Chemical Engineering September 2012 - 51

NOMENCLATURE
Q
w
Exchanged heat, Btu
Flowrate of the cooling water, lb/h
Cp Heat capacity, Btu/(lb)(°F)
U
A Area of heat transfer, ft2
FG
Constant overall coefficient of heattransfer
determined at optimum conditions,
Btu/(h) (ft2)(°F)
Geometrical factor (depends on the
geometrical arrangement of the shelland-tube
passes in the exchanger),
dimensionless
LMTD Log mean temperature difference driving
force over heat
exchanger, °F
T1
T2
t1
Temperature of the hot process stream
entering the heat
exchanger, °F
Temperature of the hot process stream
leaving the heat
exchanger, °F
Temperature of cooling water entering
the heat exchanger, °F
t2
Temperature of cooling water leaving
the heat exchanger or temperature of
the cooling water return stream to the
tower, °F
CO Operational cost, $/yr
Hy
Cw
Hours the exchanger is operated per
year, h/yr
Cooling water cost assumed as directly
proportional to amount of water
supplied, $/lb
CF Annual fixed costs, $/yr
KF
CA
Annual fixed charges including maintenance,
expressed as a fraction of
initial cost for completely installed
equipment, dimensionless
Installed cost of heat exchanger per
square foot of heat-transfer area, $/
ft2
CT Total annual costs, $/yr
CS,u
CS,f
Cooling water price for use in Equation
(14), $/m3
Fuel price for use in equation (14), $/GJ
CEPCI Chemical Engineering Plant Cost
Index, which is an inflation parameter
for projects in the U.S.5
a
b
q
RSI
S
t
B
Cooling water cost coefficient, $/m3
Cooling water cost coefficient, $/m3
Total water capacity, m3/s
Ryznar Stability Index, dimensionless
pH pH value of studied water
T Water temperature, °F
pHS
pH value of water saturated in CaCO3
Coefficient of the equation to calculate
pHS, dimensionless
Coefficient of the equation to calculate
pHS, dimensionless
D Coefficient of the equation to calculate
pHS, dimensionless
Coefficient of the equation to calculate
pHS, dimensionless
TDS Total dissolved solids, mg/L
TH
TAlkalinity Total alkalinity, mg/L
5. Calculated with a weighted average of the most common fuels used in the U.S. data obtained from the May 2011 Monthly Energy Review published
by the U.S. Energy Information Administration
TABLE 3. TYPICAL WATER ANALYSIS, PPM
Parameter
pH
Total alkalinity
Total hardness
Lake
water
(VS)
6.3
2
10
Total dissolved solids 33
VS: Very soft
MS: Moderately soft
Surface
water
(MS)
6.8
38
53
88
SH: Slightly hard
calcium carbonate scale can be predicted
from calculations involving calcium
hardness, total alkalinity, total
dissolved solids, pH and temperature.
The most commonly used indicators
are the Langelier Saturation Index
(LSI), the Ryznar Stability Index
(RSI), and the Puckorius (Practical,
Predictive) Scale Index (PSI) [5].
For this article, the RSI was chosen
to predict the scale tendencies. The
RSI has several advantages over the
other techniques: it always gives positive
values, provides better estimates
of the severity of scaling tendencies
[6], and it is not possible for low-hardness
and high-hardness waters to have
the same value (which can sometimes
happen with the LSI [7]).
RSI is defined by Equation (15) [8]:
RSIpHpH=−2
s
lowing relation [8]:
pH
s =+ +− −
93.
Where:
STDS
.log
= ()−()01
1
(17)
St DB
(15)
Usually, pHs is calculated by the fol(16)
River
water
(SH)
7.4
River
water
(MH)
7.5
Borehole
water
(H)
7.1
90
180 250
120 230 340
185 332 400
MH: Moderately hard
t =−13 12
DTH
log
.log
 +

T
BTAlkalinity
=
= ()− .04
lo ()g
Ground
water
(VH)
7.1
470
559
1,670
H: Hard
VH: Very hard
459 67
18
.
.


+ 34.55
(18)
(19)
(20)
Some typical values corresponding to
different types of water for calculating
the parameters S, D and B are shown
in Table 3 [9].
For practical purposes, the RSI was
calculated considering a wide range of
temperatures and the values of the parameters
shown in Table 3 for all types
of water. The results are presented as
a graph in Figure 3. This graph helps
one to easily determine the RSI, given
a particular type of water and a cooling
water temperature.
Using the optimum temperatures
obtained from the example for year
1990 and year 2011, and considering
river water (slightly hard), RSI can be
determined easily from Figure 3.
For year 1990 and t2 = 119°F, the
value of RSI according to the graph is
7.5. From Table 4, it is found that with
this RSI value, scale may be dissolved.
It is suggested to use the value of 7 >
RSI > 6 as a breaking point, instead of
using the published value of RSI = 6.
Now for year 2011, where the temperature
to evaluate for scale-forming
tendency is higher, the following exercise
analyzes also the effect of the type
of water on the RSI value. The results
of evaluating the RSI for all types of
water, considering t2 = 121.5°F, are
shown in Table 5.
As it can be observed, the optimum
temperature obtained for year 2011
is higher than that for year 1990. For
both years, comparing the results of
the RSI obtained for the same type of
water (river water, slightly hard), this
temperature increase gives a lower
RSI value (7.4). In this case, given the
characteristics of the water, scale also
may be dissolved, but the RSI value
tends to be in the limit of being in
chemical balance.
For the same example, and considering
the case of borehole water that
is relatively hard, this increase on the
temperature of the cooling water return
stream to the tower (t2) is even
more convenient, because, according
to Table 4, the RSI (6.0) shows that
the system is in chemical balance -
thus, the water is essentially neutral.
Hence, operating with a higher cooling
water outlet temperature is justified
and should provide no additional
problems in terms of added scale.
Readers should note that the RSI
relates only to scaling - not to corroCHEMICAL
ENGINEERING WWW.CHE.COM SEPTEMBER 2012 49
Total hardness as Ca2+, mg/L
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Chemical Engineering September 2012

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