OPERATIONAL ISSUES INVOLVINGUSE OF SUPPLEMENTARY COOLING TOWERS TO MEET STREAM TEMPERATURE STANDARDS

WITH APPLICATION TO THE BROWNS FERRYNUCLEAR PLANT by Keith D. Stolzenbach, Stuart A. Freudberg Peter Ostrowski and JohnA. Rhodes Energy Laboratory Report No. MIT-EL 79-036 January 1979COO-4114-7
OPERATIONAL ISSUES INVOLVINGUSE 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 1979ABSTRACT A mixedmode 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 tomeet 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 bemet, and the monitoring system and associated decision rules used to determinewhen 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 bothwith 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 bya 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 themixed 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 ofan interdisciplinary effort by the IT Energy Laboratory to examine issues of power plant cooling system design and operationunder environmental constraints. The effort has involved participation byresearchers in the R.M. Parsons Laboratory for ater Resources and Hydrodynamicsof the CivilEngineering Department and the Heat Transfer Laboratory of theMechanical Engineering Department. Financial support for this research effort has beenprovided by the Division of EnvironmentalControl Technology, U.S. Dept. of Energy, under ContractNo. EY-76-S-02-4114.A001. The assistance of Dr. WilliamMott, Dr.MyronGottlieb andMr. Charles Grua of DOE/ECT is gratefullyacknowledged. Reports published under this sponsorship include: "Computer Optimization ofDry 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 theMITAdvancedWet/Dry Cooling Tower Concept for Power Plants," by Choi, M., and Glicksman, L.R., MIT Energy LaboratoryReport 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 EnergyLaboratory 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: ANational 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 PredictiveModels for Cooling onds and Lakes," Part B: User's Manual andApplications of 'ITE:P by Octavio, K.H., Watanabe,M., Adams, E.E., Jirka, G.H., Helfrich, K.R., and Harleman, D.R.F.; andPart C: A Transient nalyticalModel for Shallow Cooling Ponds, byAdams, E.E., and Koussis, A., MIT Energy LaboratoryReport No. IT-EL 79-039, December 1979. "SummaryReport 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 sitewas provided by the Water Systems Development Branch, Division ofWater Management, of the TennesseeValley Authority. The studywould nothave been possiblewithout the cooperation of Mr. ElyDriver, Dr. William Waldrop, Mr. Christopher Ungate, andMr. Charles W.Almquist of TVA.

ivTABLE OF CONTENTS Page TITLE PAGE i ABSTRACT ii ACKNOWLEDGEMENTS iii TABLE OF CONTENTS V I. Introduction 1 II. Description of the Browns FerryNuclear 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 V5.2 Base Cases 39 5.3 Effects of Spatial and TimeAveraging 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 ofModel Results with Measured Temperature 105 Differences REFERENCES 113 APPENDIX A 114

viOPERATIONAL ISSUES INVOLVING USE OF SUPPLEMENTARY COOLING TOWERS TO MEET STREAM TEMPERATURE STANDARDS

WITH APPLICATION TO THE BROWNS FERRYNUCLEAR 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 examplehas 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. 1First, 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 simulationmodel is then used to compare ayear 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 simulationmodel 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 significantvariability in water temperature over awide range of space and time scales. 2

### The difference between temperatures measuredupstream and downstream from the plant during apre-operational period are the same order of magnitude (5°F) as themaximum induced temperature increase permitted by the regulatory standard. 2. Apredictivemodel for the upstream - downstream natural temperature differences iscapable of accounting for 40% of the observedvariability. This estimate,which isbased upon local hydrological andmeteorological data,primarily addresses the temperature changes occurring overperiods of days tomonths rather than diurnal variations which are found to be quite random innature. 3. Theplant simulationmodel provided agood estimate of the induced river temperature rise (within 10

### F)except for periods when the upstream temperaturemonitors were affectedby seasonal stratifications not accounted for in the natural temperature model whichwas used to isolate the plant induced effect from thenaturally 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) Amixed 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 inlost capacity. Compared to the influence ofenvironmental 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 amixed 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 reductionmay be obtained by spatial and temporal averaging of temperature monitor measurements.

