Simulation of Infiltration Processes in the Unsaturated Zone Using a Multiscale Approach

Kissling, Frederike; Helmig, Rainer; Rohde, Christian

doi:10.2136/vzj2011.0193

Cited by 9 publications

(5 citation statements)

References 35 publications

(44 reference statements)

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“…[], Chapwanya and Stockie [], Kissling et al . [], and Rätz and Schweizer [] have also produced physical looking fingering displacements using the dynamic extensions with the latter including hysteresis.…”

Section: Saturation Overshoot Paradigmmentioning

confidence: 99%

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

DiCarlo

2013

Water Resources Research

112

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Gravity‐driven multiphase flow in porous media is ubiquitous in the geophysical world; the classic case in hydrology is vertical infiltration of precipitation into a soil. For homogenous porous media, infiltrations are sometimes observed to be stable and laterally uniform, but other times are observed to be unstable and produce preferential flow paths. Since Saffman and Taylor (1958), researchers have attempted to define criteria that determine instability. Saffman and Taylor's analysis consisted of two regions of single phase flow, while Parlange and Hill (1976) integrated this analysis with the multiphase flow equations to provide testable predictions. In the subsequent 40 years, great advances have been made determining the complex interactions between multiphase flow and instability. Theoretically, the stability of the standard multiphase flow equations has been verified, showing the necessity of extensions to the multiphase flow equations to describe the observed unstable flow. Experimentally, it has been shown that the instability is related to a phenomena in 1‐D infiltrations called saturation or pressure overshoot. In this review, the connection between overshoot and instability is detailed, and it is described how models of overshoot can simplify the analysis of current and future models of instability and multiphase flow.

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Section: Saturation Overshoot Paradigmmentioning

confidence: 99%

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

DiCarlo

2013

Water Resources Research

112

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“…The appearances and disappearances of instabilities and overshoots during two-phase flow in porous media are shown theoretically by means of travelling wave analysis by van Duijn et al [47]. Fingering is also discussed in detail by Rohde and Kissling [48], Kissling et al [49] and DiCarlo [50]. As the dynamic saturation front in a porous domain could vary within the domain and K r relationships are primarily point relationships, it becomes important to know the location dependent K r -S w relationship.…”

Section: Introductionmentioning

confidence: 99%

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

et al. 2016

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Capillary pressure-saturation-relative permeability relationships (P c -S w -K r ) are functions of importance in modeling and simulations of the hydrodynamics of two-phase flow in porous media. These relationships are found to be affected by porous medium and fluid properties but the manner in which they are affected is a topic of intense discussion. For example, reported trends in fluid viscosity and boundary conditions effects have been found to be contrary to each other in different studies. In this work, we determine the dependency of dynamic K r -S w relationships (averaged data) on domain scale in addition to investigating the effects of fluid viscosity and boundary pressure using silicone oil (i.e. 200 and 1000 cSt) and water as the respective non-wetting and wetting fluids with a view to eliminating some of the uncertainties reported in the literature. Water relative permeability, K rw , was found to increase with increasing wetting phase saturation but decreases with the increase in viscosity ratio. On the other hand, the oil relative permeability, K rnw , was found to increase with the increasing non-wetting phase saturation in addition to the increase in viscosity ratio. Also, it was found that with the increasing boundary pressure K rw decreases while K rnw increases. The influence of scale on relative permeability was slightly indicated in the non-wetting phase with K rnw decreasing as domain size increases. Effect of measurement location on dynamic relative permeability was explored which is rarely found in the literature. Comparison was also made between K r -S w relationships obtained under static and dynamic condition. Finally, mobility ratio (m) and dynamic coefficient (s) were plotted as a function of water saturation (S w ), which showed that m decreases as s increases at a given saturation, or vice versa.

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“…From the solution, the approximate plateau value S ij = S ε ij is determined. OUTPUT: Plateau value S ij For solving (6.2) and for the approximation of the plateau value, we use a semi-implicit Euler discretization and refer to [23,25] and the discussions therein. Alternatively, one can use the methods discussed in [1,11,16,20].…”

Section: Computationalmentioning

confidence: 99%

“…In this section, we consider the effect of a perturbation given by the inflow condition. For computations with various inflow conditions S inflow and the development of fingers we refer to Kissling et al [23]. The aim in this section is to show the tracking of the discrete front and the behaviour of the element sets T w,n h , T m,n h and T nw,n h for the case that we do not have a constant inflow condition.…”

Section: Dmentioning

confidence: 99%

The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case

Kissling¹,

Rohde²

2015

Multiscale Model. Simul.

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We consider two-phase flow problems in porous media with overshooting waves. If higher order effects are neglected, such problems are governed by a hyperbolic conservation law with non-convex flux function as macroscale model. It is well known, that there can be multiple weak solutions. To ensure uniqueness, we use on the microscale either a kinetic relation or in a second approach an extended system, taking rate-dependent capillary pressure effects into account. We present a new multidimensional mass-conserving numerical method to solve the macroscale model. The method belongs to the class of Heterogeneous Multiscale Methods in the sense of E&Engquist (2003) and is L ∞-stable. A key part of the approximation is a novel numerical flux function for the multidimensional setting, which captures undercompressive waves and generalizes the one-dimensional approach of Boutin et al. (2008). Furthermore, we improve the overall computational complexity, using a data-based approach. Finally, we validate the numerical method and test it on several infiltration problems.

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Simulation of Infiltration Processes in the Unsaturated Zone Using a Multiscale Approach

Cited by 9 publications

References 35 publications

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

Stability of gravity‐driven multiphase flow in porous media: 40 Years of advancements

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

The Computation of Nonclassical Shock Waves in Porous Media with a Heterogeneous Multiscale Method: The Multidimensional Case

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