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Environmental solutions delivered uncommonly well
Performance of AERMOD vs. CALPUFF on
Fugitive Emission Sources in the Nearfield
Paper No. 816
Prepared By:
Ian Donaldson - Consultant
Divya Harrison - Consultant
Jonathan Hill - Consultant
TRINITY CONSULTANTS
12700 Park Central Drive
Suite 2100
Dallas, TX 75251
+1 (972) 661-8881
trinityconsultants.com
June 24, 2008
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Performance of AERMOD vs. CALPUFF on Fugitive Emission Sources in the Nearfield

  • 1. Environmental solutions delivered uncommonly well Performance of AERMOD vs. CALPUFF on Fugitive Emission Sources in the Nearfield Paper No. 816 Prepared By: Ian Donaldson - Consultant Divya Harrison - Consultant Jonathan Hill - Consultant TRINITY CONSULTANTS 12700 Park Central Drive Suite 2100 Dallas, TX 75251 +1 (972) 661-8881 trinityconsultants.com June 24, 2008
  • 2. . / / ) * #+ & , -." " /0,1 2 $,/1 ) % 3 ! ! #3 4$ % # ." " /0,' 33 2 # 5 5 $ 6 # 5 # %" ,70.88# 2 # ." " /0,' 33 # 3! 2 2' 2 3 # ! + 9 5 ! '+ '! + !! 2 ,33 4: 5 ; 5 58 1 2 0 $ " . 5 # 5 ! 5 3 # 2 - 5! " 1 2 5 # 9 5 3 # 2 5 # ! 2 2 3 ! 5 33 2 5 < 3 # 22 2 2 3 ! ! 3 !# # # 5! 2 3 # 2 # 33 3 # 5 3 2 52 3 ! # $0 % # ! # " 3 ! # # #3 ! 5 # =' 52 0 # ! 3! 3 22 2 25! " : # 2 2 ! 3 2 ! = # 52 3 ! # ! ! ! # + 3 # 5 # ! ! 3 3 3 + # ! 2 # 2 4 ! ! ! = 0 5 2 5! $0 % 3 # 2" 5! 3! 0 # ! ! 2 3 # 5 ! 22 2 2 5! " 3 !5! 3 3 !#3 3 5 # ! 5 ,70.88 ,/1 ) # 2 # = # 2 52 0 ! 5 $" " ! 6#%" 0 / /0 + ." " /0,> < # 5 5 < # 2 33 ! " ! 33 # # 5 2 ,/1 ) # " ) * #+ & ,/1 ) 3 ! ! #3 4 # ? @ $ @% # 2 # 5 5 $ 6 # 5 # %" ,/1 ) # 2 # !#3 5 # !#3 A ) !3 2 3 2 # $,/1 ,0% ) 2! 3 3 ! $,/1 / % ,/1 .18, /
  •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
  • 4. 55 ! + = ,70.88 ,/1 ) # 2 # ! + ! ! 9 5 = A โ€ข ,70.88 = 5 + ! E! $" " ' ' 3 % = ,/1 ) # 2 E! $" " # ' 3 %" โ€ข ,70.88! !#3 ! ! 5 ! # = = 3 # 2! + " โ€ข ,70.88 9 # 2! 3 #3 " โ€ข ,70.88 5 # # 5 # 3 = 3 # # 2 # 2 # " โ€ข ,70.88 = 5 5 ' ! # ! 5 # # ! # 3 = 3 # 2!3 + = ,/1 ) " 3 + 5 ! + - !#3 4 !#3 4 # 2! # $" " ! 2 % ! 5 ,70.88 ,/1 ) ! + = 0 5 2 5! $0 % # 2 " 2 !2 9 3 # # #3 ! 5 # =' 52 0 # ! 3 2 ! # 2 2 ! 