Page 62 - gas transport in porous media

CHAPTER 5

TWO-PHASE GAS TRANSPORT

STEPHEN W. WEBB
Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185, USA

Chapter 2 was limited to all-gas conditions. This chapter addresses two-phase, or
unsaturated, gas transport in the presence of a liquid. While the same general transport
mechanisms (advection and diffusion) exist as discussed in Chapter 2, gas transport
under two-phase conditions must consider the influence of the liquid phase. Not only
does the liquid phase interfere with gas-phase transport in the gas phase, but gas
transport may occur in the liquid phase as a dissolved species. The presentation in
this chapter complements the discussion given in Chapter 2.
As in Chapter 2, energy transport is not discussed in this chapter. It is treated by
Plumb (Chapter 27 of this book), Nield and Bejan (1999), and Kaviany (1995).

5.1 GAS-PHASE ADVECTION

5.1.1 Darcy’s Law
Darcy’s law as presented in Section 2.1.1 is often extended to two-phase conditions
with separate equations for the gas and liquid phases. Relative permeabilities for each
phase are introduced into the momentum equations to account for the influence of the
other phase. Each phase may be at a different pressure due to interfacial curvature, so
a pressure relationship between the two phases (capillary pressure) is also included.
For unsaturated flow conditions, the Darcy equations for mass flux can be written as

k g k r,g
F g =− ρ g (∇P g − ρ g g)
µ g
k k r,
F =− ρ (∇P − ρ g)
µ
The equation for the gas mass flux is the same as in Section 2.1.1 except for the
addition of the term k r,g , which is the gas-phase relative permeability. The relative
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C. Ho and S. Webb (eds.), Gas Transport in Porous Media, 55–70.
© 2006 Springer.