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.

Numerical simulation for separation of multi-phase immiscible fluids in porous media

Based on a lattice Boltzmann method and general principles of porous flow, a numerical technique is presented for analysing the separation of multi-phase immiscible fluids in porous media. The total body force acting on fluid particles is modified by axiding relative permeability in Nithiarasu＇s expression with an axiditional surface tension term. As a test of this model, we simulate the phase separation for the case of two immiscible fluids. The numerical results show that the two coupling relative permeability coefficients K12 and K21 have the same magnitude, so the linear flux-forcing relationships satisfy Onsager reciprocity. Phase separation phenomenon is shown with the time evolution of density distribution and bears a strong similarity to the results obtained from other numerical models and the flows in sands. At the same time, the dynamical rules in this model are local, therefore it can be run on massively parallel computers with well computational efficiency.

Dissipative Particle Dynamics Simulations of Domain Growth and Phase Separation in Binary Immiscible Fluids

It was investigated that the domain growth processes of spinodal decomposition with different quenching depth in two and three dimensional binary immiscible fluids by using parallel dissipative particle dynamics simulations. In two dimensions, the dynamic scaling exponent 1/2 for coalescence and 2/3 for inertial regimes in the shallow quench and strong finite size effects in the cases of deep quenching were obtained. In three dimensions, it was used that the diffusive regime with exponent n=l/3 in the shallow quench and the inertial hydrodynamic regime with n=2/3 for different quenches. The viscous effects are not clearly reflected, showing n=1/2 in both shallow and deep quenches in this time period, due to the soft nature of interaction potential adopted in dissipative particle dynamics.

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.

Averaged Dynamics of Fluids near the Oscillating Interface in a Hele-Shaw Cell

The steady flow in a Hele-Shaw cell filled with fluids with a high viscosity contrast in the presence of fluid oscillations is experimentally studied.The control of oscillatory dynamics of multiphase systems with interfaces is a challenging technological problem.We consider miscible(water and glycerol)and immiscible(water and high-viscosity silicone oil PMS-1000)fluids under subsonic oscillations perpendicular to the interface.Observations show that the interface shape depends on the amplitude and frequency of oscillations.The interface is undisturbed only in the absence of oscillations.Under small amplitudes,the interface between water and glycerol widens due to mixing.When the critical amplitude is reached,the interface becomes unstable to the fingering instability:Aqueous fingers penetrate the high-viscosity glycerol and induce intensive mixing of miscible fluids and associated decay of the instability.After the disappearance of the fingers,the interface takes a U-shape in the central part of the cell.A similar effect is observed for immiscible fluids:The oscillating interface tends to bend to the side of a high-viscosity fluid.Again,when the critical amplitude is reached,the fingering instability arises at the convex interface.This paper focuses on the causes of bending of the initially undisturbed interface between miscible or immiscible fluids.For this purpose,we measure the steady flow velocity near the interface and in the bulk of a high-viscosity fluid using Particle Image Velocimetry(PIV).

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.

Interface profile evolution between binary immiscible fluids induced by high magnetic field gradients

A mechanical analysis is done to find the evolution of the interface profile between binary immiscible fluids induced by a three-dimensional orthogonal magnetic field gradient.In the experiments,the changes of the interface profile between four groups of binary immiscible fluids are investigated under the same horizontal magnetic field gradients.The binary immiscible fluids are made of benzene and other liquids,like CuSO4,Fecl3,FeSO4 or Cucl2 aqueous solutions.In addition,the interface profile between the benzene and CuSO4 aqueous solution is examined under different horizontal magnetic field gradients.The experimental results are consistent with the theoretical analysis.This study explains the enhanced Moses effect from a mechanics standpoint.Furthermore,a new method for susceptibility measurement is proposed based on this enhanced Moses effect.

