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.,

Adams, E.E., Jirka, G.H., and Harleman, D.R.F., IT Energy.

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,"

by Shaw, J.J., Adams, E.E., Barbera, R.J., Arntzen, B.C,, and

Harleman, D.R.F., MIT Energy I.abl)oratory Report o. MIT-EL 79-038,

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 5

Study

2.1 Wheeler Reservoir 5

2.2 The Cooling System 7

2.3 Temperature Data Collected in Wheeler Reservoir 9

III. Modeling the National Temperature Difference in Wheeler 12

Reservoir

3.1 One-Dimensional Formulation 13

3.2 Input Data 17

IV. Simulation of Plant Operation 26

4.1 Main Simulation Cycles 26

4.2 Simulation Subroutines 28

4.2.1 Input 28

4.2.2 Browns Ferry Flow 28

4.2.3 Plant Subroutine 28

4.2.4 Running Averages 32

4.2.5 Best Mode 32

4.2.6 Cumulative Energy Lost 33

4.2.7 Output 33

4.3 Source of Performance 33

V. Results of Computer Simulation of Plant Operation 34

5.1 An Explanation of the Forms Used to Display Results of 34

Computer Simulation

5.1.1 Power Output of the Plant in Best Mode of Operation 34

5.1.2 Sorted Power Losses 35

5.1.3 Cumulative Hourly Power Losses 39

V
5.2 Base Cases 39

5.3 Effects of Spatial and Time Averaging 44

5.3.1 Monitor Location and Spatial Average 44

5.3.2 Time Averaging 54

5.3.3 Combined Spatial and Time Averaging 63

5.4 Sensitivity to Changes in Environmental Standards 63

of Plant Design

5.4.1 Changes in Environmental Thermal Standards 67

5.4.2 Existence of Various Modes of Operation 72

5.4.3 Changes in Plant Design 76

5.5 Summary and Display of Cumulative Hourly Power Losses 81

VI Comparison with Operating Data 88

6.1 Recalibration of Natural Temperature Difference Model 88

6.2 1977 Natural Temperature Difference Prediction 90

6.3 Revised Plant Induced Temperature Simulation Model 97

6.4 Comparison of Model Results with Measured Temperature 105

Differences

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 10F) 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

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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 SHALLOW AREA

Figure 2.2 Location of Diffuser In Tennessee River

Near Browns Ferry Nuclear Plant Station

100
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. The location of the sampling stations is depicted

in Fig. 2.4. 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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C , j ' '1 2o tx

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w w H~~~~~~~~S '- z z 40H

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~~~~~~

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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. The period of record is from April 1, 1975

through March 31, 1976. 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 temperatures 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

- gd (A T) ()gn x (3.1-1)

where: T is

A is

t is

x is

E is

~n(t)

B (x)

is

and c is

the cross-sectional average temperature

the cross-sectional area

time

the longitudinal position from the upstream station

a diffusion coefficient

is the net heat flux, a function of time

is the width, variable with distance along the river

the density of water, assumed constant

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 = 4 (E '0 ) , * x (F£ 0 ) 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

9TA

al t

4- A"

GI x
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 ate 0a2e Ar ~._.~.T -I- U ~..__~T = E 09 ~ T /~ z~'7'c ~ (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 . -d

,~ , y 7' E< 2 ~g X 7(3.1-4)

z L2 h

If each parameter above is divided through by VT'/L to produce nondimensional parameters, then this results in:

[-1 Ii [ I

®0 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. Using the

1/'
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 ~__0 + a ~_r - ( 6) (3.1-6)

t k e- oh

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 = () (3.1-7)

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

76V= b 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

{-of (3.1-10)

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

i-de (3.1-11)

Thus, it is seen that t is itself a function of time.

For the natural AT at time t defined by:

7 = (-) 7 A F () (3.1-12) d a

16
equation 3.1-9 combined with 3.1-12 yields:

Ao£ =-/z Jf;; ,(' y-[;6J4K--{ (3.1-13)

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
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Io

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1t

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r-I

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fa

r4

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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.

19

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
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

1975. Only 3/4 of the year is shown because the flow and meteorological

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 -D

model. 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. The best

20O
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

Figure 3.2. As is seen, the model is a reasonable fit on a monthly

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

dramatically illustrated in Figure 3.3, As is seen the model

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 cooldown in the fall is a far more complex process. Unlike the spring

21
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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. This residual series has a mean of 0.12'F and a variance of

2 0.34°F 2. Thus the variance of the data has been reduced roughly 40%

using the 1-D model.

24
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25
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. The results of the

simulation are presented in the next section. 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:

1. Releases from the upstream (Guntersville) and downstream

(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 TIME = BEGINNING HOUR

TIME + ONE HOUR

1

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

CALCULATE RIVER FLOW AT BROWNS FERRY

| , a, , -

| ~PLANT OPERATION SUBROUTINE|

_~~~~~~~~t

| ~~MONITOR DATAl

MODE SELETO

,~~~~ I

COMUT CUMULATIVE ENERGY LOST|

4~~~~~~~~~~~~

I

I , , ,11 , .!@~

OUTPUT

T

K TIME < FINAL HOUR T__

Figure 4.1 Overall Logic Diagram for Simulation of Plant Operation

27

I

r- I

t

[

4

-- __ { [[[

w [[ [~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I II ~ 1 [ [ 

- . .I[
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) of the previous hours

flow calculation. 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 temperature 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
MODE = HELPER M

CONDENSER INTAKE TEMP. = RIVER TEMP.

- 4-- 

COOLING TOWER PERFORMANCE:

CALCULATE TOWER COLD SIDE TEMP.

