Transient multiphase multicomponent flow in porous media. Page: 4 of 36
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the petroleum industry because of its
importance to the secondary recovery of
petroleum. As a result, most of the
available literature on such flows 1-12
deals with conditions that may be found
in petroleum reservoirs. Multiphase
flow resulting from an underground
nuclear explosion, however, passes
through considerably larger ranges of
temperature ad pressure. Consequently,
assumptions in these studies usually
prohibit their application to the problem
of interest here. For example, the
fluids are c-dinarily considered incom-
pressible -4 or barotropic.5-10 Although
such restrictive assumptions are not
made in Refs. 11 and 12, the formulation
of the first law of thermodynamics is in
error in both cases,
The flow will be assumed to :.e a two-
phase, two-component flow. When
applying the analysis to flow of the cavity
gas, the two components are taken to be
air and water. Air is initially present
in the porous medium. The gas flowing
from the cavity is predominantly steam.
Because the tnperature of th- gas
entering the nurous medium is consider-
ably higher than the ambient temperature
of the medium, condensation will occur
and a two-phase flow results.
The equations governing this 'low may
be formulated in a straightforward man-
ner. The equations will be written for
a one-dimensional flow; the extension to
more dimensions being obvious.
Conservation of mass is expressed by
a continuity equation for each component.
For air, this equation is
i (aum) + e (pa m) 0.
Here, air is assumed to be present only
in the vapor phase, Any air dissolved in
the liquid phase is negligible; x is tWe
distance in the direction of flow from the
surface of the porous medium; t is the
time; pa is the mass density of the air;
um is tht apparent velocity, i.e., volume
flow rate/unit area normal to flow, of
the mixture of air and water vapor. The
two phases will ordinarily have different
apparent velocities. Sm is the saturation
of the vapor phase. The saturation of a
phase is the void volume fraction occupied
by that phase.
The corresponding equation for water
g pu+ ovum)
+ c (PO + Pv m) = 0.
The additional terms result from the
presence of water in both phases. The
subscript P refers to the liquid and the
subscript v refers to water vapor. The
air and water vapor have the same ap-
parent velocity, diffusion being neglected.
The flow res.ats from the pressure
gradient in the medium. Flow due to
gravity is not considered. For sufficiently
small Reynolds numbers, the apparent
velocity of a phase will be given by Darcy's
law with the permeability reduced by the
presence of the other phase:
up = - S'
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Morrison, F.A. Jr. Transient multiphase multicomponent flow in porous media., report, January 1, 1973; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc1034085/m1/4/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.