Page 46 - gas transport in porous media

Chapter 3: Vapor Transport Processes
Solid 39
Vapor flux Liquid Vapor flux
A B

Solid

Figure 3.6. Water vapor flux across liquid islands driven by thermal gradients. Condensation occurs on
the “hot” side (A) and evaporation occurs on the “cool” side (B) (from Ho and Webb, 1998, reprinted with
permission)

B B
A A

Figure 3.7. Pore-scale transport paths: (A) enhanced vapor-diffusion mechanisms and (B) Fickian
diffusion (from Ho and Webb, 1998)

3.5.1 Analytical Model
As detailed in Ho and Webb (1998), a simple pore-scale analysis can be performed to
estimate the steady-state mass flow of water across liquid islands due to condensation
and evaporation mechanisms (Path A in Figure 3.7). A comparison between the flux
due to condensation and evaporation mechanisms and the flux caused by Fickian
diffusion (Path B in Figure 3.7) is made to discern the relative importance of enhanced
vapor-diffusion mechanisms.

3.5.1.1 Path A
Consider the space between two solid particles that contains entrapped liquid water
as shown in Figure 3.8. A thermal gradient in the water-wet porous medium induces
vapor diffusion from the hot region (left side) to the colder regions (right side). Con-
densation on the upstream side of the liquid interface occurs because of vapor pressure
lowering. An energy balance is performed on a control volume of the surface of the
liquid island exposed to the hotter side (Figure 3.8). The latent heat of condensation