Miscible Flow Research Articles

An experimental study of transient front velocity for miscible exchange flow in a rectangular channel

ABSTRACT This experimental study considers the exchange flow of two miscible fluids in a rectangular channel. The main purpose is to understand the mixing dynamics and explore how mixing and different channel inclinations can affect variations in front velocity. In contrast to previous studies, no steady state is assumed. The larger channel cross-section used in the current study provides an opportunity to visualize and analyze the inertia dominated regime in finer details. For horizontal channels, after opening the gate valve and allowing the transient phase to pass, it is observed that the front velocity remains almost constant for a period before gradually decreasing. In inclined flows, the mixing and transition to inertia dominated flow begin when the viscous flow rate of the main flow increases. This flow rate may exceed the maximum flow rate that the front can tolerate according to the equations describing the momentum balance at the front. At sufficiently high density contrasts or large inclinations, the front velocity may continue to decrease as the flow progresses due to interfacial instabilities and mixing. Under such conditions, the results may also cast doubt on the presence of a true steady state front velocity in miscible exchange flow.

Two-Layer Equilibrium Model of Miscible Inhomogeneous Fluid Flow

Two-layer flow of a density-stratified fluid with mass transfer between the layers is considered. In the Boussinesq approximation, the equations of motion are reduced to a homogeneous quasilinear system of partial differential equations of mixed type. The flow parameters in the intermediate mixed layer are determined from the equilibrium conditions in a more general model of three-layer flow of a miscible fluid. In particular, the equilibrium conditions imply the constancy of the interlayer Richardson number in velocity-shift flows. A self-similar solution to the problem of breakdown of an arbitrary discontinuity (the lock-exchange problem) in the domain of hyperbolicity of the system under consideration is constructed. The transcritical flow regimes over a local obstacle are studied and the conditions under which the obstacle determines the upstream flow are determined. A comparison of steady-state and time-dependent solutions with the solutions obtained for the original three-layer models of miscible fluid flow is carried out.

Numerical investigation of the divergence-free constraint for the miscible fluids interaction in a lock-exchange arrangement

The present work scrutinizes the implementation of the divergence-free constraint in miscible fluids flow algorithms. In general, the flow solvers handling the interaction of the miscible fluid enforce the zero divergence condition, considering the fluids to be incompressible. In these algorithms, however, a convection-diffusion equation for the mass fraction, in conjunction with the Navier-Stokes equation, is solved for incorporating the mixing effects. This equation leads to a non-zero velocity field in the numerical modeling and the derived velocity divergence is a function of Reynolds and Schmidt numbers. Therefore, in this work, a quasi-incompressible formulation is presented for such flows wherein weak compressibility effects exist, but Mach numbers are very small. This novel approach is tested extensively in the classical lock-exchange setup where the effects of Reynolds and Schmidt numbers are analyzed. The role of density ratios is also investigated to realize whether the quasi-incompressible formulation generates a different mixing behavior or is similar to the conventional incompressible approach. The results demonstrate the convincing differences in these two formulations subjected to the specific combinations of Reynolds number, Schmidt number, and density ratio. A lenient criterion is also suggested by investigating the numerical tests carried out in this work, which may predict the possibilities of generating consistent results in both formulations.

A new optimal error analysis of a mixed finite element method for advection–diffusion–reaction Brinkman flow

AbstractThis article deals with the error analysis of a Galerkin‐mixed finite element methods for the advection–reaction–diffusion Brinkman flow in porous media. Numerical methods for incompressible miscible flow in porous media have been studied extensively in the last several decades. In practical applications, the lowest‐order Galerkin‐mixed method is the most popular one, where the linear Lagrange element is used for the concentration and the lowest‐order Raviart–Thomas element, the lowest‐order Nédélec edge element and piece‐wise constant discontinuous Galerkin element are used for the velocity, vorticity and pressure, respectively. The existing error estimate of this lowest‐order finite element method is only for all variables in spatial direction, which is not optimal for the concentration variable. This paper focuses on a new and optimal error estimate of a linearized backward Euler Galerkin‐mixed FEMs, where the second‐order accuracy for the concentration in spatial directions is established unconditionally. The key to our optimal error analysis is a new negative norm estimate for Nédélec edge element. Moreover, based on the computed numerical concentration, we propose a simple one‐step recovery technique to obtain a new numerical velocity, vorticity and pressure with second‐order accuracy. Numerical experiments are provided to confirm our theoretical analysis.

