HWAHAK KONGHAK Vol. 41, No. 2, April, 2003, pp. 167-173 * 449-701 1 * 608-739 100 (2002 9 5, 2003 2 15 ) Manipulation of Cooling Water Flow Rates in a Cooling Water Exhangers Network Jin-Kyeong Kim, Gyeongbeom Yi* an Bomsok Lee Department of Chemial Engineering, Kyunghee University, Seoheonli 1, Giheung-eup, Yongin 449-701, Korea *Department of Chemial Engineering, Pukyung University, San 100, Yongang-ong, Nam-gu, Busan 608-739, Korea (Reeive 5 September 2002; aepte 15 February 2003)!" #$% & ' () # *+,-. / 0123. 45!" 6 &7 89, 6 :; '< 01 => *+6 01? @A,!2 3B 45 C :; 'D EF< 7G 23. H I J 45 :; '< KL MN> '< OPM Q '$ C 01 RS TU< VWX3. YI YI '< Z[L\ RS *+,-.6! => ]^_ RS 4`< Za$%, 4` RS /6 I => RS b Cef GAMS/ MINOS6 X3. Abstrat In a large, omplex ooling water heat s network, ooling water flow rates are manipulate by ajusting the valves loate at the rear of eah heat. Sine the heat s are onnete to a network, the manipulation of the ooling water flow rate in a heat by ajusting the valve results in the hanges of the ooling water flow rates in the other heat s. Therefore, the manipulation tehniques of ooling water flow rates in a ooling water heat s network are require in orer to operate the ooling water networks effiiently. This paper presents the analysis an the manipulation metho of the ooling water flow rates in all heat s in a network simultaneously. A nonlinear programming(nlp) formulation is propose to etermine the optimal ajustment of the valves for the require flow rates of the ooling water in the heat s. Solution of this formulation is obtaine with a ommerial NLP solver (GAMS/MINOS). Key wors: GAMS/MINOS, Optimization, Exhanger Network Cooling Water Flow Rates 1.!" #$%&' ( ) %* +) #$, -./ 0 (ooling water network)1 2),3. 4 5(6 / 5) 78 9 %&': /3. ;< => %-?@ A9% BC, 01 DE % To whom orresponene shoul be aresse. E-mail: bslee@khu.a.kr 4 5F GH I 5 J K),3. </ BC JK 51 L M N OP 9 0 #$%& ( QR 3S OP JK 5 T 9' U),3. 78.E / 5VW 51 LM N XC &Y@ 3. B>, 6 Z[ OP 5\ ]^E 5 1 _ N `9a QR[11], 01 JK bb 5F e1 fg N 5 LM h ij Lk,3. lm 01 JK n o=1 p \qe: /3. r fq s 167
168 tuv 5 fg 9 w xy% =z{ Hazen- Williams {1 } {1 xye e ~ m J K!" J1 ) ƒ 3[3]. #4 0 n b!"9 #$ % H 1 noe 3. n noe ˆ1 JK 5 n noes ˆ e ~!" ŠBF m 4ƒ }, Q xy% =z{ Hazen-Williams {3. Œ/ "Ž (- 9 '9 noe.m r H{1 YE : /3. 0 JK 51 LM lm š%&' œ L E: /3. Q OP 9 0 #$%& ( QR./ 51 LM le ; œ L ƒ BC 3S OP JK 5 žÿ1 ),3. ;< OP JK 51.E / 5 G LM lm OP./ J1 YE: /3. œ m JK 51 LMƒ 3. œ ; m %!" 9 3[8]. Œ/ Hazen-Williams {!" 9 T xy%&h*, ;Q xy%!" =>!" œ 9 ª & xy),3. 01 JK 51 LM le # 4 «/ O LM T!" 9 %* š%& œ T /3. 