orvallis
EVAPORATION FROM POPLAR
RIVER COOLING RESERVOIR
Mostafa A. Shirazi
CERL - 033
April 1977
nvironmental
gjesearch
^laboratory
%

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EVAPORATION FROM POPLAR
RIVER COOLING RESERVOIR
Mostafa A. Shirazi
CERL - 033
April 1977
Prepared for EPA Region VIII
Dennis Nelson, Project Officer
CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330

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I. Introduction
An electric generation project proposed by the Saskatchewan
Power Corporation impounds the East Branch of Poplar River to form
a cooling reservoir. Since this is an international river and the
proposed dam would be located within five miles of the United
States-Canada border, the project raises water quality concerns to
the State of Montana and to Environmental Protection Agency Region
VIII.
The impoundment of the river and the use of the reservior for
cooling within the Canadian border is subject to certain water
apportionment agreements as well as maintaining acceptable water
quality. Evaporative water losses provide a first order link
between water quantity and quality. It is important, therefore, to
establish an estimate of such loss at the outset.
The purpose of this report is to provide estimates of water
loss by evaporation under specific conditions of power generation.
Adequate details are outlined in this report to enable assessment
of assumptions and comparison with other methods.
II. Meteorological data
Saskatchewan Power Authority supplies (a) dew point tempera-
ture, (b) solar radiation, (c) natural water surface temperature
and (d) wind speed for Coronach, Province of Saskatchewan, corre-
sponding to the geographical location of the proposed reservoir
within the Canadian border. These data are listed in Table 1 and
will be used for all calculations in this report.
III. Engineering data
There are four coal-operated units, each generating 300 mega-
watts of electric power. They totally reject 5.89 billion Btu/hr
1

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at 11.67°C (21°F) condenser aT. The volume flow rate of cooling
water is 34.4m3s_1. The reservoir when flooded to its highest
elevation is nearly 1800 acres (728 ha). Calculations are
performed for a reservior area as small as 700 acres (283 ha). The
distance between intake and discharge, measured along the river
bed, is about 5 km.
The discharge is a rectangular, open end conduit 3X5 meters
with an invert elevation of 739 m. There is no skimmer wall con-
sidered at the intake end of the reservoir.
IV. Intermediate Calculations
Table 2 shows a list of items that are common to all forth-
coming calculations. These items are explained below:
A) Wind speed function f(M)--Heat loss by evaporation and by
conduction from the water surface are strong functions of
ambient air flow. The greater the wind speed, the greater
would be both losses. The functional form of wind speed for
evaporation losses is not well known. Numerous wind functions
have been compared by Edinger and Brady (1974). For example,
fj (W) = 9.2 + 0.46 W2 Wnf2 rrenHg"1
where W is wind speed in ms"1 and fi(W) is expressed in Watts
(W) per m2 per mmHg .
For the range of wind speed used in this work, the above
wind function yields low values. Higher, but realistic values
of wind speed function were obtained from visual inspection of
upper bound of data presented in Reference 2 and identified by
f2 (W) in Table 2. Both quantities will be used in our cal-
2

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culations, yielding conservative and more liberal evaporation
estimates for the purpose of comparison.
B)	Humidity ratio w--This is defined as the ratio of mass of
vapor per unit mass of dry air. It was obtained from a stand-
ard psychrometric chart, from the intersection of the dew
point temperature and saturated vapor line.
C)	Ambient air vapor pressure e --This was obtained from the
a
definition of humidity ratio for a mixture of water vapor at
e3 and air water vapor mixture at a standard pressure e =
a
760 mmHg, i.e.,
w Rs 760
= (85^6° = 1222w mmHg
Q	Os5 • j
where R, and Rp are, respectively, the universal gas constants
a	S
for air and for steam.
V. Natural evaporation
Heat loss by evaporation per unit area can be calculated from:
He = e(Ts - Td) f (W), Wnf2
p = .35 + .015 Tm + .0012 Tm2, (mmHg/°C)
Tm = (Ts + V/2' °C
T$ = Surface water temperature, °C
Td = Dew point temperature, °C
For total natural evaporation, Hg is multiplied by the surface area
either of the reservoir or the area of the 5 km stretch of the
river without impoundment. The heat loss Hg can also be calculated
more directly from
3