Recipes for mixing vortices in a microchannel using electric field

Application of an electric field on the pressure-driven flow of a fluid inside a microchannel can create mixing vortices. The Coulombic force at electrode–fluid interface generates the additional stress to engender the instability. While the previous studies show the phenomena at the two-layer immiscible or miscible flows, we show the same for a single fluid system. Linear stability analysis (LSA), non-linear simulations, and experiments together uncover the conditions for onset and propagation of such instabilities with Reynolds (Re) and electric field Rayleigh (Raψ) numbers. The LSA uncover that a higher critical field (larger Racψ) is required to destabilize a flow with a higher flow rate (higher Re), highlighting the stabilizing nature of the inertia. Subsequently, the non-linear simulations and experiments uncover that such systems can develop localized steady or unsteady vortices with time in order to dissipate the excess localized electrical energy originating from the applied field. Example cases are shown wherein the size, number, and recirculation strength of the vortices have been tuned inside the microchannel with the variations in the external field intensity and the arrangements of the electrodes for a fixed Re. The study further unveils that while at lower Raψ only be steady vortices may show up for the fluids with higher viscosities, at the significantly higher Raψ the fluids with a lower viscosity may manifest an array of unsteady counter-rotating vortices. Such vortices may translate due to the flow of the fluid inside the confined microfluidic channel to eventually form a “vortex-street” inside the microchannel.

Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media

Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media

Buoyant miscible viscoplastic displacements in vertical pipes: Flow regimes and their characterizations

We experimentally study miscible displacement flows of a light Newtonian fluid by a heavy viscoplastic fluid, in a vertical pipe with a large aspect ratio (δ−1≫1). We use camera imaging, laser-induced fluorescence, and ultrasound Doppler velocimetry techniques, to capture and process data. Four dimensionless parameters, namely, the Reynolds (Re), Bingham (B), viscosity ratio (M), and densimetric Froude (Fr) numbers (or their combinations), mainly govern the flow dynamics. We identify and characterize three distinct flow regimes, including plug, separation, and mixing regimes, while we describe each regime's dynamics in detail, particularly in terms of the velocity and concentration fields as well as the displacement front velocity. In addition, we analyze the plug regime concerning the residual wall layers, the separation regime in terms of the separation dynamics, spatiotemporal separation zone, and viscoplastic layer thinning, and the mixing regime regarding the mixing index and macroscopic diffusion. Finally, we develop a simplified model to help delineate the flow regime classification, in the plane of Re/Fr2 and M.

Investigation of gravity influence on EOR and CO2 geological storage based on pore-scale simulation

Gravity assistance is a critical factor influencing CO2–oil mixing and miscible flow during EOR and CO2 geological storage. Based on the Navier–Stokes equation, component mass conservation equation, and fluid property–composition relationship, a mathematical model for pore-scale CO2 injection in oil-saturated porous media was developed in this study. The model can reflect the effects of gravity assistance, component diffusion, fluid density variation, and velocity change on EOR and CO2 storage. For non-homogeneous porous media, the gravity influence and large density difference help to minimize the velocity difference between the main flow path and the surrounding area, thus improving the oil recovery and CO2 storage. Large CO2 injection angles and oil–CO2 density differences can increase the oil recovery by 22.6% and 4.2%, respectively, and increase CO2 storage by 37.9% and 4.7%, respectively. Component diffusion facilitates the transportation of the oil components from the low-velocity region to the main flow path, thereby reducing the oil/CO2 concentration difference within the porous media. Component diffusion can increase oil recovery and CO2 storage by 5.7% and 6.9%, respectively. In addition, combined with the component diffusion, a low CO2 injection rate creates a more uniform spatial distribution of the oil/CO2 component, resulting in increases of 9.5% oil recovery and 15.7% CO2 storage, respectively. This study provides theoretical support for improving the geological CO2 storage and EOR processes.

