The foam drainage equation for unsaturated flow in porous media

2013 ◽  
Vol 49 (10) ◽  
pp. 6258-6265 ◽  
Author(s):  
Dani Or ◽  
Shmuel Assouline
Keyword(s):  
Porous Media ◽  
Unsaturated Flow ◽  
Flow In Porous Media ◽  
Foam Drainage Equation ◽  
Foam Drainage

scholarly journals Modelling Unsaturated Flow in Porous Media Using an Improved Picard Iteration Scheme

2021 ◽  
Author(s):  
S.R. Zhu ◽  
L.Z. Wu ◽  
T. Ma ◽  
S.H. Li
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
Unsaturated Flow ◽  
Control Volume ◽  
Linear Equations ◽  
Solution Process ◽  
Coefficient Matrix ◽  
Picard Iteration ◽  
Flow In Porous Media ◽  
Richards Equation

Abstract The numerical solution of various systems of linear equations describing fluid infiltration uses the Picard iteration (PI). However, because many such systems are ill-conditioned, the solution process often has a poor convergence rate, making it very time-consuming. In this study, a control volume method based on non-uniform nodes is used to discretize the Richards equation, and adaptive relaxation is combined with a multistep preconditioner to improve the convergence rate of PI. The resulting adaptive relaxed PI with multistep preconditioner (MP(m)-ARPI) is used to simulate unsaturated flow in porous media. Three examples are used to verify the proposed schemes. The results show that MP(m)-ARPI can effectively reduce the condition number of the coefficient matrix for the system of linear equations. Compared with conventional PI, MP(m)-ARPI achieves faster convergence, higher computational efficiency, and enhanced robustness. These results demonstrate that improved scheme is an excellent prospect for simulating unsaturated flow in porous media.

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.

Phase-Field Models of Gravity-Driven Unsaturated Flow in Porous Media

2008 ◽  
Author(s):  
Luis Cueto-Felgueroso ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Preferential Flow ◽  
Unsaturated Flow ◽  
Flow In Porous Media ◽  
Macroscopic Model ◽  
Wetting Front ◽  
Forming Mechanism ◽  
Gravity Driven ◽  
Pattern Forming ◽  
Models Of Gravity

Existing continuum models of multiphase flow in porous media are unable to explain why preferential flow (fingering) occurs during infiltration into homogeneous, dry soil. We identify a relevant pattern-forming mechanism in the dynamics of the wetting front, and present a macroscopic model that reproduces the experimentally observed features of fingered flows. The proposed model reveals a scaling between local and nonlocal interface phenomena in imbibition, and does not introduce new independent parameters. The predictions based on this model are consistent with experiments and theories of scaling in porous media.

scholarly journals Influence of heterogeneous air entry pressure on large scale unsaturated flow in porous media

2014 ◽  
Vol 62 (5) ◽  
pp. 1179-1191 ◽  
Author(s):  
Adam Szymkiewicz ◽  
Insa Neuweiler ◽  
Rainer Helmig
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Unsaturated Flow ◽  
Flow In Porous Media ◽  
Entry Pressure

The foam drainage equation for drainage dynamics in unsaturated porous media

2017 ◽  
Vol 53 (7) ◽  
pp. 5706-5724 ◽  
Author(s):  
P. Lehmann ◽  
F. Hoogland ◽  
S. Assouline ◽  
D. Or
Keyword(s):  
Porous Media ◽  
Unsaturated Porous Media ◽  
Foam Drainage Equation ◽  
Foam Drainage

scholarly journals An Improved Picard Iteration Scheme for Simulating Unsaturated Flow in Layered Porous Media

2021 ◽  
Author(s):  
S.R. Zhu ◽  
L.Z. Wu ◽  
S.H. Li
Keyword(s):  
Porous Media ◽  
Convergence Rate ◽  
High Speed ◽  
Unsaturated Flow ◽  
Correction Method ◽  
Iteration Scheme ◽  
Picard Iteration ◽  
Flow In Porous Media ◽  
Richards Equation ◽  
Layered Porous Media

Abstract Picard iteration method is commonly used to obtain numerical solution of unsaturated flow in porous media. However, because the system of linear equations derived from Richards equation is seriously ill-conditioned, Picard iteration has slow convergence rate and low computational efficiency, particularly in layered porous media. In this study, control volume method based on non-uniform nodes is used to discrete Richards equation. To improve the convergence rate of Picard iteration, we combine the non-uniform multigrid correction method with the multistep preprocessing technology. Thus, an improved Picard iteration scheme with multistep preconditioner based on non-uniform multigrid correction method (NMG-MPPI(m)) is proposed to model 1D unsaturated flow in layered porous media. Three test cases were used to verify the proposed schemes. The result shows that the condition number of the coefficient matrix has been greatly reduced using the multistep preconditioner. Numerical results indicate that NMG-MPPI(m) can solve Richards equation at a faster convergence rate, with higher calculation accuracy and good robustness. Compared with conventional Picard iteration, NMG-MPPI(m) shows a very high speed-up ratio. As a result, the improved Picard iteration scheme has good application for simulating unsaturated flow in layered porous media.

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