4II. 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 anet 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 2dams: 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-H 0 4J 4- 0 P-4 pH a)

I) 0 0 

### ~4) P-- U

0 4 0 F.>> (f2 O-J Fa) Uc 3 to rl 4z c) Co .1H

6 f z

### 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 systemwhich 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
0 10

### construct 6mechanical draft cooling towers. To increase their versatility, the cooling towers were designed to operate in twomodes: "helper-mode" and "closed-cyclemode." In thehelper mode, condenser cooling waterpasses through the towers, is cooled down to within several degrees fahrenheit of the wetbulb temperature, and returned to the river. The discharge rate for helper mode is 3675 cfs. As ageneral rule, the discharge temperature usinghelper mode isless than that of openmode, although this may not be the case during times of high wet bulb temperature. In closed-cyclemode, 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 waterneeded for the unit due to evaporative losses in this mode isapproximately 220 cfs. The option of three cooling modes (open, helper, and closed-cycle) make the cooling system at Browns Ferryunique among power stations. A schematic of the condenser coolingmodes isgiven inFig. 2.3. 2.3 Temperature Data Collected inWheelerReservoir Because of the presence of the Browns Ferry Station, extensive water temperature records have been collected documenting conditions in Wheeler Reservoir since 1968. Atpresent, there are 12 stations located along the river at which temperature data is collected at least every hour. In addition the temperature ismeasured at Guntersville andWheeler Dams. The location of the sampling stations isdepicted in Fig. 2.4. At the monitors closest to Browns Ferry (these are labelled Station 1,9,10 and 11) and at the furthest upstreammonitor (Station 6), temperature data is collected every 15 minutes. 9(3~~~~~~~~~~~~,

- C~~~~~~~~. - '4 rp~~~~~~~~~~~~~~~~$ -.- I >? t..i f- j l C,- C '1 , j ' 2o tx
1'4 C
140~~~~~~~~~~ . .O0 Ua ww H~~~~~~~~S '- z z

40H a:
- 

## ~~~~~~ ~~~~o ww.

4C 0 .'I-

a:. Z W 0 , 4 0 0 

### ~4 a, I U Z 4ass 0 a:~~~~~~~~~~~~~tt

.Za)

: C) U) 03 Cd~~~~~~~~~~: V

*.*A A 'C.. I -A C-) 10Each of the stations has avertical 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 ameteorological 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 theWater Systems Development Branch of TVA in Norris, Tennessee. The period of record is fromApril 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.

11III. 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 frommonitor #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 1will be large.

123.1 One-Dimensional Formulation The basic 1-dimensional convective diffusion equation is given by

- 

## gd (A T) 

## ()gnx (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 adiffusion coefficient

is the net heat flux, a function of time is the width, variable with distance along the river the density ofwater, assumed constant the heat capacity of water, assumed constant. If itis assumed that the cross-sectional area is constant along the reach from Station 6to Station 1,that thewidth is also constant, (their values are given bymeans) and that the flowdoes not vary as a function of distance butmayvary as afunction of time, then equation 3.1-1 becomes, upon dividing throughbyA:



## - 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 alt 

### 4- A" GIxIf 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 0 9~

### 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< ~g 

### 2 X 

### 7(3.1-4) 

# z L2 

# h If each parameter above is divided through by VT'/L to producenondimensional 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 6and 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 Vand L,Ewouldhave to be approximately 40,000 ft2

### /sec to make this parameter about 1. Almquist (1977) states that for the Tennessee River, avalue an order of magnitude lower of 1000 ft /sec isprobably a good estimate. Therefore, using the value 1000 ft /sec, [E/VL] has avalue <<1, and therefore the dispersion term shall be neglected. So the -Dequation 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 aparcelof water as it travels downstream from Station 6to Station 1. In Lagrangian coordinates, this may bewritten as amaterial derivative: 

