Theory of Operation
4-3
The mass balance equations for CO
2
, water vapor and air take the form
storage = flux in - flux out.
We neglect the effects of leaks for now, but we will consider them later.
CO
2
Mass Balance
v
c
c
t
= sf
c
c
c
u
4-1
H
2
O Mass Balance
v
c
w
t
= sf
w
w
c
u
4-2
Air Mass Balance
v
c
t
= sf
c
+ sf
w
u
4-3
c
c
is the number density of CO
2
in the chamber,
c
w
is the number density of
water vapor in the chamber, and
c
is the total number density of air in the
chamber (all in mol m
-3
);
c
=
c
a
+
c
c
+
c
w
, where
c
a
is the number density of
dry air in the chamber.
The number density of air is given by the ideal gas law,
c
= p (RT
K
)
-1
, where R is
the gas constant (8.314 Pa m
3
K
-1
mol
-1
), and T
K
is the absolute temperature (K).
From equation (4-3), with p and T
k
constant, and sf
w
>> sf
c
,
u = sf
w
4-4
Combining equations (4-2) and (4-4), and noting that
c
w
=
c
w
c
, we find
sf
w
=
v
c
1 w
c
w
c
t
4-5
Combining equations (4-1), (4-4) and (4-5) gives
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