Flow Of Multicomponent Mixtures Research Articles

Theoretical Investigation of the Nonlinear General Rate Model with the Bi-Langmuir Adsorption Isotherm Using Core-Shell Adsorbents.

Core-shell particles enable the separation of intricate mixtures in a highly efficient and rapid manner. The porous shell particles increased the separation efficiency with expedited flow rates due to an abatement in the pore volume accessible for longitudinal diffusion and a decrease in diffusion path length. This study focuses on the numerical approximation of a nonlinear isothermal general rate model applied to stationary bed columns that are replete with inert core adsorbents featuring double adsorption sites. The transport of solute in heterogeneous porous media can be modeled by a nonlinear convection acquiescent partial differential equation system together with a specific nonlinear algebraic relation: the bi-Langmuir adsorption isotherm. Therefore, it is important to develop accurate and reliable numerical techniques that can perform accurate numerical simulations of these models. We extended and implemented a second-order, semidiscrete, high-resolution finite volume method to simulate the governing equations of the model. Single solute flow and multi component mixture flows are assessed through a series of numerical experiments to theoretically illustrate the repercussions of intraparticle diffusion, film mass resistance, axial dispersion, and the size of the inert core radius upon simulated elution curves. Standard performance criteria are assessed to determine the optimal core radius fraction range for optimizing the separation performance.

Investigation of the efficiency of gas and water injection into an oil reservoir

Oil displacement by a miscible fluid in a porous medium, which is related to injection of hydrocarbonic gas into an oil reservoir, is investigated. A compositional model is used to describe flow of multicomponent mixtures through the porous medium. The thermophysical properties of the mixtures are given by the equation of state of the van der Waals type. The reservoir simulation software for compositional modeling of flow through a porous medium is developed within the framework of this model. The efficiencies of oil displacement from the porous medium by methane or water are compared using the above software. It is shown that in the initial stages of injection oil displacement by water is more efficient under a fixed volume flow rate of the injected fluid. However, in the last stages gas injection becomes more efficient for displacement of light hydrocarbon components.

Two-phase explicit CBS procedure for compressible viscous flow transport in porous materials

PurposeIn this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.Design/methodology/approachEven though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.FindingsThe numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.Social implicationsThe present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.Originality/valueFor the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

Математическая модель течения многокомпонентной смеси газов с учетом возможности возникновения жидкой фазы

Математическая модель течения многокомпонентной смеси газов с учетом возможности возникновения жидкой фазы

Lattice Boltzmann model for thermal binary-mixture gas flows

A lattice Boltzmann model for thermal gas mixtures is derived. The kinetic model is designed in a way that combines properties of two previous literature models, namely, (a) a single-component thermal model and (b) a multicomponent isothermal model. A comprehensive platform for the study of various practical systems involving multicomponent mixture flows with large temperature differences is constructed. The governing thermohydrodynamic equations include the mass, momentum, energy conservation equations, and the multicomponent diffusion equation. The present model is able to simulate mixtures with adjustable Prandtl and Schmidt numbers. Validation in several flow configurations with temperature and species concentration ratios up to nine is presented.

Modeling of Two‐Phase Flashing Flow of Multicomponent Mixtures in Large Diameter Pipes

AbstractA two‐phase flashing flow model is developed to predict the distributions of pressure, temperature, velocity and evaporation rate in a transfer line, which is a typical example of a two‐phase flow pipe in the petrochemical industry. The model is proposed based on the pressure drop model and the multi‐stage flash model. The results indicate that pressure drop, temperature drop, and change of evaporation rate mainly occur in the transition section and the junction site of the transfer line. The predictions of the model have been tested with reliable field data and the good agreement obtained may lead to a better understanding of the two‐phase flashing flow phenomenon, as well as demonstrating the feasibility of applying the model into the design and optimization of pipelines.

Description of the Flows of Two-Phase Mixtures with Phase Transitions in Capillaries by the Density-Functional Method

The problem of mathematical modeling of flows of multicomponent mixtures with phase transitions has been considered. The free energy of a mixture is given as a functional containing squared density gradients of the components. This permits continuous description of multiphase mixtures without discontinuities at the interfaces. Numerical solutions for the flows of two-phase mixtures in capillaries with different wall wettability conditions have been obtained.

