring in circular geometry, these two-dimensional jets are absolutely stable. Focusing on situations where the inner fluid is more viscous than the outer one, we evidence a range of parameters where droplets are produced through a blocking and pinching mechanism. In this particular case, the flow is unstable, the growing perturbations are convected upstream. This induces the clogging of the channel by the internal phase and its pinching by the external one. In a future presentation we will give a comparison between this model and experimental data.

Investigations of Interfacial Coupling Phenomena and its Impact on Recovery Factor

Abstract Interfacial coupling phenomena in multiphase flow through porous media and its impact on the recovery factor have been of interest for sometime, especially in the SAGD process and in fractured reservoirs. In this study, a numerical simulator that takes into account inlet end effects was developed to solve the modified transport equations proposed by Bentsen(1, 2), Ayub and Bentsen(3), Ayub(4) and Ayodele(5) to account for interfacial coupling phenomena and hydrodynamic effects. Moreover, the simulator was validated using experimental data. Finally, sensitivity analysis studies were carried out with the simulator to show the effect of interfacial coupling phenomena on the recovery factor. Introduction It is well known that Darcy's equation was developed on the basis of experiments involving single-phase flow through porous media. To account for multiphase flow, Darcy's equation was modified by Muskat et al.(6) into a form that has been widely used in petroleum reservoir engineering. However, as pointed out by several researchers(1, 3, 7–13), the modified equation can not give accurate recovery predictions when used to simulate multiphase flow in petroleum reservoirs. This is because, in multiphase flow, the presence of one fluid affects the flow of the other fluids; that is, interfacial coupling effects (viscous and capillary coupling effects) influence the flow. The viscous coupling effect, first identified by Yuster(14), refers to the coupling that arises due to the viscous drag exerted by one fluid on the other when they flow through the same porous medium, and it is usually associated with the mobility of the fluids(5). The capillary coupling effect, recently postulated by Babchin and Yuan(15) and by Bentsen(16), refers to the coupling that arises due to coupling, through the capillary function(2), of pressure across the interfaces of the fluids. Moreover, counter-current experimental data(17–19) has been used to show that Muskat's extension of Darcy's equation does not correctly describe the physics of multiphase flow through porous media, because the magnitude of the relative permeabilities for a given phase obtained from counter-current flow is always less than that acquired from a co-current experiment conducted in the same porous medium. To closely capture the physics of flow, Bentsen(1, 2), Ayub and Bentsen(3), Ayub(4) and Ayodele(5) developed a set of modified transport equations that incorporate interfacial coupling and hydrodynamic effects. In the following sections, a one-dimensional form of these modified transport equations is solved numerically by developing an Interfacial Coupling Simulator (ICS). Simulation results are compared with immiscible displacement experimental data and some conclusions are drawn as well. Mathematical Formulation To describe the one-dimensional immiscible displacement flow by using the fractional flow concept, two governing equations, the fractional flow equation and the frontal advance equation, are needed. Fractional Flow Equation With the assumption that two immiscible and incompressible fluids flow through a homogenous and isotropic water-wet porous medium, Bentsen(1, 2), Ayub and Bentsen(3), Ayub(4) and Ayodele(5) developed a set of modified transport equations whose one-dimensional form is as follows: V1 = Equation 1 Available In Full Paper V2 = Equation 2 Available In Full Paper The definitions for the relat

Molecular dynamics of immiscible fluids in chemically patterned nanochannels

Molecular dynamics simulations of chain molecules are used to elucidate physical phenomena involved in flows of dense immiscible fluids in nanochannels. We first consider a force driven flow in which the channel walls are homogeneous and wetting to one fluid and nonwetting to the other fluid. The coating of the walls by the wetting fluid provides a fluctuating surface that confines the flow of the nonwetting fluid. The resulting dissipation yields stationary Poiseuille-like flows in contrast to the accelerating nature of flow in the absence of the coating. We then consider walls consisting of patches whose wetting preferences to a fluid alternate along the walls. In the resulting flow, the immiscible components exhibit periodic structures in their velocity fields such that the crests are located at the wettability steps in contrast to the behavior of a single fluid for which the crest occurs in the wetting region. We demonstrate that for a single fluid, the modulated velocity field scales with the size of the chain molecules.

