## Example

A defective gas-fueled space heater is unwisely operated in a room 8 ft high by 12 ft wide by 20 ft long. The heater generates CO, a toxic combustion product, at the rate of 100 g/h. Although the room is closed, it is ventilated at a relatively typical air exchange rate of 0.5 h-1. Air exchange rate is a term used by heating and air-conditioning engineers which is equivalent to the first-order rate constant for contaminant removal due to the infiltration of fresh, uncontaminated air into a room and the corresponding exhaust of contaminated air to the outside. It is equal to the volumetric flow rate into and out of a room divided by the volume of the ventilated space.

(a) What would be the maximum concentration of CO if steady state were reached?

(b) What is the concentration of CO in the room after 2 hours?

(c) There are no regulatory standards for carbon monoxide levels in the home. The Environmental Protection Agency limit on outdoor exposures is approximately 10 mg/m3. The concentration obtained is considerably higher than this. If the heater were to be turned off after 2 hours, how long would it take to reach this level?

Solution

(a) The constant-source first-order removal model (Eq. 2.13) can be applied to this problem:

The steady-state concentration is given by the leading term. The volume is V = (8 ft) (12 ft) (20 ft) = (1920 ft3) (0.02832 m3/ft3) = 54.4 m3. Substituting gives

(c) When the heater is turned off, there is no longer a source of carbon monoxide, and Eq. 2.12 reduces to Eq. 2.8 for first-order removal. The solution is Eq. 2.10:

Solving for time gives

t = — ln—— k Cn and substituting values yields t = — ln—— =--T ln-

k Co 0.5h 2330

Clearly, if someone knew the hazard, they should have opened all the doors and windows in the room and used a fan to enhance clearance of the CO. Mathematically, this would have increased the removal rate constant (see Problem 2.7).

2.3.2.3 Instantaneous Partitioning In risk assessment there are a number of important physicochemical processes in which a contaminant undergoes dynamic exchange between two different media. A conceptual model applicable to these systems is shown in Figure 2.6, which illustrates contaminant partitioning between compartments A and B. The kinetics are illustrated in Figure 2.7 for a contaminant introduced into compartment A at t = 0. As time passes, the concentration in A decreases (Figure 2.7a) and the concentration in B increases (Figure 2.7b) until equilibrium is achieved and the concentrations stabilize.

Contaminant partitioning between the two compartments is described by a partition factor, PF (Figure 2.7c), which is given by

If the time required to reach equilibrium is small compared to the time scale of interest, partitioning is approximated as occurring instantaneously; and the partition factor becomes the ratio of the equilibrium concentrations:

where the subscript e refers to equilibrium. This is the instantaneous partitioning model. It is used to describe a wide variety of environmental systems, including the sorption of contaminants in aqueous solution to rock, soil, and sediment; the uptake of contaminants by plants from soil; the uptake of contaminants by aquatic animals (fish, mollusks) from water; and the exchange of a contaminant between air and raindrops.

COMPARTMENT A

COMPARTMENT B

Figure 2.6 Instantaneous partitioning between two compartments. (a) (b) Figure 2.7 Partitioning of a contaminant between two compartments. At t = 0, a contaminant is introduced into compartment A, at which time it begins to partition between compartments A and B.