OPERATIONAL ISSUES INVOLVING USE OF SUPPLEMENTARY
COOLING TOWERS TO MEET STREAM TEMPERATURE STANDARDS
WITH APPLICATION TO THE BROWNS FERRY NUCLEAR PLANT
by
Keith D. Stolzenbach, Stuart A. Freudberg
Peter Ostrowski and John A. Rhodes
Energy Laboratory Report No. MIT-EL 79-036
January 1979
COO-4114-7
OPERATIONAL ISSUES INVOLVING USE OF SUPPLEMENTARY
COOLING TOWERS TO MEET STREAM TEMPERATURE STANDARDS
WITH APPLICATION TO THE BROWNS FERRY NUCLEAR PLANT
by
Keith D. Stolzenbach
Stuart A. Freudberg
Peter Ostrowski
and
John A. Rhodes
Energy Laboratory
and
Ralph M. Parsons Laboratory
for
Water Resources and Hydrodynamics
Department of Civil Engineering
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
Prepared under the support of
Environmental Control Technology Division
Office of the Assistant Secretary for Environment
U.S. Department of Energy
Contract No. EY-76-S-02-4114.AOOl
Energy Laboratory Report No. MIT-EL 79-036
January 1979
ABSTRACT
A mixed mode cooling system is one which operates in either the open,
closed, or helper (once-through but with the use of the cooling towers) modes.
Such systems may be particularly economical where the need for supplementary
cooling to meet environmental constraints on induced water temperature
changes is seasonal or dependent upon other transient factors such as streamflow. The issues involved in the use of mixed mode systems include the
design of the open cycle and closed cycle portions of the cooling system,
the specification of the environmental standard to be met, and the monitoring
system and associated decision rules used to determine when mode changes
are necessary. These issues have been examined in the context of a
case study of TVA's Browns Ferry Nuclear Plant which utilizes the large
quantity of site specific data reflecting conditions both with and without
plant operation. The most important findings of this study are: (1) The
natural temperature differences in the Tennessee River are of the same order
of magnitude (5°F) as the maximum allowed induced temperature increase.
(2) Predictive estimates based on local hydrological and meteorological
data are capable of accounting for 40% of the observed natural variability.
(3) Available algorithms for plant induced temperature increases provide
estimates within 1°F of observed values except during periods of strong
stratification. (4) A mixed mode system experiences only 10% of the
capacity losses experienced by a totally closed system, (5) The capacity
loss is relatively more sensitive to the environmental standard than to
changes in cooling system design.
(6) About one third of the capacity
loss incurred using the mixed mode system is the result of natural
temperature variations. This unnecessary loss may be halved by the use
of predictive estimates for natural temperature differences.
ii
ACKNOWLEDGMENTS
This report is part of an interdisciplinary effort by the
IT
Energy Laboratory to examine issues of power plant cooling system design
and operation under environmental constraints.
The effort has involved
participation by researchers in the R.M. Parsons Laboratory for
ater
Resources and Hydrodynamics of the Civil Engineering Department and the
Heat Transfer Laboratory of the Mechanical Engineering Department.
Financial support for this research effort has been provided by the
Division of Environmental Control Technology, U.S. Dept. of Energy, under
Contract No. EY-76-S-02-4114.A001.
The assistance of Dr. William Mott,
Dr. Myron Gottlieb and Mr. Charles Grua of DOE/ECT is gratefully acknowledged.
Reports published under this sponsorship include:
"Computer Optimization of Dry and Wet/Dry Cooling Tower Systems
for Large Fossil and Nuclear Plants," by Choi, ., and
Glicksman, L.R., MIT Energy Laboratory Report No. MIT-EL 79-034,
February 1979.
"Computer Optimization of the MIT Advanced Wet/Dry Cooling Tower
Concept for Power Plants," by Choi, M., and Glicksman, L.R.,
MIT Energy Laboratory Report No. IT-EL 79-035, September 1979.
"Operational Issues Involving Use of Supplementary Cooling Towers
to Meet Stream Temperature Standards with Application to the
Browns Ferry Nuclear Plant," by Stolzenbach, .D., Freudberg, S.A.,
Ostrowski, P., and Rhodes, J.A., MIT Energy Laboratory Report No.
MIT-EL 79-036, January 1979.
"An Environmental and Economic Comparison of Cooling System
Designs for Steam-Electric Power Plants," by Najjar, K.F., Shaw, J.J.,
IT Energy.
Adams, E.E., Jirka, G.H., and Harleman, D.R.F.,
Laboratory Report No. MIT-EL 79-037, January 1979.
"Economic Implications of Open versus Close Czle Cooling for
New Steam-Electric Power Plants: A National and Regional Survey,"
Adams, E.E., Barbera, R.J., Arntzen, B.C,, and
by Shaw, J.J.,
o. MIT-EL 79-038,
Harleman, D.R.F., MIT Energy I.abl)oratory Report
September 1979.
iii
"Mathematical Predictive Models for Cooling onds and Lakes,"
Part B: User's Manual and Applications of 'ITE:P by Octavio, K.H.,
Watanabe, M., Adams, E.E., Jirka, G.H., Helfrich, K.R., and
Harleman, D.R.F.; and Part C: A Transient nalytical Model for
Shallow Cooling Ponds, by Adams, E.E., and Koussis, A., MIT
Energy Laboratory Report No. IT-EL 79-039, December 1979.
"Summary Report of Waste Heat Management in the Electric Power
Industry: Issues of Energy Conservation and Station Operation
under Environmental Constraints," by Adams, E.E., and Harleman,
D.R.F., MIT Energy Laboratory Report No. MIT-EL 79-040, December
1979.
Site specific data collected at the Browns Ferry Nuclear Plant site was
provided by the Water Systems Development Branch, Division of Water
Management, of the Tennessee Valley Authority.
The study would not have
been possible without the cooperation of Mr. Ely Driver, Dr. William
Waldrop, Mr. Christopher Ungate, and Mr. Charles W. Almquist of TVA.
iv
TABLE OF CONTENTS
Page
TITLE PAGE
i
ABSTRACT
ii
ACKNOWLEDGEMENTS
iii
TABLE OF CONTENTS
V
I.
Introduction
1
II.
Description of the Browns Ferry Nuclear Power Station Case
Study
5
2.1
2.2
2.3
III.
Modeling the National Temperature Difference in Wheeler
Reservoir
3.1
3.2
IV.
Wheeler Reservoir
The Cooling System
Temperature Data Collected in Wheeler Reservoir
One-Dimensional Formulation
Input Data
12
13
17
Simulation of Plant Operation
26
4.1
4.2
26
28
Main Simulation Cycles
Simulation Subroutines
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
4.2.7
4.3
V.
5
7
9
Input
Browns Ferry Flow
Plant Subroutine
Running Averages
Best Mode
Cumulative Energy Lost
Output
33
Source of Performance
Results of Computer Simulation of Plant Operation
5.1
An Explanation of the Forms Used to Display Results of
Computer Simulation
5.1.1
5.1.2
5.1.3
28
28
28
32
32
33
33
Power Output of the Plant in Best Mode of Operation
Sorted Power Losses
Cumulative Hourly Power Losses
V
34
34
34
35
39
5.2
5.3
Base Cases
Effects of Spatial and Time Averaging
5.3.1
5.3.2
5.3.3
5.4
VI
63
Changes in Environmental Thermal Standards
Existence of Various Modes of Operation
Changes in Plant Design
67
72
76
Summary and Display of Cumulative Hourly Power Losses
Comparison with Operating Data
6.1
6.2
6.3
6.4
44
54
63
Sensitivity to Changes in Environmental Standards
of Plant Design
5.4.1
5.4.2
5.4.3
5.5
Monitor Location and Spatial Average
Time Averaging
Combined Spatial and Time Averaging
39
44
Recalibration of Natural Temperature Difference Model
1977 Natural Temperature Difference Prediction
Revised Plant Induced Temperature Simulation Model
Comparison of Model Results with Measured Temperature
Differences
81
88
88
90
97
105
REFERENCES
113
APPENDIX A
114
vi
OPERATIONAL ISSUES INVOLVING USE OF SUPPLEMENTARY
COOLING TOWERS TO MEET STREAM TEMPERATURE STANDARDS
WITH APPLICATION TO THE BROWNS FERRY NUCLEAR PLANT
I.