3 = # 52 0 # ! ! ! # + 3 # 5 # ! " , ! 3 3 5 = !#3 3 5 # ! 5 ,70.88 ,/1 ) # = # 2 52 0 ! 3! 5 22 2 2 3 ! ! 3 !# # # 5! 2 3 " 3 ! 5! 3 5 # ! 5 ! 5 # 2 # = ! 2 3! 52 0 ! ! 2 3 # 5 = 55 ! A ! 2 3 3 4! 2 3 3 " / 1 /0 ! ' 2 3 # !#3 5! 3 ! 52 0 # ! $"2" # 5 3 % 3 ! " 3 ! ,/1 ) ,70.88 3 5 # ! = # 2 3 5 ! + !#3 2 # 3 ! ! + $" " 6#% !3 "
  • 5. 2 5 2 # #3 ! 5 = 5 # 5 ,70.88 ,/1 ) 3 5 # ! = # 2 52 0 # ! " 1 !3 5! ! + ,/1 ) ,70.88 # 2 ! !3 2 " 5 F5 G2 5 !3 4 33 4# @ 6# 5 # ! 5 ! = '# 3 ! 2" * 5 2 ! !3 3 ! 2 3 3 = '# 3 ! 2" ! 2 ! '# 3 ! !3 4 ( 6# 5 # !" 8 F! G2 ! 2 ' 6# 3 ! !3 33 4# 6# 5 # ! = ! !#3 3 5 # ! 5,/1 ) ,70.88 ! ! " ,3 5 !3 2 3 82 " 04 $( / / 0 / 0 / 5 / 5 2 !3 2 ,70.88# 2 # < 5 5 = 9 # A # 2! ,7 / # !#3 ,70.88 # " 8 3 3 5 ,7 / ,70.88 # =
  • 6. ! 5 ! ! ! " 9 5 # = 2 4 6# + # !3 5! ! " = 5 3 + ! ! 5 3 55 + 5! !3 + 2 " 9 # !#3 52 ! ! ! 2 ! 2 3 = ! # 2! !#3 3 # ! ! ! # 3" ,2 3 ! 2 5 6# = ! 5 = # = ! 2 5 + !#3 # 3 E 55 " B 9 5 9 # # ! 5 6# $2 ! % + 6# $2 ! %" + ## 9 ! 2 ! ! 5 ! 5 9 # 2 ! " ! 5! 2 5 ! ! ! ! 4 " ! # !#3 5 '5 = 22 ! #+ 9 5= ! ! ! + = ! 3 ! # ! 5 # 6 3 !" 2 ! 5! = ! + ; # ! 5 # 4# # # 4 2 2 5 @ # " * ! ,70.88# 2 # = 7 #+ 5 # + 2 5 ? + #3 # + , ! 5 $? , % 1 2 9 1 $1 1% # 2"; ! 2 5; H* H: = 3 5@@H* ; H*" * ,/1 ) = ! ! 2 ! ! #" / . $ 6 /0 4 0 / / 6 4 7 2 3 ; @ ( ; & @ & &; ( @ ;
  •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
  •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
  • 9. 3 5 # " 3 # = 5 2 = 5 5 + + 5= 5 # 5! 33 = 2 ,7 / # " = 3 5 ? , ,7 / = 5 5# 3 5! # 2! 33 3 !3 = " #3 55 ! + = ,70.88 ,/1 ) # 2 # ! 5# 3 # 5 ' # 5 # 2! + 5 # 2 ! = ,/1 ) B 3 # " , 5! 33 3 !3 + 9 ,7 / 3 ! 2= # = ! 3 ? , 1 1 !#3 + ? , ! ! " , #3 ! 5 ! = 2 + ! # = ! #3 ! " # 2! 3 # + 5 # 5! #3 ! + 3 ! = 3 ! #3 ! ! ! 2 # 3 !3 3 " .33 3 3 5 5 + ! 5 # 5! 2 3 5 + = ! 3 !! = # # 5 3 = 3 ! #3 $# 2 3 # % + 2 # 3 " 8 # 3 !3 ! = ! 2 55! 5! # ! 5 # = 3 3 ! #+ 3 ! ! " ) = = 5 ! 9 # 4 , !)! " = !2 9 ! ! 55 ! + 5 # + # 3 ! 3 3 # !! 2 = ! 2# 3 ! ! 3 3 53 2 2 55! ! " L 3 # !! 2 ! # 55! 3 3 ! - ' + 9 ! ! ! 5 3 # #3 # 3 2 # 4 2 2 ! ' 5! # + ! ! 5# 2 ! ! " ) = = ! ! + + 5 # * C $*C % 3 ! = #3 # # = # ! + 5 5 # 3 =3 + " 4 2 2 #3 2 5 # + 33 + ,7 / = # 2 !