Numerical study on nonisothermal reactive viscous fingering

The numerical study examines the dynamics of viscous fingering in a miscible flow displacement involving an exothermic reaction between displacing and displaced fluids producing nanoparticles. The exothermic reaction alters fluid properties by producing nanoparticles and/or by releasing heat at the front, both competitive in nature. The front changes from stable to forward (reverse) fingering when the contribution of temperature (concentration) to the viscosity dominates. For a fixed viscous behavior, decreasing reaction rate weakens the forward movement of fingers and reverse fingering is obtained. For a fixed injection rate, the thermal diffusivity can weaken the thermal gradients leading to a stable displacement even when the system is viscously unstable and can also trigger double-diffusive instability in a viscously stable system. Overall, the study suggests that the interplay between the mass and thermal contribution to the fluid properties and chemical reaction rates governs the fingering dynamics.

Diffusive–layered convection in Y-shaped continuous-flow microreactor

Efficient and rapid mixing of fluids in continuous-flow microfluidic devices plays an important role in a wide range of applications. Although there are many different methods to enhance mixing in such reactors, the potential of natural convection to mix fluids has been overlooked because of its possible limitations at the microscale. Recent studies have challenged this statement by demonstrating the significance of both gravity-dependent and gravity-independent types of natural convection in improving mixing efficiency. It was shown that inducing double-diffusive convection, Marangoni convection, or Rayleigh–Taylor convection can greatly enhance the mixing of two aqueous solutions in a continuous-flow microreactor. In this study, we experimentally investigate the influence of another type of differential-diffusion instability, known as diffusive–layered convection, on the mixing of two aqueous solutions of chemically inert substances in a Y-shaped continuous-flow microreactor. We consider the scenario when two miscible solutions flow into the main channel through distinct tubes, in which they come into contact and mix, thus causing the onset of diffusive–layered convection. We used two experimental methods, including laser interferometry and dye visualization, to analyse the mixing process. Surprisingly, despite the vigorous convective motion driven by diffusive–layered convection, the intensity of mixing of pumped fluids remains comparable to the scenario when solutions mix only via a diffusion mechanism. We explain this unexpected result by the unique structure of the convective motion, which prevents system homogenization. A comparison with the results previously obtained for double-diffusive convection is performed, and pure diffusive mixing scenarios are implemented.

Primary cementing of vertical wells: displacement and dispersion effects in narrow eccentric annuli. Part 2. Flow behaviour and classification

We present results for Newtonian laminar miscible displacement flows in a narrow, vertical, eccentric annulus, obtained from experiments carried out in a scaled laboratory set-up. These are compared with two computational models introduced in Part 1, Zhang & Frigaard (J. Fluid Mech., vol. 947, 2022, A732). Quite close matches have been found for different approaches, regarding the overall evolving displacement process: front shape, dispersion levels and front velocities. Standardized criteria have been established to identify whether a flow has steady/unsteady and dispersive/non-dispersive displacement front, applicable to both concentric and eccentric annuli. Three characteristic flows have been observed, unsteady and dispersive, dispersive with steady front, and non-dispersive with steady front. Through both qualitative and quantitative studies, the importance of the buoyancy number has been established: it both restrains dispersion on the annular gap scale and induces secondary flows in the azimuthal direction.

