Hydrodynamics and Heat Transfer at Single-Phase Flow through Porous Media

2009 ◽  
pp. 17-40
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Single Phase ◽  
Phase Flow ◽  
Flow Through Porous Media ◽  
Single Phase Flow ◽  
Flow Through

Single phase flow through porous media and pore structure

1975 ◽  
Vol 10 (1) ◽  
pp. 1-34 ◽  
Author(s):  
F.A.L. Dullien
Keyword(s):  
Porous Media ◽  
Pore Structure ◽  
Single Phase ◽  
Phase Flow ◽  
Flow Through Porous Media ◽  
Single Phase Flow ◽  
Flow Through

Single-phase flow through porous media

AIChE Journal ◽  
1969 ◽  
Vol 15 (6) ◽  
pp. 866-872 ◽  
Author(s):  
John C. Slattery
Keyword(s):  
Porous Media ◽  
Single Phase ◽  
Phase Flow ◽  
Flow Through Porous Media ◽  
Single Phase Flow ◽  
Flow Through

Incorporation of Interfacial Areas in Models of Two-Phase Flow

1999 ◽  
Author(s):  
William G. Gray ◽  
Michael A. Celia
Keyword(s):  
Porous Media ◽  
Hydraulic Conductivity ◽  
Single Phase ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Hydraulic Gradient ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Α Phase ◽  
Flow Through

The mathematical study of flow in porous media is typically based on the 1856 empirical result of Henri Darcy. This result, known as Darcy’s law, states that the velocity of a single-phase flow through a porous medium is proportional to the hydraulic gradient. The publication of Darcy’s work has been referred to as “the birth of groundwater hydrology as a quantitative science” (Freeze and Cherry, 1979). Although Darcy’s original equation was found to be valid for slow, steady, one-dimensional, single-phase flow through a homogeneous and isotropic sand, it has been applied in the succeeding 140 years to complex transient flows that involve multiple phases in heterogeneous media. To attain this generality, a modification has been made to the original formula, such that the constant of proportionality between flow and hydraulic gradient is allowed to be a spatially varying function of the system properties. The extended version of Darcy’s law is expressed in the following form: qα=-Kα . Jα (2.1) where qα is the volumetric flow rate per unit area vector of the α-phase fluid, Kα is the hydraulic conductivity tensor of the α-phase and is a function of the viscosity and saturation of the α-phase and of the solid matrix, and Jα is the vector hydraulic gradient that drives the flow. The quantities Jα and Kα account for pressure and gravitational effects as well as the interactions that occur between adjacent phases. Although this generalization is occasionally criticized for its shortcomings, equation (2.1) is considered today to be a fundamental principle in analysis of porous media flows (e.g., McWhorter and Sunada, 1977). If, indeed, Darcy’s experimental result is the birth of quantitative hydrology, a need still remains to build quantitative analysis of porous media flow on a strong theoretical foundation. The problem of unsaturated flow of water has been attacked using experimental and theoretical tools since the early part of this century. Sposito (1986) attributes the beginnings of the study of soil water flow as a subdiscipline of physics to the fundamental work of Buckingham (1907), which uses a saturation-dependent hydraulic conductivity and a capillary potential for the hydraulic gradient.

Pressure drop, gas hold-up and heat transfer during single and two-phase flow through porous media

2005 ◽  
Vol 26 (1) ◽  
pp. 156-172 ◽  
Author(s):  
M. Jamialahmadi ◽  
H. Müller-Steinhagen ◽  
M.R. Izadpanah
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Pressure Drop ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Flow Through Porous Media ◽  
Two Phase ◽  
Flow Through

scholarly journals  A Simplified Model of Low Reynolds Number, immiscible, Gas-Liquid Flow and Heat Transfer in Porous Media (Numerical Solution with Experimental Validation)

2021 ◽  
Author(s):  
Gamal B. Abdelaziz ◽  
M. Abdelgaleel ◽  
Z.M. Omara ◽  
A. S. Abdullah ◽  
Emad M.S. El-Said ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solution ◽  
Single Phase ◽  
Energy Equation ◽  
Numerical Results ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Two Phase

Abstract This study investigates the thermal-hydraulic characteristics of immiscible two-phase flow (gas/liquid) and heat transfer through porous media. This research topic is interested among others in trickle bed reactors, the reservoirs production of oil, and the science of the earth. Characteristics of two-phase concurrent flow with heat transfer through a vertical, cylindrical, and homogeneous porous medium were investigated both numerically and experimentally. A generalized Darcy model for each phase is applied to derive the momentum equations of a two-phase mixture by appending some constitutive relations. Gravity force is considered through investigation. To promote the system energy equation, the energy equation of solid matrix for each phase are deemed. The test section is exposed to a constant wall temperature after filled with spherical beads. Numerical solution of the model is achieved by the finite volume method. The numerical procedure is generalized such that it can be reduced and applied to single phase flow model. The numerical results are acquired according to, air/water downward flow, spherical beads, ratio of particle diameter to pipe radius D=0.412, porosity φ=0.396, 0.01≤Re≤500, water to air volume ratio 0≤W/A≤∞, and saturation ratio 0≤S1≤1. To validate this model an experimental test rig is designed and constructed, and the corresponding numerical results are compared with its results. Also, the numerical results were compared with other available numerical results. The comparisons show good agreement and validate the numerical model. One of the important results reveals that the heat transfer is influenced by two main parameters; saturation ratios of the two fluids; S1 and S2, and the mixture Reynolds number Re. The thermal entry length is directly dependent on Re, S1, and the thermofluid properties of the fluids. A modified empirical correlation for the entrance length; Xe =0.1 Re.Pr.Rm is predicted, where Rm =Rm(S1, S2, ρ1, ρ2, c1, c2). The predicted correlation is verified by comparing with the supposed correlation of Poulikakos and Ranken (1987) and El-Kady (1997) for a single-phase flow; Xe/Pr=0.1 Re.

On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media

2004 ◽  
Vol 27 (6) ◽  
pp. 669-677 ◽  
Author(s):  
Mostafa Fourar ◽  
Giovanni Radilla ◽  
Roland Lenormand ◽  
Christian Moyne
Keyword(s):  
Porous Media ◽  
Single Phase ◽  
Three Dimensional ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Linear Behavior ◽  
Non Linear ◽  
Flow Through
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