Introduction
The basic motivation for this study has been the need to assess
the energy consumption consequences of environmental regulations applied
to waste heat discharges from steam electric power plants.
This
report describes the results of an investigation focussing solely on
the operation of mixed mode systems e.g. the real time choice of
supplementary cooling mode (open, helper, or closed) to be used to meet
a given constraint on induced temperatures in the receiving water body.
The investigation of mixed mode operation has been conducted
in the context of a case study involving TVA's Browns Ferry Nuclear
Plant.
The use of a specific example has provided the opportunity to
produce quantitative results associated with actual combinations of
environmental and plant design parameters.
However, it should be noted
that in performing this study it was both necessary and advisable to
make a number of assumptions which are not based on actual conditions
at Browns Ferry.
Accordingly, the results of this investigation are
in no way intended to represent past or future actual operation of the
Browns Ferry Nuclear Plant by the Tennessee Valley Authority.
The remainder of the report is divided into five sections.
1
First, the most important general details of the case study problem
are outlined, e.g., the characteristics of the Browns Ferry Plant site
and design and the associated environmental constraints on waste heat
discharges.
Following this section, a semi-empirical model for predicting
natural temperature differences is presented.
The next section describes
a model for simulating the river temperature changes due to natural and
plant induced causes, for selecting the necessary plant cooling mode,
and for calculating the associated energy consumption by the plant.
The simulation model is then used to compare a year of plant operation
as a function of the following:
- choice of temperature monitor location
- spatial and temporal averaging of temperature monitor values
- correction of monitor values for computed natural temperature
differences
- changes in environmental standard
- changes in plant design
The results of this sensitivity study are presented in terms of plant
output as a function of time and in terms of total energy requirements.
Finally, the plant simulation model and the natural temperature difference
model are applied to a year during which the Browns Ferry Nuclear Plant
has been operating.
This application provided a direct evaluation of
the validity of the simulation model results.
The most important findings of this study are the following:
1.
The Tennessee River in the vicinity of the Browns Ferry Nuclear
Plant (Wheeler Reservoir) exhibits significant variability
in water temperature over a wide range of space and time scales.
2
The difference between temperatures measured upstream and
downstream from the plant during a pre-operational period are
the same order of magnitude (5°F) as the maximum induced
temperature increase permitted by the regulatory standard.
2. A predictive model for the upstream - downstream natural
temperature differences is capable of accounting for 40% of the
observed variability.
This estimate, which is based upon local
hydrological and meteorological data, primarily addresses the
temperature changes occurring over periods of days to months
rather than diurnal variations which are found to be quite
random in nature.
3. The plant simulation model provided a good estimate of the
induced river temperature rise (within 10 F) except for periods
when the upstream temperature monitors were affected by seasonal
stratifications not accounted for in the natural temperature
model which was used to isolate the plant induced effect from
the naturally occurring temperature differences.
4. The simulation study of capacity losses resulting from the necessity
to use cooling towers to meet the specified environmental
temperature standard indicates the following:
(a) A mixed mode cooling system experiences only 10% of the
capacity losses experienced by a totally closed system.
(b) The capacity loss is sensitive to the specified limit on
induced temperature increases.
A decrease in the allowable
river temperature increase from 5F to 3F produced a 300%
increase in lost capacity.
Compared to the influence of
environmental standard, changes in plant design, such as
cooling tower size or open cycle diffuser mixing, have
significantly less influence on plant capacity losses.
(c) About one third of the capacity loss incurred using a mixed
mode system is the result of natural temperature variations
that are interpreted as plant induced effects by the
monitoring system.
This unnecessary loss may be cut in
half by the use of the predictive model for natural
temperature variations.
Further reduction may be obtained
by spatial and temporal averaging of temperature monitor
measurements.
4
II.
Description of the Browns Ferry Nuclear Power Station Case Study
The Browns Ferry Nuclear Power Station consists of three
identical General Electric Co. Boiling Water Reactors (BWR), each with a
nameplate
rating of 1152 megawatts electric (MWe), and a net rating of
1067 MWe.
The station is located on an 840 acre site in Limestone
County in northern Alabama on the north bank of the Wheeler Reservoir
at Tennessee River Mile 294 (TRM 294).
This is approximately 10 miles
northwest of Decatur, Alabama and 10 miles southwest of Athens, Alabama.
(See Fig. 2.1).
2.1
Wheeler Reservoir
Wheeler Reservoir, along which Browns Ferry is located, was
constructed by TVA for electric power generation, flood control and
navigation, sport and commercial fishing, industrial water supply,
and public water supply.
The hydraulic regime of Wheeler Reservoir is
controlled by the operation of 2 dams:
Guntersville, located upstream
of Browns Ferry at TRM 349, and Wheeler, located downstream of Browns
Ferry at TRM 274.9.
These dams, constructed in the 1930's are operated
primarily for hydroelectric power production and secondarily for flood
control.
The long term average flow at Wheeler Dam is 49,000 cfs;
its drainage area is 29,590 sq. miles, and it was designed to generate
356.4
MWe.
Upstream at Guntersville Dam, the long term average flow
is about 40,000 cfs, the drainage area is 24,250 sq. mi. and the hydrostation there is capable of generating 97.2 MWe.
The elevation in the
predominantly flat pool portion of Wheeler Reservoir is normally 556.3
ft., although this varies by several feet throughout the year, as a
5
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0
4J
4-
0
P-4
pH
a)
I)
P--
U
0
~4)
0
Fa)
Uc
3
to
0
O-J
04
F.>>
(f2
rl
4z
c)
Co
.1H
f
z
6
function of flood control and power production constraints.
2.2
The Cooling System
Browns Ferry Station was originally designed to operate in an
"open-cycle" cooling mode, pumping cooling water from the Tennessee
River through the condensers at a rate of 4410 cubic feet per second
(cfs) for all three units, and then returning it back to the river at
an elevated temperature.
The temperature of the discharge from the
condensers is approximately 25° hotter than the river intake temperature,
which corresponds to a net heat rejection rate (for all three units)
of 2.467 x 1010 BTU/hr, and thus a plant efficiency of about 30.7%.
The discharge in open mode is passed through a submerged multiport
diffuser system which consists of three perforated, corrugated galvanized
steel pipes laid in parallel across the bottom of the main river channel
a short distance downstream from the plant (see Fig. 2.2).
The
operation of the diffuser has been studied extensively (Harleman, 1968);
its main purpose is to facilitate better mixing of the plant's thermal
discharge with the river.
The Tennessee River cross-section at this point (TRM 294)
consists of navigation channels dredged to a 30-foot depth and approximately
1800 feet laterally across, which is bordered by shallow overbank areas
that vary from 2 to 10 feet in depth and 2000 to 6000 feet in width.
Although the main channel at this point contains only 1/3 of the total
river width, through it passes approximately 65% of the flow (AEC, 1971).
Due to the implementation of the more stringent Alabama water
temperature standards, TVA decided in 1971 to spend $59,000,000 and
7
BROWNS FERRY
NUCLEAR PLANT
ik
A
~
INTAKE
Figure 2.2
SHALLOW AREA
Location of Diffuser In Tennessee River
Near Browns Ferry Nuclear Plant Station
0
10
construct 6 mechanical draft cooling towers.
To increase their
versatility, the cooling towers were designed to operate in two modes:
"helper-mode" and "closed-cycle mode."
In the helper mode, condenser
cooling water passes through the towers, is cooled down to within several
degrees fahrenheit of the wet bulb temperature, and returned to the river.
The discharge rate for helper mode is 3675 cfs.
As a general rule, the
discharge temperature using helper mode is less than that of open mode,
although this may not be the case during times of high wet bulb
temperature.
In closed-cycle mode, only 110 cfs are released to the
river - the so-called "blowdown" - and the remainder of the flow is
circulated through the cooling towers and then back into the intake
channel.
Makeup water needed for the unit due to evaporative losses
in this mode is approximately 220 cfs.