Hydrodynamic Effects in Two-Phase Multicomponent Mixture Flow through a Porous Medium in Oil Reservoirs with a Complex Structure

The features of the hydrodynamic processes in stratified inhomogeneous oil reservoirs are investigated using a numerical solution of the equations of two-phase multicomponent flow through a porous medium. The structures of the two-phase flows caused by the reservoir structure and the hydrodynamic interaction between the phases are analyzed in relation to problems of the displacement of oil by water in ordinary flooding and in the presence of moving thickener slugs.

The use of the moment method to derive the gas and plasma transport equations with transport coefficients in higher-order approximations

Grad's moment method is used to derive the linear equations of mass momentum and energy transfer of the components and to obtain all the transport coefficients (kinetic coefficients) for a multicomponent mixture of monatomic gases. A system of equations for the expansion coefficients of the non-equilibrium correction to the distribution function using a system of irreducible tensorial Hermite polynomials (the equations of moments) is obtained on the basis of the linearized Boltzmann equations for the components of the mixture. The assumptions under which these equations reduce to a system of algebraic equations for determining of the mass diffusion fluxes, the heat fluxes of the components and the partial viscous stress tensors are analysed. The advantage in writing the transport equation in a “forces in terms of fluxes” representation for solving actual problems of the flows of multicomponent mixtures as compared with the classical “fluxes in terms of forces” representation in the standard Chapman-Enskog method [1–3] is demonstrated. Different ways of representing the transport equations and expressions for the transport coefficients are considered in an arbitrary order of approximation with respect to the number of Sonine polynomials which are retained in the expansion of the distribution function (the Chapman-Cowling method). This enables one, in particular, to establish a direct link between results obtained by different methods and to track more clearly the constraints which are actually used when employing classical method [1–3] and the modified method [4, 5] of deriving the transport equations and calculating the transport coefficients in the Chapman-Enskog scheme

Multicomponent Mixture Flow in an Axisymmetric Capillary in the Presence of a Mobile Surface Phase

Within the framework of the density-functional method, the hydrodynamics of a multicomponent mixture in the presence of a mobile surface phase is investigated. A system of interrelated three- and two-dimensional hydrodynamic equations for isothermal volume and surface flows is formulated. For flow in a thin axisymmetric capillary, the principal term of the asymptotic expansion of the solution in powers of the characteristic capillary radius to length ratio is obtained. For slow motion, the solution is found in quadratures.

Solving Practical Industrial Problems in Two-Phase Multicomponent Mixture Flow - Critical Velocity

A method for evaluation of the critical velocity in the case of two (vapor?liquid)-phase mixtures transported in pipelines was developed. This method is based on a theoretical background of complex hydrocarbon mixture thermodynamics with respect to application in the petrochemical industry. Methods published so far have focused on applications in the power industry, where the water?steam two-phase system is considered. The method presented allows one to calculate pressure drop, velocity, and temperature profiles for two-phase complex hydrocarbon systems and to identify the critical flow presence. In this method the critical condition means a singular discontinuity where the finite pressure and/or velocity change corresponds to an infinitesimal change in space coordinate. An example of applying the method in the case of a furnace-to-distillation column transfer line is shown. It can be observed that using this method can be considered a contribution to solving practical industrial cases. This method was verified in industrial practice for a long time, and satisfactory results were obtained.

Solving Practical Industrial Problems in Two-Phase Multicomponent Mixture Flow - Critical Velocity

Solving Practical Industrial Problems in Two-Phase Multicomponent Mixture Flow - Critical Velocity

Binary two-phase flow with phase change in porous media

Flow of multicomponent mixtures with interphase mass transfer through porous media has been analyzed by combining thermodynamics of real fluids, the use of immiscible Boltzmann code and reconstructed porous media. A general algorithm is detailed and applied for comparison with Poiseuille flow where a semi-analytical solution can be found. A series of structures and phenomena are then analysed; attention is mostly focused on liquid to gas transition (or vaporization) and retrograde condensation; phase distribution and macroscopic quantities such as composition, liquid saturation and pressure evolution are systematically plotted. The role of the location of nucleation sites is shortly investigated with a periodically constricted tube. The total mass flow rate influenced the phase distribution and circulation in a two-dimensional network. Finally, relative permeabilities of a reconstructed medium are discussed; an interesting feature is that they follow hysteresis cycles for retrograde condensation.

