Insight into evolution of invasive patterns on fingering phenomenon during immiscible two-phase flow through pore structure

Understanding fingering, as a challenge to stable displacement during the immiscible flow, has become a crucial phenomenon for geological carbon sequestration, enhanced oil recovery, and groundwater protection. Typically governed by gravity, viscous and capillary forces, these factors lead invasive fluids to occupy pore space irregularly and incompletely. Previous studies have demonstrated capillary numbers,describing the viscous and capillary forces, to quantificationally induce evolution of invasion patterns.While the evolution mechanisms of invasive patterns have not been deeply elucidated under the constant capillary number and three variable parameters including velocity, viscosity, and interfacial tension.Our research employs two horizontal visualization systems and a two-phase laminar flow simulation to investigate the tendency of invasive pattern transition by various parameters at the pore scale. We showed that increasing invasive viscosity or reducing interfacial tension in a homogeneous pore space significantly enhanced sweep efficiency, under constant capillary number. Additionally, in the fingering crossover pattern, the region near the inlet was prone to capillary fingering with multi-directional invasion, while the viscous fingering with unidirectional invasion was more susceptible occurred in the region near the outlet. Furthermore, increasing invasive viscosity or decreasing invasive velocity and interfacial tension promoted the extension of viscous fingering from the outlet to the inlet, presenting that the subsequent invasive fluid flows toward the outlet. In the case of invasive trunk along a unidirectional path, the invasive flow increased exponentially closer to the outlet, resulting in a significant decrease in the width of the invasive interface. Our work holds promising applications for optimizing invasive patterns in heterogeneous porous media.

Influence of reservoir heterogeneity on immiscible water-alternating-CO_(2)flooding:A case study

Currently,limited studies of immiscible water-alternating-CO_(2)(imWACO_(2))flooding focus on the impact of reservoir heterogeneity on reservoir development outcomes.Given this,using the heterogeneous reservoirs in the Gao 89-1 block as a case study,this study conducted slab core flooding experiments and numerical simulations to assess the impact of reservoir heterogeneity on imWACO_(2)flooding efficiency.It can be concluded that imWACO_(2)flooding can enhance the sweep volume and oil recovery compared to continuous CO_(2)flooding.As the permeability difference increases,the difference in the swept volume between zones/layers with relatively high and low permeability increases.To optimize the exploitation of reservoirs in the Gao 89-1 block,the optimal timing and CO_(2)injection rate for imWACO_(2)flooding are determined at water cut of 40%and 10000 m^(3)/d,respectively.A short injection-production semi-period,combined with multiple cycles of water and CO_(2)injection alternations,is beneficial for enhanced oil recovery from imWACO_(2)flooding.

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation（capillary pressure）.So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory.The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported.In our work,wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived.Furthermore,the wavefield and its characteristics are studied using the numerical finite element method.The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band.The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase.More specifically,the displacement decreases with increasing relaxation coefficient.

Comparison of dendrite and dispersive structure in rapidly solidified Cu-Co immiscible alloy with different heat flow modes

Rapid solidification of Cu-Co immiscible alloy was investigated by glass-fluxing, spray casting and melt-spinning techniques. Both the transition from dendrite to dispersive structure and corresponding scale evolution were revealed and further elucidated in terms of the heat flow mode, nucleation and growth processes under different solidification conditions. With the increase of undercooling, columnar dendrite is replaced by dispersive structure due to the immiscible effect. In contrast, equiaxed dendrite forms in spray cast alloy due to multiple nucleation events and becomes thinner for the case of higher cooling rate. Ascribed to the enhanced non-equilibrium effect and insufficient period for collision and coagulation processes between separated droplets, fine globular dispersion appears upon the diameter of spray casting reaching 4 mm. As for the melt-spun ribbon with the highest cooling rate, a single-phase solid solution microstructure with refined grain of cellular morphology can be obtained, which is attributed to the suppression of liquid phase separation by instant solidification.

Two stages of immiscible liquid separation in the formation of Panzhihua-type Fe-Ti-V oxide deposits,SW China