4 5F \ q, 5F ~1 ± N3. >²Lk noe r H{F noe x JK 51 Hazen- Williams {*, >² Lk{ ³ µ, O m 4 le by "; [ GAMS/MINOS[1] xy 3. 0 O mž / 51 On V!" 9 4 ƒ 3. E $%&!" 9 š, œ, $¹ / 51 LMƒ œ $ƒ 3. 2. 2-1.!" JK º 5F ef»\ w =z { ¼ ½¾ 51 ef!" ŠB / Hazen- Williams { ÀF ˆÁ [m XC y) xy,3[4, 7, 9]. 01 4À!" ŠBF ) Â, #4 J1 le ÃÄ { (1) %&H Hazen-Williams {1 y 3. Q C H D 2.63 ---------------- H 0.54 = 6.819L E H º9 JK n H ˆ n ~(6 e~) * D L!" ŠBF Å3. \ q%& 5 Q [m 3 /s] Æl Ç3. Hazen-Williams { 41 2 2003 4 (1) Table 1. Values of roughness oeffiient for Hazen-Williams equation[10] Pipe material C H Asbestos ement 140 Dutile iron Cement line 130 to 150 New, unline 130 5-year-ol, unline 120 20-year-ol, unline 100 Conrete 130 Copper 130 to 140 Plasti 140 to 150 New wele steel 120 New rivete steel 110 -È \[ C H» É, xy #/ 78 3S Ê1 Ç 3. Table 1 Hazen-Williams { xy% -È \[ C H Ë 9H Ê1 Ì3. 0 OP noe.e 5F 5 ͵1 2&: /3. r H{ m Î }, n noe 2& 0.E noe j noe i JK J.E noe i r H{ ÃÄ { (2) Ï,3. n j = 1 Q ext, i + = 0 ( i = 1,, n) E noe j noe i JK 51 * (+) ŽÐ noe j noe i Ñ1 Ò, (-) ŽÐ noe i noe j Ñ1 Ò/3. Q ext,i noe i ÓŽŽ Œ % 5(Ô: "Ž, Œ [ blow own)1 /3. Œ/ Q ext,i BC (+) Ê1, [ BC (-)Ê,3. ;p noe i #$%H I noe j.m 0,3. Õ ]Ö/ Hazen-Williams { noe ˆ1 JK 51 Ô_ } xy,3. n noe 2& 0 noe i r H{ { (1)1 { (2). 3Ø { (3) & 3. n j = 1 2.63 C H D H j H i ji -------------------- 0.54 Q 6.819L ji + ext, i = 0 ( = i, 1, n) E H j H i noe j i n(6 e) * ; Ê noe Ù Ú /3. D ji L ji noe j i #$!" ŠBF Å3. n noe./ ³ µ #Û Ü{ O >² Lk{,3. 2-2. 0 => JK 5 4 5./ Ýx LM%&: /3. ;< O / 5F O m \q, 5F U~ ± N,3. { (4) #4 «, O Å3. Q ji ( ji, ) S Minimize ------------------- (4) (2) (3)
E Þª S noe j noe i9 4 4 BC /3. Q noe j noe i ß!" * ; 9 ]\ $, 4 5 Q ij,(j, i)àsf eá ]\Ê ;p Ž 9 DF ✠ŠB1 Hazen-Williams { ã. E 4/!" Ê1 xy/3../ \q Ô Ô >1 ]Ö 3. Œ/, Q ij, (j, i)às O mg1 D E \q, JK 51 /3. 2-3. #4 O LMT xy% N JK 51 LMƒ š, œ 3. œ œ äå 78 3æ/!" 9 3[5, 8]. #4 Ô> xy, š, œ )t œ8 ƒ Q œ9 š,! " ŠBF œ 7S 9 Table 2 Ì 3. >² Lk1 On V Ê1 ± m LMT Ê œ 9 4mH),3. m 4/!" Table 2 y/ œ 4 ç JK 4 5 G š, œ $ƒ ),3. 2-4. NLP Õ ]Ö/ >² Lk{F Lª/ O 3ØF Table 2. Equivalent lengths of gate valve for egrees of valve losing[8] Equivalent length of gate valve, L v Diameter D Degree of valve losing000 75% lose 50% lose 169 25% lose 0% lose 0.0254 21.34 5.18 1.07 0.18 0.0318 27.43 6.71 1.37 0.24 0.0889 76.20 18.29 3.66 0.61 0.1524 128.02 30.48 6.10 0.98 Ï ƒ 3. Q ji ( ji, ) S Minimize ------------------- (5) n 2.63 Subjet to C H D H j H i ji -------------------- 0.54 + Q (6) 6.819L ji ext, i = 0 ( = i, 1, n) j = 1 2.63 C H D H j H i ji -------------------- 0.54 = ij 6.819L ji (, ) S E Þª (j, i)às noe