The option of three cooling
modes (open, helper, and closed-cycle) make the cooling system at
Browns Ferry unique among power stations.
A schematic of the condenser
cooling modes is given in Fig. 2.3.
2.3
Temperature Data Collected in Wheeler Reservoir
Because of the presence of the Browns Ferry Station, extensive
water temperature records have been collected documenting conditions in
Wheeler Reservoir since 1968.
At present, there are 12 stations
located along the river at which temperature data is collected at least
every hour.
In addition the temperature is measured at Guntersville
and Wheeler Dams.
in Fig. 2.4.
The location of the sampling stations is depicted
At the monitors closest to Browns Ferry (these are labelled
Station 1, 9, 10 and 11) and at the furthest upstream monitor (Station 6),
temperature data is collected every 15 minutes.
9
(3~~~~~~~~~~~~,
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-
-
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2o
j
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-.-
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rp~~~~~~~~~~~~~~~~$
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'
tx
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C
14 0~~~~~~~~~~
.
.O0
z
a:
w w
z
40H
Ua
H~~~~~~~~S
'-
-
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Z
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W
0
,
4
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Z
0
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A
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I
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C-)
10
Each of the stations has a vertical string of sensors covering
the total water depth.
Some of the sensors are located at a fixed
height relative to the river bottom, and others are attached to floating
moorings so that the reference height is the water surface, which
fluctuates during the year by several feet.
The measurements are
considered to be accurate to ±0.3°F (TVA, 1974).
The means of data collection is via telemetry from the monitor
which is initiated by a signal sent from a meteorological station
located at Browns Ferry,
All the data is punched onto paper tape and
each week this tape is retrieved and the data copies to magnetic
tape which may then be processed.
The actual data used for analysis in this study was contained on
a magnetic tape obtained from the Water Systems Development Branch of
TVA in Norris, Tennessee.
through March 31, 1976.
The period of record is from April 1, 1975
During this time Browns Ferry Power Station
was not operating due to the fire of March 22, 1975.
Thus the record
is essentially of pre-operational or "natural" conditions in the
reservoir without the plant's influence.
11
III.
Modeling the National Temperature Difference in Wheeler Reservoir
This section will present a one-dimensional (longitudinal)
model for predicting the
naturally
occuring difference between tem-
peratures in Wheeler Reservoir upstream and downstream from the Browns
Ferry Nuclear Plant.
This one dimensional approach essentially neglects
a variety of natural temperature variations that are known to be more
complex resulting in vertical and lateral temperature gradients as well
as longitudinal differences.
A more complete discussion of these
phenomena may be found in Freudberg (1977).
The one-dimensional model was developed using temperature
data from monitor #6 (upstream) and monitor #1 (downstream) for the
study year described in the previous section.
These predictions are
also used for the simulation studies (presented in section 5.0 of this
report) in which the downstream temperature measurement is defined
using stations 9, 10 or 11.
Because of the close proximity of these
monitors, it is not expected that the error incurred in basing
natural temperature difference on Station 1 will be large.
12
3.1
One-Dimensional Formulation
The basic 1-dimensional convective diffusion equation is given by
9TA
al t
4-
A"
GI x
-
gd
(A
()gn x
T)
(3.1-1)
T
is the cross-sectional average temperature
A
is the cross-sectional area
t
is time
x
is the longitudinal position from the upstream station
E
is a diffusion coefficient
where:
~n(t)
is the net heat flux, a function of time
B (x) is the width, variable with distance along the river
is the density of water, assumed constant
and
c
is the heat capacity of water, assumed constant.
If it is assumed that the cross-sectional area is constant along
the reach from Station 6 to Station 1, that the width is also constant,
(their values are given by means) and that the flow does not vary as
a function of distance but may vary as a function of
time, then equation 3.1-1 becomes, upon dividing through by A:
-
U
e
* x
=
(E 0'0 ))
4
(F£
,
o___h
(3.1-2)
where u is the cross-section average velocity, given by Q/A, and h
is the average depth, given by B/A.
13
If E is taken as a constant dispersion coefficient, and for
scaling purposes
(t) is replaced by -K(T-TE) or -KATE and
then the 4th term is rewritten so that k = K/pc is substituted,
equation 3.1-2 becomes:
4WEQT
Tk7'
It U ~..__~T
ate = E
~._.~.T
-I-
Ar ~
/~ z~'7'c
00a2e
9~ T
(3.1-3)
If the temperature is scaled by T', the time by 0, the velocity by V,
and the x-coordinate by L, then the scaled parameters corresponding
to each term of equation 3.1-3 are:
7-z
~
,~
,
~
~
TLz
y
7'
E<
z
2
~g
X
L2
. -d
h
7(3.1-4)
If each parameter above is divided through by VT'/L to produce nondimensional parameters, then this results in:
[-1
®0
Ii
I
[
0
M
(3.1-5)
Besides the balance between the 2nd and 4th parameters, in equation
3.1-5, what other terms need be retained?
[-] would have a value on
V®
the order of 1 if the distance between Station 6 and 1, 85000 ft, were
used for L, an average velocity of 0.5 ft/sec were used for V, and
were about 2 days.
Since the time scale of interest for the natural
AT is on the order of 2 days, this term must be retained.
The third parameter scales the dispersion coefficient.
1/'
Using the
same values as above for V and L, E would have to be approximately
40,000 ft2 /sec
to make this parameter about 1. Almquist (1977)
states that for the Tennessee River, a value an order of magnitude
lower of 1000 ft /sec
is probably a good estimate.
Therefore,
using the value 1000 ft /sec, [E/VL] has a value <<1, and therefore
the dispersion term shall be neglected.
So the
-D equation becomes
(returning to the original formulation of the heat term),
i~__0t
+
a
-
~_r
k
(3.1-6)
(6)
eoh
The left hand side of equation 3.1-6 represents the changes in the
temperature of a parcel of water as it travels downstream from
Station 6 to Station 1. In Lagrangian coordinates, this may be written
as a material derivative:
)r
()
=
7
(3.1-7)
cA
Integrating this equation over time for the parcel yields:
t
7,Hi) =
4
(I - zt) =
|
C
6d)
A
(3.1-8)
where Td is the temperature of the downstream monitor (Station 1), and
T
is the temperature of the upstream monitor (Station 6).
A moment's thought concerning equation 3.1-8 indicates
A moment's thought concerning equation 3.1-8 indicates
15
its physical foundation.
If equation 3.1-8 is rewritten as
b
76V=
d)
(3.1-9)
then it is seen that the downstream temperature at time t is a result
of the water parcel's temperature when it was at the upstream monitor
At earlier plus the integrated net heat flux over At the parcel
received during its journey downstream.
The correct definition for
this At is the travel time for the parcel to move from Station 6 to
Station 1. At is thus determined from:
udrz~L
(3.1-10)
{-of
where L is the distance between upstream and downstream sections.
Utilizing the assumptions that the area is a constant between monitors,
and that Q, the flow, is a function of time only, equation 3.1-10
becomes:
A
(3.1-11)
i-de
Thus, it is seen that
t is itself a function of time.
For the natural AT at time t defined by:
7= (-)
7
A
d
Fa ()
16
(3.1-12)
equation 3.1-9 combined with 3.1-12 yields:
Ao£
=-/z
Jf;;
,('
(3.1-13)
y-[;6J4K--{
Thus, the temperature difference between the two stations consists of
two effects:
the net heat input over At and the change in temperature
at the upstream monitor during At.
Equation 3.1-13 represents the
desired formulation for the 1-dimensional model.
3.2
Input Data
There are many aspects which make up the natural AT.
The time
scale of many of the more random events are hourly, whereas the 1-dimensional (l-D) influences are felt over longer time periods on the order
of a day.
Therefore, it was decided to use the 1-D model to fit a
2-day running average of the natural AT, which was expected to have
more 1-D character.
A plot of the natural AT after a 49-hour running
average was made (49 hours was used so that a symmetric averaging
interval occurred) is given in Fig. 3.1.
From this signal, "storm
cycles" may be observed which appear as wide temperature swings
persisting up to a week that are believed to be associated with the
weather patterns.
