A macroscopic description of multiphase flow in porous media involving spacetime evolution of fluid/fluid interface

Kalaydjian, F.

doi:10.1007/bf00192154

Cited by 126 publications

(100 citation statements)

References 18 publications

(8 reference statements)

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“…These mechanisms have been incorporated into network models to predict three-phase relative permeability and saturations path [12][13][14], under the ansatz of each phase flowing independently in its own network. * dicarlo@mail.utexas.edu Viscous coupling, where the pressure gradient of a particular phase affects the flow of the other phase, has been investigated for two-phase flow through experiments [15][16][17], analytical calculations [18,19], and simulations at the pore-scale [20].…”

Section: Department Of Petroleum and Geosystems Engineering The Univmentioning

confidence: 99%

Flow coupling during three-phase gravity drainage

et al. 2011

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We measure the three-phase oil relative permeability kro by conducting unsteady-state drainage experiments in a 0.8m water-wet sandpack. We find that when starting from capillary-trapped oil, kro shows a strong dependence on both the flow of water and the water saturation and a weak dependence on oil saturation, contrary to most models. The observed flow coupling between water and oil is stronger in three-phase flow than two-phase flow, and cannot be observed in steadystate measurements. The results suggest that the oil is transported through moving gas/oil/water interfaces (form drag) or momentum transport across stationary interfaces (friction drag). We present a simple model of friction drag which compares favorably to the experimental data.When the single-phase Darcy equation is generalized to multi-phase flow in porous media, it is assumed that each phase flows due to the pressure gradient within that phase, albeit with a reduced permeability [1,2]. Conceptually, each phase flows in a capillary-stable reduced network compared to single phase flow. The change in permeability is parameterized by the relative permeability, k ri , that is assumed to be a function of the saturation of the phase, S i (the local volume fraction of the pore space filled by the phase i). Mathematically this is expressed through the Darcy-Buckingham equation [1].Here, q i , µ i , ρ i and P i are flux, viscosity, density and pressure of phase i flowing through porous media of permeability k. While this multi-phase flow equation is widely used due to its simplicity, it is known to break down at high capillary numbers (the network is fluid) [3], unstable flow [4], high viscosity ratio (due to viscous coupling between the mobile phases) [5], and three-phase flow (the network for the intermediate phase depends on the other two phases) [6].Here we concentrate on the combined effects of threephase flow and viscous coupling. Three-phase flow occurs when three mobile fluid phases co-exist in a porous media; typically water is the most wetting phase and oil the intermediate wetting phase. Three-phase relative permeability has been measured using steady state experiments [6], and many empirical models of the oil relative permeability k ro have been introduced [7]. These models have a dependence on both saturations, k ro (S o , S w ), based on the idea that the connected oil network depends on the amount of water. From observations in micromodels [8,9] and capillary stability arguments based on geometry [10] and thermodynamics [11] various three-phase pore level fluid configurations and flow mechanisms have been recognized. These mechanisms have been incorporated into network models to predict three-phase relative permeability and saturations path [12][13][14], under the ansatz of each phase flowing independently in its own network. * dicarlo@mail.utexas.edu Viscous coupling, where the pressure gradient of a particular phase affects the flow of the other phase, has been investigated for two-phase flow through experiments [15][16][17], analytical...

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Section: Department Of Petroleum and Geosystems Engineering The Univmentioning

confidence: 99%

Flow coupling during three-phase gravity drainage

et al. 2011

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“…have considered some of the similarities and differences between capillary pressure as viewed from the micro-and macroscales. Despite that effort, and those of other researchers (e.g., Kalaydjian, 1987;Pavone, 1989) the comment of Scheidegger (1974) still holds true: "A consistent theory of capillary pressure in porous solids should provide an explanation of the fundamental relationship between saturation and capillary pressure (or interfacial curvature).…”

Section: Motivation and Needmentioning

confidence: 99%

Establishing a Quantitative Functional Relationship between Capillary Pressure Saturation and Interfacial Area

