DETERMINING UNDISTURBED GROUND ...

Rudarsko-geološko-naftni zbornik

Vol. 22

!"#$$%&'()$$$

Zagreb, 2010.

!"#"$%&'()"*$+",)'-%-*! Originalni znanstveni rad

UDC 504.43 UDK 504.43 Language/Jezik:English/Engleski

DETERMINING UNDISTURBED GROUND TEMPERATURE AS PART OF SHALLOW GEOTHERMAL RESOURCES ASSESSMENT !"#$%&'()#*+,',%-.#*,#/0#"',1"#*,2'*.' *!%)#2'* &")#!( &'()'*02%,.%3*4# ,#"/'2(%3*0 ,#(5%)'2' TOMISLAV KUREVIJA, DOMAGOJ VULIN University of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Pierottijeva 6, 10000 Zagreb, Croatia

.67*89:; ' :/*' 3$4"(+3!5*4' #!03$4' +*6-*!%+3!*' "(' 0$*' 0;' +/*' 8*' :/*' three regions are: Northern Croatia, Adriatic region, and the regions of Lika and Gorski Kotar.

+?H6>?I* ' G+%+"E8%' +*6-*!%+3!%' +&%' F*4%$' F*' 04' $%F9%H$"F"/' +*!60#*0&0I8"/' -%!%6*+%!%'$3H$"/'=%'9!F*4$09%$F*'"'"(80!"I+%9%$F*'-&"+8"/'#*0+*!6%&$"/' !*(3!(%>'?*0+*!6%&$06'*$*!#"F06'(6%+!%'(*'*$*!#"F%'-0/!%$F*$%'3'+&3'$%' 435"$%6%'#4F*'$*6%'3+F*)%F%'(3$E*90#'=!%E*$F%'('-09!I"$*>'J!"F*4$0(+' 435"$*' $%' 80F0F' (*' -0F%9&F3F*' (+%+"E8%' +*6-*!%+3!%' +&%1' $*09"($%' 0' (*=0$(8"6' -!06F*$%6%' +*6-*!%+3!*' =!%8%' $%' -09!I"$"1' 3' ;3$8)"F"' F*' 8&"6%+(8"/'-%!%6*+%!%'$%'-09!I"$"'"'+*!60#*0&0I8"/'8%!%8+*!"(+"8%'(%60#' +&%>' K%80$' 435"$*' #4F*' (*' -0F%9&F3F*' (+%+"E8%' 9!"F*4$0(+' +*6-*!%+3!*1' $F*="$'4%&F$F"'-0!%(+'39F*+09%$'F*'9*&"E"$06'#*0+*!6%&$0#'#!%4"F*$+%>' ' :0E$0' 4*+*!6"$"!%$*' 9!"F*4$0(+"' (+%+"E8*' +*6-*!%+3!*' +&%' "' 435"$%' -0F%9&F"9%$F%' $3H$*' (3' =%' -!%9"&$0' 604*&"!%$F*' 43&F"$*' 53I0+"$(80#' "=6F*$F"9%E%'+0-&"$*'3'(3(+%93'('4"=%&")06'+0-&"$*1'8%0'$%F3E"$809"+"F*' +*/$0&0#"F*' =%' "(80!"I+%9%$F*' -&"+8"/' #*0+*!6%&$"/' !*(3!(%>' L' !%43' (31' +*6*&F*6' 6F*!*$"/' -04%+%8%' +*6-*!%+3!%' +&%' (' #&%9$"/' 6*+*0!0&0I8"/' -0(+%F%1' 4*,$"!%$*' +!"' (-*)",E$*' +*6-*!%+3!$*' !*#"F*.' (F*9*!$"' 4"0' M!9%+(8*1'N%4!%$(80'-04!3EF*'"'O"8%'"'?0!(8"'80+%!>

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

>= %"1+)$"* *1#1 1$" )'101&31,3"9 1'')13 #"%5"$1#)$" -+6&331#&-' 1# *&=="$"'# *"5#2+ 61' ," "+#&%1#"* ,4 )+&'( a sinusoidal function in order to solve the differential "B)1#&-' 8' #2" ?'13 "@5$"++&-' 8AB.C:9 0 &+ #2" #&%" 31( =$-% 1' 1$,&#$1$4 +#1$#&'( %-'#2 8#1D"' 1+ E1')1$4 &' #2&+ 1'134+&+: #- #2" -66)$$"'6" -= #2" %&'&%)% #"%5"$1#)$" &' 1 4"1$.

