Solidification With a Throughflow in a Porous Medium

1992 ◽  
Vol 114 (3) ◽  
pp. 675-680
Author(s):  
T. Banerjee ◽  
C. Chang ◽  
W. Wu ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Analytical Solutions ◽  
Peclet Number ◽  
Flow In Porous Media ◽  
Circular Pipe ◽  
Parallel Plates ◽  
Péclet Number ◽  
Solid Interface

A steady throughflow in a porous medium is studied in the presence of a solidified layer due to cooling of the walls. Under the assumption of a moderately sloped melt-solid interface, analytical solutions are obtained for both a flow between parallel plates and a circular pipe. Differences and similarities are examined between the Darcian and the Brinkman porous media, as well as the effects of various parameters, such as the Peclet number, the ratio of diffusivities in the longitudinal and the lateral directions, and a parameter indicating the degree of wall cooling and flow heating, on thermofluid structure of a flow in porous media accompanied by solidification.

scholarly journals How to use solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media

2021 ◽  
Vol 60 (3) ◽  
pp. 229-240
Author(s):  
Jetzabeth Ramírez Sabag ◽  
Dennys Armando López Falcón
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Solute Transport ◽  
Dispersion Equation ◽  
Analytical Solutions ◽  
Peclet Number ◽  
Reactive Solute Transport ◽  
Péclet Number ◽  
Advection Dispersion ◽  
Outlet Boundary Condition

ResumenLas soluciones de la Ecuación de Advección-Dispersión son usadas frecuentemente para describir el transporte de solutos a través de medios porosos, considerando adsorción en equilibrio, de tipo lineal y reversible. Para indicar algunas sugerencias acerca de este tema, se hizo una revisión de las soluciones analíticas disponibles. Hay soluciones para Problemas con Condiciones de Frontera, de primer y tercer-tipo en la entrada así como de primer y segundo-tipo a la salida. Se analiza el comportamiento de las soluciones equivalentes, para sistemas finitos y semi-infinitos, observando que las soluciones de los sistemas semi-infinitos se aproximan a las correspondientes de los sistemas finitos conforme la condición de frontera de salida en el infinito se aproxima a la ubicación de medición del sistema finito. Solamente se presentan las soluciones analíticas con condiciones de frontera de segundo-tipo a la salida, ya que son iguales a las correspondientes soluciones analíticas con frontera de primer-tipo a la salida, para ambos tipos de condiciones de frontera de entrada usadas. Un análisis paramétrico, basado en el número de Peclet, muestra que todas las soluciones convergen cuando el número de Peclet es mayor que veinte. Los sistemas investigados deben tener un número de Peclet mayor que cinco para usar con confianza las soluciones de la Ecuación de Advección-Dispersión para describir el transporte de soluto en medios porosos.Palabras Clave: Ecuación de Advección-Difusión, Soluciones Analíticas, Transporte de Solutos Reactivos, Medios Porosos.AbstractThe solutions of Advection-Dispersion Equation are frequently used to describe solute transport through porous media when considering lineal and reversible equilibrium adsorption. To notice some warnings about this item, a review of analytical solutions available was done. There are solutions for Boundary Value Problems with first and third-type inlet boundary conditions as well as first and second-type outlet boundary condition. The behavior of equivalent solutions for finite and semi-infinite systems are analyzed, observing that semi-infinite system solutions approximates to the corresponding finite ones as the “infinite” outlet boundary condition approach to the finite measurement location. Because the analytical solutions with a first-type outlet boundary condition are equal to the corresponding analytical solutions with a second-type one, for both inlet boundary condition type used, only the latter is presented. A parametric analysis based on Peclet number shows that all solutions converge for Peclet number greater than twenty. Systems under research must have Peclet number greater than five to use confidently the solutions of Advection-Dispersion Equation to describe reactive solute transport through porous media.Keywords: Advection-Diffusion Equation, Analytical solutions, Reactive Solute Transport, Porous Media.

scholarly journals Hydrodynamic Dispersion in Porous Media and the Significance of Lagrangian Time and Space Scales

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 79
Author(s):  
Vi Nguyen ◽  
Dimitrios V. Papavassiliou
Keyword(s):  
Porous Media ◽  
Peclet Number ◽  
Dispersion Coefficient ◽  
Flow In Porous Media ◽  
Hydrodynamic Dispersion ◽  
Length Scale ◽  
Packed Beds ◽  
Péclet Number ◽  
Molecular Diffusivity ◽  
Effective Lagrangian