Calculation of minimum miscibility pressure

A method is described and tested for calculation of minimum miscibility pressure (MMP) that makes use of an analytical theory for one-dimensional, dispersion-free flow of multicomponent mixtures. The theory shows that in a displacement of an oil by a gas with n c components, the behavior of the displacement is controlled by a sequence of n c−1 key tie lines. Besides, the tie lines that extend through the initial oil and injection gas compositions, there are n c−3 tie lines, known as crossover tie lines, that can be found from a set of conditions that require the extensions of the appropriate tie lines to intersect each other. The MMP is calculated as the pressure at which one of the key tie lines becomes a tie line of zero length that is tangent to the critical locus. The numerical approach for solving the tie line intersection equations is described; slim tube test and compositional simulation data reported in the literature are used to show that the proposed approach can be used to calculate MMP accurately for displacements with an arbitrary number of components present.

Characterizing adsorbate passage in molecular sieve pores

The rate at which molecules can pass one another inside the pores of crystalline microporous materials can be an important factor in determining the transport properties of these systems, particularly for materials with unidimensional pores. An efficient method for characterizing adsorbate passage in micropores is presented and applied to a variety of adsorbates in AlPO 4-5. It is shown that adsorbate passage can be an activated process in some cases. The implications of rare adsorbate passage for the experimental characterization of tracer diffusion and for the flow of multicomponent mixtures through zeolitic membranes are briefly considered in the context of a simplified lattice gas model.

A two-phase mixture model of liquid-gas flow and heat transfer in capillary porous media—I. Formulation

A model for two-phase transport in capillary porous media is presented, in which the two phases are viewed as constituents of a binary mixture. The conservation equations are derived from the classical separate flow model without invoking additional assumptions. The present formulation, owing to its analogy to conventional multicomponent mixture flow theories and to a considerable reduction in the number of the differential equations required for the primary variables, provides an alternative for the theoretical analysis and numerical simulation of two-phase transport phenomena in porous media. Several complicated problems such as boundary layer two-phase flows, conjugate two- and single-phase flows in multiple regions and transient flows are shown to become more tractable within the framework of this new formulation.

An exact solution for shearing flow of multicomponent mixtures

When a nondilute multicomponent fluid is placed in a viscometric testing device, the flow that is produced is not a viscometric flow. Rather, relatively thin layers of fluid with relatively few suspended particles accumulate near the boundaries. These layers exhibit high shear rates. The suspended particles accumulate far away from the boundaries, giving a high local viscosity and a low shear rate. We consider a simple but properly invariant theory of multicomponent fluids. We investigate steady flow between parallel plates with one plate stationary and the other plate moving parallel to it at constant speed. We give exact solutions to the field equations.

Numerical simulation of flow of multicomponent mixtures in porous media

A study is made of the isothermal flow of multicomponent mixtures in a porous medium, accompanied by phase transitions, interphase mass exchange, and change in the physicochemical properties of the phases [1–3], It is assumed that at each point of the flow region, phase equilibrium is established instantaneously and the flow velocities of the separate phases conform to Darcy's law. Approximate solutions of problems of displacing oil by high-pressure gas were obtained in [1]. By generalizing the theory developed in [4], a study is made in [5] of the structure of the exact solutions of the problems of the flow of three-component systems which describe the displacement of oil by different reactants (gases, solvents, micellar solutions). The numerical solutions of the problems of multicomponent system flow are considered in [2, 3, 6, 7]. This paper presents a numerical method which is distinguished from the well-known ones [2, 3, 6, 7] by the following characteristics. The flow equations are approximated by a completely conservative finite-difference scheme of the implicit pressure-explicit saturation type, the calculation being carried out using Newton's method of iteraction with spect to both the pressure and the composition of the mixture. The minimum derivative principle [8] is used in the approximation of the divergence terms of the equations. The phase equilibrium is calculated using the equation of state.

Asymptotic form of the solution to the problem of multicomponent mixture flow through a porous medium with a boundary layer

In problems of two-phase mixture flow through a porous medium in a subterranean stratum a boundary layer phenomenon arises caused by the fact that relative phase motion exists in the system, and so having no analogy with the single-phase case. The physical nature of boundary layer phenomena is explained, and an asymptotic solution is constructed for the self-similar problem with an arbitrary number of components in the system, by using the method of matched asymptotic forms. The conditions are established for the motions of a multicomponent and a binary mixture to be equivalent, and a study is made of the role of convective factors in the formation of averaged working indices for the stratum.

A note on multicomponent mass transfer in turbulent flow

We consider mass transfer in turbulent flow of multicomponent mixtures, taking into account the molecular diffusional coupling between the constituent species. For steady state transport across an effective ‘film’, we develop a simple analytic procedure for calculating the matrix of multicomponent mass transfer coefficients.