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He =¦ (es - efl) f (W), Wm"2
where e$ is the saturated vapor pressure at the surface water
temperature; eg is found from the standard steam tables.
A graph of this function is shown plotted in Figure 1. Also
on the same figure, one finds a graph of the slope of e$ with
temperature. The latter will be needed in the calculations of
forced evaporation. A listing of heat lost from water surfaces
under natural conditions can be found in Table 3.
In order to calculate the equivalent rate of water volume
escaping from the surface in the form of vapor, we need to multiply
He by the conversion factors .0408 and .0699, respectively, for the
700 acre and 1200 acre ponds. The results are thus expressed in
cubic feet per second which are pro-rated for the entire year even
though water loss by evaporation occurs only from April through
October. Under natural conditions, surface ice is present from
November through March.
VI. Forced evaporation
Induced heating of the water results in excess evaporation
above the natural evaporation by a magnitude that is proportional
to the change in the vapor pressure. An estimate of the vapor
pressure above a heated reservoir can be obtained from the knowledge
of the effective surface temperature Tg of the reservoir. We shall
assume for the purpose of these calculations that Ts is an average
temperature between the intake temperature T. and the discharge
temperature (aT + T^) i.e.,
T. . T, ~ T,)
S ~1
where AT is the temperature differential across the condenser taken
to be 11.67°C.
4

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The intake temperature is an important parameter. It must be
calculated from meteorological and engineering data. Ideally,
details of temperature distribution from intake to discharge must
be predicted to account for the reservoir geometry, discharge
condition, and induced flow circulation. Since this is very dif-
ficult to do, simplifing assumptions that are typical for these
problems are made to find an estimate of the temperature. Accord-
ingly, it is assumed that the temperature decays exponentially from
discharge to intake, i.e., there exist no vertical and lateral
temperature gradients in any cross section along the reservoir.
Temperature gradient exists only along the length of the reservoir,
decreasing from discharge to the intake.
This longitudinal temperature decay depends on the equilibrium
temperature T , the flow rate Q, the surface area A, the heat
exchange coefficient K, water denisity p and its specific heat Cp.
Thus,
VTe -r
vr6
where r = K^/p^pQ and Tq = T^ + AT
Using.approximate expressions for K and Tg given in Reference
2, we have
de
K = 4.5 + .05 T$ + f(W)(^ + .47)
and
Te = Td + VK
where Td is the dew point temperature and Hs the solar radiation.

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Calculations are straightforward except for the fact that K is
dependent on Ts which can't be calculated without the unknown
For this reason initial estimates must be made of Tg and inserted
in the equations for K. Corresponding initial estimates are then
obtained for the equilibrium temperature Tg and the intake temper-
ature Ti. The latter will be used to obtain better values of T$
and K. In this manner, iterations continue until convergence is
obtained. Results of such calculations for 700 and 1200 acre ponds
are presented respectively in Tables 4 and 5.
Lower values of wind speed function [i.e., f^w)] were used in
these tables. To compare similar results obtained with the higher
value of wind speed function, f2(w), Tables 6 and 7 were prepared.
The Sunmary of all results are presented in the next section.
VII. Summary and discussion of results
1.	The average natural evaporation during seven months, April
through October, is 8.1 cfs for a 1200 acre impoundment and
4.7 cfs for a 700 acre impoundment. These translate to 3360
and 1960 acre-feet per year respectively, for 1200 and 700
acre impoundments. If there were no impoundments at all, the
average loss for the same period is 0.6 cfs or 250 acre-foot
per year. The yearly average is less than the seven month
average by a factor of 1.7. See Table 3.
2.	The average yearly total evaporation for a 1200 acre impound-
ment is at least 12.8 cfs or 9120 acre-foot. See Table 5.
3.	The average yearly total evaporation for a 700 acre impound-
ment is at least 10.8 cfs or 7730 acre-foot. See Table 4.
6

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4.	More conservative estimates of the total evaporation using
appropriate wind functions [i.e. f2(w)] are: 11,300 acre-foot
(15.8 cfs) and 8500 acre-foot (11.9 cfs) respectively, for
1200 acre and 700 acre reservoirs. These values were obtained
indirectly from Tables 7 and 6. Since partial calculations
were made in these tables, comparisons were made with corre-
sponding months in Tables 5 and 6 and average yearly evapor-
ation from these tables was increased proportionally.
5.	The above do not include effects of recirculation. It is
difficult to say, but recirculation of uncooled water is
unlikely to become a problem with the given design. Recircu-
lation, if it occurs, will increase evaporation, however.
6.	The estimates presented in this report are lower than those
presented in Reference 1, making the latter estimates ade-
quately conservative. No calculations were performed for
sites B and C at this time.
7.	Reference 1 did not present documentation of the method used.
In this report, such documentation is presented for the method
used. Additional calculations can be made, of course, to
check new conditions. Detailed water quality models, if
available, will provide further refinements of temperature
distribution in the reservoir. Considerably more effort is
required to achieve a relatively small improvement in the
accuracy of the estimates.
7

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References
1.	Sheppard T. Powell Consultants Limited, C. W., Systems Study for
Saskatchewan Power Corporation, Appendix I, undated.
2.	Edinger, John E. and Derek K. Brady. 1974. Heat exchange and
transport in the environment. Report No. 14, The Johns Hopkins
University.