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,

Instantaneous deformation characteristics of a single bubble in immiscible fluids

The passage of a rising bubble through immiscible fluids is encountered in bath smelting.In order to investigate characteristics of bubble deformation in immiscible fluids,the bubble shape change at the interface and the relationship between the bubble aspect ratio(E)and dimensionless number of forces were obtained.A three-dimensional model was established,and the free-floating behavior of a single bubble in immiscible fluids was numerically simulated by phase-field method.The simulation results are in good agreement with experimental results.The results indicate that when the bubble passes through the interface,the bubble shape is divided into four types in turn:“pear”,inverted“pear”,“convex”and“droplet”shape.In the lower liquid,the relationship of E to Weber number(We),Tadaki number(Ta),and Reynolds number(Re)is distributed between two intersecting lines.The relationship of E to Eötvös number(Eo),a dimensionless group,and Galilei number(Ga)is distributed near the lines with slopes of−3.325×10^(-5),−0.0855,and−8.73×10^(-4),respectively.In the upper liquid,the relationship of E to We,Ta,and Re is distributed between two parallel lines.Compared with gravity,the inertial force plays a leading role in the bubble shape in the lower and upper liquid.Compared with the viscous force,the surface tension dominates the bubble shape in the lower liquid.

Dynamics of Low-Viscosity Liquids Interface in an Unevenly Rotating Vertical Layer

The behavior of two immiscible low-viscosity liquids differing in density and viscosity in a vertical flat layer undergoing modulated rotation is experimentally studied.The layer has a circular axisymmetric boundary.In the absence of modulation of the rotation speed,the interphase boundary has the shape of a short axisymmetric cylinder.A new effect has been discovered,under the influence of rotation speed modulation,the interface takes on a new dynamic equilibrium state.A more viscous liquid covers the end boundaries of the layer in the form of thin films,which have the shape of round spots of almost constant radius;with increasing amplitude of the velocity modulation,the wetting boundary expands.It is found that upon reaching the critical amplitude of oscillations,the film of a viscous liquid loses stability,and the outer edge of the wetting spot collapses and takes on a feathery structure.It is shown that this threshold is caused by the development of the Kelvin-Helmholtz oscillatory instability of the film.The spreading radius of a spot of light viscous liquid and its stability are studied depending on the rotation rate,amplitude,and frequency of rotation speed modulation.The discovered averaged effects are determined by different oscillatory interaction of fluids with the end-walls of the cell,due to different viscosities.The effect of films forming can find application in technological processes to intensify mass transfer at interphase boundaries.

Origin of the Yueguang gold deposit in Xinhua, Hunan Province, South China: insights from fl uid inclusion and hydrogen–oxygen stable isotope analysis

The Yueguang gold deposit is located in Fengjia,Xinhua County,Hunan Province,South China.It represents a recently discovered small-scale gold deposit situated in the southwestern region of the Jiangnan Orogenic Belt,west of the Baimashan granitic batholith.In order to discern the characteristics of the ore-formingfluids,the underlying mineralization processes,and establish a foundation for the origin of the Yueguang gold depositfluid inclusion micro-thermometry,as well as quartz hydrogen and oxygen isotope analysis,have been carried out on samples obtained from various stages of mineralization.The hydrothermal miner-alization stages within the Yueguang gold deposit can be categorized into three stages:(i)the barren,pre-ore quartz-pyrite stage(Stage Ⅰ),the quartz-pyrite-gold stage(Stage Ⅱ),and the post-ore quartz-carbonate stage(Stage Ⅲ),with the second stage being the main mineralization stage.Thefluid inclusions identified in samples from the main min-eralization stage can predominantly be described with the NaCl–H_(2)O and CO_(2)–NaCl–H_(2)O systems.These inclusions display homogenization temperatures ranging from 158.8 to 334.9℃,and thefluid salinity ranges from 0.3%to 4.0%(wt.%NaCl equiv.).Laser Raman spectroscopy analysis of individual inclusions further reveals the presence of gas-phases such as CO_(2),CH_(4),and N_(2).Isotopic analysis indicatesδ^(18)Ofluid values ranging from 3.95 to 6.7‰ and δDH_(2)O values ranging from-71.9 to-55.7‰.These results indi-cate that the ore-formingfluid of the Yueguang gold deposit belongs to metamorphic hydrothermalfluids of middle-low temperature and low salinity.In the process of ore formation,gold is transported in the form of Au(HS)2-complexes,with gold deposition being driven byfluid immiscibility.Therefore,the Yueguang gold deposit is categorized as an orogenic gold deposit dominated by metamorphic hydrother-malfluid.It may become a new target for gold exploration in the Baimashan region,central Hunan Province.

