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NUREG-0693, "Analysis of Ultimate Heat Sink Cooling Ponds."

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NUREG-0693, NUREG-0693 Analysis of Ultimate Heat Sink Cooling Ponds R. Codell, W. K. Nuttle Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission Available from GPO Sal es Program Division of Technical Information and Document Control S. Nuclear Regulatory Commission U. Washington, C. D. 20555 and National Technical Information Service Springfield, Virginia 22161 NUREG-0693 Analysis of Ultimate Heat Sink Cooling Ponds Manuscript Completed: July 1980 Date Published: November 1980 R. Codell, W. K. Nuttle Division of Engineering Office of Nuclear Reactor Regulation U.S. Nuclear Regulatory Commission Washington, D.C. 20656 ABSTRACT A method to analyze the performance of ultimate heat sink cooling pond s is presented. A simple mathematical model of a cooling pond is used to scan weather data to determine the period of the record for which the most adverse pond temperature or rate of evaporation would occur . Once the most adverse conditions have been determined, the peak pond temperature can be calculated . Several simple mathematical models of ponds are described; these could be used to determine peak pond temperature, using the identified meteorological record . Evaporative water loss may be found directly from the scanning a simp le and conservative heat-and-material balance . by Methodology by which short periods of onsite data can compared with offsite records developed , so that the adequacy ofbe th e offsite datalonger pond performance iscomputations can be established . for iii CONTENTS Page ABSTRACT.. .. .. i ii . .. .. x SYMBO LS. i I NTRODUCT I ON. 1. 1 2. HEAT AND TRANSFER RELATIONSHIPS IN PONDS.................... MASS 3 2.1 Equil ibrium Temperature Heat Transfer Model................. 3 2.2 Devel opment of the Basis for Surface Heat and Mass Transfer From a Pond. ...... ........... ................... ... S 2.3 Conservatism of Equilibrium Temperature Formulation. ....... 10 3. POND MODELS...................................................... 13 Mixed-Tank 3.1 Model........ ...... ...... ....... ...... ...... ..... 14 Heat Balance ....... .... .................. ......... 3.1.1 IS Heat oa Into Pond...................... 15 3.1.1.1 L d 3.1.1.2 Heat Out From Surface ............. ....... 15 Heat Out in l ow own or Leakage Stream. .. 15 3.1.1.3 B d 3.1. 2 Mass Balance .. ................................... 15 3.2 Stratified- Flow Model....................................... 16 Heat Balance .... ... .... .. ... .. 16 3.2.1 ... ..... .. .. .. 3. 2.1.1 Heat Enteri ng From Above................. 16 d . 3.2.1.2 Heat Leaving From Segment by A vection . 16 Change in Heat Content During Time 3.2.1.3 at.... 16 3.2.1.4 Heat Entering Segment 1 From Plant.. ..... 18 H a A . ... ... .. 18 3�2.1.S e t Transferred to tmosphere . 3.2.2 Mass Sal ance ........ ........... ....... .......... 18 F . • . • . 3. 3 P 1 ug- l ow Mode 1 . .. .. .. 18 3.3.1 Heat Sal ance ............ .................. ........ 18 3. 3.1.1 Heat Enteri ng by Advection From Previous Segment. .... � .. .. .. ... .. 18 t Advection.. ...... 3.3.1.2 Heat Leaving Segmen by 19 3.3.1.3 Heat Transfer to Atmosphere From Segment. 19 3.3.1.4 Change in Segment Heat Content During Time at....... .... ............... ..... .. 19 3.3.1.S Heat Enteri ng From Plant........ ......... 20 v CONTENTS (Continued ) Page DATA SCREENING METHODOLOGy ....................................... 4. 21 4.1 Meteorological Inputs to Sc reening Model . ............. ...... 22 APPL ICABIL ITY OF WEATHER RECORD. ................................. 5. 25 DESCR IPTION OF COMPUTER PROGRAMS AND THE IR OPERAT ION ............. 6. 29 6.1 Introduction .... ...... ...................................... 6.2 Meteorological Data Sc reening Program UHSPND. ........... .... 29 29 6.2.1 Prog ram Ope ration ................................. 29 6.2.2 Program Outputs .................•................. 6.2.3 Prog ram Inputs .................................... 30 31 6.2.3.1 Pond Data Card ........................... 6.2,3 .2 Monthly Average Card ..................... 31 6.2.3.3 End Card ...................... ........... 31 31 6.2.4 Data Input Examp e ................................ 1 32 6.3 Program COMET .... ........... ............... '................. 33 6.3.1 Prog ram Inputs ...... .....'.. ...................... 34 6.4 Prog ram UHS3 ......................................... ....... 34 6.4. Prog ram Inputs .................................... 1 35 6.4.2 Uti zati on of Prog ram UHS3 ....................... 1 i 36 SAM PLE CA LCU LAT IONS .............................................. 7. 39 7.1 Finding the Pe riod of Worst-Case Cooling Perfo rmance and 30-Day Evapo rative Water loss--Prog ram UHS PND. .......... 