t 8 H 9 : ( tm ,a ) A0 * e

% H /! +

& 2$ " % * +&' + 12 -+

0

#%

H

!+

%

$'

, 2 .,

8C:

and t gm &+ #2" 10"$1(" 1'')13 #"%5"$1#)$" 8F;: 1'* A0 8F;: &+ #2" 1'')13 1%53&#)*" -= 1&$ #"%5"$1#)$" 8*&=="$"'6" ,"#G""' #2" 10"$1(" %1@&%)% #"%5"$1#)$" -= #2" G1$%"+# %-'#2 1'* #2" 10"$1(" %&'&%)% #"%5"$1#)$" -= #2" 6-3*"+# %-'#29 H&()$" C:. I2" 1'')13 1%53&#)*" -= ($-)'* #"%5"$1#)$" 621'("+ &+ *"6$"1+&'( G *"5#29 < 8%:J

()*!+,#$-%*&"$.#)*&,%/0%$1,#$%&2.$$%31,!.)&

/t " H ,

where

8L:

A H= e

% H /! +

8K:

!1%5&'( *"5#2 $"="$+ #- #2" *"5#2 1# G2&62 #2" 1'')13 #"%5"$1#)$" 1%53&#)*" -= #2" ($-)'* *"6$"1+"+ #- 1/e of #2" +)$=16" 1&$ #"%5"$1#)$" 8H1$-)D&9 LMNO:.

Rud.-geol.-naft. zb., Vol. 22, 2010. !"#$%&'()*+",!"-$.(/0" Determining undisturbed ground ...

29

!"#$%&'&1-/%2$&'-"/3 4))+45"4(&"%$'6$&4%+&$"4'65(%+,$-"()"78"4-"&$9/&,$,".:"'$%$/&/5/*(945"-%4%(/)-;"()%$&6/54%$,"?"$>(&'( #1" $"+)5#+ -@ 8A8 %">+)$"* +>%B5"+ #1># 1>* ,""' 0-55"0#"* @$-% +1>55-= ="55+ 3C % *""B(" ($-)'* *"'+ =>+ = 89CE F :E G(H%3. g IB"0&J0 1"># -@ #1" +>%B5"+ =>+ 0>50)5>#"* ,>+"* -' #1" %">+)$"%"'#+ -@ #1" ?-5)%"#$&0 0-'#"'# -@ %-&+#)$" >'* >&$7 B-$-+ %>#$&K *"'+ >'* +B"0&J0 1"># -@ ">01 0-%B-'"'#. D1" >?"$>(" 0>50)5>#"* +B"0&J0 1"># -@ #1" +>%B5"+ =>+ C!" = 1420 4HG( LM

N""B&'( &' %&'* #1" ?>5)"+ -@ #1"$%>5 *&@@)+&? @-$ O>($",7 '>%"52 E7EPC %2H*7 @$-% 1&+ ">$5&"$ $"+">$01 34"5&67 89;9# #1" #"%B"$>#)$" >%B5&#)*" ># > *"B#1 -@ 8AEE 0% "S)>5+ E.8LM7 >'* #1" )'*&+#)$,"* ($-)'* #"%B"$>#)$" "S)>5+ 8T.8LM. D1&+ &+ -'" -@ #1" %-+# &%B-$#>'# B>$>%"#"$+ &' %-*"5&'( -@ > ,-$"1-5" 1"># "K01>'("$.

!"#$%&' U">+)$"* >?"$>(" %-'#152 #"%B"$>#)$"+ -@ #1" ($-)'* ># *"B#1+ #- 8EE 0% >+ $"B-$#"* ,2 #1" %"#"-$-5-(&0>5 +#>#&-' O>($",VU>G+&%&$ >'* 0>50)5>#"* %-'#152 ($-)'* #"%B"$>#)$" -+0&55>#&-'+ 3N)$"?&W>7 AE8E< Slika 3.#$%&'&(&#)'&*(%&#+%&)&,(&#-&+!&'.-/'&#-0.#*1#233#4+#5#56'.,/(.-'5%&*(1)-5#!'5"/857.(%.#-&+!&'.-/'&#-0.#/#6.75)(1)-5#1#!'1+%&(5#*/95(&# za lokaciju Zagreb- Maksimir (Kurevija 2010)

