Page 44 - gas transport in porous media

Chapter 3: Vapor Transport Processes
Equations (3.24) and (3.25) yield the following expression:
DAC s dδ(t) 37
= φS l ρ l A (3.26)
δ(t) dt
Equation (3.26) can be integrated and solved for δ(t):

2DC s t
δ(t) = (3.27)
φS l ρ l
Equation (3.24) can then be used to calculate the bulk advective concentration,
C flow , and the transient evaporation rate, dm/dt, of a liquid receding into a stagnant
region:

A φS l ρ l DC s
C flow = (3.28)
Q 2t

dm φS l ρ l DC s
= A (3.29)
dt 2t

3.4.4 Steady Through-Flow Evaporation
In the preceding sections, the evaporation rate was limited by diffusion. In this section,
we consider the case where a gas is flowing through a homogenous, unsaturated region
containing a single liquid. Assuming that the flowing gas reaches local equilibrium
with the stationary liquid that it passes through, the rate of evaporation of the bulk
liquid can be expressed as follows:
dm
=−QC sat (3.30)
dt
where the left-hand side is the time derivative of the mass, m [kg], of liquid in the
3
control volume, Q is the air flow rate [m /s], and C sat is the saturated gas concentration
coming out of the control volume. Assuming macro-scale equilibrium, the effluent
gas concentration, C sat , can be obtained using the ideal gas law:
o
P M
C sat = (3.31)
RT
o
where P is the saturated vapor pressure [Pa] at the system temperature, T [K], M
is the molecular weight of the liquid [kg/kmol], and R is the universal gas constant
[8300 J/kmol · K]. Integration of Equation (3.30) yields a simple expression for the
time required to remove the total mass of liquid in the system:
m o
t = (3.32)
QC sat