j noe i9 4 4 BC /3. l O b &H Ê è[ 4 5 Q ij, (j, i)àsf 01 4À!" ŠB D ji œ9 š,!" >Ó/ OP!" L ji *, Q \q, 51 9 JK!" Æ é ê 9 4mH),3. => Lë!" JK º ê ìí1 le [ @îlk(ô: 1-3 m/s)1 Hï:./ >²Lk1 O A9/3 3ØF Ï Lk{1 A9ƒ 3. ; Ó b &H Ê 1 noe n(fig. 1 H 40 ) ;p "Ž % ð 5 (Fig. 1 Q ext,1 )3. v min 2 --------- π v min, ij --D 4 ji ( ) S l ³ µ O m bëy "; [ GAMS/MINOS 5.3[1] ye 4ƒ 3. m 4 ç Ê $%&H T DF \q, 5 Q ij,(j, i)àsf 1 >Ó/ noe n H i (i=1,...,n- 1) % 5(Fig. 1 Q ext,40 ) ;p!" 3. m 4/! "!" => š, œ 9 ª/ m 4/!" => ñ Ê œ 9 3. +) 4 (7) (8) Fig. 1. The heat s network for example 1. HWAHAK KONGHAK Vol. 41, No. 2, April, 2003
170 / œ 9 Table 2 ye œ 4 ç 4% 51 G œ $ƒ ),3. 0 5 L M./ => xy Ô> 3Ø ]Ö 3. 4. 4-1. 1 Fig. 1F Ï 10 9 0 #$%& ( 0 3. 01 4À» 5ò ó xy, ô»3. Table 1 m Hazen-Williams { -È \ 1201 xy /3. "(noe 1) DE 0 % 5 Q ext,1 =0.0891 m 3 /s *, 9 % 1 noe 40 n õb H 40 =103 m9 H,3. )t œ9 Žš%& 3. ö b œ 25% lose 8 9 3. O LM T xy% œ l => xy% 25-75% lose / 3. Õ ]Ö/ ø Ï 4% 4 5(Q ij,(j, i)às)f DF eá ]\Ê( H ji, (j, i)às), ;p 9 DF ✠ŠB(D ji,(j, i)às)1 Hazen-Williams { ã. E m %!" 9 (L ji,(j, i) às) 4E Table 3 Ì3. Table 4 œ On 25% ö b BC.E Õ ]Ö/ O >/ Lk{ (6)F (7) 1 xye JK 51 \qe Ì3. ö b \q, 5 4 Table 3. Equivalent length an esire flow rate for eah heat of example 1 Desire flow rate [m 3 /s] Pressure rop H ji Tube size D ji Equivalent length L ji A(noe 11-12) 0.0019 3.20 0.0508 081.0 B(noe 13-14) 0.0230 13.860 0.1524 734.0 C(noe 15-16) 0.0205 2.67 0.1524 175.0 D(noe 17-18) 0.0205 6.39 0.1524 419.0 E(noe 19-20) 0.0014 6.06 0.0508 270.0 F(noe 21-22) 0.0010 3.25 0.0508 270.0 G(noe 23-24) 10.00080 6.66 0.0381 206.0 H(noe 25-26).0.0078. 7.10 0.1016 386.0 I(noe 27-28) 0.0100 9.53 0.1016 327.0 J(noe 29-30) 10.00220 1.89 0.0381 009.0 4 5F b / U~ ùú1 Table 4 û 3. JK 5./ U~ ± le #4 «/ O 1 bëy "; [ GAMS/ MINOS ü& m 4 3. m 4/!"!" => š, œ 9 ª/ m 4/!" => ñ Ê œ 9 3. +) 4/ œ 9 Table 2 ye 4/ œ 9 25-75% x H I BC m %!" ŠB1 ºE m 3 4 Üý1 xy 3.!" ºE œ 9 => @î l[ 25-75% x On QþH ÿ m 4 ç 4% 51 LMƒ œ $ƒ ) %Ì3. ; $F Table 5 Ì3. Table 6 º,!" ŠBF $, œ 7S DF \q, 5F 9 4 5F ~ Ì3. O 4/ \q, 5 4 5F ~9 ) ±/ N1  3. Table 5!" ŠB º œ @îƒ BC 0 #$, 10.E JK 51 4 5 XC Ý Ø1  3. Table 5. The egrees of valve losing after ajustment for example 1 Noe Pipe iameter* from to D L e L v Valve ajustment 12 39 0.0254 22.70 111.07 29% lose 14 35 0.0889 164.20 139.27 64% lose 16 35 *0.0889* 113.72 145.79 66% lose 18 37 0.0889 116.73 158.80 70% lose 20 34 0.0318 34.70 125.07 73% lose 22 33 0.3048 267.69 256.06 74% lose 24 32 *0.0254* 21.41 114.70 49% lose 26 31 0.0762 33.69 118.39 56% lose 28 31 0.3810 359.28 337.98 75% lose 30 36 *0.0381* 