Also visible, though less clearly, is the weak
annual cycle.
17
r
C
- - - -,-
-
r
-
-
rI
-
"
,
'
_,
0
5i
Io
co
.1IJ
r-I
.
co
zfa
r4
ci
U)
0
t
'.4
O r)
Ze n
0
PL4
CJ
'r-I
I
S 'L
09
S -F
0G'E
S I
O'
a0
1t
-
IV
O'E-
5'h-
0 9-
S'L-
To apply equation 3.1-13, tables of flow, measured upstream
temperature, and computation of net heat flux are required.
In
addition, values for the area, A, and depth, h, must be specified.
Since only for certain locations are measurements for A and h available,
there is some leeway with their values, and these two parameters were
used to tune the model within physically reasonable limits.
The means
of producing a best fit is described briefly below where the actual
results are presented.
The net heat flux was computed using the methods outlined by
Ryan (1971).
Table 3.1 summarizes the input needed.
The actual
equations used to compute the net flux are given in Appendix A.
TABLE 3.1
DATA REQUIRED TO COMPUTE NET FLUX
1. Air Temperature
2. Relative Humidity
3. Wind Speed
4. Air Pressure
5. Solar Flux
6. Atmospheric Flux
19
Necessary inputs to apply equation 3,1-13 are (all 49-hour running
averages of) the flow, station 6 bottom temperature, and meteorological
inputs measured at Huntsville, Alabama (30 miles from Browns Ferry).
For these computations, values of cloud cover and air temperature
measured at Huntsville were used.
The period of record for this data is April 1975 through December
Only 3/4 of the year is shown because the flow and meteorological
1975.
data happened to be available from January 1975 to December 1975 and
the natural temperature measurements which were not available until
April 1975 as the plant operated until then.
The data record of 6598
points is still quite sufficient for applying and testing the
model.
-D
The upstream monitor at Station 6 at the bottom was used as the
upstream temperature (Tu(t)) in equation 3.1-13 as this location is less
susceptible to diurnal effects and it is believed to be closer to the
cross-sectional temperature.
The choice of depth and cross-sectional area to use was made after
several iteratations with the model.
The values chosen were h = 12.5
feet and A = 50,000 ft2 , values which are physically reasonable in
light of the measured cross-sectional data.
The criteria used to
choose these values was when the best agreement was obtained between
monthly averages of the model prediction and monthly averages of the
measured AT at the 5-foot depth and bottom monitors.
20O
The best
monthly averages of the model prediction and monthly averages of the
measured AT at the 5-foot depth and bottom monitors.
The best
result, using h - 12.5 feet and A - 50,000 ft2 is plotted in
As is seen, the model is a reasonable fit on a monthly
Figure
3.2.
basis.
Fig. 3.2 is somewhat misleading however, because neither the
top nor bottom measured AT values actually are true cross-sectional
averages, and due to the monthly averaging scale, the ability of the
model to fit the storm cycles is obscured.
The ability of the
-D model to fit tc 49-hour averaged. data
s
As is seen the model
dramatically illustrated in Figure 3.3,
prediction is a very credible fit of the peaks and valleys of the
measured AT, although this fit is somewhat worse in the fall and
winter.
It is suspected that the model fit is better in the spring
and summer than the fall or early winter because the valley-wide
longitudinal driving force is much smaller in the latter portions of
the year, (Freudberg, 1977).
In addition, the nature of the river
is fundamentally different during heating periods than during cooling
periods.
Stratification, although weak, occurs particularly in the
spring when the river begins to warm.
Further, the seasonal
eat-up
is a relatively steady process which induces very little turbulence
as it acts.
The flow is not particularly disrupted from its usual
1-dimensional course by density effects.
O the other hand, the cool-
down in the fall is a far more complex process.
21
Unlike the spring
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when the warmed, bouyant surface water tends to remain at the surface,
the cooled surface water in the fall sinks down due to its greater
density and thus non-one-dimensional mixing takes place.
Thus the 1-D model produces a better result during periods when
the river flow itself is generally one-dimensional, the water body is
more homogenous, and no complex mixing process is taking place.
The statistics of the mean and variance for the measured data and
the 1-D model are presented below, for the period April 1975 - Dec. 1975.
TABLE 3.2
Comparison of Statistics of 1-D Model and
Measured Natural AT
MEASURED DATA
1-D
MODEL
MEAN
0.26
0.14
VARIANCE
0.53
0.69
These values show that the model is close to the measurements, although
there is clearly some error.
In Fig. 3.4,
a time series plot of this
residual obtained via subtracting the 1-D model fit from the data
is given.
2
0.34°F 2 .
This residual series has a mean of 0.12'F and a variance of
Thus the variance of the data has been reduced roughly 40%
using the 1-D model.
24
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IV.
Simulation of Plant Operation
This section describes a simulation routine developed for the
purpose of investigating a year of plant operation at an hourly time
scale for a variety of different conditions.
simulation are presented in the next section.
The results of the
Also, because of the
complexity of some of the algorithms used to describe the plant operation,
diffuser mixing, etc., only the general logic of the simulation program
will be presented here.
4.1
Main Simulation Cycles
The logic governing the overall simulation is shown in flow
chart form in Figure 4.1.
As indicated in the figure, the simulation
routine assumes the following quantities are known for the last hour
of the period of simulation:
Releases from the upstream (Guntersville) and downstream
1.
(Wheeler) dams
2.
Browns Ferry Plant Target Load
3.
Wet bulb air temperature
4.
Upstream and downstream natural water temperature
5.
The estimated natural temperature difference between
upstream and downstream
From the above quantities the simulation program computes for each
hour the cooling mode needed to meet the applicable temperature
standard.
A plant efficiency algorithm is then used to compute the
actual power output for each hour.
26
C
1
TIME = BEGINNING HOUR
I
r-
TIME + ONE HOUR
I
INPUT: GUNTERSVILLE AND WHEELER FLOWS, TARGET PLANT
LOAD,WET BULB, UPSTREAM AND DOWNSTREAM RIVER TEMPERATURES
AND THE ESTIMATED AT PREDICTED BY THE ONE DIMENSIONAL
MODEL
t
CALCULATE RIVER FLOW AT BROWNS FERRY
I
|
,
a,
,
,
,
,11
,
[I
.!@~
-
~PLANT OPERATION SUBROUTINE|
|
_~~~~~~~~t
~~MONITOR DATAl
|
MODE SELETO
,~~~~
I
COMUT
CUMULATIVE ENERGY LOST|
4
4~~~~~~~~~~~~
OUTPUT
-- __
T
Figure 4.1
{ [[[
K
II ~
1
[
[
[~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I
w[[
TIME < FINAL HOUR
-
I[
T__
.
.
Overall Logic Diagram for Simulation of Plant Operation
27
4.2
Simulation Subroutines
The following section describes the individual algorithms that
are used in the simulation routine.
4.2.1
Input
Hourly values of river flows at Guntersville and Wheeler dams;
wet bulb temperatures; upstream and downstream temperatures; and when
desired the one dimensional models estimates of the natural temperature
difference between upstream and downstream monitors, are supplied to
the program.
4.2.2
Browns Ferry Flow
The river flow at Browns Ferry is calculated with a two term
equation utilizing flow values at Guntersville dam five hours previous
to the time of calculation, and flow at Wheeler dam two hours previous.
The flow was then time averaged using a fraction (R) of the present
flow calculation added to the fraction (-R)
flow calculation.
of the previous hours
With the diffuser performance a function of flow and
using the simple two term model for flow without time averaging causes
the plant induced temperature fluctuations to be instantly and strongly
respondant to flow variations.
We know in reality the induced tempera-
ture is not so highly sensitive to flow and the inclusion of time
averaging of flows at this point is a means to smooth the induced
temperatures response to flow.
4.2.3
Plant Subroutine
The subroutine simulating plant operation is executed three
28
times per hour to include three possible modes of operation, open,
helper and closed. (see Figures 4.2)
Condenser Intake Temperatures:
For open and helper modes
condenser intake temperatures are approximated by the upstream river
temperature.
Closed mode iteration is used until the temperature
rise across the condensers is equal to the temperature drop across
the cooling towers.
