On the Inclusion of the Interfacial Area Between Phases in the Physical and Mathematical Description of Subsurface Multiphase Flow

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The mathematical description of multiphase flow and transport in the subsurface should be based on conservation principles. In practice, however, equations used for modeling multiphase flow are actually obtained by starting with the single fluid equation and then enhancing the simple empirical coefficients that arise with complex functional dependences. These manipulations are also supplemented by equilibrium expressions for capillary pressure as a function of saturation that is equal to the pressure difference between adjacent phases. The shortcoming of this approach is that the governing flow equations do not account for some of the important physical phenomena. Therefore accurate simulation is ... continued below

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Gray, William G.; Tompson, Andrew & Soll, Wendy E. June 1999.

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Description

The mathematical description of multiphase flow and transport in the subsurface should be based on conservation principles. In practice, however, equations used for modeling multiphase flow are actually obtained by starting with the single fluid equation and then enhancing the simple empirical coefficients that arise with complex functional dependences. These manipulations are also supplemented by equilibrium expressions for capillary pressure as a function of saturation that is equal to the pressure difference between adjacent phases. The shortcoming of this approach is that the governing flow equations do not account for some of the important physical phenomena. Therefore accurate simulation is more of an art than a scientific exercise. Experimental and field programs designed to measure data in support of these equations may actually be seeking curve fitting coefficients rather than information characteristic of physical phenomena. A more general approach to the description of multiphase flow physics has been evolving over the last thirty years. This approach relies on a series of mathematical procedures that allow for derivation of conservation principles at a length scale on the order of tens to hundreds or more of pore diameters. The components of this procedure are: (1) derivation of conservation equations for phases, interfaces between phases, and common lines where interfaces intersect; (2) use of thermodynamic considerations to obtain the functional dependence of energy; (3) followed by imposition of thermodynamic constraints to restrict the generality of these expressions. The product of this approach is a set of balance equations which provides a framework in which the assumptions inherent in a hypothesized model of multiphase flow are clearly stated. However, support for the coefficients in these models is still required.

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  • Other Information: PBD: 1 Jun 1999

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  • Report No.: EMSP-54576--1999
  • Grant Number: FG07-96ER14701
  • DOI: 10.2172/825755 | External Link
  • Office of Scientific & Technical Information Report Number: 825755
  • Archival Resource Key: ark:/67531/metadc781535

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  • June 1999

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  • Dec. 3, 2015, 9:30 a.m.

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  • April 21, 2016, 3:19 p.m.

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Gray, William G.; Tompson, Andrew & Soll, Wendy E. On the Inclusion of the Interfacial Area Between Phases in the Physical and Mathematical Description of Subsurface Multiphase Flow, report, June 1999; United States. (digital.library.unt.edu/ark:/67531/metadc781535/: accessed August 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.