ITERATION

T CHECK:

AT ACROSS TOWERS

= AT ACROSS

CONDENSER

_ J ,

DIFFUSER PERFORMANCE:

CALCULATE INDUCED TEMP. CHANGE

I E 

(RETURN

Figure 4.2 Flow Chart for Plant Subroutine

30

fl 

INITIAL ITERATION:

CONDENSER INTAKE

TEMP. = RIVER

TEMP.

1'

CONDENSER INTAKE

TEMP. = COOLING

TOWER COLD SIDE

TEMP.

CALCULATE ACTUAL PLANT LOAD AND CONDENSER HOT SIDE TENP.

,F wIt

DISCHARGE TEMP.

= CONDENSER HOT

SIDE TEMP.

DISCHARGE TEMP.

= TOWER COLD

SIDE TEMP.

F

-I

MODE = OPEN

.

MODE = CLOSED

Il !

. __ _ .

i i II r~~~~~~~ 

_ !

ii !

- .

.

L

F

I!i, I

_ .

i

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

J

T

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

!

I _
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. Evaluations were done comparing the individual

downstream stations. 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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The change in temperature estimating D model described in Section

3.0 was used on the Base Case A analysis. The use of the model by

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. Figure 5.11 shows the power

output in best mode plot for the results. The spatial averaging offers

44
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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. In all cases the use of the D model lowers the power

losses. 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. The use

of the 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. This is probably due to its midchannel location. An interesting result occurs for the addition of

the estimated AT 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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53
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. Note there is

54
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one case (Station 9 including the D Model's estimated AT) where going

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 D Model, and the

Base Cases. An interesting situation occurs when the use of the combined

averaging with the estimated AT D Model gives lower temperatures

than the upstream station. 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. It

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

67
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T
the entire period.

Figure 5.30 shows a comparison of the sorted power loss curves for

the sensitivity of the thermal standards. Station 9 is plotted as the

Base Case A. 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). The no open analysis just shifts all open mode use

to helper mode. In the no helper mode,all helper mode use is shifted

72
co

Cl)

c~

c4XEo

4-J U)

L.,. p0.t-J

r. 4.J

Ca

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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. In this

case all open mode is considered as having no losses. The other results

are shown in Table 5.1.

Table 5.1

Mode Cumulative Hourly Power Loss, M- hr

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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41
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. The evaluations are grouped as appears in

text. 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. Combining

spatial and time averaging plus the AT D model gave the lowest power

81
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-------

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APL,

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'" Decreased Conling Tover Performance

.-e s Came 

increased CoolingX Tower Performance

Figure 5.39 Comparison of Sorted Power Loss Curves for

Cooling Tower Performance Study

I

I
Table 5.2 Display of Cumulative Hourly Power Losses

Cumulative Hourly

Analysis Power Loss (MW hr.)

5.2 Base

Base

Base

Base

Cases

Case A, Downstream Station 9

Case B, Upstream Equals Downstream

Case A With Estimated AT lD Model

5.3 Spatial and Time Averaging

5.3.1 Monitor Location and Spatial Averaging

Downstream Station 10

Downstream Station 11

Spatial Average of Downstream Stations 9,10, & 11

Downstream Station 10 With Estimated AT D Model

Downstream Station 11 With Estimated AT D Model

Stations 9,10, & 11 Spatial Average With Estimated

AT D Model 

96,044

63,542

83,018

80,865

78,327

82,485

69,504

69,557

71,599

5.3.2 Time Averaging

2 Hour Running Average of

24 Hour Running Average of

48 Hour Running Average of

2 Hour Running Average of

AT 1D Model

24 Hour Running Average of

AT 1D Model

48 Hour Running Average of

AT 1D Model

Station 9

Station 9

Station 9

Station 9 With Estimated

Station 9 With Estimated

Station 9 With Estimated

85

95,963

92,280

90,490

83,280

78,890

77,726
Table 5.2 (cont.)

Cumulative Hourly

Analysis Power Loss (MW hr.)

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 67,188

Running Average with Estimated AT 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 10 0F 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 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

5.4.3 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. This work consisted

of: 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). The model

88
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0

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e
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

minus the predicted variation. The model does quite well except for a

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 to coiiipWtte nut flux s des, rlibcd In Sectioon 11. Th'le resultting

net flux is shown in Figure 6.7. The magnitudes of the flux during various

seasonal periods agree with te previous 1975, 1976 data.

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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. These

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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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 = net heat flux, BTU/ft -day n

r = net solar plus atmospheric flux, BTU/ft2 -day

T = water surface temperature, °F s

T = ambient air temperature, °F

a

e = saturated vapor pressure (mm Hg) at the temperature

of the water surface given by:

23

e = - 2.4875 + 0.2907T - 0.00445T + 0,0000663T s s S s

ea = vapor pressure of ambient air, mm Hg, given by:

ea = (oo) x (- 2.4875 + 0.2 9 07Ta - 0.00445Ta + 0.0000663T 3 )

where RH = relative humidity in %

f(W2) is a wind function based on a virtual temperature difference and

the wind speed at 2 meters, W2, (in miles per hour) above the water

surface given by either:

(w 2 ) = 22./ (, + ( A-2)

f(w 2 ) = / ( A-3)

114
The choice of A-2 or A-3 depends on:

a Ov - 7,sv - "7t

where Tv = (T + 460)/(1 - 0.378 e /p) SV S S

T = (T + 460)/(1 - 0.378 e /p) av aa

p = ambient air pressure, mm Hg

3 - If A < 0.0024W23, use A-3

Else use A-2

Else use A-2

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.