At this point the condenser intake temperature
is approximated by the cooling towers cold side temperature.
Actual Plant Load and Condenser Hot Side Temperature: Actual
plant load is a function of the target plant load (held constant at
3300 MWefor the three units considered here), water temperatures, and
the mode of operation.
The condenser hot side temperature is a
function of the actual plant load, the intake temperature and the
condenser flow rate (constant within a given mode).
However, the ratio
of actual plant load to target plant load is a function of the actual
plant load and condenser hot side temperature.
Hence, iteration is used
alternatingly computing the condenser hot side temperature and the
actual plant load until both values converge to a final value (for
a given intake temperature and mode of operation).
An additional 56
MWe issubtracted from the actual plant load in helper and closed
modes to account for the operation of the cooling towers pumps. (see
Figure 4.3)
Cooling Tower Performance:
The temperature drop across the
cooling towers is calculated using a fitted polynomial with tower
intake temperature and wet bulb temperature as arguments,
Discharge Temperatures:
In open mode the condenser hot side
29
-I
MODE = OPEN
.
M
MODE
= CLOSED
MODE = HELPER
Il
!
fl
INITIAL ITERATION:
CONDENSER INTAKE
TEMP. = RIVER
TEMP.
F
r~~~~~~~
i __
.
_
i
CONDENSER INTAKE TEMP. = RIVER TEMP.
_
!
Ii,
I!
!
ii
1'
.
II
CONDENSER INTAKE
TEMP. = COOLING
TOWER COLD SIDE
TEMP.
,F
wIt
CALCULATE ACTUAL PLANT LOAD AND CONDENSER HOT SIDE TENP.
.
-
-
4--
COOLING TOWER PERFORMANCE:
CALCULATE TOWER COLD SIDE TEMP.
_
DISCHARGE TEMP.
= CONDENSER HOT
SIDE TEMP.
.
DISCHARGE TEMP.
= TOWER COLD
SIDE TEMP.
L
.
_
,
J
i
DIFFUSER PERFORMANCE:
CALCULATE INDUCED TEMP. CHANGE
F
E
I
ITERATION
T
CHECK:
AT ACROSS TOWERS
= AT ACROSS
(RETURN
Figure 4.2
CONDENSER
Flow Chart for Plant Subroutine
30
F
INITIAL ITERATION
ACTUAL PLANT LOAD = TARGET PLANT LOAD
CALCULATE CONDENSER HOT SIDE TEjfP.
= FUNCTION (ACTUAL PLANT LOAD, MODE)
CALCULATE NEW ACTUAL PLANT LOAD
=FUNCTION (OLD ACTUAL PLANT LOAD, CONDENSER
HOT SIDE TEMPERATURE)
/
CONVERGENCE
CHECK:
NEW ACTUAL PLANT
LOAD = OLD ACTUAL
PLANT LOAD
!
T0=
T+
MODE = OPEN
T
J
I
_
SUBTRACT 56 MW FROM ACTUAL PLANT
LOAD FOR OPERATION OF COOLING TOWERS
Figure 4.3
Flow Chart of Actual Plant Load and Condenser Hot
Side Temperature Algorithm
31
temperature at the open mode flow rate of 4410 ft3 /sec for the three
units is discharged.
Helper mode makes use of one pass through the
cooling towers and discharges the resulting tower cold side temperature
3
at the helper flow rate of 3675 ft3/sec to the river.
Induced River Temperature:
The induced river temperature is
a function of river flow and temperature, discharge flow and temperature,
and diffuser performance.
The diffuser performance is described by
curves fitting the three multiport bottom diffusers in place at Browns
Ferry.
Complete mixing in higher river flows and the recirculation
around the diffuser in lower flows are modeled.
4.2.4
Running Averages
If spatial or temporal averages of temperature monitor values
are desired they are performed after the plant subroutine by operating
on the observed upstream
and downstream temperatures, and the calculated
plant induced river temperatures.
4.2.5
Best Mode
The best mode of operation is selected on the basis of the time
averaged or unaveraged temperatures depending on the objective of the
particular run.
In selecting the mode,power production is maximized
within the constraints of a maximum downstream river temperature and
a maximum change in temperature between the upstream and downstream
monitors.
This change in temperature is taken as the natural temperature
difference given by the upstream and downstream monitors plus the
calculated plant induced temperature change.
When the AT estimated by
the one-dimensional model is included,it is subtracted giving the total
32
AT=natural measured AT + calculated induced AT -1-D model's estimated
AT.
4.2.6
Cumulative Energy Lost
The hourly reduced power output caused by the plants compliance
to the river temperature standards is accumulated for the years operation.
This gives a measure of the energy lost in comparison to operating
entirely in open mode.
4.2.7
Output
Output from the program includes the calculated Browns
Ferry flow; induced AT and actual power output for each mode of operation
every hour, the condenser hot side temperature in closed mode, the
optimum mode within the temperature constraints, and the cumulative hourly
power lost by operating in the constrained modes rather than in open
mode.
4.3
Source of Performance
The condenser heat rejection curve and the power reduction
curve used in the actual plant load calculation; the cooling tower
performance curves; and the diffuser performance curves describing
the mixing of thermal discharge with the river were obtained from and
at one point used by TVA for the Browns Ferry Plant.
33
V
RESULTS OF COMPUTER SIMULATION OF PLANT OPERATION
A number of sensitivity studies of plant operation were carried
out with the model described in Section IV.
Sensitivity analysis
considered monitor location, spatial averaging of monitors, time averaging of monitors, and changes in environmental standards or plant
design.
The following subsections describe the results of these
studies along with the methods used to display the results and the
basis for result evaluation.
5.1
An Explanation of the Forms Used to Display Results of Computer
Simulation
The results of the computer evaluations for the sensitivity analyses
are presented in three ways:
1) a graph of the power output of the
plant in the best mode of operation, 2) a sorted display of how many
hours the plant had a reduced power output due to running in either
helper or closed mode and 3) the total cumulative output power loss for
the period of observation.
5.1.1
Power Output of the Plant in Best Mode of Operation
It is assumed that the plant would like to operate at full power,
3300 MWe, at all times during the year.
Some loss of power results when
higher water temperatures reaching the condenser cause a loss of thermal efficiency in the plant.
When river water temperatures reach
certain levels it is necessary to use a helper or closed mode of
operation to meet thermal standards.
These other modes of operation
require a significant amount of energy over and above the losses due
34
to thermal efficiencies.
The results of the sensitivity analyses are
graphically displayed as the power output of the plant in megawatts
electric (MWe) for each hour of the observation period (grouped by
Julian days).
The change in output for the plant often shows up as long
spikes due to the switching between various modes of operation in
response to changing river temperatures.
Figure 5.1 contains three
separate graphs showing what the power output of the plant would be
if it were run entirely in each mode of operation for the entire
period.
Each graph of the power output of the plant in best mode
can be thought of as a mixture of these curves.
The graphs take into
account the thermal inefficiency caused by higher river temperatures.
Figure 5.2 displays a typical evaluation result identifying basic
items that are common to most of the results.
This includes the
range of each mode of operation, seasonal periods, and constant open
cycle operations.
5.1.2
Sorted Power Losses
The power values determined frot the plant output in best mode
graphs were subtracted from the power of the plant if it was in open
mode.
These values of power losses, due to running the plant in helper
or closed modes, were sorted and displayed versus the number of hours
these values of power loss occurred.
Figure 5.3 shows a typical
example of a sorted power loss evaluation and points out the ranges
of open and closed modes of operation as well as some common factors
in some of the results.
35
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5.1.3
Cumulative Hourly Power Losses
Finally, the power losses, due to running the plant in helper
or closed mode, during the entire observation period were totaled and
are reported as the cumulative hourly power lost in megawatt hours.
These values do not consider the thermal inefficiencies of running
the plant (i.e. open mode losses have been kept out of the total).
Comparing the cumulative hourly power losses provides a good quick
method of comparing the results of each sensitivity analysis.
5.2
Base Cases
Two base cases are used in comparing the results of the sensitivity
analyses.
