Environmental Engineering Reference
In-Depth Information
then diffuse into the sorbent particle. The configuration of a process can also affect the
overall mass transfer resistance. Therefore, the flux, or rate per unit area, of a component
A is usually expressed in words as:
Flux of A
=
(Overall Mass Transfer Coefficient)
×
(Driving Force)
.
(3.78)
This equation can be rearranged as:
Driving Force
Total Mass Transfer Resistance =
×
,
Flux of A
=
OMTC
Driving Force
(3.79)
where the OMTC includes all system contributions to mass transfer resistance.
The value of the total mass transfer resistance is the inverse of the overall mass transfer
coefficient value. This equation is analogous to Ohm's Law which relates current flow
(flux) to applied voltage (driving force):
=
V
R .
i
(3.80)
There are different approaches that can be taken to estimate the OMTC (or resistance).
The first is to directly measure the flux and driving force and calculate the coefficient.
The second uses correlations that are available to estimate the value based on the par-
ticular process and operating conditions. Examples of this approach will be included in
later chapters that deal with a particular separation technology. The third is to determine
each mass transfer resistance and combine the terms to calculate the total resistance.
This approach is analogous to the calculation of an equivalent resistance for an electrical
circuit.
The two-film model is a simple example of this approach. A system of two fluids
exists, with a distinct interface between the two (gas/liquid or two immiscible liquids).
For purposes of this example, we assume a gas/liquid interface; Figure 3.33 illustrates
the region near the interface. There will be a film (or boundary layer) on each side of the
interface where, due to mass transfer from one phase to the second (gas to liquid in the
figure), the concentration of A is changing from its value in the bulk phase, P A , b in gas
and C A , b in liquid. The thickness of the boundary layer on each side of the interface will
typically be different and a function of the fluid and flow conditions in each phase. At
steady-state, the flux of A can be described as:
k g ( P A , b
P A , i )
k L ( C A , i
C A , b )
J A =
=
Liquid Phase ,
(3.81)
Gas Phase
where k g and k L are the mass transfer coefficients in each phase. These values can be
estimated from correlations based on flow conditions and configuration. An equation can
also be written for the equilibrium at the interface (such as Henry's Law):
P A , i =
mC A , i .
(3.82)
Search WWH ::




Custom Search