Influence of initial plume shape on miscible porous media flows under density and viscosity contrasts

The effect of the initial condition upon the transport dynamics of miscible flowing fluids in a porous medium is investigated under viscosity and density contrasts. Such flows have attracted significant attention due to their importance in many fields of science and engineering, such as $\mathrm {CO}_2$ sequestration and aquifer remediation. Using high-resolution two-dimensional numerical simulations, we illustrate the impact of viscosity and density contrasts on the temporal evolution of the spreading and mixing quantities. We show that such impact depends on the initial shape of the source distribution where the solute is injected and on the intensity of the horizontal background flux. We find that rates of mixing are dependent on whether the solute is more or less viscous than the ambient fluid, a result usually not taken into consideration in studies on gravity fingering. At higher background flux, the effects due to horizontal viscous fingering dominate over gravitational fingering. Our computational analysis also suggests a non-trivial relationship between mixing and the length of the plume's interface under fingering instabilities. Finally, we show how a stratified permeability field can interact with these sources of instabilities and affect the transport behaviour of the plume.

Numerical simulation of miscible multiphase flow and fluid–fluid interaction in deformable porous media

AbstractThe focus of the underlying research work is on the macroscopic modeling of unstable multiphase fluid flow in deformable porous media, where a lower‐viscous fluid is displaced by a more viscous fluid. This process leads to the formation of channel‐like networks, called viscous fingering. The instability effect is involved in a wide range of different fields in engineering. Some of the most common applications include carbon sequestration to store carbon dioxide (CO2) in underground reservoirs, contaminant transport in geostructures, in industrial processes, such as filtration, catalytic reactions, and in the operation of polymer electrolyte membrane fuel cells with multiphase flow in the gas diffusion layers. In this work, ideal miscible water–glycerin fluids are considered. It is assumed that the interacting fluids in the deformable porous media are incompressible. In addition, a dispersion–diffusion law is applied to capture the fluid–fluid interactions. The presence of a deformable porous material adds additional effects to the problem of the multiphase flow in porous media. The stresses in the porous solid matrix lead to changes in the porosity and influence the flow velocity of the fluids. To couple the deformable porous media with the multiphase flow, a macroscopic approach is used that relies on the theory of porous media. For the porous solid matrix, a linear elastic material model within small strains assumption is applied. The influence of the deformation‐dependent porosity on the instability is studied for 2D simulations, such as a multilayered geometry with different elastic parameters. The presented coupled nonlinear system of differential equations is simulated with the finite element method. Furthermore, a stabilization technique based on the quasi‐compressibility method is used.

Comparison of exchange flow of two miscible fluids in curved and slanted straight tubes

The front velocity in miscible exchange flow along the straight and curved tubes has been investigated. Almost the entire flow lies within the range of inertia dominated regime in the current experimental setup. Available data for straight pipes at different Atwood numbers have been revisited to provide an appropriate ground for better understanding and evaluation of the observations made for the flow in curved tubes. A 19.05 mm diameter and 2.40 m long tube has been formed to follow 55°of an arc in the vertical plane with the radius of curvature of 2.5 meters. The upper and lower parts are separated by a gate valve and filled with heavier and lighter fluids, respectively. The observations and analyses demonstrate how the continuous variations of the flow inclination along the curved path and the change in mixing dynamics associated with it can affect the velocity of downward and upward moving fronts. Most notably it has been detected that the velocity of upward moving front follows a similar trend as in straight pipes due to the continuously increasing mixing. However, the velocity of downward moving heavy front slightly decreases as opposed to the case of straight pipes, signifying the effect of curvature on mixing enhancement.

Analysis of critical water flow and solute transport parameters in different soils mixed with a synthetic zeolite