Magmatic-hydrothermal Evolution and Mineralization Mechanisms of the Wangjiazhuang Cu(-Mo)Deposit in the Zouping Volcanic Basin,Shandong Province,China:Constraints from Fluid Inclusions

The Wangjiazhuang Cu(-Mo)deposit,located within the Zouping volcanic basin in western Shandong Province,China,is unique in this area for having an economic value.In order to expound the metallogenetic characteristics of this porphyry-like hydrothermal deposit,a detailed fluid inclusion study has been conducted,employing the techniques of representative sampling,fluid inclusion petrography,microthermometry,Raman spectroscopy,LA-ICP-MS analysis of single fluid inclusions,as well as cathode fluorescence spectrometer analysis of host mineral quartz.The deposit contains mainly two types of orebodies,i.e.veinlet-dissemination-stockwork orebodies in the K-Si alteration zone and pegmatiticquartz sulfide veins above them.In addition,minor breccia ore occurs locally.Four types of fluid inclusions in the deposit and altered quartz monzonite are identified:L-type one-or two-phase aqueous inclusions,V-type vapor-rich inclusions with V/L ratios greater than 50%-90%,D-type multiphase fluid inclusions containing daughter minerals or solids and S-type silicate-bearing fluid inclusions containing mainly muscovite and biotite.Ore petrography and fluid inclusion study has revealed a three-stage mineralization process,driven by magmatic-hydrothermal fluid activity,as follows.Initially,a hydrothermal fluid,separated from the parent magma,infiltrated into the quartz monzonite,resulting in its extensive K-Si alteration,as indicated by silicate-bearing fluid inclusions trapped in altered quartz monzonite.This is followed by the early mineralization,the formation of quartz veinlets and dissemination-stockwork ores.During the main mineralization stage,due to the participation and mixing of meteoric groundwater with magmatic-sourced hydrothermal fluid,the cooling and phase separation caused deposition of metals from the hydrothermal fluids.As a result,the pegmatitic-quartz sulfide-vein ores formed.In the late mineralization stage,decreasing fluid salinity led to the formation of L-type aqueous inclusions and chalcopyrite-sulfosalt ore.Coexistence of V-type and D-type inclusions and their similar homogenization temperatures with different homogenization modes suggest that phase separation or boiling of the ore-forming fluids took place during the early and the main mineralization stages.The formation P-T conditions of S-type inclusions and the early and the main mineralization stages were estimated as ca.156-182 MPa and 450-650℃,350-450℃,18-35 MPa and 280-380℃,8-15 MPa,respectively,based on the microthermometric data of the fluid inclusions formed at the individual stages.

THREE DIMENSIONAL SIMULATION OF UNSTABLE IMMISCIBLEDISPLACEMENT IN THE POROUS MEDIUM

In this study changes of uncontinuous potential functions at the interface were used to simulate the immiscible displacement in porous media. The elliptic partial differential equation was changed to a seven-point molecule form algebraic equation in three dimensions using the finite difference method. The strongly implicit procedure was adopted to determine the potential functions at every tone instant. Then the change of interface was determined. The simulation was continued until the displacement changed to unstable state. The effect of capillary pressure, wetting property, and nonuniformity of permeability were considered.

Unsteady flow and heat transfer of porous media sandwiched between viscous fluids

The problem of unsteady oscillatory flow and heat transfer of porous medin sandwiched between viscous fluids has been considered through a horizontal channel with isothermal wall temperatures. The flow in the porous medium is modeled using the Brinkman equation. The governing partial differential equations are transformed to ordinary differential equations by collecting the non-periodic and periodic terms. Closed-form solutions for each region are found after applying the boundary and interface conditions. The influence of physical parameters, such as the porous parameter, the frequency parameter, the periodic frequency parameter, the viscosity ratios, the conductivity ratios, and the Prandtl number, on the velocity and temperature fields is computed numerically and presented graphically. In addition, the numerical values of the Nusselt number at the top and bottom walls are derived and tabulated.

