Page 133 - Materials Chemistry, Second Edition

116 Practical Design Calculations for Groundwater and Soil Remediation

Assumption of steady-state is frequently used in the analysis of flow reac-
tors. It should be noted that a batch reactor is operated under unsteady state
because the concentration in the reactor is changing, and it is not a flow reac-
tor because there is no flow in and out of the reactor when it is in operation.
The general mass-balance equation (i.e., Equation 4.1) can also be expressed as:

dC
V = ∑ QC in − ∑ QC out ± ( V × γ ) (4.5)
in
out
dt
where V is the volume of the system (reactor), C is the concentration, Q is the
flow rate, and γ is the reaction rate. The following sections will demonstrate
the role of the reaction in the mass-balance equation and how it affects the
reactor design.

Example 4.1: Mass-Balance Equation: Air Dilution (No
Chemical Reaction Occurring)
A glass bottle containing 900 mL of methylene chloride (CH Cl , specific grav-
2
2
ity = 1.335) was accidentally left uncapped in a poorly ventilated room (5 m ×
6 m × 3.6 m) over a weekend. On the following Monday it was found that two-
thirds of methylene chloride had volatilized. An exhaust fan (Q = 200 ft /min)
3
was turned on to vent the fouled air out of the laboratory. How long will it take
to reduce the concentration down below the Occupational Safety and Health
Administration (OSHA’s) short-term exposure limit (STEL) of 125 ppmV?

Strategy:
This is a special case (no reactions occurring) of the general mass-
balance equation. For this case Equation 4.5 can be simplified into:
dC
V = ∑ QC in − ∑ QC out (4.6)
in
out
dt
The equation can be further simplified with the following assumptions:
1. The air leaving the laboratory is only through the exhaust fan,
and the air ventilation rate is equal to the rate of air entering the
laboratory (Q = Q = Q).
out
in
2. The air entering the laboratory does not contain methylene chlo-
ride (C = 0).
in
3. The air in the laboratory is fully mixed; thus the concentration of
methylene chloride in the laboratory is uniform and is the same
as that of the air vented by the fan (C = C ).
out
dC
V =− QC (4.7)
dt