Modelling Water Flow in Unsaturated Porous Media

Szymkiewicz, Adam

doi:10.1007/978-3-642-23559-7

Cited by 68 publications

(60 citation statements)

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“…In the case of drainage, the coarse-textured inclusions surrounded by fine-textured matrix cannot be drained until the matrix entry pressure is exceeded. These effects were observed in laboratory experiments (Vasin et al 2008, Szymańska 2012) and numerical simulations (Szymkiewicz et al 2011(Szymkiewicz et al , 2012Szymkiewicz 2013). They can be represented using the full two-phase model, but not the Richards equation.…”

Section: Upscaled Richards Equation For Media With Heterogeneous Air mentioning

confidence: 85%

“…Some small differences between the models always exist, because air is not infinitely mobile. The typical water air viscosity ratio is about 50 to 60, while for a perfect agreement of the two-phase model with the Richards equation a ratio of about 100 or more is required (Tegnander 2001, Szymkiewicz 2013. Other sources of discrepancies seem to be the lack of connectivity between the pore air and the atmosphere, which may lead to air pressure buildup ahead of the infiltration front during ponded infiltration (e.g., Vachaud et al 1973) or to formation of regions of trapped pore air (e.g., Leśniewska et al 2009).…”

Section: Two-phase Flow Model and Richards Equationmentioning

confidence: 99%

“…All numerical calculations were made using a program developed by the first author, based on a fully implicit finite volume discretization; for details see Szymkiewicz (2013). We used a uniform numerical grid of 10 cells in x direction by 100 cells in y direction.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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

2014

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A b s t r a c tThe paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embedded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. However, its performance can be improved by introducing appropriately defined effective capillary and permeability functions, representing largescale behaviour of the heterogeneous medium.

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Section: Upscaled Richards Equation For Media With Heterogeneous Air mentioning

confidence: 85%

Section: Two-phase Flow Model and Richards Equationmentioning

confidence: 99%

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

2014

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“…[45]). Such an approach is also being used for defining extended pressure conditions in the case of porous media with block-type heterogeneities, and if models involving an entry pressure are adopted (see e.g.…”

Section: G(s)dsmentioning

confidence: 99%

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

Duijn

Mitra

Pop

2018

Nonlinear Analysis: Real World Applications

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The Richards equation is a mathematical model for the unsaturated flow through porous media. This paper considers an extension of the Richards equation, where non-equilibrium effects like hysteresis and dynamic capillarity are incorporated in the relationship that relates the water pressure and the saturation. The focus is on travelling wave solutions, for which the existence is investigated first for the model including hysteresis and subsequently for model including dynamic capillarity effect. In particular, such solutions may have non monotonic profiles, which are ruled out when considering standard, equilibrium type models, but have been observed experimentally. The paper ends with numerical experiments confirming the theoretical results. In this sense the original system of partial differential equations is solved by means of an implicit scheme. This relies on an equivalent, mixed formulation of the system. For solving the resulting nonlinear, time-discrete problems, a linear iterative scheme is proposed.

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“…Numerous researchers have worked on this particular hydrodynamics and mathematical problem [44,45], and the books by Prof. Bear collect these study cases [46][47][48], which are essential reading for researchers working in this field. It is also noteworthy that Prof. Bear highlights in his books the goodness of Darcy's law, and that its application range is wider (more useful) than it was expected at first (i.e., unsaturated flow, high Reynolds number, etc.…”

Section: The Effect Of Saturationmentioning

confidence: 99%

Wetting and Navier-Stokes Equation — The Manufacture of Composite Materials

Caccia¹,

Camarano²,

Sergi³

et al. 2015

Wetting and Wettability

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It is well known that there are several processes to manufacture composite materials, a large part of which consist in the infiltration of a liquid (matrix) through a porous medium (reinforcement). To perform these processes, both thermodynamics (wetting) and kinetics (Navier-Stokes) must be considered if a good quality composite material is sought. Although wetting and the laws that govern it have been well known for over 200 years, dating back to the original works of Young and Laplace, this is not the case with the Navier-Stokes equation, which remains so far unsolved. Although the Navier-Stokes equation, which describes the motion of a fluid, has been solved for many particular cases, such as the motion of a fluid through a pipe, which has resulted in the well-known Poiseuille equation, or the motion of a fluid through a porous media, described by the Darcy's law (empirical law obtained by Darcy), its general solution remains one of the greatest challenges of mathematicians today. Therefore, the objective of this chapter is to present the resolution of the Navier-Stokes equation with the laws of wetting for different cases of interest in the manufacture of composite materials.

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Modelling Water Flow in Unsaturated Porous Media

Cited by 68 publications

References 0 publications

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

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

Travelling wave solutions for the Richards equation incorporating non-equilibrium effects in the capillarity pressure

Wetting and Navier-Stokes Equation — The Manufacture of Composite Materials

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