Page 12 - gas transport in porous media

CHAPTER 2

GAS TRANSPORT MECHANISMS

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

Gas-phase momentum transport in porous media consists of advective and diffu-
sive components. In this chapter, the individual advective and diffusive components
will be presented separately first, followed by a discussion of the combined mecha-
nisms. Gas-only situations will be discussed for all the mechanisms. Two-phase, or
unsaturated, flow effects are included in Chapter 5.
The conservation equations presented below are given in a simplified form. For
a complete derivation of the various conservation equations, including underlying
assumptions, see Whitaker (Chapter 6 of this book).
Energy transport is not discussed in this chapter. Gas-phase energy transport in
porous media is treated by Plumb (Chapter 27 of this book). Energy transport is also
discussed in Nield and Bejan (1999) and Kaviany (1995).

2.1 GAS-PHASE ADVECTION
2.1.1 Darcy’s Law

Gas-phase advection in porous media is generally analyzed using Darcy’s law (Darcy,
1856), which simply states that the gas Darcy velocity, u g , is directly proportional
to the gas-phase pressure gradient, ∇P g , and the gas-phase permeability, k g . Darcy’s
law can be written as

k g
u g =− ∇P g − ρ g g
µ g
where µ g is the gas-phase viscosity and g is the gravitational constant. In terms of
mass flux, the equation is

k g
F g = ρ g u g =− ρ g (∇P g − ρ g g)
µ g
5
C. Ho and S. Webb (eds.), Gas Transport in Porous Media, 5–26.
© 2006 Springer.