Transport in porous media is critical for many applications in the environment and in the chemical process industry. A key parameter for modeling this transport is the hydrodynamic dispersion coefficient for particles and scalars in a porous medium, which has been found to depend on properties of the medium structure, on the dispersing compound, and on the flow field characteristics. Previous studies have resulted in suggestions of different equation forms, showing the relationship between the hydrodynamic dispersion coefficient for various types of porous media in various flow regimes and the Peclet number. The Peclet number is calculated based on a Eulerian length scale, such as the diameter of the spheres in packed beds, or the pore diameter. However, the nature of hydrodynamic dispersion is Lagrangian, and it should take the molecular diffusion effects, as well as the convection effects, into account. This work shifts attention to the Lagrangian time and length scales for the definition of the Peclet number. It is focused on the dependence of the longitudinal hydrodynamic dispersion coefficient on the effective Lagrangian Peclet number by using a Lagrangian length scale and the effective molecular diffusivity. The lattice Boltzmann method (LBM) was employed to simulate flow in porous media that were constituted by packed spheres, and Lagrangian particle tracking (LPT) was used to track the movement of individual dispersing particles. It was found that the hydrodynamic dispersion coefficient linearly depends on the effective Lagrangian Peclet number for packed beds with different types of packing. This linear equation describing the dependence of the dispersion coefficient on the effective Lagrangian Peclet number is both simpler and more accurate than the one formed using the effective Eulerian Peclet number. In addition, the slope of the line is a characteristic coefficient for a given medium.

Heat Transfer and Fluid Flow in Porous Media With Two Equations Non-Darcian Model

2005 ◽  
Author(s):  
A. Nouri-Borujerdi ◽  
M. Nazari
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Peclet Number ◽  
Saturated Porous Medium ◽  
Flow In Porous Media ◽  
Local Thermal Equilibrium ◽  
Conductivity Ratio ◽  
Parallel Plates ◽  
Péclet Number ◽  
Wide Range

In the present study criterion for local thermal equilibrium assumption is studied. It concerns with the fluid flow and heat transfer between two parallel plates filled with a saturated porous medium under non-equilibrium condition. A two-equation model is utilized to represent the fluid and solid energy transport. Numerical Finite Volume Method has been developed for solving coupled energy equations and the Non-Darcian effects are considered for description of momentum equation. The effects of suitable non dimensional parameters as Peclet number and conductivity ratio has been studied thoroughly. A suitable non dimensional equation proposed in wide range of Peclet number and conductivity ratio. This equation shows the temperature difference between solid and fluid phases.

Conservation of Mass

1997 ◽  
Author(s):  
David Jon Furbish
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Unsaturated Flow ◽  
Flow In Porous Media ◽  
Degree Of Saturation ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Conservation Of Mass ◽  
Special Case

The concept of conservation of mass holds a fundamental role in most problems in fluid physics. For a given problem this concept is cast in the form of an equation of continuity. Such an equation describes a condition—conservation of mass—that must be satisfied in any formal analysis of a problem. Thus an equation of continuity often is one of several complementary equations that are solved simultaneously to arrive at a solution to a flow problem, for example, the flow velocity as a function of coordinate position in a flow field. (Typically these complementary equations, as we will see in later chapters, involve conservation of momentum or energy, or both.) Although we did not explicitly use this idea in analyzing the one-dimensional flow problems at the end of Chapter 3, it turns out that continuity was implicitly satisfied in setting up each problem. We will return to these problems to illustrate this point. We will develop equations of continuity for three general cases: purely fluid flow, saturated single-phase flow in porous media, and unsaturated flow in porous media. The most general of the three equations is that for unsaturated flow, where pores are partially filled with the fluid phase of interest, such that the degree of saturation with respect to that phase is less than one. We will then show that this equation reduces, in the special case in which the degree of saturation equals one, to a simpler form appropriate for saturated single-phase flow. Then, this equation for saturated flow could be reduced further, in the special case in which the porosity equals one, to a form appropriate for purely fluid flow. For pedagogical reasons, however, we shall reverse this order and consider purely fluid flow first. In addition we will consider conservation of a solid or gas dissolved in a liquid, and take this opportunity to introduce Fick’s law for molecular diffusion. For simplicity we will consider only species that do not react chemically with the liquid, nor with the solid phases of a porous medium. Most of the derivations below are based on the idea of a small control volume of specified dimensions embedded within a fluid or porous medium.

Foams as Blocking Agents in Porous Media

1970 ◽  
Vol 10 (01) ◽  
pp. 51-55 ◽  
Author(s):  
Robert A. Albrecht ◽  
Sullivan S. Marsden
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Natural Gas ◽  
Gas Flow ◽  
Gas Storage ◽  
Flow In Porous Media ◽  
Porous Rocks ◽  
Experimental Conditions ◽  
Storage Reservoirs