## )r = 

## () (3.1-7) 7 

### cA Integrating this equation over time for theparcel yields: t 7,Hi)

## = 4 

## (I

## -zt)= | C 

## 6d) A 

### (3.1-8) where Td is the temperature of the downstreammonitor (Station 1), and T is the temperature of the upstreammonitor (Station 6). Amoment'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= d) 

# b (3.1-9) then it is seen that the downstream temperature at time t is aresult of thewater parcel's temperaturewhen itwas at the upstreammonitor At earlier plus the integrated net heat flux overAt the parcel received during its journey downstream. The correct definition for thisAt is the travel time for the parcel tomove from Station 6to Station 1. At is thus determined from: 

## udrz~L {-of (3.1-10) 

### whereL 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 afunction of time only, equation 3.1-10 becomes: 

## A i-de (3.1-11) Thus, it is seen that tis itself afunction of time. For the natural AT at time tdefined 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 differencebetween the two stations consists of two effects: thenet heat input overAt and the change in temperature at the upstreammonitor during At. Equation 3.1-13 represents the desired formulation for the 1-dimensional model. 3.2 Input Data There aremany aspectswhichmake up the naturalAT. The time scale ofmany of themore random events are hourly, whereas the 1-dimensional(l-D) influences are felt over longer time periods on the order of aday. Therefore, itwas decided to use the 1-D model to fit a 2-day runningaverage of the natural AT, whichwas expected tohave more 1-D character. Aplot of thenatural AT after a49-hour running average wasmade (49hourswas used so that asymmetric averaging interval occurred) is given in Fig. 3.1. From this signal, "storm cycles" may be observed which appear aswide temperature swings persisting up to aweek that are believed to be associatedwith the weather patterns. Also visible, though less clearly, is the weak annual cycle.

17r C ----,- - r - - r I

- " , ' 

# Io

.

1t 0

5i

co .1IJ r-I

co z fa r4 ci U) 0 t '.4

O r-

) Ze n
0 PL4 CJ 'r-I S'L 09 S-F 0G'E S I O' - O'E- 5'h- 0 9- S'La0 IV _,

I

### To apply equation 3.1-13, tables of flow,measured upstream temperature, and computationofnetheat flux arerequired. In addition, values for the area, A,anddepth,h,mustbe specified. Since only for certain locations aremeasurements forAandhavailable, there issome leewaywith theirvalues, and these twoparameterswere usedto tune themodelwithinphysicallyreasonable limits. The means of producingabest fit isdescribed brieflybelowwhere the actual resultsarepresented. Thenetheat fluxwas computed using themethodsoutlinedby Ryan (1971). Table3.1 summarizes the inputneeded. Theactual equations used to compute thenet fluxare given inAppendixA.

19 TABLE3.1 DATA REQUIRED TO COMPUTE NET FLUX 1. Air Temperature 

### 2. RelativeHumidity 3. Wind Speed 4. Air Pressure 5. Solar Flux 6. Atmospheric FluxNecessary inputs to apply equation 3,1-13 are (all 49-hour running averages of) the flow, station 6 bottom temperature, andmeteorological 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 whichwere 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 bottomwas 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 themodel. The values chosenwere 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 andmonthly averages of the measuredAT at the 5-foot depth and bottommonitors. The best

20O

### monthly averagesof themodelpredictionandmonthly averagesof the measuredAT at the 5-footdepth andbottommonitors. Thebest result, usingh- 12.5 feetand A- 50,000 ft2 