Data available from the plant consisted of temperature
readings at upstream station 6 and downstream stations 1,9,10 & 11
as shown in Figure 5.4.
downstream stations.
Evaluations were done comparing the individual
Station 9 showed the largest cumulative power
losses for all the downstream stations, hence, this case was chosen as a
basis for comparison.
Figures 5.5 and 5.6 show the base power output
in best mode graph and the sorted power losses curve, respectively for
Base Case A.
Base Case B used the idealized case where the natural upstream
temperature is considered equal to the natural downstream temperature.
In this case all the effect on the change in temperature in the river
between these two points its plant induced.
This base case can be
thought of as the lowest possible power losses since this only includes
the effects of river temperatures on the thermal efficiency of the
plant.
Figures 5.7 and 5.6 show the power output in best mode plot and
sorted power losses.
39
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D model described in Section
The use of the model by
3.0 was used on the Base Case A analysis.
itself cuts down on power losses significantly.
The sorted power
losses curve, Figure 5.6, actually comes about one half the way
between the two Base Cases.
A comparison of the power output in
best mode graphs Figure 5.8 to Figure 5.6 shows effects mostly in
the spring and the fall.
More use of helper mode occurs in the fall,
however, in the spring reduced power losses are shown where less
helper and closed modes are used.
5.3
Effects of Spatial and Time Averaging
The first set of sensitivity analyses considered the location of
the downstream monitor, the effect of averaging a set of monitors,
and time averaging a specific monitor.
The estimated AT
D model
was then used on each case to see if any monitors or averaging
techniques were specifically affected.
5.3.1
Monitor Location and Spatial Average
Data for downstream monitors offerred possible analysis of
Stations 9,10 & 11.
The Base Case chosen was Station 9 which resulted
in the worst power losses.
Figures 5.9 and 5.10 show the power output
in best mode plots for individual stations 10 & 11 respectively.
The
results show progressively less use of both helper and closed
modes as you go from Station 9 to Station 10 to mid-channel Station 11.
Downstream stations 9,10 & 11 data were averaged and analyzed to
determine the effect of spatial averaging.
output in best mode plot for the results.
44
Figure 5.11 shows the power
The spatial averaging offers
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less power losses in both the spring and the fall, but, actually uses
slightly more closed mode operation during the late summer period.
The estimated AT
D model was applied to the above cases with the
resulting power output in best mode plots shown in Figures 5.12,
5.13 and 5.14.
losses.
In all cases the use of the
D model lowers the power
In Figure 5.12 (Station 10) closed mode operation doesn't occur
in the spring.
Figure 5.13 (Station 11) shows only one hour of closed
mode operation except for the late summer periods.
Both stations
also show reductions in the use of helper mode operation.
of the
The use
D model with the Stations 9,10 & 11 (Figure 5.14) spatial
average reduces the use of cooling towers throughout the observation
period, except during late summer.
Reductions of helper mode are
also noticeable, but, not as much as with Station 10 & 11 separately.
Figure 5.15 shows a composite of the sorted power loss curves
for the above evaluations.
Station 10 shows slightly less losses than
the Stations 9,10 & 11 spatial average.
This is probably the case
due to the influence of Station 9 in the spatial average.
Station 11,
however, shows a lot less use of helper mode than the Station 10 or
Stations 9,10,11 spatial average.
channel location.
the estimated AT
This is probably due to its mid-
An interesting result occurs for the addition of
D model.
The model does better using the individual
stations than the spatial average, much more so than the difference
between the single station versus the spatial average without the
model.
49
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5.3.2
Time Averaging
The power output in best mode graphs shown in Figures 5.16 through
5.21 represent the effects of time averaging using Station 9 as the
downstream station.
Upstream, downstream, and induced river temperatures
were all time averaged before selecting the best mode of operation
within the standards constraints.
Periods of 2,24, and 48 hours were
examined both without the estimated AT
D model(Figures 5.16, 5.17,
and 5.18)and with it (Figures 5.19, 5.20, and 5.21). The Figures are
compared with Base Case A, Figure 5.5, and Base Case A with estimated
AT
D Model, Figure 5.8.
In general increased time averaging of river temperatures and
induced temperatures decreases power loss by removing or decreasing
some of the temperature excursions above the standard's limit.
In
decreasing this variance, some short term violations causing the plant
to switch from open to helper (or helper to closed) have been reduced.
This is particularly true during spring heat up periods (see the spring
periods of the power output in the best mode graphs). Note, however,
that the same mechanism operates in reverse.
There are periods where
short term temperature dips allowing the plant to switch from helper
to open (or closed to helper) are being removed by increased time
averaging resulting in increased power loss.
This reverse mechanism
is most important during fall cool down (see fall portions of power
output graphs).
The net effect for the year is decreased power loss with increasing
temperature averaging, but a few exceptions in our results demonstrate
the importance of the mechanism operating in reverse.
54
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60
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D Model's estimated AT) where going
one case (Station 9 including the
from no averaging to a two hour running average increased the year's cumulative power loss (see Table of Cumulative Power Loss, Sec. 5.5) in contrast
to the general trend.
Also observe the reversal in the sorted power
loss curves (Figure 5.22).
Here generally curves with increasing time
averaging are lower than curves with less time averaging and spend less
time off of closed mode as illustrated by the intersection point with
the time axis.
The result is lower cumulative power loss (the area
under the sort curves) for cases with more time averaging.
There's
one area where the curves cross however, between 10-20 days which
represents in terms of operating time the shift from closed to helper.
The crossing here suggests time averaging is causing the plant to
operate more hours in closed mode.
Power loss is decreased for all running averages by including the
1D Model's estimated AT.
Neglecting that gain, the gain in power
production for going to a 48 hour running average from no time averaging
is about the same if we include the
D model's AT or not.
If running
averaging is increased beyond 48 hours, the gain in power production
can be expected to approach a limit.
The limit will be less than our
limiting case where natural downstream temperature was set equal to
the natural upstream temperature (see Base Case B curve Figure 5,22)
and in some cases the power production of the 48 hour time average of
the spatial average of Stations 9,10, & 11 was better than the natural
upstream = natural downstream temp. Base Case B (see following
section).
61
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5.3.3
Combined Spatial and Time Averaging
In order to assess the limit of various averaging techniques a
spatial average of downstream Stations 9, 10, & 11 was combined with
a 48 hour running average of the downstream temperatures.
Figure 5.23
shows the results as the power output in best mode graph.
The general
character of the graph follows the effect of the 48 hour running
average by smoothing out the operation periods.
The addition of
the spatial average cuts down on losses primarily in late summer
and the early spring.
Adding the estimated AT
D Model to the combined averages cuts
out more helper and closed more operation especially in the spring,
but, adds some helper operation in the fall.
This is shown in Figure
5.24.
Figure 5.25 shows the composite of the sorted power loss curves
for the combined averaging, combined averaging with
Base Cases.
D Model, and the
An interesting situation occurs when the use of the combined
averaging with the estimated AT
than the upstream station.
D Model gives lower temperatures
This appears during the closed mode-operation
at the top of the curve.
5.4
Sensitivity to Changes in Environmental Standards of Plant Design
All the following analyses used upstream Station 6 and downstream
Station 9 as a basis and an observation period of April 1 through
November 1. Analyses of the effects of using the estimated change in
temperature
D Model or averaging methods were not considered.
was our effort to get an idea of critical areas in the standards
63
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and plant design that may significantly influence power losses,
and to gain an approximate magnitude of their significance.
5.4.1
Changes in Environmental Thermal Standards
Both the maximum allowable change in temperature from upstream to
downstream station plus the maximum allowable temperature in the
river were considered.
At the present these standards are 5F for
maximum change in temperature and 86°F maximum allowable temperature.
The first case considered changing the maximum allowable change
in temperature to 3F. The results are shown in Figure 5.26 as the
power output in best mode graph.
Considerable use of both helper
and closed modes of operation is needed except for the late summer
period.
The second case used an allowable change in temperature of 10°F,
Figure 5.27.
The late summer period is unaffected since maximum
temperature is the overriding factor in this period.
However, during
the fall and the spring a substantial savings of power loss can be
found.
The third case considered a 90°F maximum allowable temperature.