Abstract Although foam usually will flow in porous media, under certain controllable conditions it can also be used to block the flow of gas, both in unconsolidated sand packs and in sandstones. After steady gas or foam flow has been established at a certain injection pressure pi, the pressure is decreased until flow pressure pi, the pressure is decreased until flow ceases at a certain blocking pressure pb. When flow is then reestablished at a second, higher pi, blocking can again occur at another pb that will usually be greater than the first pi. The relationship between pi and Pb depends on the type of porous medium and the foamer solution saturation in the porous medium. A process is suggested whereby porous medium. A process is suggested whereby this phenomenon might be used to impede or block leakage in natural gas storage projects. Introduction The practice of storing natural gas in underground porous rocks has developed rapidly, and it now is porous rocks has developed rapidly, and it now is the major way of meeting peak demands in urban areas of the U. S. Many of these storage projects have been plagued with gas leakage problems that have, in some cases, presented safety hazards and resulted in sizeable economic losses. Usually these leaks are due to such natural factors as faults and fractures, or to such engineering factors as poor cement jobs and wells that were improperly abandoned. For the latter, various remedies such as spot cementing have been tried but not always with great success. In recent years several research groups have been studying the flow properties of aqueous foams and their application to various petroleum engineering problems. Most of this work has been done under problems. Most of this work has been done under experimental conditions such that the foam would flow in either tubes or porous media. However, under some extreme or unusual experimental conditions, flow in porous media becomes very difficult or even impossible. This factor also has suggested m us as well as to others that foam can be used as a gas flow impeder or as a sealant for leaks in gas storage reservoirs. In such a process, the natural ability of porous media to process, the natural ability of porous media to generate foam would be utilized by injecting a slug of foamer solution and following this with gas to form the foam in situ. This paper presents preliminary results of a sandy on the blockage of gas flow by foam in porous media. It also describes how this approach might be applied to a field process for sealing leaks in natural gas storage reservoirs. Throughout this report, we use the term "foam" to describe any dispersed gas-liquid system in which the liquid is the continuous phase, and the gas is the discontinuous phase. APPARATUS AND PROCEDURE A schematic drawing of the apparatus is shown in Fig. 1. At least 50 PV of filtered, deaerated foamer solution were forced through the porous medium to achieve liquid saturation greater than 80 percent. Afterwards air at controlled pressures was passed into the porous medium in order to generate foam in situ. Table 1 shows the properties and dimensions of the several porous media that were used. The beach sands were washed, graded and packed into a vibrating lucite tube containing a constant liquid level to avoid Stoke's law segregation over most of the porous medium. JPT P. 51

Magnetohydrodynamics and Soret Effects on Bioconvection in a Porous Medium Saturated With a Nanofluid Containing Gyrotactic Microorganisms

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
S. Shaw ◽  
P. Sibanda ◽  
A. Sutradhar ◽  
P. V. S. N. Murthy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Sherwood Number ◽  
Peclet Number ◽  
Volume Fraction ◽  
Soret Effect ◽  
Magnetic Field Effect ◽  
Lewis Number ◽  
Solute Concentration ◽  
Péclet Number

We investigate the bioconvection of gyrotactic microorganism near the boundary layer region of an inclined semi infinite permeable plate embedded in a porous medium filled with a water-based nanofluid containing motile microorganisms. The model for the nanofluid incorporates Brownian motion, thermophoresis, also Soret effect and magnetic field effect are considered in the study. The governing partial differential equations for momentum, heat, solute concentration, nanoparticle volume fraction, and microorganism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations and solved numerically. The effects of the bioconvection parameters on the thermal, solutal, nanoparticle concentration, and the density of the micro-organisms are analyzed. A comparative analysis of our results with previously reported results in the literature is given. Some interesting phenomena are observed for the local Nusselt and Sherwood number. It is shown that the Péclet number and the bioconvection Rayleigh number highly influence the local Nusselt and Sherwood numbers. For Péclet numbers less than 1, the local Nusselt and Sherwood number increase with the bioconvection Lewis number. However, both the heat and mass transfer rates decrease with bioconvection Lewis number for higher values of the Péclet number.

Nanofluid Impinging Jets in Porous Media

2016 ◽  
Vol 7 ◽  
pp. 84-113
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca ◽  
Sergio Nardini ◽  
D. Ricci
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Rayleigh Number ◽  
Peclet Number ◽  
Pure Water ◽  
Particle Diameter ◽  
Target Surface ◽  
Impinging Jets ◽  
Local Thermal Equilibrium ◽  
Péclet Number

Heat transfer enhancement technology has the aim to develop more efficient systems as demanded in many applications in the fields of automotive, aerospace, electronics and process industry. A possible solution to obtain efficient cooling systems is represented by the use of confined impinging jets. Moreover, the introduction of nanoparticles in the working fluids can be considered in order to improve the thermal performances of the base fluids. In this paper a numerical investigation on mixed convection in confined slot jets impinging on a porous media by considering pure water or Al2O3/water based nanofluids is described. A two-dimensional model is developed and different Peclet numbers and Rayleigh numbers were considered. The particle volume concentrations ranged from 0% to 4% and the particle diameter is equal to 30 nm. The target surface is heated by a constant temperature value, calculated according to the value of Rayleigh number. The distance of the target surface is five times greater than the slot jet width. A single-phase model approach has been adopted in order to describe the nanofluid behaviour while the hypothesis of non-local thermal equilibrium is considered in order to simulate the behaviour in the porous media which is featured by a porosity value of 0.87. The aim consists into study the thermal and fluid-dynamic behaviour of the system. Results show increasing values of the convective heat transfer coefficients for increasing values of Peclet number and particle concentration. This behaviour is more evident at low Peclet number values and Rayleigh number ones.

Sign in / Sign up

Export Citation Format

Share Document