### isplotted in Figure 3.2. As isseen, themodel isareasonable fit onamonthly basis. Fig. 3.2 is somewhatmisleadinghowever,becauseneither the top norbottommeasuredAT values actuallyare true cross-sectional averages, anddue to themonthlyaveraging scale, the abilityofthe model to fit the storm cycles isobscured. Theability of the -Dmodel to fit tc 49-hour averaged.data s dramatically illustrated inFigure 3.3, As isseen themodel prediction is avery credible fit of thepeaksand valleys ofthe measuredAT, although this fitis somewhatworse in the fall and winter. Itissuspected that themodel fit isbetter in the spring and summer than the fall orearlywinterbecause thevalley-wide longitudinal driving force ismuch smaller inthe latterportions of theyear, (Freudberg, 1977). In addition, thenature of the river isfundamentallydifferent duringheatingperiods thanduring cooling periods. Stratification, althoughweak, occursparticularly inthe springwhen the riverbegins towarm. Further, the seasonal eat-up isarelatively steadyprocesswhich inducesvery little turbulence as itacts. The flow isnot particularlydisrupted from its usual 1-dimensional courseby densityeffects. O the otherhand,the cooldown inthe fall isafarmore complexprocess. Unlike the spring 210

44j '-H P4 10 44J CO, aL) 

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0 4 0 0 II Il ¢o 4 c4 W C4 a) .S OI[ ' - I r - r - S'L 09 ' h O'E ;.'

Q.) to at CO 0 s-i Cd e CO

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-4

S'L O'9 q'h Olt sIt I r - '--- - - - - - - -- ----i 1 I1- 0'E- ., - ,, 'L d

IC 4-i

I O.) O70r-4 S HO =Do 4i 

# ?{mm 1.00 :p I P4r- 

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-on, I i. M- ;=M

.1w 19=- >- CO p .1 

### M=- r. CO r-I r-4 .1 0

I I I I I S 1- O't- S'h- 09- 5'L- . o'~,V 23 CA 0 -H *,-4 4 Ps 4= .r E-4 CO4-i s-i4-i <:3

4.JQ 4.-}0 d 0 Zo Q) o Z o)

O 1 ClII 

## =3 J 04-4 0ilJ CJ)II4

UO)

0 CN 0 1I o ,-- CY) qJ cv) 0 bo

.- i .,, -



### .L

_ _
_ .

### when the warmed, bouyant surfacewater tends to remain at the surface, the cooled surface water in the fall sinks down due to its greater density and thus non-one-dimensionalmixing takes place. Thus the 1-Dmodel produces abetter result duringperiodswhen the river flow itself is generally one-dimensional, thewaterbody is morehomogenous, andno complexmixing process is taking place. The statistics of the meanand variance for themeasured data and the 1-Dmodel are presented below, for theperiod April 1975 - Dec. 1975. TABLE 3.2 Comparison of Statistics of 1-DModel and Measured NaturalAT 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 obtainedvia subtracting the 1-Dmodel fit from the data is given. This residual series has amean of 0.12'F and avariance of 2 0.34°F2

### . Thus the variance of the data has been reduced roughly 40% using the 1-D model.

24Pd
6., o a) 0 Ca o Cd o
0o 4-i Pd 0

5-4 .a 0 a) 4-4 0
Q)sPC-4 co 

### ~4- C4
0 

### ~X 5'tL 09 'h E I 0 S'i 1- 0'E- 'h- 09- sL

### a0 

### 'IV 25IV. 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 avariety 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 = BEGINNINGHOUR 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 