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.

Simulation of the Influence of Surface Wettability on Viscous Fingering Phenomenon in Porous Media

Fingering phenomena are common occurrence in the natural world. It generally takes place when a less viscous fluid displacesa more viscous fluid typically in porous media. Nowadays, such phenomena have extensively been studied due to itsimportance in many industrial fields. In this paper, the effects of surface wettability on finger pattern are studied and simulatednumerically by the Lattice Boltzmann method (LBM). The displacement efficiency is investigated by using two parameters,namely, the breakthrough time and the areal sweep efficiency. The simulation has demonstrated that surface wettability willinfluence the finger pattern no matter the gravity is considered or not, but in the presence of gravity, the finger pattern is muchmore complicated and irregular due to the coexistence and competition of capillary force, viscous force and gravity.

The Solely Use of the “Hydraulic-Diameter” Concept Is Not Sufficient to Describe Correctly Non-Symmetric Flow in Conduits

A well-known cornerstone in fluid mechanics is the equations that relate the friction factor to the Reynolds number obtained from the measurements in cylindrical cross-sectional tubes. The extension of these equations to different geometries failed to give reliable results. The introduction of the Hydraulic Diameter has fixed this issue particularly for the square ducts. However, for non-symmetric flows, as in concentric annuli, the discrepancies were unacceptable. Several attempts have been made to fix these problems with finally the introduction of a new concept like, “Laminar Equivalent Hydraulic Diameter” or “Efficient Hydraulic Diameter” provided satisfactory results. This approach seems to have fixed the problem and hence has been widely accepted. Nevertheless, it is based on a non-robust theoretical argument. In the present paper, it has been demonstrated that the solely use of the “Hydraulic Diameter” concept is insufficient to describe non-symmetric flows as in concentric annuli. It appears the need to use the Z axis component of the skew driving force for the laminar flow and the parameter λ for the turbulent one. At the same time, instead, it has been shown that in the case of flow in square and rectangular ducts, the “Hydraulic Diameter” is sufficient to describe it. In this case, the flow is practically symmetric. Moreover, several new straightforward equations are provided, which simplify a lot dealing with non-cylindrical cross-sectional conduits. In doing so, the concept of “Eigenvectors-Eigenvalues” has been implemented. This theoretical approach could help to simplify other non-symmetric cases in fluid dynamics. To mention, “Flow past immersed non-symmetric bodies”, “Flow in curved conduits” etc.

Seismic reflection and transmission coefficients of a single layer sandwiched between two dissimilar poroelastic solids

The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.

Simulation of Thermocapillary Convection in a TwoLayer Immiscible Fluid System Using a Boundary Element Method

A boundary element method for simulating thermocapillary convection in a two-layer immiscible fluid system with flat and free interface has been developed.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity gradients are eliminated and the complete formulation is written in terms of velocity.This avoids the difficulty of convective discretizations and provides considerable reductions in storage and computational requirements while improving accuracy.In this paper,we give the influence of different parameters(Marangoni number, Reynolds number)on thermocapillary convection in cavity with two-layer immiscible fluids.As shown by the numerical results,when the physical parameters between liquid encapsulant and melt are chosen appropriately, the detrimental flow in the bottom melt layer can be greatly suppressed.The influence of the free interface on thermocapillary convection is also shown.

Cavity dynamics of water drop impact onto immiscible oil pool with different viscosity

In this work,we numerically study the impact of a water droplet onto a deep oil pool.Two fluids are immiscible and the viscosity of the pool liquid is changed systematically.We focus on the cavity dynamics during the impact and especially the effects of the pool liquid viscosity and the impacting velocity.For the parameter range explored,we identify the regime where splashing occurs with corolla breaking into droplets,and the regime where no splashing is observed.Similarity is found for the time evolution of cavity depth for fixed impact velocity and different viscosity,if the cavity depth and time are nondimensionalized by the maximal depth and the time when the maximal depth is reached.Effective power-law scalings are also proposed to describe the dependence of the maximal cavity depth and the corresponding time on the impact velocity and pool liquid viscosity,in the term of Froude and Reynolds numbers.