Page 277 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

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7.6 Water Quality Modeling 237
7.6.2 Trace Modeling

Identifying the origin of flow at a point in the system is referred to as flow tracking or trace
modeling. In systems that receive water from more than one source, trace studies can be
used to determine the percentage of flow from each source at each point in the system.
These studies can be very useful in delineating the area influenced by an individual source,
observing the degree of mixing of water from several sources, and viewing changes in origins
over time.

7.6.3 Constituents Modeling
Reactions can occur within pipes that cause the concentration of substances to change as
the water travels through the system. Based on conservation of mass for a substance within
a link (for extended-period simulations only),
0c 0c
= v + u(c) (7.9)
0t 0x
where
c substance concentration as a function of distance and time
t time increment
v velocity
x distance along the link
(c) substance rate of reaction within the link.
In some applications, there is an additional term for dispersion, but this term is usually
negligible (plug flow is assumed through the system).
Assuming that complete and instantaneous mixing occurs at all junction nodes, addi-
tional equations can be written for each junction node with the following conservation of
mass equation:
a Q C ƒ + Q C
e e
j j x=L
ƒ
C k x=0 = (7.10)
a Q + Q e
j
where
C k concentration at node k
j pipe flowing into node k
L length of pipe j
Q j flow in pipe j
C j concentration in pipe j
Q e external source flow into node k
C e external source concentration into node k.
Once the hydraulic model has solved the network, the velocities and the mixing at the
nodes are known. Using this information, the water quality behavior can be derived using
a numerical method.

7.6.4 Initial Conditions

Just as a hydraulic simulation starts with some amount of water in each storage tank, ini-
tial conditions must be set for a water age, trace, or constituent concentration analysis.
These initial water quality conditions are usually unknown, so the modeler must esti-
mate these values from field data, a previous water quality model, or some other source
of information.