  • 10. # 3 " + + ,7 / # + 55! + !#3 2 5! ! ' )+ 6 2 5! 2 # 4 2 2 = 5!" 5 5 # 5# 3 2 # 3 ! # !!#3 2 ,70.88 # 2 #" ,7 / < 2 3 ! + # ! ! 9 3 # 3 55! 3 " 5 55! 5 = ! + ! # 3 3 +E! 2 ! ! 5 3 55" 55 4 + + ! ! ! ! 5! 2 + C = 5' 4 55! + ! 3 " ! = + 5 # . B ' 2 $A ! 33 4# '# % 2 5 # " 3 3 ! = 5 # # 2 2 3 ! 5 5 3 ! 2+ ,7 / " 82 @ 3! ! # 2 # 3 ,7 / 3 ! " 5! ! ! 5 # 2 # " 04 *(/ 0 6 /0 0 0 4 0
  • 11. 04 8( 6 0 0 4 0 ) ! < # 2! 2 3 ! = + 5 # ,7 / = + " , # 3 ,7 / # 5 5! 33 3 !3 2 3 ! # ! ! + 3 ! 2 2 5 5 + ,70.88" ,7 / 3 5 ! 2 5 5= #3 # ! # 2! + + ! 3 # ! 5 ,70.88 !#3 !#3 $" " 3 ! # ! 5 # 3 % 5 ! #
  •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
  • 13. 51 1 = ! # 5 6# + ! 5 $ 6# @& 6#% = 5*: + " C ,/1 ) ,70.88 3 # = # + 3 3 # ! " : # 2 3 ! = + ! ! 33 3 ! !6 3 # $" " 2 # 4 2 #3 2 4 ! % # 2 " = 3 3 5 !#3 3 5 # ! 5 ,70.88 ,/1 ) = ! 2 52 3 ! ! ! 3 5 " 5 52 ! # # ! " 8 # 5 3 = 3 # ! = 3 = 3 ! " C ! 2 # ! # ! ! 2 !#3 5,/1 ) ,70.883 5 # ! 5 ! ! ! ! 9 " + @ ! 3 # 5 # ! 3 ! " * + 5 5! # ! = 33 4# & 5 $ # % + # " / . * 5 / ! $- 2 9 : * 3 7 2 3 0 6 2 3 1 2 3 5 2 3 2 3 0 ;" &/' " " " " " 0 " /' &" "( @" ; "( ( " 0 1 @" ;/' "( ;"& @ (" @ "( @ "( . 3 1 &" /' "( ;"& @"@ @ "( '(&"
  •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
  •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
  • 16. < ' ! ' ! ) ! 43 = 3 5 # ! 5 ,/1 ) ,70.88 # 2 # ! ! 2 0 ! ! = 4! 2 55! 5 3 3 " + 3! # 3 0 ! ! $ P2-#@ % 5 ! " / . = 0 $- / /0 / / >0/7 / 5 0/0 5 /0 ! 4 2? 9 8 3 2? 9 8 3 @ 2 2 &" ( ;" & ' "@ 8 2 2 ;"(& "@ '@ "@ 2 2 "@ " ' " # 2 2 " & " @ ';@" 2 2 " " ( ' " ;' 2 2 "&; "@( '; "& 8 2 " " ' "; # 2 " " (( '&;"(, 2 " " '&@" 8 ! # !3 2 $" " 5 # # ! % + 2 2 2 2 ;' 2 ! ! = + " 2 ! ! 5 ! 5 !3 2 # 3! " , + # 4# # ;' 2 0 ! ! 5 # ,70.88 = + O 3 ! + ,/1 ) " = 55 ! # 4# # 3 ! ! ! ! # 3 2 = 5 # " = + @ O 55 ! # 4# # ;' 2 # ! ! ! 2 $" " ( 6# 5 # %" : !#3 2 2 2 ;' 2 ! ! 0 ! # $@ P2-#@ 5 ( P2-#@ 5 % * ,#+ , D $ P2-#@ %
  • 17. 5 0 + !# 33 # 52 ! 5 2 3 ! = " ! 5E 2 $(% 52 0 ! # # 3 ! ! 5 2 = 4! 0 0 ! # = !! 5 @ O O 5 0 0 ! # " # ! ! + # # 2 #3 ! + ! + 43 ! # ! !! 5 33 4# O 5 0 # 5 # 9 " = 43 ! ,70.88 3 ! = ! ! ,/1 ) 3 ! = ! 2 # # ! 2 2 2 2 3 $" " 2 ! ! %" = 2 5 # 55 ! + = = # " ,70.883 ! = #3 ! ! ,70.88 ' 7 2 2 # = ,/1 ) ' B # " ! ,70.88 3 ! 3 ! ! + = 2 ! 3 55 # # 3 ! 3 2 2 # 2 # 2 = ,/1 ) " , 5! # #3 ! # 3 5 # ! = 3 ! 3 ! 2 ! !" 0 5 # 4# # # ! ! ! !3 5 ! # 2 23 = ! 5 2 5! 3 # 3 " 82 ; 2 3! = # 3 0 ! ! # 2 # 5 ! # 2 23 "