The addition of natural or synthetic zeolites alters a soil’s chemical, physical and biological properties. Due to the existence of a complex internal structure, zeolites have the potential to modify soil structure and texture with a direct impact on soil hydrological properties, introducing the possibility of controlling soil and groundwater pollution as well as irrigation management practices.In the present study, a series of laboratory tests were conducted on soil samples mixed with zeolite to investigate the possible changes in hydraulic and solute transport properties and related parameters. To determine the above properties, four soils of different textures were selected and two distinct groups of experiments were conducted on disturbed (i.e., repacked) soil samples by adding known amounts of zeolite (i.e., 1, 2, 5 and 10%; w/w). Solute transport properties were determined on one group of soil samples using the so-called Kachanoski approach to monitor miscible flow experiments. Soil hydraulic properties were determined on the second group of soil samples by measuring soil water retention curves (SWRCs) and saturated hydraulic conductivity (Ks). In general, we observed significant changes in the measured properties with zeolite percentages of 5% and 10%. However, some changes were also evident at 1% and 2% of zeolite addition. These observed differences may be mainly ascribed to changes in the soil’s pore size distribution due to the addition of a finer fraction (i.e., zeolite) to soils. This fraction reduces macropores (that are occluded in proportion to their amount) and thus enhances the formation of meso- and micropore regions.

Molecular dynamics simulation of CO2-oil miscible fluid distribution and flow within nanopores

CO2 Huff-n-Puff is a promising technology for recovering unconventional oil reservoirs nowadays. Studying the structural properties of CO2-oil inside nanoscale pores and the transport mechanism during production can help further improve crude oil recovery. In this work, molecular dynamics simulations are performed to explore the distribution and flow of CO2-decane within a 6 nm SiO2 nanopore under reservoir conditions. CO2 will substitute the decane adsorbed on the surface under the strong electrostatic interactions with the SiO2 surface. The variation of CO2 content in the adsorbed layer was quantitatively described. The flow behavior of CO2-decane on the pore surface does not obey the continuous hydrodynamics theory. The adsorbed CO2 forms an adhesion layer on the pore surface, shifting the flow boundary condition from slip to negative slip. The CO2-decane permeability model is established to investigate the influences of the negative slip on the permeability. The adhesion layer reduces the permeability of CO2-decane in pores. By contrast, the dissolved CO2 reduces the bulk phase viscosity and raises the decane mobility. The flux analysis results indicate that viscosity reduction contributes more than the flux loss due to negative slip, and CO2 improves the decane transport ability within the nanopore. Besides, sensitive factors such as oil content, pore pressure, and pressure gradient are considered. This study provides new insights into the surface flow behavior of CO2-oil in nanopores, which is essential for the accurate prediction of CO2-oil transport behavior under confined conditions.

A new Runge–Kutta–Chebyshev Galerkin-characteristic finite element method for advection–dispersion problems in anisotropic porous media

We propose a new approach that combines the modified method of characteristics with a unified finite element discretization for the numerical solution of a class of coupled Darcy-advection–dispersion problems in anisotropic porous media. The proposed method benefits from advantages of the method of characteristics in its ability to handle the nonlinear convective terms, while taking advantage of a unified formulation that allows the use of equal-order finite element approximations along with the L2-projection method for all solutions in the problem. In the proposed Galerkin-characteristic finite element framework, the standard Courant–Friedrichs–Lewy condition is relaxed, and time truncation errors are reduced since no stability criterion restricts the choice of time step. For time integration, we use a Runge–Kutta scheme with the Chebyshev polynomials (RKC). The RKC method has an extensive stability field and it is explicit and second-order accurate. In order to assess the quality of the proposed approach, we perform numerical experiments for several categories of test cases. The first category concerns accuracy test examples with known analytical solutions, while the second category focuses on a benchmark problem of miscible flow in a heterogeneous porous medium. The numerical results obtained show high performance and demonstrate the ability of the method to capture dispersion effects in porous media problems.

