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

Abstract

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.

Observations of capillary barriers and preferential flow in layered snow during cold laboratory experiments

“…The use of the Richards equation for modeling wetting front instability in porous media is still a matter of debate (Egorov et al, 2003;Waldner et al, 2004;DiCarlo, 2013) due to the occurrence of peculiar pore-scale processes when water infiltrates as fingers (Egorov et al, 2003;DiCarlo, 2013;Katsushima et al, 2013;Baver et al, 2014). Observations reveal that in soils an unstable infiltration profile may be marked by an overshoot profile in terms of θ (saturation overshoot) or ψ (capillary pressure overshoot; see DiCarlo, 2004DiCarlo, , 2007DiCarlo, , 2013Baver et al, 2014).…”

“…Observations reveal that in soils an unstable infiltration profile may be marked by an overshoot profile in terms of θ (saturation overshoot) or ψ (capillary pressure overshoot; see DiCarlo, 2004DiCarlo, , 2007DiCarlo, , 2013Baver et al, 2014). Examples of pressure overshoots have been observed in homogeneous snow samples during preferential infiltration by Katsushima et al (2013).…”

“…These water input rates are a compromise between the need for exploring the properties of capillary barriers over a broad range of W , expected melt rates in natural conditions (DeWalle and Rango, 2011), and operational constraints (specifically the expected duration of the tests). Because the saturated conductivity of snow is rather high compared with the chosen input rates, most existing instability criteria (Saffman and Taylor, 1958;Baker and Hillel, 1990;de Rooij, 2000;DiCarlo, 2013) will predict unstable flow in these conditions. Accordingly, Katsushima et al (2013) have already observed preferential infiltration in snow with average g S between 0.421 and 1.439 mm for different water input rates (21.7 mm h −1 ≤ W ≤ 205.5 mm h −1 ).…”

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

“…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.…”

Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media

“…A strong motivation for these studies were mathematical results excluding the existence of overshoot profiles for the traditional Richards equation from hydrology (Nieber 1996;Otto 1996Otto , 1997Geiger and Durnford 2000;Glass 2001, 2002;Egorov et al 2003;DiCarlo 2005DiCarlo , 2013Duijn et al 2007;Juanes 2008, 2009). It has been conjectured that new theoretical approaches might be unavoidable (Eliassi and Glass 2002;Duijn et al 2007Duijn et al , 2013Juanes 2008, 2009;Hilfer et al 2012;Nieber et al 2005) to reconcile theory and experiment.…”