126.08 130.83 73% lose *Change iameter: new pipe iameter when the moel was not optimize with the ol pipe iameter Table 4. Initial state(eah valve 25% lose) of example 1 Valve state Desire flow rate Q [m 3 /s] Calulate flow rate Q [m 3 /s] Error [%] A 25% lose 0.0019 10.00137 27.9 B 25% lose 0.0230 0.0198 13.9 C 25% lose 0.0205 00.03036 48.1 D 25% lose 0.0205 00.01896 17.5 E 25% lose 0.0014 10.00115 17.9 F 25% lose 0.0010 10.00075 25.0 G 25% lose 10.00080 10.00071 11.3 H 25% lose.0.0078. 10.00583 25.3 I 25% lose 0.0100 10.00699 30.1 J 25% lose 10.00220 0.0.00319 45.0 Table 6. The optimize results for example 1 Desire flow rate Q [m 3 /s] Calulate flow rate after ajustment Q [m 3 /s] Error [%] A 0.0019 0.0019 0 B 0.0230 0.0230 0 C 0.0205 0.0205 0 D 0.0205 0.0205 0 E 0.0014 0.0014 0 F 0.0010 00.00105 5.0 G 10.00080 0.0008 0 H.0.0078. 0.0078 0 I 0.0100 0.00995 0.5 J 10.00220 0.0022 0 41 2 2003 4
171 Fig. 2. The heat s network for example 2. Table 7. Equivalent length an esire flow rate for eah heat of example 2 Equivalent length L ji Tube size D ji Desire flow rate Q ji [m3 /s] H1 206 0.0387 20.0 H2 206 0.0387 13.0 H3 206 0.0387 16.0 H4 206 0.0387 18.0 H5 206 0.0387 10.0 H6 206 0.0387 16.0 H7 320 0.1524 85.0 H8 235 0.4318 1975.0 H9 73 0.1524 166.0 H10 206 0.0387 10.0 H11 206 0.0387 8.0 H12 206 0.0387 15.0 H13 206 0.0387 15.0 H14 235 0.4318 1975.0 H15 52 0.0762 24.0 H16 54 0.0387 20.0 H17 54 0.0387 13.0 H18 54 0.0387 16.0 H19 54 0.0387 18.0 H20 54 0.0387 10.0 H21 54 0.0387 16.0 H22 270 0.0504 85.0 H23 75 0.2032 1975.0 H24 749 1.2954 166.0 H25 749 1.6510 10.0 H26 182 0.1524 8.0 H27 184 0.1524 15.0 H28 289 0.3048 15.0 H29 189 0.3048 1975.0 H30 838 1.0161 24.0 4-2. 2 Ô> 2 Fig. 2 ùe ø Ï 30 120 noe9 ÿ) #$, 0.E ù /3. 01 #$!" É? ô», Table 1 Hazen-Williams -È \ 1301 xy /3. 51 LM} xy% œ )t œ, ö b œ 25% lose* L l 25-60% lose /3. m m $% œ 9 V² L l[ 25-60% lose x & BC! " º ï L l Ê $% R> m %üe 4/3. îº 5 Q ext,1 =11,852.0 m 3 /s *, n 1 DE 9,3. Q noe 118 I n9 H 118 =103 m * noe 120 II n H 120 =94 m 3. 9 4 5, e á ]\Ê, 9 DF ✠ŠB, ; p Ê1 { (1) ã. E 4/ 9 Table 7 Ì3. ö b \q, 5F 4 5F ~9 & [H!m ù /3. Table 8 Ô> 2 0 OP œ1 25% lose b >² Lk{ (6)F (7) 1 xye 4/ JK 51 Ì 3. Table 8 ø Ï \q, 5F 4 5F U~9 10% 9 3 É/3. #4 «/ O m 4 ç!" 9 4 Ê!" => œ $ 9 4ƒ 3. ç 4/ œ 9 Table 2 y œ 4ƒ } Table 9 Ì3. Œ/ Table 9 ùeh Ê!" ŠB1 º œ @î 1 Q, JK 51 Table 10 Ì3. Table 10 $ F ù JK \q, 5F 4 5 HWAHAK KONGHAK Vol. 41, No. 2, April, 2003