Figure 5.28 shows that less power losses occur during the summer
period as expected since the maximum allowable temperature is the
overriding factor in cooling tower usage during this period.
Last of all, both a maximum allowable change in temperature of
3°F and a maximum allowable temperature of 90°F were used for an analysis.
Figure 5.29 shows use of the helper mode only during the late summer
period and in late April.
Cooling towers were only used once during
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Figure 5.30 shows a comparison of the sorted power loss curves for
the sensitivity of the thermal standards.
Base Case A.
Station 9 is plotted as the
All sorted power loss curves show reduced power losses
except AT = 3°F, which has a large amount of losses in this analysis.
The tradeoff between the maximum allowable temperature of 90 °F
and the maximum AT of 10°F can be seen quite explicitly.
The AT = 10°F
analysis does not save as much on the helper mode, but, does save on
high power losses occuring in the spring, and the fall.
The maximum
temperature of 90 °F shows a reduction in a lot of the helper mode
operation, but, the high spring time losses are not influenced
at all.
The combination of AT = 10°F and the maximum temperature
of 90°F shows the expected drastic reduction in losses for the
observation period.
5.4.2
Existence of Various Modes of Operation
The possibilities for analyzing various possible modes of operation
included all open mode, no open mode, no helper mode (open/closed) and
no open or helper mode (only closed).
All open mode operation and all closed mode of operation is shown in
Figure 5.1.
Oen mode losses occur when there is a reduced plant thermal
efficiency due to high natural river temperatures.
All closed mode always
has power losses attributed to it due to cooling tower operation.
The other possibilities are no open (Figure 5.31) and no helper
mode (Figure 5.32).
to helper mode.
The no open analysis just shifts all open mode use
In the no helper mode,all helper mode use is shifted
72
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to closed mode.
The results of these analyses are shown in the composite
sorted power loss Figure 5.33.
The significance of each is better
described by the use of the cumulative hourly power losses.
case all open mode is considered as having no losses.
In this
The other results
are shown in Table 5.1.
Table 5.1
Cumulative Hourly Power Loss, M- hr
Mode
All Open
0
No Open
481,040
No Helper
145,664
No Open or Helper (All Closed)
911,858
Base Case A (Station 9)
96,044
5.4.3
Changes in Plant Design
Diffuser mixing and cooling tower performance were the two
areas in plant design that were evaluated.
Increased or decreased
performance was considered for each design.
For diffuser mixing the area of the jet ports was varied to
either increase or decrease mixing.
In the first case (Figures 5.34)
the total area was decreased by 50%. This has the effect of increasing
exit velocity out the diffuser and increasing mixing.
The second case
(Figure 5.35) increased the total area of the jet ports by 400%.
This has the effect of modeling decreased mixing.
Figure 5.36 shows
the sorted power losses for both cases as compared to the Base Case A
(Station 9).
As expected the decreased mixing case shows significantly
76
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more losses for the helper mode of operation, but, not much for the
closed mode.
An interesting result is found for the increased mixing
case which is almost exactly the same as the Base Case.
Hence, the
design of the diffusers at the present time does about as best as
can be done.
Cooling tower performance was varied by subtracting 5°F from
the wet bulb temperature to model increased cooling performance and
adding 5F to the wet bulb temperature to model decreased cooling
performance.
Figures 5.37 and 5.38 show the power output in best mode
graphs for the increased cooling and decreased cooling respectively.
Figure 5.39 shows the combined sorted power loss curves as compared
to the Base Case A. As expected differences only appear in the closed
mode of operation range.
5.5
Summary and Display of Cumulative Hourly Power Losses
This section summarizes the results of the sensitivity analyses
by displaying the cumulative hourly power losses for each of the
evaluations, Table 5.2.
text.
The evaluations are grouped as appears in
These numbers represent losses greater than the plant thermal
inefficiencies that would be experienced if the plant ran in open
mode.
It is apparant for spatial and time averaging that selection of
the downstream monitor is important.
Adding various time running
averages will decrease power losses somewhat.
Using the estimated AT 1D
model reduces power losses significantly in all cases.
spatial and time averaging plus the AT
81
Combining
D model gave the lowest power
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Figure 5.39
Comparison of Sorted Power Loss Curves for
Cooling Tower Performance Study
Table 5.2 Display of Cumulative Hourly Power Losses
Cumulative Hourly
Power Loss (MW hr.)
Analysis
5.2
5.3
Base Cases
Base Case A, Downstream Station 9
96,044
Base Case B, Upstream Equals Downstream
63,542
Base Case A With Estimated AT lD Model
83,018
Spatial and Time Averaging
5.3.1
Monitor Location and Spatial Averaging
Downstream Station 10
80,865
Downstream Station 11
78,327
Spatial Average of Downstream Stations 9,10, & 11
82,485
Downstream Station 10 With Estimated AT
D Model
69,504
Downstream Station 11 With Estimated AT
D Model
69,557
Stations 9,10, & 11 Spatial Average With Estimated
AT
5.3.2
71,599
D Model
Time Averaging
2 Hour Running Average of Station 9
95,963
24 Hour Running Average of Station 9
92,280
48 Hour Running Average of Station 9
90,490
2 Hour Running Average of Station 9 With Estimated
83,280
AT 1D Model
24 Hour Running Average of Station 9 With Estimated
78,890
AT 1D Model
48 Hour Running Average of Station 9 With Estimated
AT 1D Model
85
77,726
Table 5.2 (cont.)
Cumulative Hourly
Power Loss (MW hr.)
Analysis
5.3.3
Combined Spatial and Time Averaging
Stations 9,10,& 11 Spatial Average and 48 Hour
76,650
Running Average
Stations 9,10,& 11 Spatial Average and 48 Hour
Running Average with Estimated AT
67,188
D Model
5.4.0 Sensitivity to Changes in Environmental Standards
or Plant Design
5.4.1
Changes in Environmental Thermal Standards
Maximum Allowable AT of 3 F
268,732
Maximum Allowable AT of 100F
68,667
Maximum Allowable River Temperature of 90°F
41,734
Maximum Allowable AT of 10°F and Maximum Allowable
7,543
River Temperature of 90 F
5.4.2
5.4.3
Existence of Various Modes of Operation
All Open Mode Operation
0
No Open Mode Operation
481,040
No Helper Mode Operation
145,664
All Closed Mode Operation (No Open or Helper)
911,858
Changes In Plant Design
Increased Diffuser Mixing
95,960
Decreased Diffuser Mixing
120,807
Increased Cooling Tower Performance
91?438
Decreased Cooling Tower Performance
103,718
86
losses and approached the Base Case B value,
In the environmental standards and plant design analyses the
values speak for themselves.
Interestingly, the maximum allowable
river temperature of 90°F has significantly less losses than the
maximum allowable change in temperature of 10°F.
Also, as seen from
analyses of the power output in best mode graphs, the savings occur
during the late summer period when maximum power output is more
important.
87
VI.
Comparison with Operating Data
The Browns Ferry Nuclear Plant went back into full operation
late in the year 1976.
From available data,the period January through
October 1977 was used to compare the natural and plant induced temperature models with a period of actual plant operation.
of:
This work consisted
recalibrating the natural temperature difference model (Section III)
to take into account a new set of instream monitors; utilizing meteorological
data, river flows,and instream monitor data to produce a natural temperature
difference prediction for the year 1977; revising the plant simulation
model (Section IV); and finally, comparing the two model results with
1977 data from the instream monitors used for compliance purposes.
6.1
Recalibration of Natural Temperature Difference Model
On several occasions during the years 1975 and 1976, the
thermal instream monitors showed the plant in violation of its maximum
allowable temperature rise of 5F.
After analyzing the situations, it was
discovered the violations were caused by natural temperature variations
and not the plant.
TVA decided to change the primary upstream monitor
to station 4 thereby decreasing the distance between upstream and downstream
monitors from 15 miles to about 5 miles.
It was also decided to remove
station 6, and replace station 9 with station 13 (which is farther from
the right bank and less affected by natural heating).
Figure 6.1
shows the locations of the new monitors.