On the Stress Singularities at Multimaterial Interfaces and Related Analogies With Fluid Dynamics and Diffusion

Abstract Joining of different materials is a situation frequently observed in mechanical engineering and in materials science. Due to the difference in the elastic properties of the constituent materials, the junction points can be the origin of stress singularities and a possible source of damage. Hence, a full appreciation of these critical situations is of fundamental importance both from the mathematical and the engineering standpoints. In this paper, an overview of interface mechanical problems leading to stress singularities is proposed to show their relevance in engineering. The mathematical methods for the asymptotic analysis of stress singularities in multimaterial junctions and wedges composed of isotropic linear-elastic materials are reviewed and compared, with special attention to in-plane and out-of-plane loadings. This analysis mathematically demonstrates in a historical retrospective the equivalence of the eigenfunction expansion method, of the complex function representation, and of the Mellin transform technique for the determination of the order of the stress singularity in such problems. The analogies between linear elasticity and the Stokes flow of dissimilar immiscible fluids, the steady-state heat transfer across different materials, and the St. Venant torsion of composite bars are also discussed. Finally, advanced issues for the stress singularities due to joining of angularly nonhomogeneous elastic wedges are presented. This review article contains 147 references.

Disturbance growth in two-fluid channel flow: The role of capillarity

This work examines the role of capillarity in the non-modal linear stability properties of three-dimensional disturbances in sheared two-layer flow of immiscible fluids of similar density. Capillarity reduces the transient growth of energy that occurs due to the non-normality of the linear stability problem according to a scaling of peak energy with We 1/2 over a wide range of Weber number, viscosity ratio and wavenumber. More importantly, the participation of capillary modes in non-modal growth leads to oscillatory energy growth and to larger disturbance growth rates, features that are confirmed by computing the numerical range and numerical abscissa of the non-normal disturbance evolution operator. Examination of energy components and disturbance structure reveals that early rapid growth and subsequent oscillations are due to the coupling of streamwise vortices – the two-fluid analog of lift-up – to the displaced interface.

Estimation of Permeability and Permeability Anisotropy From Straddle-Packer Formation-Tester Measurements Based on the Physics of Two-Phase Immiscible Flow and Invasion

Summary We describe the successful application of a new method to estimate permeability and permeability anisotropy from transient measurements of pressure acquired with a wireline straddle-packer formation tester. Unlike standard algorithms used for the interpretation of formation-tester measurements, the method developed in this paper incorporates the physics of two-phase immiscible flow as well as the processes of mudcake buildup and invasion. An efficient 2D (cylindrical coordinates) implicit-pressure explicit-saturation finite-difference algorithm is used to simulate both the process of invasion and the pressure measurements acquired with the straddle-packer formation tester. Initial conditions for the simulation of formation-tester measurements are determined by the spatial distributions of pressure and fluid saturation resulting from mud-filtrate invasion. Inversion is performed with a Levenberg-Marquardt nonlinear minimization algorithm. Sensitivity analyses are conducted to assess nonuniqueness and the impact of explicit assumptions made about fluid viscosity, capillary pressure, relative permeability, mudcake growth, and time of invasion on the estimated values of permeability and permeability anisotropy. Applications of the inversion method to noisy synthetic measurements include homogeneous, anisotropic, single and multilayer formations for cases of low- and high-permeability rocks. We also study the effect of unaccounted impermeable bed boundaries on inverted formation properties. For cases where a priori information can be sufficiently constrained, our inversion methodology provides reliable and accurate estimates of permeability and permeability anisotropy. In addition, we show that estimation errors of permeability inversion procedures that neglect the physics of two-phase immiscible fluid flow and mud-filtrate invasion can be as high as 100%.

Mesoscopic Simulation of Binary Immiscible Fluids Flow in a Square Microchannel with Hydrophobic Surfaces

Mesoscopic Simulation of Binary Immiscible Fluids Flow in a Square Microchannel with Hydrophobic Surfaces

Lattice Boltzmann model for simulating immiscible two-phase flows

The lattice Boltzmann equation is often promoted as a numerical simulation tool that is particularly suitable for predicting the flow of complex fluids. This paper develops a two-dimensional 9-velocity (D2Q9) lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio using a single relaxation time for each fluid. In the macroscopic limit, this model is shown to recover the Navier–Stokes equations for two-phase flows. This is achieved by constructing a two-phase component of the collision operator that induces the appropriate surface tension term in the macroscopic equations. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. The model is also shown to predict Laplace's law for surface tension and Poiseuille flow of layered immiscible binary fluids. The spinodal decomposition of two fluids of equal density but different viscosity is then studied. At equilibrium, the system comprises one large low viscosity bubble enclosed by the more viscous fluid in agreement with theoretical arguments of Renardy and Joseph (1993 Fundamentals of Two-Fluid Dynamics (New York: Springer)). Two other simulations, namely the non-equilibrium rod rest and the coalescence of two bubbles, are performed to show that this model can be used to simulate two fluids with a large density ratio.

