Page 461 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

442 14 Indoor Air Quality

Consider the schematic diagram in Fig. 14.3, where air flow through the building
envelop is ignored. There is also an internal air cleaner to help clean the air. The
mass balance of an air pollutant leads to

dc i
V ¼ Q o c o 1 gð½ o Þ þ Q r c i 1 g Þ þ _ sŠ Q e c i þ Q i c i g Þ ð14:18Þ
ð
ð
i
r
dt
where Q o , Q r , Q i ; and Q e are the volumetric flow rates of fresh air, recirculating air,
internal air cleaning, and exhaust air, respectively. V is the volume of the space of
concern, and the total area within the space is A. The internal source rate with
respect to the air pollutant is _ s. At any moment the indoor air concentration is c i and
that in the fresh air is c o . The last term ðQ e c i þ Q i c i g Þ stands for the removal rate of
i
the pollutant from the room air.
Since air pollutant is the main concern in this analysis, the change of moisture
level in the air can be ignored; then the mass balance of air leads to
Q o ¼ Q e ð14:19Þ

Then Eq. (14.18) becomes,

dc i
V ¼ Q o Q r 1 gð½ r Þ þ Q i g Šc i Q o c o 1 g Þ þ _ sŠ: ð14:20Þ
ð
½
i
o
dt
If we assume only c i and t are variables, then integration leads to

Q o c o 1 g Þ þ _ s Q o Q r 1 g Þ þ Q i g i
ð
ð
r
o
c i ¼ c i0 exp t
Q o Q r 1 gð r Þ þ Q i g i V
ð14:21Þ
Q o c o 1 g Þ þ _ s
ð
o
þ :
Q o Q r 1 gð r Þ þ Q i g i
It can be presented in a simple form as
t

c i ðtÞ¼ c i0 c i1 Þ exp þ c i1 ð14:22Þ
ð
s
where C i = C i0 at t = 0
Q o c o 1 g Þ þ _ s
ð
o
c i1 ¼ ð14:23Þ
Q o Q r 1 gð r Þ þ Q i g i
V
s ¼ ð14:24Þ
Q o Q r 1 gð r Þ þ Q i g i
In the above equation, c i1 is the steady state concentration in the indoor space
when t !1, and s can be considered as a time constant that is used to characterize
the transient concentration in the space.