  • 18. 04 +( / / / 7047 / $ / 7047 *+:7 6 4 $- / /0 04 =( / / / 7047 / $ / 7047 *+:7 6 4 $- / /0
  • 19. 04 %( / / / 7047 / 6 4 $- / /0 04 A( / / / 7047 / 6 4 $- / /0 , 5 52 = # 3 ! 2 ! ! 5 # ! "
  • 20. ! 5# 3 # = ! = # 2 !#3 " 3 # = ! ! + # 5 # = 5 # 2! ,/1 ) ! 82 (" = # ! ! ! ! = # 4# # ,70.88 3 ! ! $ 82 ; &% = !#3 ! 5 # 4# # ,/1 ) 3 ! ! = ! 5 ,70.88 = 25 3 -3 55 = 2 # 2 # = = # 3 !" 04 #(>0 0 / >0/7 /7 / 40 / 0 2*--8 / .0 , /7 0 3 < ' ! ' ! ! 43 = 3 5 # ! 5 ,/1 ) ,70.88 # 2 # ! ! 2 0 ! ! = ! 2 55! 5 3 3 " + & 3! # 3 0 ! ! $ P2-#@ % 5 ! "
  • 21. / . % 0 $- / /0 / / >0/7 5 0/0 5 /0 ! 4 2? 9 8 3 2? 9 8 3 @ 2 2 " ;" '&"& 8 2 2 ;" @ ("&& '@ " 2 2 " " & ' " # 2 2 " " '@&"& 2 2 " ";( ' " ;' 2 2 "; "@ ' &" 8 2 " " & ' &"; # 2 " " ( ' ", 2 " @& " & ' "& + & 3! 2 2 2 2 ;' 2 ! ! 5 ! # !3 2 $" " 5 # # ! % = ! 2 55! 5 3 3 # ! ! 3 " 2 ! ! 5 ! 5 !3 2 # 3! " , 43 ! # 3 ! ! = ! 2 3 3 + (O = 4! 2 55! 5 3 ! # # ! # $ + %" # 3 ! ! 4! 0 ! # 5 0 = 33 ! 5 3 3 #3 55 ! + = ,/1 ) ,70.88 3 ! ' # ! ! " 3 5 2 #3 ,70.88 3 ! = ! ! ,/1 ) 3 ! = ! 2 # # ! 2 2 2 2 3 $" " 2 ! ! %" , ! 5 2 ! + 43 55 ! + = = # $" " ,70.88 ' 7 2 2 # ,/1 ) ' B # %" 0 5 # 4# # # ! ! ! !3 5 ! # 2 23 = ! ! 2 5! 3 # 3 = ! 2 55! 5
  • 22. 3 3 " 82 2 3! = # 3 0 ! ! # 2 # 5 ! # 2 23 " = 5 # 3 # 2 ! 2 ! + = 43 ! 2 # = 3 ! 3 3 ,70.88 ,/1 ) " # # 2= 3 3 5 52 = ! = = = !" 82 2 ! # 4# # # 3 ! ! 4 5 5 # = ! 2 3 3 " = 43 ! ! 3 3 2 # 3 # # ! # " : 3 + 2 # 5 # 3 # -3 55 = = 3 ! ! = # + " 04 B( / / / 7047 / $ / 7047 *+:7 6 4 $- / /0 >0/7 5 0/0 /0
  • 23. 04 $-( / / / 7047 / $ / 7047 *+:7 6 4 $- / /0 >0/7 5 0/0 /0 04 $$( / / / 7047 / 6 4 $- / /0 >0/7 5 0/0 /0
  • 24. 04 $*( / / / 7047 / 6 4 $- / /0 >0/7 5 0/0 /0 0 ,70.88 !2 9 # 5 !#3 4 5 " B 6 = 2 # ! < # 5 ! 2 3 # 2! 5 ,/1 ) ,70.88= 6 + 5 # 5 3 # 2 ! 2 0 ! # 5 " = 2 ! ! 5 # = #3 3 '5 ' ! # ! 5 # ! 3 5 ,70.88 # 2 # ,/1 ) !3 + 5 2 = 4! 5 # " , #3 2 ! ! 3 = # ! 3 3 5 '6# ,70.88 # 3 ! 2 3 + + # !#3 + 3 ! ! = + 3 ! !#3 4 # 2! ! " 8 = + + 5! 2 3 5 # ! 5 ,70.88 ,/1 ) 3 ! 2 # ! # 2! 9 + ,70.88 + 3 ! ,70.88= + + # 5 = ! 252 3 ! ! "
  • 25. : 3 5! = 5 # # 2 55 3 ! ! = # 5!#3 2 B # $" " ,/1 ) % 7 2 2 # $" " ,70.88%" !#3 2 # 23 5 # ! 5 52 0 ! 5 = ! ! ! 5 = 2A โ€ข ,70.883 ! # ! = 5 2' # 2 23 $" " 2 % 5 !3 5 5 # # ! ,/1 ) " โ€ข ,70.88!#3 5 + ,/1 ) = 3 ! 2 ' # 2 # 3 ! ! " โ€ข ,/1 ) 3 ! # 2 #3 ! 4 5 5 # 52 ! ,70.88" โ€ข , 43 ! ! 5 3 3 = # 3 ! ! I = # ! 2 = ! 5 3 # # ! #" โ€ข , ! + # 2 5 # 3 ! ! 5 # 5= 52 ! # 52 0 ! 3 ! = "
  •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