Environmental Engineering Reference
In-Depth Information
For a more general description it is assumed that there is an additional vector of
fluxes
f
i
into the lakes (
i
for influx). Additional fluxes out of the system can be taken
into account.
There are connections to compartments, which are not included in the model, as
the atmosphere and the ocean in the examples represented by Figs.
18.1
and
18.2
.
These fluxes are also donor controlled. For that reason they are best represented by
a matrix-vector product
E
o
c
, with a diagonal matrix
E
o
(
o
for outflow). The mass
conservation equations within the network can then be expressed in the more
general form
Sidebar 18.1: Indoor Air Quality Modeling
Various compounds from different sources affect Indoor air quality. There are
random short-term on/off sources, like cigarettes for example, long-term on-
off sources like heaters, long-term steady-state sources, like moth crystals.
Sources may have a high initial emission rate, which is decreasing in time
with quite different rates. Wax or painted surface emissions decline within
hours, while others show modest decay. Sources for volatile organic
compounds (VOCs) may be located outdoors (air quality in vicinity of
industrial emissions, landfills or contaminated sites) or within the building
(combustion, human activities, surface emissions).
Problems of indoor air quality, due to VOCs, can be treated by linear
compartment models, as demonstrated by Bouhamra and Elkilani (
1999
). The
approach is presented here briefly. In analogy to (
18.3
) for each room the
concentration of VOC is described by two differential equations:
V
@
c
@t
¼ Qc
in
Qc k
a
Ac
i
þ k
d
Ac
s
þ q
@
c
s
@t
¼ k
a
c k
d
c
s
where
c
denotes the concentration within the room,
c
in
the inflow concentra-
tion,
V
the volume of the room,
Q
air inflow and outflow, and
q
the rate of the
sources within the room, if there is any. Two terms and the second differential
equation are introduced to account for sorption effects. Especially furniture
and soft tissues may act as temporary sinks of sources for the VOC due to ad-
and desorption processes. The corresponding ad- and desorption coefficients
are denoted by
k
a
and
k
d
, while
c
s
denotes the sorbed concentration and
A
the
area of the reacting surface.
When the source is described by
q ¼ k
c
ðc
source
cÞ
a set of two linear
equations results. The approach can be extended to a complete apartment,
floor or building, when the set of equations, given above, is formulated for a
network of room compartments:
(continued)