In order to represent the actual situation at the site, the
natural temperature difference model was re-evaluated for the stretch
of the river from station 4 to stations 10, 11 and 13 (the previous analysis
presented in SectionIII was for station 6 to station 1).
88
The model
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corrections needed consisted of a change in the river length and the
average cross sectional area.
Figure 6.2 shows the calibration of the
model using average cross sections as compared to measured data for
the years 1975 and 1976.
An area equal to 100,000 ft2 was found to
best fit the measured data (stations 9, 10, 11 minus station 4) for the
period when the plant was not
n operation.
The increase in cross
sectional area is physically reasonable since the previous stretch of
river (station 6 to station 1) consisted of narrower channeled flow in
the upstream region.
Figure 6.3 shows the difference of the measured
The model does quite well except for a
minus the predicted variation.
slight negative offset occurring in the summer months.
6.2
1977 Natural Temperature Difference Prediction
Meteorological data for Huntsville, Alabama were obtained from
the National Weather Service for the period January 1, 1977 to the end
of October, 1977, which was the latest verified data available at the
time of our analysis.
It was determined that the temperature effects
in November and December were not significant since this is usually a
time when the plant complies very well to its thermal standards.
Figures
6.4, 6.5, 6.6 show forty-nine hour running averages of the ambient air
temperatures,
relative humidity, and wind speeds for this period.
This
meteorological information along wth forty-nine hour running averages
of air pressure, completed solar flux, and computed atmospheric flux
we re ulsed
net flux is
to coiiipWtte
shown in
nut flux
s des, rlibcd
Figure 6.7.
In Sectioon
11.
Th'le resultting
The magnitudes of the flux during various
seasonal periods agree with te previous 1975, 1976 data.
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The recalibrated natural temperature model (Section 6.1) was
run using the following 1977 data:
forty-nine hour running averaged river
flows at the Browns Ferry site and upstream station 4 temperature
measurements, and the net flux (calculated using forty-nine hour averaged
inputs).
The river flow at the Browns Ferry site was determined from
a two term equation utilizing flow values from Guntersville and Wheeler
Dams.
The discharges from Guntersville and Wheeler Dams are shown in
Figures 6.8 and 6.9 respectively.
The calculated hourly flow at
Browns Ferry is shown in Figure 6.10 while the forty-nine hour running
averages are shown in Figure 6.11.
Figures 6.12 and 6.13 show the
temperature measurements at station 4, 5 foot depth, for hourly and
forty-nine hour running averaged values.
The resulting natural temperature
difference prediction for the 1977 period is shown in Figure 6.14.
The
magnitudes of the natural temperature variation are lower than the
previous analysis (Section III) since the travel distance was cut
down substantially.
However, variations approach .75 to 1.0°F frequently
during the year showing there is still a significant natural temperature
difference to be accounted for.
6.3
Revised Plant Induced Temperature Simulation Model
The simulation model described in Section IV was modified to
better describe real time plant operation.
The major revisions to the
model centered around accepting individual unit load values (as opposed
to one target plant load), using given cooling mode usage, and considering
only predicted plant induced temperature rise.
The revised model uses
hourly wet bulb temperatures, unit loads, cooling modes, and river flows
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at Browns Ferry for input and determines the total plant induced
temperature rise predicted for the total three units.
The total hourly
plant loads (3 units combined) are shown in Figure 6.15.
6.4
Comparison of Model Results with Measured Temperature Differences
The results of the 1-D natural temperature difference model
and the plant induced temperature simulation model were compared with
the measured temperature difference from the instream monitors.
Evaluations of the differences in instream monitor readings show there
is quite a variation in values of measured temperature differences (ATs).
Figure 6.16 shows the individual ATs for downstream stations 10, 11 and
13 minus station 4.
To alleviate this problem, an average of the three
downstream stations is used in the model comparisons.
Figure 6.17
shows this averaged value minus station 4 on an hourly basis.
Figure
6.18 shows a forty-nine hour running average of measured spatially
averaged ATs that are used in the actual comparison.
The predicted natural temperature difference was subtracted
from the measured averaged temperature difference to obtain a corrected
measured AT.
This corrected measured AT was then compared to the
plant temperature rise prediction, Figure 6.19.
The residual series
obtained by subtracting the corrected measured AT from the predicted
plant induced temperature difference is shown in Figure 6.20.
There is
better agreement of the predicted plant versus corrected measured values
for winter, early spring, and fall periods.
Several occurances of high predicted
plant temperatures versus low corrected measured temperatures are apparent.
occurances appear to be correllated with minimums in river flows.
It is
possible that during these low flow situations upstream station 4 may be
105
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4J
influenced by warmer water resulting from plant operation or natural
solar heating causing the measured temperature difference to be small.
The influence of natural or artificial heat at station 4 may also be the
cause of the overestimation of upstream-downstream temperature differences.
112
REFERENCES
Almquist, Charles W., "A Simple Model for the Calculation of Traverse
Mixing in Rivers with Application to the Watts Bar Nuclear Plant,"
TVA Division of Water Management, Water Systems Development Branch,
Report No. 9-2012, Norris, Tennessee, March, 1977.
Atomic Energy Commission, Browns Ferry Nuclear Plant Units 1,2,3 Environmental Statement, July, 1971.
Freudberg, S.A., "Modeling of Natural River Temperature Fluctuations,"
S.M. Thesis, M.I.T., September, 1977.
Harleman, D. R. F., Hall, L., and Curtis, T. G., "Thermal Diffusion of
Condenser Water in a River During Steady and Unsteady Flows with
Application to the T.V.A. Browns Ferry Nuclear Power Plant," M.I.T.
Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics,
Technical Report No. 111, Sept., 1968.
Ryan, Patrick J., and Harleman, Donald R. F., "An Analytical and
Experimental Study of Transient Cooling Pond Behavior," M.I.T. Parsons
Laboratory for Water Resources and Hydrodynamics, Technical Report No.
161, January, 1973.
Tennessee Valley Authority, "Monitoring of Water Temperatures in Wheeler
Reservoir to Determine Compliance of Browns Ferry Nuclear Plant with
Water Temperature Standards," TVA Division of Water Control Planning,
Browns Ferry Nuclear Plant Advance Report No. 21, Norris, Tennessee,
May, 1974.
113
APPENDIX
A
EQUATIONS TO COMPUTE NET HEAT FLUX
The basic equation used is:
*'
Fin
6e2)
4 '+Jwa)
[(e6- e')a])
0255(s
( A-i)
where
n
n
r
= net heat flux, BTU/ft -day
=
net solar plus atmospheric flux, BTU/ft 2 -day
T
= water surface temperature, °F
T
= ambient air temperature, °F
e
= saturated vapor pressure (mm Hg) at the temperature
s
a
of the water surface given by:
e
s
= - 2.4875 + 0.2907T
s
- 0.00445T
23
S
+ 0,0000663T
s
ea = vapor pressure of ambient air, mm Hg, given by:
x (- 2.4875 + 0.2 9 07 Ta - 0.00445Ta
ea = (oo)
where
+ 0.0000663T 3 )
RH = relative humidity in %
f(W2 ) is a wind function based on a virtual temperature difference and
the wind speed at 2 meters, W 2,
(in miles per hour) above the water
surface given by either:
(w
2
) =
f(w 2 )
=
22./
(,
+
( A-2)
( A-3)
/
114
The choice of
A-2 or
A-3 depends on:
a Ov -
where
A
"7t
Tv = (T + 460)/(1 - 0.378 e /p)
S
S
SV
T
= (T
p
= ambient air pressure, mm Hg
av
If
7,sv -
aa
+ 460)/(1 - 0.378 e /p)
3
< 0.0024W23, use
Elseuse
A-2
Else use
A-2
A-3
115
Work reported in this document was sponsored by the Department of Energy
under contract No. EY-76-S-02-4114,AO01. This report was prepared as an
account or work sponsored by the United States Government. Neither the
United States nor the United States Department of Energy, nor any of their
employees, makes any warranty, express or implied, or assumes any legal
liability or responsibility for the accuracy, completeness, or usefulness of
any information, apparatus, product or process disclosed or represents that
its use would not infringe privately owned rights.