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### 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 andWheeler dams; wet bulb temperatures; upstream and downstream temperatures; andwhen desired the one dimensional models estimates of the natural temperature difference between upstreamand downstreammonitors, are supplied to theprogram. 4.2.2 Browns Ferry Flow The river flow at Browns Ferry is calculatedwith atwo term equation utilizing flowvalues at Guntersville dam five hours previous to the time of calculation, and flowat Wheeler dam twohours previous. The flowwas then time averaged using a fraction (R)of thepresent flow calculation added to the fraction (-R) of theprevious hours flow calculation. With the diffuser performance afunction of flow and using the simple two termmodel for flowwithout time averaging causes the plant induced temperature fluctuations to be instantlyand strongly respondant to flowvariations. Weknow in reality the induced temperature is not so highly sensitive to flowand the inclusion of time averaging of flows at this point is ameans 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 possiblemodes of operation, open, helper and closed. (see Figures 4.2) Condenser Intake Temperatures: For open andhelper modes condenser intake temperatures are approximated by the upstream river temperature. Closed mode iteration is used until the temperature rise across the condensers isequal to the temperature drop across the cooling towers. At this point the condenser intake temperature isapproximated by the cooling towers cold side temperature. Actual Plant Load and Condenser Hot Side Temperature: Actual plant load is afunction of the target plant load (held constant at 3300MWefor the three units considered here), water temperatures, and the mode of operation. The condenserhot side temperature is a function of the actual plant load, the intake temperature and the condenser flow rate (constantwithin a givenmode). However, the ratio of actualplant load to target plant load is a function of the actual plant load and condenserhot side temperature. Hence, iteration isused alternatingly computing the condenser hot side temperature and the actualplant load until both values converge to a final value (for agiven intake temperature andmode of operation). An additional 56 MWeissubtracted 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 TowerPerformance: The temperature drop across the cooling towers iscalculated using a fitted polynomial with tower intake temperature andwet bulb temperature as arguments, DischargeTemperatures: In openmode the condenserhot side 29MODE = HELPER M

CONDENSER INTAKE TEMP. = RIVER TEMP.

- 4--

COOLING TOWER PERFORMANCE: CALCULATE TOWER COLD SIDE TEMP.

ITERATION T CHECK: ATACROSS 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 COLDSIDE TEMP. CALCULATE ACTUAL PLANT LOAD AND CONDENSER HOT SIDE TENP. ,F wIt

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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 !

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### 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. InducedRiver 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 threemultiportbottom diffusers in place at Browns Ferry. Complete mixing inhigher river flows and the recirculation around the diffuser in lower flows aremodeled. 4.2.4 Running Averages If spatial or temporal averages of temperaturemonitor values are desired they are performed after theplant 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 themode,power production is maximized within the constraints of amaximum downstream river temperature and amaximum change in temperature between the upstreamand downstream monitors. This change in temperature istaken as the natural temperature difference given by the upstream and downstreammonitors plus the calculatedplant induced temperature change. When the AT estimatedby the one-dimensional model is included,it issubtracted giving the total 32AT=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 ameasure of the energy lost in comparison to operating entirely in openmode. 4.2.7 Output Output from the program includes the calculated Browns Ferry flow; induced AT and actual power output for eachmode of operation every hour, the condenser hot side temperature in closedmode, the optimummode 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.

33V RESULTS OF COMPUTER SIMULATION OF PLANT OPERATION A number of sensitivity studies of plant operationwere 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 alongwith 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 higherwater 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 34to thermal efficiencies. The results of the sensitivity analyses are graphically displayed as the power output of the plant inmegawatts 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 betweenvarious modes of operation in response to changing river temperatures. Figure 5.1 contains three separate graphs showing what the power output of the plantwould be if it were run entirely in eachmode of operation for the entire period. Each graph of the power output of the plant in bestmode can be thought of as amixture 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 inbest mode graphs were subtracted from the power of the plant if it was in open mode. Thesevalues of power losses, due to running the plant inhelper or closed modes, were sorted and displayedversus 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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0 .15.1.3 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 inmegawatt hours. These values do not consider the thermal inefficiencies of running the plant (i.e. openmode losses have been kept out of the total). Comparing the cumulative hourlypower 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. 39Zr 40~~~~~~~~~~, a a: wIZ4a:U w' a:CaL 0 W Z U 0 cc a) IL l_ on a I-

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r-- -- -T- - T- - ----I- I I I T - - - T - - --- - --- crThe change in temperature estimating D model described in Section 3.0 was used on the Base Case A analysis. The use of themodel by itself cuts down on power losses significantly. The sorted power losses curve, Figure 5.6, actually comes about one half theway 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 9which 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 showprogressively less use of both helper and closed modes as you go from Station 9 to Station 10 tomid-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 bestmode plot for the results. The spatial averaging offers 44