Magmatic oxide deposits in the～260 Ma Emeishan Large Igneous Province（ELIP）,SW China and northern Vietnam,are important sources of Fe,Ti and V.Some giant magmatic Fe-Ti-V oxide deposits, such as the Panzhihua,Hongge,and Baima deposits,are well described in the literature and are hosted in layered mafic-ultramafic intrusions in the Panxi region,the central ELIP.The same type of ELIP- related deposits also occur far to the south and include the Anyi deposit,about 130 km south of Panzhihua,and the Mianhuadi deposit in the Red River fault zone.The Anyi deposit is relatively small but is similarly hosted in a layered mafic intrusion.The Mianhuadi deposit has a zircon U-Pb age of～260 Ma and is thus contemporaneous with the ELIP.This deposit was variably metamorphosed during the Indosinian orogeny and Red River faulting.Compositionally,magnetite of the Mianhuadi deposit contains smaller amounts of Ti and V than that of the other deposits,possibly attributable to the later metamorphism.The distribution of the oxide ore deposits is not related to the domal structure of the ELIP.One major feature of all the oxide deposits in the ELIP is the spatial association of oxide-bearing gabbroic intrusions,syenitic plutons and high-Ti flood basalts.Thus,we propose that magmas from a mantle plume were emplaced into a shallow magma chamber where they were evolved into a field of liquid immiscibility to form two silicate liquids,one with an extremely Fe-Ti-rich gabbroic composition and the other syenitic.An immiscible Fe-Ti-（P） oxide melt may then separate from the mafic magmas to form oxide deposits.The parental magmas from which these deposits formed were likely Fe-Ti-rich picritic in composition and were derived from enriched asthenospheric mantle at a greater depth than the magmas that produced sulfide-bearing intrusions of the ELIP.

Modeling and Simulation of the Microstructure Evolution during a Cooling of Immiscible Alloys in the Miscibility Gap

The microstructure development during a cooling period of alloys being immiscible in the liquid state such as Al-Pb or AI-Bi has gained renewed scientific and technical interest during the last decades. Experiments have been performed to investigate the phase transformation kinetics in the liquid miscibility gap and numerical models have been developed to simulate and analyze the solidification process. The recently developed computational modeling techniques can, to some extent, be applied to describe the decomposition, the spatial phase separation and the microstructure evolution during a cooling period of an immiscible alloy through the miscibility gap. This article overviews the researches in this field.

Effect of high magnetic field on solidification microstructure evolution of a Cu-Fe immiscible alloy

The liquid phase separation behavior and the evolution of the solidification microstructure of a binary Cu_(50)Fe_(50) alloy were investigated under the conditions of without and with a 10 T magnetic field,with different undercooling during the solidification process.Results show that the combined effect of Stokes motion and Marangoni convection leads to the formation of the core-shell structure under the condition without the magnetic field.In addition,specific gravity segregation is reinforced by increasing the undercooling,resulting in Fe-rich phase drifts towards the sample edge.In the 10 T magnetic field,the Fe-rich phase is elongated in the parallel direction of the magnetic field under the action of demagnetization energy due to the difference of static magnetic energy and surface energy.In the vertical direction,through the action of Lorentz force,the convection in the melt is inhibited and Fe-rich phase becomes more dispersed.Meanwhile,the diffusion of the two phases and the coagulation of the Fe-rich phases are also restrained under the magnetic field,therefore,the phase volume fraction of the Fe-rich phase decreases at the same undercooling in the 10 T magnetic field.The magnetic field inhibits the segregation behavior in the vertical direction of the magnetic field,and at the same time,improves the gravitational segregation to a certain extent,which has a very important impact on microstructure regulation.

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,

Calculation of Activity Coefficient from Immiscible Binary Alloy Phase Diagram by Means of Modified Sub-regular Solution Model

The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.

Large-Scale Segregation of Immiscible Liquids in the 1780 Ma Taihang Dykes to Produce the Bimodal Xiong'er Volcanics(North China)

It is yet unclear whether large-scale segregation of immiscibile liquids and eruption of high-Si lavas exist in nature(Charlier et al.,2013).We present a possible case of segregation of immscible liquids in the 1780 Ma Taihang

Mechanical Alloying of Ag-Cu Immiscible Alloy System

Mechanical alloying has been performed in Ag-Cu immiscible alloy system with five different compositions. X-ray diffraction analysis was carried out to determine the structural characterization of the milled powders. Lattice constants of the milled powders were determined and the solubility for Ag in Cu was calculated. The results demonstrated that MA indeed produced a face center cubic (f.c.c.). Cu-based Cu-Ag solid solution and the solid solubility has been extended to x(Ag)=30% for Ag in Cu when the grain size of Cu-based Cu-Ag solid solution is about 10 nm after MA. There is a three-phases co-existence during the process of MA in this alloy system which agrees well with other experimental and theoretical results. Based on the experimental results a formation model was proposed in this paper to understand the formation of Ag-Cu solid solution during MA.

A FINITE ELEMENT COLLOCATION METHOD FOR TWO-PHASE INCOMPRESSIBLE IMMISCIBLE PROBLEMS

Two-phase, incompressible, immiscible flow in porous media is governed by a coupled system of nonlinear partial differential equations. The pressure equation is elliptic, whereas the concentration equation is parabolic, and both are treated by the collocation scheme. Existence and uniqueness of solutions of the algorithm are proved. A optimal convergence analysis is given for the method.

Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solu- tion of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.

Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schr6dinger equations （1-NLS） with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoret- ically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.

Calculation of Interaction Parameters from Immiscible Phase Diagram of Alkali Metal or Alkali Earth Metal-Halide System by Means of Subregular Solution Model

In this paper, the interaction parameters in the subregular solution model, λ1 and λ2, are regarded as a linear function of temperature, T. Therefore, the molar excess Gibbs energy of A-B binary system may be reexpressed as follows:Gm^E=xAxB[(λ11+λ12T)+(λ21+λ22T)xB]The calculation of the model parameters, λ11, λ12, λ21and λ22, was carried out numerically from the phase diagrams for 11 alkali metal-alkali halide or alkali earth metal-halide systems. In addition, artificial neural network trained by known data has been used to predict the values of these model parameters. The predicted results are in good agreement with the .calculated ones. The applicability of the subregular solution model to the alkali metal-alkali halide or alkali earth metal-halide systems were tested by comparing the available experimental composition along the boundary of miscibility gap with the calculated ones which were obtained by using genetic algorithm. The good agreement between the calculated and experimental results across the entire liquidus is valid evidence in support of the model.

A NEW NUMERICAL METHOD FOR TWO-PHASE IMMISCIBLE INCOMPRESSIBLE PROBLEM

Two-phase, immiscible, incompressible flow in porous media is governed by a system of nonlinear partial differential equations. In most practical applications convection physically dominates diffusion, and the object of this paper is to develop a finite difference method combined with the method of characteristics and the lumped mass method to treat the parabolic equation of the differential system. This method is shown satisfy the maximum principle and its error analysis is presented.

Numerical simulation of the Liquid-liquid phase separation and microstructure evolution of Al-In immiscible alloys during cooling

A numerical model has been developed to describe the microstructural evolution of Al In immiscible alloys through the miscibility gap. The model considers the common action of nucleation, diffusible growth, Brownian collision and motion collision between the second phase droplets. The simulation results are dynamically visualized and show that the volume fraction, distribution and size of the second phase droplets satisfactorily agree with the experimental results. So the model can be used to predict the microstructural evolution of Al In immiscible alloys during the cooling process.

Unsteady mixed convective heat transfer of two immiscible fluids confined between long vertical wavy wall and parallel flat wall

The combined effects of thermal and mass convection of viscous incom- pressible and immiscible fluids through a vertical wavy wall and a smooth flat wall are analyzed. The dimensionless governing equations are perturbed into a mean part （the zeroth-order） and a perturbed part （the first-order）. The first-order quantities are ob- tained by the perturbation series expansion for short wavelength, in which the terms of the exponential order arise. The analytical expressions for the zeroth-order, the first-order, and the total solutions are obtained. The numerical computations are presented graph- ically to show the salient features of the fluid flow and the heat transfer characteristics. Separate solutions are matched at the interface by using suitable matching conditions. The shear stress and the Nusselt number are also analyzed for variations of the governing parameters. It is observed that the Grashof number, the viscosity ratio, the width ratio, and the conductivity ratio promote the velocity parallel to the flow direction. A reversal effect is observed for the velocity perpendicular to the flow direction.

Microstructural Features of Spray-Deposited Immiscible Bearing Alloys Al-43Sn and Al-7Sn-1.3Cu-1.3Ni

Two commercial grade aluminum based immiscible bearing alloys were spray-deposited using convergent-divergent type of nozzle. The processing parameters for spray-deposition were adjusted in such a way that most of the droplets arrived on the deposition substrate in either liquid or semi-liquid state. The microstructural features of spray-formed and as-cast alloys are compared. In spray-formed alloys equiaxed grains were observed. The cell boundaries and intercellular regions were observed to be decorated with sub-micron sized particles whereas in normal casting the second phase was observed to be segregated along grain boundaries. The morphology and distribution of second phase were observed to have similarity with those in over-spread and atomized powders produced under similar processing conditions. The microstructural features observed with variation in spray conditions are discussed in detail.

Effect of the liquid temperature on the interaction behavior for single water droplet impacting on the immiscible liquid

The interaction of single water droplet impacting on immiscible liquid surface was focused with the temperature varying from 50℃ to 210℃.The impact behavior is recorded with a high-speed camera running at 2000 frames per second.It is found that droplet diameter,oil temperature,andWeber number have important influences on impact behaviors.Three typical phenomena,including penetration,crater-jet,and crater-jet–secondary jet,were observed.Penetration only occurs when the Weber number is below 105.With Weber number increasing to 302,the jet begins to appear.Moreover,to gain deeper physical insight into the crater formation and jet formation,the energy of droplet impingement onto the liquid pool surface was estimated.The oil temperature has a significant effect on the energy conversion efficiency.High temperature is beneficial to improve energy conversion efficiency.