X'*&+#)$,"* ($-)'* #"%B"$>#)$" 0>' ," *"#"$%&'"* ,2 %">'+ -@ 0-$$"5>#&-' &' #1" @-$% -@ "KB-'"'#&>5 @)'0#&-'. D1" ?>5)"+ -@ #1" >?"$>(" %">+)$"* %-'#152 #"%B"$>#)$" >%B5&#)*"+ @-$ *"B#1+ -@ A7 C7 8E7 AE7 TE7 CE >'* 8EE 0% ="$" J##"* &'#- #1" "KB-'"'#&>5 @)'0#&-'Y AH Zg

25, 767e

0,0054 H

!"#

where AH Zg $% &'( )*+,$&-.( /0 12/-3. &(*+(2)&-2(% )& ) .(%$2(. .(+&' !0/2 &'( 4)12(5 %$&(%# $3 67 )3. H is the .(+&' !8*#9 :'(3 %/,;(. 3-*(2$8),, +0-;+ :27)"+ -3 #0" 8"2$78 ($-)'* #"%1"$2#)$"+5 '2%"78 %&'&%)%5 %2=&%)%5 2'* 2:"$2(" #"%1"$2#)$"+5 2+ ;"77 2+ :27)"+ -3 8"2$78 2%17&#)*"+. ?&:" %"#"-$-7-(&627 +#2#&-'+ ;"$" 60-+"' &' -$*"$ #- -,#2&' @)27 %"2+)$"* *2#2 2'* ("-($210&6 +"##&'(. ?&()$" A +0-;+ 8"2$78 2:"$2(" 2%17&#)*"+ B2 *&33"$"'6" ,"#;""' #0" 2:"$2(" 8"2$78 %&'&%)% #"%1"$2#)$"+ 2'* #0" 2:"$2(" 8"2$78 %2=&%)% #"%1"$2#)$"+C 2# (&:"' *"1#0+. 90" 6-$$"72#&-' ;� #0" "=1-'"'#&27 3)'6#&-' +0-;+ #02# #0" %2=&%)% *&33"$"'6" &' 2%17&#)*"+ &+ >D4.

!2%1&'( 3)'6#&-' -3 #0" ($-)'* #"%1"$2#)$" 2%17&#)*" 3-$ #0" '-$#0"$' 12$# -3 4$-2#&2 &+ 2+ 3-77-;+E AH Panon

>A5FG> ! e

0,0053 H

!" # $%&'#()*+,)-#'%./'#0%+0#0%*#123*,&(+)#'.)20&.1#4.,#+1# +35)&026*# .4# 789:;# (.,,*'5.16'# 0.# +# 6*50%# .4# 97&?1

'&?1

@A&?1

Extrapolation of ground temperature in Adriatic region >A&?1

R' #5" 8-0+#01 $"(&-'H ("-1-(&801 0'* 81&%0#" 850$08#"$&+#&8+ 0$" %-$" *&:"$+&9"*. S5" ($-)'* &+ 8-%3-+"* %0&'12 -4 80$,-'0#" $-8T+H -4#"' 850$08#"$&U"* ,2 +"8-'*0$2 3-$-+ AT0$+#E. M1&%0#&8 O)8#)0#&-'+ 0$" 0330$"'# &' #5" '-$#5"$'H %&**1" 0'* +-)#5"$'

# g ST BC8ADEFG " 1' H ! H9IAJJK # 9EA I $C t g DU =-0,1637 " ln H ! +18,586 # 17, 4 $C

=9D>

/0" )'*&+#)$,"* ($-)'* #"%4"$3#)$" 3+ 5315)13#"* ,@ )+" -7 1-(3$�%&5 7)'5#&-'+ 7-$ #0" *"4#0+ 3# 60&50 #0" 3%41&#)*" "2)31+ 8.9:; &+ #0"' =?&()$" K.>< # g OG BC8A88PK " 1' H ! H9JAJKK # 99AG $C

=9E>

!"#$%& QN"$3(" %"3+)$"* ($-)'* #"%4"$3#)$"+ &' #0" O()1&' $"(&-' 7-$ 3 4"$&-* 9GG8CJ88P =$36 )'4),1&+0"* !RST *3#3>. Tablica 4.# $%&'()&# *&+,&%-*.%&# */-# (-# /01-23)3# 4 ./3(# 5-# %-5'06/)&# 0'# 7889:;990'3?()&#-+,/3*.'&#+)&%&(3@#*&+,&%-*.%-#*/-#5-#/01-23).#4 ./3(#'0#'.63(�'#799#2+

