A LOCAL EXPANSION METHOD FOR SOLVING THE MACROSCOPIC MOMENTUM EQUATION OF THE SINGLE PHASE FLOW IN HIGHLY PERMEABLE POROUS MEDIA

2018 ◽  
Vol 21 (10) ◽  
pp. 977-992
Author(s):  
Jun-wen Liu ◽  
Zhi-Fan Liu ◽  
Zhi-Feng Liu ◽  
Xiao-Hong Wang ◽  
An-Feng Shi
Keyword(s):  
Porous Media ◽  
Single Phase ◽  
Expansion Method ◽  
Momentum Equation ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Local Expansion

Topology Optimization for the Single Phase Flow Using Two Point Flux Approximation Model

2013 ◽  
Author(s):  
Guang Dong ◽  
Yulan Song
Keyword(s):  
Porous Media ◽  
Topology Optimization ◽  
Optimization Problem ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Approximation Model ◽  
Single Phase Flow ◽  
Topology Optimization Problem ◽  
Flux Approximation

The topology optimization method is extended to solve a single phase flow in porous media optimization problem based on the Two Point Flux Approximation model. In particular, this paper discusses both strong form and matrix form equations for the flow in porous media. The design variables and design objective are well defined for this topology optimization problem, which is based on the Solid Isotropic Material with Penalization approach. The optimization problem is solved by the Generalized Sequential Approximate Optimization algorithm iteratively. To show the effectiveness of the topology optimization in solving the single phase flow in porous media, the examples of two-dimensional grid cell TPFA model with impermeable regions as constrains are presented in the numerical example section.

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.

scholarly journals On the Inertial Single Phase Flow in 2D Model Porous Media: Role of Microscopic Structural Disorder

2019 ◽  
Vol 128 (1) ◽  
pp. 201-220
Author(s):  
Yibiao Wang ◽  
Azita Ahmadi ◽  
Didier Lasseux
Keyword(s):  
Porous Media ◽  
Single Phase ◽  
Structural Disorder ◽  
Phase Flow ◽  
Single Phase Flow ◽  
2D Model

scholarly journals A two-pressure model for slightly compressible single phase flow in bi-structured porous media

2013 ◽  
Vol 96 ◽  
pp. 55-70 ◽  
Author(s):  
Cyprien Soulaine ◽  
Yohan Davit ◽  
Michel Quintard
Keyword(s):  
Porous Media ◽  
Single Phase ◽  
Phase Flow ◽  
Single Phase Flow ◽  
Slightly Compressible
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