40 7.2 Statistical Treatment of UHSPND Output ...................... 7.3 Dete rmining the Applicability of the Offsite Data 41 Set--Prog ram COMET .......................................... 41 7.4 Final Design Basis Pond Tempe rature and Water Loss Computat ions- -Prog ram UHS3 .................................. 50 Evaporative Loss .................................. 7.4.1 67 7.4.2 Correction Factors fo r Peak Temperature and Water loss ........... ............................. 68 REFERENCES ...................................... ................ ',' . .. 73 vi CONTENTS (Continued) Page APPENDIX A--STATISTICAL TREATMENT OF OUTPUT........................... 75 A.I Additional Statistical Manipulation......................... 76 .........................•.. A.2 Maximum Likeli hood Curve �. ...... A. 3 Error Bands................................................. 76 79 APPENDIX B"-COMPUTER CODES............................................ 81 vii LIST OF FIGURES Page 2.1 Definition of Equ i libri um Coefficients.................... ....... · 4 4 2.2 Pond Temperature Computati ons (Steady State) ..................... 2. 3 Heat Loads on a Pond. ... ........................ ................. 6 2.4 Steady-State Surface Temperatures . ... ............................ 12 3.1 Mixed -Tank Model . 14 Stratifi ed- Flow ModeL ........................................... 17 3.2 1 3.3 Pl ug-Fl ow Model....... 9 4. 1 Insolation as a Function of Time ..........................'. ...... 24 7.1 sting of Input for Program ULTSNK.............................. 41 Li 7. 2 Output From Program UHSPND.................... .................. 42 Yearly Maximum Ambient Pond Tempera tures . ................ ... ..... 48 7.3 7.4 Yearly Maximum Ambient Po nd Temperatures, Max imum Likelihood Frequency Curve , 0.05 and 0.95 Error Bands............ 49 I nput to Program COMET........................... .............. 49 7.67. 5 Output of Program COMET .......................................... 51 7.7 Correlation of Equilibri um Temperatures , Susquehanna River Site Versus Harrisburg Station . .................................. 59 7. 8 Program UHS3 Data Deck, rst Set................................ 60 Fi 7.9 Output From Program UHS3 , First Set........ ........ .............. 61 7.10 Ambient Pond Temperature as a Function Time................... 66 of Pond Temperature With Externa l Plant Heat Load , 7.11 and Constant E i and as a Funct on of Time. .... .................. 66 ·7.12 Data Deck for ProgramK UHS3 , Second Set........................... 67 7.13 Output From Program UHS3 , Second Set............................. 68 7.14 Pond Temperature (Final Calculation) as a Function of Time. ..... 70 A.1 Pearson Type I II Coordi nates.. ... .. .. 77 A.2 Table of Versus P in Percent.. .................. ............. PN 00 78 Errors of Esti mated Va lues........................... ...... ...... A. 3 8083 B.1 L isti ng of Program UHSPND ... ...... .....·. ..... ... ...... .......... B.2 Listing of Prog ram COMET......................................... 99 B.3 Listing of Program UHS3 .......................................... 101 B.4 Li st i ng of Psychrometri c Subrout i nes. .. .. .. .. .. ... 104 LIST OF TABLES 5.1 Estimated Correction Factor 6E(x) Compared to Actual Transient Model Response 6T True Correction Factors ......... 27 max ( } 6.1 Pond Data Card Input Parameters .................................. 32 Monthly Average Card Input Parameters............................ 33 6.2 6.3 Meteorological Input for Program UHS3. .... .... .... ...... ......... 36 6. 4 NA LI T INLIST for Program UHS3 ................................. 37 U ME3 FiSnal Temperature RUns Varying Starting Time ................ 7.1 HS 71 viii SYMBOLS pond surface area, ft2 or acres A one-half the daily insolation , Btu/ft2 AO surface area of nth segment of the plug-flow model , ft2 AnC cloud cover in tenths of the total sky obscured Bowen's ratio, mm Hg/oF C1 �O.26 heat capacity of water , Btu/lb/oF Cp E equilibrium temperature, of estimation of equilibrium temperatures using data from offsite E2 E1, and onsite records, respectively , of E(x) estimation of equilibrium temperature using monthly average meteorologic data, of e saturation pressure of air above pond surface , mm Hg a e saturation pressure of air at surface temperature T ' mm Hg s S g skew coefficient H heat content, Btu HN heat transfer from segment N, Btu/day heat of vaporization of water , Btu/lb �vap H net heat flux, Btu/(ft2 day) net atmospheric longwave radiation, Btu/ (ft2 day ) HAN back radiation from pond surface , Btu/ (ft2 day) HBR conductive and convective heat loss , Btu/ (ft2 day) HC H evaporative heat loss , Btu/ (ft2 day) E H heat transfer from segment n, Btu/day n net plant heat rej ctio , Btu/ (ft2 day) HRJ e n gross solar radiation HS net solar radiation, Btu/ (ft2 day) HSN K equilibrium heat
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