Montemagno¹

2002

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SUIWMARY OF OBJECTIVESWe propose to continue our collaborative research focused on advanced technologies for subsurface contamination problems. Our approach combines new multi-phase flow theory, novel laboratory experiments, and non-traditional computational simulators to investigate practical approaches to include interfacial areas in descriptions of subsurface contaminant transport and remediation. Because all inter-phase mass transfer occurs at fluid-fluid interfaces, and it is this inter-phase mass transfer that leads to the difficult, long-term ground-water contamination problems, it is critical to include interfacial behavior in the problem description. This is currently lacking in all standard models of complex ground-water contamination problems. In our earlier project, we developed tools appropriate for inclusion of interfacial areas under equilibrium conditions. These include advanced laboratory techniques and targeted computational experiments that validated certain key theoretical conjectures. However, it has become clear that to include interfacial behavior fully into a description of the multi-phase flow and contamination problems, the Molly dynamic case must be considered. Therefore, we need to develop both experimental and computational tools that can capture the dynamic nature of interfacial movements. Development and application of such tools will allow the theory to be evaluated, and will lead to significant improvements in our understanding of complex subsurface contamination problems, thereby allowing us to develop and evaluate improved remediation technologies.We propose to combine theoretical, experimental, and computational research efforts to achieve the following goals: 0 Develop new experimental techniques to measure interface dynamics, under realistic conditions of movement in porous media. 0Develop new computational algorithms that properly incorporate interface dynamics, and that include wedges and films of wetting fluid. .Test existing theory and develop new theory, in conjunction with the experiments and the computations, to provide practical definitions to fundamental terms like dynamic capillary pressure and average interfacial velocity. 0Synthesize the results of the experimental, computational, and theoretical investigations to develop a new model for multi-phase flow and contaminant transport in contaminated soils and ground waters. Compare this new approach to standard methods and evaluate the potential improvements in terms of soil characterization and remediation evaluation.The results of this research will provide guidance regarding fundamental questions of remediation efficacy. We will examine how interfacial areas need to be characterized, and under what conditions their dynamics need to be included in practical analyses of subsurface contamination problems, Given that these interfaces are the source of contaminants to the aqueous phase, it is important that we continue our ongoing investigations of the role of these interfaces in contamination problems, the influence o...

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“…Among these are a rational thermodynamics approach by Hassanizadeh & Gray (1980;1993b;a), a thermodynamically constrained averaging theory approach by Gray and Miller (e.g. Gray & Miller (2005); Jackson et al (2009)), mixture theory (Bowen (1982)) and an approach based on averaging and non-equilibrium thermodynamics by Marle (1981) and Kalaydjian (1987). While Marle (1981) and Kalaydjian (1987) developed their set of constitutive relationships phenomenologically, Hassanizadeh & Gray (1990;1993b); Jackson et al (2009), andBowen (1982) exploited the entropy inequality to obtain constitutive relationships.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Gray & Miller (2005); Jackson et al (2009)), mixture theory (Bowen (1982)) and an approach based on averaging and non-equilibrium thermodynamics by Marle (1981) and Kalaydjian (1987). While Marle (1981) and Kalaydjian (1987) developed their set of constitutive relationships phenomenologically, Hassanizadeh & Gray (1990;1993b); Jackson et al (2009), andBowen (1982) exploited the entropy inequality to obtain constitutive relationships. To the best of our knowledge, the two-phase flow models of Marle (1981); Kalaydjian (1987); Hassanizadeh & Gray (1990;1993b); Jackson et al (2009) are the only ones to include interfaces explicitly in their formulation allowing to describe hysteresis as well as kinetic interphase mass and energy transfer in a physically-based way.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…While Marle (1981) and Kalaydjian (1987) developed their set of constitutive relationships phenomenologically, Hassanizadeh & Gray (1990;1993b); Jackson et al (2009), andBowen (1982) exploited the entropy inequality to obtain constitutive relationships. To the best of our knowledge, the two-phase flow models of Marle (1981); Kalaydjian (1987); Hassanizadeh & Gray (1990;1993b); Jackson et al (2009) are the only ones to include interfaces explicitly in their formulation allowing to describe hysteresis as well as kinetic interphase mass and energy transfer in a physically-based way. In the following, we follow the approach of Hassanizadeh & Gray (1990;1993b) as it includes the spatial and temporal evolution of phase-interfacial areas as parameters which allows us to model kinetic interphase mass transfer in a much more physically-based way than is classically done.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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