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A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship

Abstract

New theories suggest that the relationship between capillary pressure and saturation should be enhanced by a dynamic term that is proportional to the time rate of change of saturation. This so-called dynamic capillary pressure formulation is supported by laboratory experiments, and can be included in various forms of the governing equations for two-phase flow in porous media. An extended model of two-phase flow in porous media may be developed based on fractional flow curves and a total pressure - saturation description that includes the dynamic capillary pressure terms. A dimensionless form of the resulting equation set provides an ideal tool to study the relative importance of the dynamic capillary pressure effect. This equation provides a rich set of mathematical research questions, and numerical solutions to the equation provide insights into the behavior of two-phase immiscible flow. For typical two-phase flow systems, dynamic capillary pressure acts to retard infiltration fronts, with responses dependent on system parameters including boundary conditions. Recent theoretical work suggests that the traditional algebraic relationship between capillary pressure and saturation may be inadequate. Instead, a so-called dynamic capillary pressure formulation is needed, where capillary pressure is defined as a thermodynamic variable, and the difference between phase pressures is  More>>
Publication Date:
Jul 01, 2002
Product Type:
Technical Report
Report Number:
BUM-166
Resource Relation:
Other Information: 13 refs., 1 fig., 2 tabs.; PBD: 2002
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; MATHEMATICS; TWO-PHASE FLOW; POROUS MATERIALS; FLUID FLOW
OSTI ID:
20243748
Research Organizations:
Bergen Univ. (Norway). Dept. of Applied Mathematics
Country of Origin:
Norway
Language:
English
Other Identifying Numbers:
Other: ISSN 0084-778X; TRN: NO0205037
Availability:
Available to ETDE participating countries only(see www.etde.org); commercial reproduction prohibited; OSTI as DE20243748
Submitting Site:
NW
Size:
9 pages
Announcement Date:
Jul 15, 2002

Citation Formats

Dahle, H K, Celia, M A, Hassanizadeh, S M, and Karlsen, K H. A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship. Norway: N. p., 2002. Web.
Dahle, H K, Celia, M A, Hassanizadeh, S M, & Karlsen, K H. A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship. Norway.
Dahle, H K, Celia, M A, Hassanizadeh, S M, and Karlsen, K H. 2002. "A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship." Norway.
@misc{etde_20243748,
title = {A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship}
author = {Dahle, H K, Celia, M A, Hassanizadeh, S M, and Karlsen, K H}
abstractNote = {New theories suggest that the relationship between capillary pressure and saturation should be enhanced by a dynamic term that is proportional to the time rate of change of saturation. This so-called dynamic capillary pressure formulation is supported by laboratory experiments, and can be included in various forms of the governing equations for two-phase flow in porous media. An extended model of two-phase flow in porous media may be developed based on fractional flow curves and a total pressure - saturation description that includes the dynamic capillary pressure terms. A dimensionless form of the resulting equation set provides an ideal tool to study the relative importance of the dynamic capillary pressure effect. This equation provides a rich set of mathematical research questions, and numerical solutions to the equation provide insights into the behavior of two-phase immiscible flow. For typical two-phase flow systems, dynamic capillary pressure acts to retard infiltration fronts, with responses dependent on system parameters including boundary conditions. Recent theoretical work suggests that the traditional algebraic relationship between capillary pressure and saturation may be inadequate. Instead, a so-called dynamic capillary pressure formulation is needed, where capillary pressure is defined as a thermodynamic variable, and the difference between phase pressures is only equal to the capillary pressure at equilibrium. Under dynamic conditions, the disequilibrium between phase-pressure differences and the capillary pressure is taken to be proportional to the time rate of change of saturation. A recent study by Hassanizadeh et al. presents experimental evidence, culled from the literature, to support this claim. Numerical simulations using dynamic pore-scale network models and upscaling also support the claim. Hassanizadeh et al. also presented numerical solutions for an enhanced version of Richards' equation that included the dynamic terms. A preliminary assessment was made regarding the magnitude of the proportionality coefficient in the dynamic equation, identifying ranges that produce significant modification to infiltration results. While the work presented by Hassanizadeh et al. provides a foundation for this problem, it only co considered the specific case of flow in unsaturated soils, under the assumption that the air phase remains at essentially atmospheric pressure everywhere in the domain. In the present work, we expand this earlier work to include the general two-phase flow case, using a fractional flow formulation for the governing equations. Into these equations are embedded the dynamic capillary pressure terms. The equations are then written in dimensionless form, and a brief discussion of the mathematical properties of the enhanced governing equations is presented. A numerical algorithm for their solution is given, and a numerical simulation is presented to demonstrate the effects of the dynamic terms. Finally the implication of these results is discussed, and a few comments on future directions for research are given.}
place = {Norway}
year = {2002}
month = {Jul}
}