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Table 1. Meteredogical Data for	Coronach, Site A, Data	Obtained
from Reference 1.
January February March April May	June	July	August	September October November
Dew point °C -16.94 -13.61 -8.06 -2.50 2.78	8.33	11.39	9.72	4.72 0	-7.5
(°F) (1.5) (7.5) (17.5) (27.5) (37)	(47)	(52.5)	(49.5)	(40.5) (32) (18.5)
Solar radiation
Langleys, Hs 128 213 350 425 500	550	600	490	355 227	125
Wind Speed
Mph 14.8 14.3 14 14.3 14.4	13	12	12	14 14	14.6
m/s 3.31 3.2 3.13 3.2 3.22	2.91	2.68	2.68	3.13 3.13	3.27
Natural water
temperature
O
C	-14.17 -9.72 -3.17 3.61 9.44 15.28 19.17 17.18 12.11	5.56 -3.06
(°F)	6.49 14.50 26.29 38.50 48.99 59.50 66.51 62.92 53.80 42.00 26.49

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January
fjtW) W^rrmHg"1	14.24
f2(W) W^nmHg"1	27.50
w	.0008
e, mmHg	.98
a
Table 2. Intermediate
February March	April May
13.91 13.71	15.50 13.97
27.00 26.00	27.00 27.50
.00115 .00185 .003 .0046
1.41 2.26 3.67 5.62
Ca I culations.
June July	August
13.10 12.05	12.05
25.00 28.00	28.00
.0068 .0082	.0075
8.25 10.02	9.17
September	October	November
13.71	13.71	14.12
26.00	26.00	27.00
.0053	.0037	.002
6.42	4.75	2.44

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Table 3a.
Heat loss He* from Water Surface
Under Natural Conditions.
es mmHg	6.0	9.10 13.30 17.00 15.20 10.90 6.40
He, Wnf2	33.96	45.26 63.19 83.60 78.92 56.84 30.56
'1
;2 V
HeoWnf2	62.91	95.70 126.30 196.40 168.80 116.50 42.90
Table 3b. Yearly Averaged Water Loss CFS.**
No Reservoir	700 Acre	1200 Acre	1800 Acre
Qe]	Qe2 Qe1 Qe2 Qe] Qe2 Qe] Qe2
.18	.35 1.42 2.75 2.44 4.72 3.65 7.08
~Indices 1 and 2 refer to different methods of calculation
as explained in this section.
~~Evaporation rates during seven months are higher than
indicated for the yearly average by a factor of 12 * 7 = 1.71.
Note that 35.31 CFS = lm^s"^
1 acre-foot/year = 1.401 x 10~3 CFS

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Table 4. Calculations for Site A, 700 Acres with Low Values of
Wind Speed Function.
Wms"^
f^(w) Wm mmHg
Hs Wm~^
Td °C
w
rrmHg
T$ °C
des/dT mmHgc"^
T °C
e
T1. °C
K Wm"2c_1
e$ mmHg
He^ Wm~2
Qe-j CFS
January
February
March
April
May
June
July
August
September
October
November
3.31
3.20
3.13
3.20
3.22
2.91
2.68
2.68
3.13
3.13
3.27
14.24
13.91
13.71
15.50
13.97
13.10
12.05
12.05
13.71
13.71
14.12
62.00
103.00
169.40
205.70
242.0
266.2
290.4
237.20
171 .80
109.90
60.50
-16.94
-13.61
-8.06
-2.50
2.78
8.33
11.39
9.72
4.72
0
-7.50
.0008
.00115
.00185
.003
.0046
.0068
.0082
.0075
.0053
.0037
.002
.98
1 .41
2.26
3.67
5.62
8.25
10.02
9.17
6.42
4.75
2.44
13.01
15.37
20.33
22.63
27.22
31.45
34.43
34.35
27.32
23.69
17.92
.76
.86
1.12
1.26
1.61
1.98
2.30
2.31
1 .64
1.34
.985
-14.20
-9.28
-1.86
3.84
9.71
15.30
18.72
18.70
9.66
3.60
-5.17
6.49
10.23
14.49
16.86
21.48
25.70
28.58
28.52
21.49
17.75
12.30
22.67
23.77
27.32
32.45
34.92
38.17
39.60
39.72
34.79
30.50
25.94
11.40
13.30
18.00
20.50
27.30
35.00
41.50
41.30
27.50
22.00
15.80
148.38
165.39
215.80
260.87
302.87
350.43
379.33
387.17
289.01
236.50
188.64
6.05
6.75
8.80
10.64
12.36
14.30
15.48
15.80
11.79
9.65
7.70