CONCLUSION /0" )'*&+#)$,"* ($-)'* #"%4"$3#)$"+ 6"$" 5315)13#"* ,3+"* -' #0" N31)"+ -7 #0" %"3+)$"* ($-)'* #"%4"$3#)$" -,#3&'"* 3# *"4#0+ -7 )4 #- 988 5%. /0&+ +),+"2)"'#1@ 1"* #- *"L'&'( #0" *"4#0 3# 60&50 #0" &'W)"'5" -7 +-13$ $3*&3#&-' 7$-% #0" +)$735" ,"5-%"+ '"(1&(&,1".

X3+"* -' #0" *3#3 5-11"5#"* 3# LN" %"#"-$-1-(&531 +#3#&-'+ &' '-$#0"$' ;$-3#&3 3 5-$$"13#&-' 63+ %3*" ,"#6""' #0" *3%4&'( -7 #0" #"%4"$3#)$" 3%41&#)*" 3'* #0" *"4#0A #0" $"+)1# -7 60&50 63+ 3 ($-)'* #"%4"$3#)$" 3%41&#)*" -7 8.9:;. X@ )+&'( #0" #"%4"$3#)$" 3%41&#)*" *3%4&'( &# 63+ *"#"$%&'"* #03# #0" )'*&+#)$,"* ($-)'* #"%4"$3#)$" 3# 3 *"4#0 -7 98.EP% &+ 9D.9:;. Y&'5" #0" )'*&+#)$,"* ($-)'* #"%4"$3#)$" *"#"$%&'"+ *&$"5#1@ #0"

Rud.-geol.-naft. zb., Vol. 22, 2010. !"#$%&'()*+",!"-$.(/0" Determining undisturbed ground ...

36 /%-)'# -0 /1/&2/,2" "'"$(3 +#-$"* &' #4" ($-)'* #4/# 5/' ," )#&2&6"* 0-$ /'3 /++)%"* #"%7"$/#)$" 54/'("8 &# %/9"+ &# -'" -0 #4" 9"3 7/$/%"#"$+ #- 5/25)2/#" #4" $":)&$"* length of a borehole heat exchanger. !)" #- 52&%/#" *&1"$+&#&"+ &' #4" ;*$&/#&5 $"(&-'8 / 5-$$"2/#&-' Q4"$%/2 T$-7"$#&"+ -0 H-&2+8 H"$&"+ -' $-59 /'* +-&2 %"54/'&5+. U-2. ??. Q$/'+ Q"54 T),2.8 B2/)+#4/2VG"22"$0"2*8 I"$%/'38 77?WS. X&22"28 !. L?ORYN> Z'#$-*)5#&-' #- +-&2 743+&5+8 ;5/*"%&5 T$"++8 H/' !&"(-8 [H;8 77.WS@ \"2&]8 J. L?OEON> Q"$%&^9" -+-,&'" +"*&%"'#/5&-'-( 9-%72"9+/ D)(-6/7/*'-( *&D"2/ T/'-'+9-( ,/6"'/8 *-9#-$+9/ *&+"$#/5&D/8 H1")^&2&_#" ) G/($",)8 C)*/$+9-V("-2-_9-V'/0#'& 0/9)2#"#8 77.ES \"2&]8 J.` J"1$&]8 Z. L?OOEN> T2 / ("-#"$%/2'/ "'"$(&D/ ) X$1/#+9-D, S. 0-$)% X$1/#+9-( "'"$("#+9-( *$)_#1/ 8 G/($",8 X$1/#+9"'"$("#+9- *$)_#1-8 77. ?R?V?OF \"2&]8 J.` K)9/^"1&]8 a. L?ORON> H-2/$ X"/# ='"$(3 &' #4" H-&2 -0 #4" T/''-'&/' b/+&' &' #4" H-5&/2+# C"7),2&5 -0 B$-/#&/8 G,-$'&9 $/*-1/ +9)7/ H-2/$ "'"$(38 Z[B !),$-1'&98 77 ?V?Y. J/77"2%/3"$8 M.` X/"'"28 C. L?OE@N> I"-#4"$%&5+ Z+7&#'/ ("-#"$%/2'/ *&6/2&5/ #-72&'" +/ +-'*-% *),&'" ?FF %"#/$/8 J2&%/ 0-$)%8 G/*/$