Civil Engineering Reference
In-Depth Information
Mixing in Storage Facilities
Most models assume that the contents of storage fa-
cilities (tanks and reservoirs) are mixed completely. The concentration in the facility
is a blend of the current contents and any entering water. At the same time, the internal
concentration could change because of reactions. The following equation expresses
these phenomena:
(
VC
)
ss
Accumulation in Storage
t
Mass flow in
Mass flow out
(22-3)
Mass generated in reactions
(
VC
)
ss
QC
C
Q
r
(
C
)
V
in
in
s
in
s
s
t
where
V
s
volume in storage at time
t
,
C
s
concentration within the storage facility,
Q
in
flow into storage from all sources, and
r
(
C
s
)
the rate of reaction.
Bulk Flow Reactions
While a substance moves down a pipe or resides in storage,
it can react with constituents in the water column. The rate of reaction generally can
be described as:
r
kC
(22-4)
n
where
k
a reaction constant and
n
the reaction order. Some examples of differ-
ent reaction rate expressions are
r
kC
for chlorine decay (first-order decay),
r
k
(
C
*
C
) for THM formation (first-order growth, where
C*
maximum THM for-
mation possible),
r
1 for water age (zero-order growth), and
r
0 for conservative
materials (e.g., fluoride).
Pipe Wall Reactions
While flowing through pipes, dissolved substances can be
transported to the pipe wall and react with materials such as corrosion products or
biofilm. The amount of wall area available for reaction and the rate of mass transfer
between the bulk fluid and the wall influences the overall rate of this reaction. The
surface area per unit volume, which for a pipe equals 2 divided by the radius, deter-
mines the former factor. The latter factor can be represented by a mass-transfer co-
efficient, the value of which depends on the molecular diffusivity of the reactive species
and on the Reynolds number of the flow.
29
For first-order kinetics, the rate of a pipe
wall reaction can be expressed as:
2
kkC
w
ƒ
r
(22-5)
R
(
k
k
)
w
ƒ
where
k
w
wall reaction rate constant (L / T),
k
ƒ
mass transfer coefficient (L / T),
and
R
pipe radius (
L
). If a first-order reaction with rate constant k
b
also is occurring
in the bulk flow, then an overall rate constant
k
(
T
1
) that incorporates both the bulk
and wall reactions can be written as