Simulation of Nonlinear Viscous Fingering in a Reactive Flow Displacement: A Multifractal Approach

fractal analysis of viscous fingering of a reactive miscible flow displacement in homogeneous porous media is investigated and multifractal spectrum, and fractal dimension are introduced as two essential features to characterize the irregularity of finger patterns. The Reaction of the two reactant fluids generates a miscible chemical product C in the contact zone. Considering the similarity between chemical products and coastline, monofractal and multifractal analyzes are performed. In monofractal analysis, the box-counting method is implemented on binary images and in multifractal analysis, due to the image processing; the fractal characteristics of viscous fingering instability are analyzed by means of fractal quantities such as Holder exponent, multifractal spectrum, f (α)-image and fractal dimension dynamics. Fractal analysis shows that the fractal dimension increases with time. Also, by considering five different nonlinear simulations, the results show that in the case both sides of the chemical product C are unstable, the multifractal spectrum curve has the highest peak, which means the more complex finger patterns lead to more values of fractal dimension. In addition, a comparison between different values of Ar is conducted and the results show similar behavior. However, small value of aspect ratio leads to a broader width of the multifractal spectrum curve. Furthermore, f (α)-images of concentration contour were investigated for different precisions and some undetectable finger patterns were observed in these images. It can be concluded that the use of f (α)-image represents more detailed image than concentration contours.

Co‐Current Fluid Flow Mechanisms Within a Complex Porous Structure at the Pore Level

AbstractThis study has been addressed the mechanisms of the co‐current fluid flow in a heterogeneous porous media using the lattice Boltzmann method. Since the smallest interaction between viscous and capillary forces at the interface is of great importance, the simulations are performed with the hybrid phase‐field model at the pore level. This is because the main advantage of this model is that due to its connection with the phase‐field theory, it has a solid physical basis to record interface dynamics. Model verification is followed by recording viscous coupling effects. The relative permeability curves and the velocity profiles are compared with the analytical solution, so that the observations confirm the accuracy claim of the model. In the following, the fluid flow through the heterogeneous porous structure is simulated, so that its sweep efficiency and corresponding velocity field at the breakthrough time are discussed. The results show that increasing the injection velocity reduces the displacement efficiency and increases the velocity field fluctuations due to the viscous fingering regime. Changing the wetting conditions to strong imbibition (SI) will increase the efficiency due to the role of capillary pressure and corner flow mechanism. Also, increasing the interfacial tension in the SI and the strong drainage will increase and decrease the sweep efficiency, respectively, so the rate of changes in fully immiscible flow is much higher than the near miscible flow. The velocity fluctuations in the fully immiscible flow are more significant than in the near miscible flow, which is reasonable given the flow properties.

Finite Element Simulations of Fluids Leakage through the Faulted Reservoir

Carbon dioxide (CO2) capture and storage (CCS) in geological formation as a supercritical fluid is a viable option to reduce anthropogenic greenhouse gas emissions. Due to the density difference between CO2 and formation fluid, CO2 shows a buoyant tendency. Thereby, if CO2 migrates towards the fault in a compromised faulted reservoir, it may escape the storage reservoir. Therefore, it is essential to predict fluids leakage through the faulted reservoir into the aquifer, associated pressure development, and fluids properties over time to assess associated risk and quantification of leakage. We present finite element simulations of miscible fluids flow through the faulted reservoir to elucidate this behavior. There are very few attempts to model multicomponent fluids non-isothermal model during phase change including the Equation of State (EoS) which we addressed by coupling the mass balance equation of fluids, the fractional mass transport, and the energy balance equation. To obtain fluids mixture thermo-physical properties, we used the Peng-Robinson EoS. For validation of the coupled formulation, we compared the simulation results with Ketzin Pilot project field monitoring data, which shows good agreement. A faulted reservoir comprised of five layers is used to investigate fluids leakage through a compromised reservoir. These layers are a CO2 storage reservoir, overlain by alternating caprocks and aquifers. We also considered three different CO2 injection rates to study the injection rate effect to assess the pressure buildup during injection process. We present the thermal effect by comparing the isothermal and the non-isothermal conditions. For the latter case, we assumed three different thermal gradients. Additionally, to assess the fault aperture effect, we studied three different apertures. We observed that developed pressure and fluids properties have effects on injection rates, temperature gradient, and fault aperture. Additionally, such responses in the near-field and the far-field from the injection well are critical to assess the risk, which we discussed in this paper.