A numerical model for two–phase immiscible fluid flow in a porous medium

Chemical grouting may be defined as the injection of chemical mixtures, known as grouts, into the pore space of the soil. It is extensively used for ground stabilization in the construction industry. The mechanism by which injected grout permeates a soil mass involves a complex interaction of both chemical and physical factors that are not well understood. The objective of this work is to develop a two–dimensional numerical model for the computation of a two–phase immiscible flow in a porous medium. The phases of flow are grout and water. It is assumed that the phase of grout is non–wetting type. An important aspect of the chemical grout—hardening of the grout mix—is considered in the model. The coefficient of hardening is a parameter that represents the gelation behaviour of the chemical grout mix. The numerical model applied is based on a finite difference scheme known as vector volumes. The model is capable of estimating the order of magnitude and distribution of pore pressures that are developed during the injection process and the effects of non–homogeneities such as variations in permeability. The results are checked against laboratory tests. In practice, the numerical model may be used to avoid the expensive and time–consuming laboratory tests.

Liquid‐liquid two‐phase flow patterns in a rectangular microchannel

AbstractIn this work, the flow of immiscible fluids in a PMMA microchannel 300 μm wide and 600 μm deep was investigated experimentally. Dyed de‐ionized water and kerosene were selected as the test fluids. Flow patterns were observed by using a CCD camera and were identified by examining the video images. Flow patterns obtained at the T‐junction and in the microchannel are presented. Superficial velocities varied between 9.26 × 10−4 ∼ 1.85 m/s for water and 9.26 × 10−4 ∼ 2.78 m/s for kerosene. The formation mechanism of slug, monodispersed droplet and droplet populations at the T‐junction was studied. Weber numbers of water and kerosene, WeKS and WeWS, were used to predict the flow regime transition and the flow patterns map. The experimental data of volume of dispersed phase were successfully correlated as a function of WeKS, WeWS, and hold‐up fraction. Considering the uncertainty associated with experimental quantification of the process, the results are in satisfactory agreement over the wide range of 1.90 × 10−3 < WeWS < 30.43 and 5.90 × 10−6 < WeKS < 0.13 with average absolute deviation of only 16.18%. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Stochastic analysis of a displacement front in a randomly heterogeneous medium

The behavior of the interface in a two-phase immiscible fluid flow in a randomly heterogeneous porous medium is investigated. The medium is described by the permeability distribution which represents a random field with given statistical characteristics. When the approach proposed is used, it turns out to be possible to relate the statistical characteristics of the interface with the statistical characteristics of the permeability field and the properties of the phases. On the basis of this relation an important characteristic of the two-phase flow, namely, the average saturation distribution in the neighborhood of the interface, can be calculated.

Two-phase viscoelastic jetting

A coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations. The ink is modeled by the Oldroyd-B viscoelastic fluid model. The coupled algorithm seamlessly incorporates several things: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection terms in the momentum and level set equations; (3) a simple first-order upwind algorithm for the convection term in the viscoelastic stress equations; (4) central difference approximations for viscosity, surface tension, and upper-convected derivative terms; and (5) an equivalent circuit model to calculate the inflow pressure (or flow rate) from dynamic voltage.

A Silicon/glass-based microfluidic device for invetigation of Lagrangian velocity field in microdroplets

We have measured the flow field inside microdroplets formed by two immiscible fluids in a microchannel using micro particle image velocimetry (micro-PIV) technique. An aqueous liquid with fluorescent particles was injected in an immiscible carrier flow. Both velocity fields during the droplet formation process and during the passage in straight, rectangular microchannels were measured and evaluated. We observed that at a certain layer the direction of the outer circulation flow in the droplet is the same as that of the droplet motion. The results indicate that the immiscible carrier fluid flows through the gaps between the aqueous droplet and the rigid channel wall at a velocity faster than the droplet itself.