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### less power losses inboth the spring and the fall, but, actually uses slightly more closedmode operation during the late summer period. The estimatedAT Dmodelwas applied to the above caseswith the resulting power output in bestmode plots shown in Figures 5.12, 5.13 and 5.14. In all cases the use of the Dmodel lowers thepower losses. In Figure 5.12 (Station 10) closed mode operationdoesn'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 showreductions in the use of helper mode operation. The use of the Dmodelwith 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 asmuch aswith Station 10 & 11 separately. Figure 5.15 shows acomposite 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 9in the spatial average. Station 11, however, shows alot less use of helper mode than the Station 10 or Stations 9,10,11 spatial average. This is probably due to itsmidchannel location. An interesting result occurs for the addition of the estimated AT Dmodel. The modeldoes better using the individual stations than the spatial average, much more so than the difference between the single stationversus the spatial average without the model.
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535.3.2 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 DModel, 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 fromhelper 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 54I I q IL I)" -L I m,! I _A 

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### one case (Station 9including the DModel's estimated AT) where going from no averaging to atwo hour running average increased theyear's cumulative power loss (see Table of CumulativePower 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 islower cumulative power loss (the area under the sort curves) for cases withmore time averaging. There's one areawhere the curves crosshowever, 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 operatemore hours in closed mode. Power loss isdecreased for all running averages by including the 1DModel's estimated AT. Neglecting that gain, the gain inpower production for going to a48hour running average from no time averaging is about the same ifwe include the Dmodel's AT or not. If running averaging is increased beyond 48hours, the gain inpower production can be expected to approach alimit. The limit willbe less than our limiting casewhere natural downstream temperaturewas set equal to thenatural 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). 61C-:4@ tC- C, 2:

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### 5.3.3 Combined Spatialand Time Averaging In order to assess the limit of various averaging techniques a spatial average of downstream Stations 9,10, & 11was combinedwith a48 hour running average of the downstream temperatures. Figure 5.23 shows the results as the power output in bestmode 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 DModel to the combined averages cuts outmore helper and closed more operation especially in the spring, but, adds some helper operation in the fall. This is shown inFigure 5.24.Figure 5.25 shows the composite of the sorted power loss curves for the combined averaging, combined averagingwith DModel, and the Base Cases. An interesting situation occurs when theuse of the combined averagingwith the estimatedAT DModel 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 usedupstream Station 6and downstream Station 9as abasis and an observation period of April 1through November 1. Analyses of the effects of using the estimated change in temperature DModel or averagingmethods werenot considered. It was our effort to get an idea of critical areas in the standards 6300
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### and plant design that may significantly influence power losses, and to gain an approximatemagnitude of their significance. 5.4.1 Changes in Environmental Thermal Standards Both the maximum allowable change in temperature from upstream to downstream stationplus themaximum allowable temperature in the riverwere considered. At thepresent these standards are 5F for maximum change in temperature and 86°Fmaximum allowable temperature. The first case considered changing themaximum allowable change in temperature to 3F. The results are shown in Figure 5.26 as the power output in best mode graph. Considerableuse of bothhelper and closed modes of operation is needed except for the late summer period. The second caseused an allowable change in temperature of 10°F, Figure 5.27. The late summer period is unaffected sincemaximum temperature is the overriding factor in thisperiod. However, during the fall and the spring asubstantial savings of power loss can be found. The third case considered a 90°Fmaximum allowable temperature. Figure 5.28 shows that less power losses occur during the summer period as expected since themaximum allowable temperature is the overriding factor in cooling tower usage during this period. Last of all,both amaximum allowable change in temperature of 3°F and amaximum allowable temperature of 90°Fwere used for an analysis. Figure 5.29 shows use of the helper mode only during the late summer periodand in lateApril. Cooling towers were only used once during 67-~