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Table 5. Calculations for Site A, 1200 Acre and Low Values of Wind
Speed Function

January
February
March
April
May
June
July
August
September
October
November
Wms-^
3.31
3.20
3.13
3.20
3.22
2.91
2.68
2.68
3.13
3.13
3.27
f-|Cw) Wm"2mmHg
14.24
13.91
13.71
15.50
13.97
13,10
12.05
12.05
13.71
13.71
14.12
Hs.W/m2
62.00
103.00
169.40
205.70
242.0
266.20
290.40
237.20
171.80
109.90
60.50
T °C
.d L
-16.94
-13.61
-8.06
-2.50
2.78
8.33
11.39
9.72
4.72
0
-7.50
w
.0008
.00115
.00185
.003
.0046
.0068
.0082
.0075
.0053
.0037
.002
mmHg
.98
1.41
2.26
3.67
S.62
8.25
10.02
9.17
6.42
4.52
2.44
Tsc °C (1DnH9"'c
5.70
9.45
14.93
18.00
23.08
27.71
30.75
28.65
22.96
18.53
11 .97
des/dT
.49
.61
.835
.99
1.30
1.64
1.92
1.73
1.28
1.02
.705
t °r
'd L
-13.58
-8.46
-.74
4.84
10.75
16.27
19.73
17.03
10.46
4.27
-4.70
Ti °C
-.12
3.62
9.09
12.22
17.25
21.81
24.92
22.88
17.13
12.70
6.13
K WnfV1
18.47
20.00
23.14
28.03
30.38
33.53
34.84
32.44
29.92
25.71
21.62
es mmHg
6.80
8.90
13.00
16.00
21.00
28.00
33.50
30.00
21.00
16.50
10.50
He Wm 2
82.88
104.20
147.25
191.12
214.86
258.73
282.93
251.00
199.89
165.25
113.81
Qe CFS.
5.74
7.28
10.29
13.36
15.06
18.08
19.78
17.55
13.97
11.48
7.96

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Table 6. Calculations for Site A, 700 Acre at Highest Values
of Wind Speed Function.

January
February
March
April
June
August
September
October
f(W)^ Wm 2mmHg
27.50
27.00
26.00
27.00
25.00
28.00
26.00
26.00
Ts °C
4.91
8.25
13.00
16.86
25.23
24.95
21.39
17.30
des/dT mmHgc"^
.47
.56
.76
.925
T .46
1.42
1.18
.96
Te °C
-14.91
-10.46
-3.53
2.28
13.26
13.76
8.26
2.58
Ti °C
.83
2.41
7.17
11.02
19.39
19.11
15.55
11.46
K Wm"2c_1
30.60
32.72
37.40
43.01
54.01
58.67
48.47
42.54
esmmHg
6.55
8.15
11.50
14.70
24.50
24.00
19.30
15.30
He Wm'2
153.20
182.00
240.20
297.90
406.25
415.24
334.88
280.28
Qe CFS
6.25
7.42
9.80
12.15
16.97
16.94
13.66
11.43

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Table
7. Calculations for Site A, 1200 Acre at
Values of Wind Speed Function.
High

May
f^(w) Wm ^mniHg
27.50
T °C
s
17.41
des/dT mmHgc"^
.96
T °C
e
8.23
T. °C
11.57
-2 -1
K Wm C
44.42
es mmHg
15.30
He^ Wm ^
266.20
Qe2 CFS
18.61
July
November
28.00
27.00
24.22
6.37
1.38
.51
16.44
-5.58
18.39
.54
57.51
31.55
23.00
7.16
363.44
127.44
25.40
8.91

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2.0
1 -8
- 1.6
- 1
- 1.2
- 1
O
C_J
o>
- .8
- .6
- .4
- .2

0>
"O
-40 -30 -20 -10 0 10 20
T = temperature C°
dt
Figure 1: Saturated vapor pressure es and its gradient 37^- as a
function of temperature

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