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71 Tthe 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 CaseA. 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 themaximum 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 possiblemodes of operation included all open mode, no open mode, no helper mode (open/closed) and no open or helper mode (only closed). All openmode operation and all closedmode 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 72co Cl) c4 X c~ E
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-- . , ; .i".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 openmode 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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### more losses for the helpermode 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 canbe done. Cooling tower performance was varied by subtracting 5°F from the wet bulb temperature tomodel increased coolingperformance and adding 5F to the wet bulb temperature to modeldecreased cooling performance. Figures 5.37 and 5.38 show thepower output inbest 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 inopen mode.It is apparant for spatial and time averaging that selection of the downstreammonitor isimportant. Addingvarious time running averageswill decreasepower losses somewhat. Using the estimated AT 1D model reduces power losses significantly in all cases. Combining spatial and time averaging plus the AT Dmodel gave the lowest power 81e~ C mC 4.J

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## I

ITable 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 CaseA With Estimated AT lD Model 

### 5.3 Spatial and TimeAveraging 5.3.1 Monitor Location and SpatialAveraging 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

2Hour Running Average of AT 1D Model 

### 24 Hour Running Average of AT 1D Model 

### 48 Hour RunningAverage of AT 1DModel Station 9 Station 9 Station 9 Station 9With Estimated Station 9With Estimated Station 9With Estimated 85 

### 95,963 92,280 90,490 83,280 78,890 77,726Table 5.2 (cont.) Cumulative Hourly Analysis Power Loss (MWhr.) 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 MaximumAllowable 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 andMaximum Allowable 7,543 River Temperature of 90 F 5.4.2 Existence of Various Modes of Operation All OpenMode 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 86losses 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 bestmode graphs, the savings occur during the late summer period whenmaximum power output is more important.

87VI. Comparison with Operating Data The Browns FerryNuclear 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 anew set of instreammonitors; utilizing meteorological data, river flows,and instreammonitor 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 instreammonitors 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 5miles. It was also decided to remove station 6, and replace station 9with station 13 (which is farther from the right bank and less affected by natural heating). Figure 6.1 shows the locations of the newmonitors. 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 SectionIIIwas for station 6 to station 1). The model 88

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### des, rlibcd In Sectioon 11. 

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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 SimulationModel The simulation model described in Section IV was modified to better describe real time plant operation. Themajor 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 97r. -

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# .-F- Iat Browns Ferry for input and determines the total plant induced temperature rise predicted for the total three units. The total hourly plant loads (3units 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 simulationmodel were compared with themeasured temperature difference from the instreammonitors. Evaluations of the differences in instreammonitor readings show there is quite avariation in values ofmeasured 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 withminimums in river flows. It is possible that during these low flow situations upstream station 4may be 105-;Vitro:~

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### influenced by warmerwater resulting fromplant operation or natural solar heating causing themeasured temperature difference to be small. The influence of natural or artificial heat at station 4may also be the cause of the overestimation of upstream-downstream temperature differences.

112REFERENCES Almquist, Charles W., "ASimple Model for the Calculation of Traverse Mixing in Rivers with Application to theWatts 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 andUnsteady 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., "AnAnalytical and Experimental Study of Transient Cooling Pond Behavior," M.I.T. Parsons Laboratory forWater Resources and Hydrodynamics, Technical Report No. 161, January, 1973. Tennessee Valley Authority, "Monitoring of Water Temperatures inWheeler Reservoir to Determine Compliance of Browns Ferry Nuclear Plantwith 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 

## *' 6 

## e2)4

## '+Jwa)[(e6- ) 

## e 0255(s

')a] 

## (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 + 0.2907Ta - 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 2meters, W2, (inmiles perhour) above the water surface given by either: 

### (w 2

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

### f(w2

### ) = / 

### ( A-3)
114

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

# aOv - 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, mmHg 

### 3 - If A < 0.0024W23, use A-3 Else use A-2 Else use A-2

115

### Workreported in this documentwas sponsoredby the Department of Energy under contract No. EY-76-S-02-4114,AO01. This reportwas prepared as an account orwork sponsoredby theUnited States Government. Neither the United States nor theUnited StatesDepartment of Energy, nor any of their employees, makes anywarranty, 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 usewould not infringe privately owned rights.