172 Table 8. Initial state(eah valve 25% lose) of example 2 Valve state Desire flow rate Q [m 3 /s] F U~ On 10% &ÌØ1  3. 4-3. HþH E< 2& 01 JK 51 LM l/ Üý1 n Ô> & ]Ö 3. n Ô> Ô xy/ 0 => x y% 0 Žf1 «/ N!" ŠB, ;p 4 5 #$ µ / Ê1 xy 3. ;< => xy% 0 100 9þ@ 2& -./ 0 R Ô P 0 ³m ) v3. Ô > 1 10 2& 3± ˆÆ/ 0 m 4 ç & 5 4 5F - ^ Ê(Table 6)1 1 Ì3. 3V Table 5 œ Ê1 ù 70% b œ b @î 9 10 ¼ 5 ~H } => œ Ï F ) b @î N y[% HV øš3 û 1 N3. lm F ) w œ9 š,! " ŠB1 º Üó > Î 3. +) Y º,! " ŠB Ê1 O. E O 1 3 ü&: i-1 &:/3. 20 2& 3± ÿ/ 4L 01 41 2 2003 4 Calulate flow rate Q [m 3 /s] Error [%] H1 25% lose 20.0 20.3 1.5 H2 25% lose 13.0 14.9 14.6 H3 25% lose 16.0 14.9 6.9 H4 25% lose 18.0 18.2 1.1 H5 25% lose 10.0 10.0 0 H6 25% lose 16.0 14.9 6.9 H7 25% lose 85.0 50.9 40.1 H8 25% lose 1975.0 1963.3 0.6 H9 25% lose 166.0 173.5 4.5 H10 25% lose 10.0 10.3 3.0 H11 25% lose 8.0 7.7 3.8 H12 25% lose 15.0 12.8 14.7 H13 25% lose 15.0 12.5 16.7 H14 25% lose 1975.0 2281.8 15.5 H15 25% lose 24.0 16.2 32.5 H16 25% lose 13.0 11.2 13.8 H17 25% lose 13.0 11.1 14.6 H18 25% lose 15.0 20.0 33.3 H19 25% lose 13.0 11.1 14.6 H20 25% lose 12.0 11.0 8.3 H21 25% lose 13.0 14.5 11.5 H22 25% lose 15.0 16.5 10.0 H23 25% lose 310.0 290.2 6.4 H24 25% lose 2100.0 2005.8 4.5 H25 25% lose 2450.0 2300.2 6.1 H26 25% lose 170.0 198.2 16.6 H27 25% lose 240.0 237.4 1.1 H28 25% lose 651.0 797.9 22.6 H29 25% lose 915.0 816.1 10.8 H30 25% lose 556.0 539.6 2.9 Table 9. The egrees of valve losing after ajustment for example 2 Noe Change iameter from to D L e L v Valve ajustment 5 9 0.0229 24.68 6.68 58% lose 8 9 0.0178 18.82 5.82 60% lose 12 13 0.0178 13.63 0.63 25% lose 16 17 0.0203 16.63 3.63 52% lose 20 21 0.0152 15.37 2.37 50% lose 23 24 0.0178 13.63 0.63 25% lose 30 31 0.1270 108.59 65.59 60% lose 28 33 0.1651 60.10 25.10 49% lose 37 38 0.0762 118.56 24.56 60% lose 43 44 0.0203 11.84 4.84 56% lose 48 44 0.0178 12.66 2.66 49% lose 51 52 0.0635 16.24 2.24 25% lose 54 52 0.1524 83.11 49.11 60% lose 56 46 0.1651* 106.78 5.78 25% lose 59 60 0.0635 35.68 20.68 60% lose 64 65 0.0152 10.53 0.53 25% lose 69 70 0.0152 10.53 0.53 25% lose 73 74 0.0178* 15.67 5.67 60% lose 77 78 0.0152 10.53 0.53 25% lose 81 82 0.0152 10.53 0.53 25% lose 85 86 0.0152 8.27 3.27 54% lose 88 86 0.0203 26.46 6.46 60% lose 92 93 0.0762 76.66 2.66 25% lose 96 97 1.1430 99.05 46.05 28% lose 99 97 0.8890 91.12 31.12 25% lose 107 105 0.0635 50.68 20.68 60% lose 104 105 0.0635 29.41 9.41 49% lose 109 110 0.1016 75.96 32.96 60% lose 113 111 0.1397 144.90 4.90 25% lose 115 116 0.5461* 558.06 148.06 56% lose *Diameter hange for the optimization Ô> 2 œ @î l ù3 9!) 60% /H l m 4 4 5F LM, 5F U~ On 10% 3ØF Ï Lk{1 A9 3. ------------------- < 0.1 (, j ) i S Table 10 $F ù JK LM, 5 4 5ÊF On 10% U~ l " V / Ê L M, N1  3. U~ l 10%ù3 # m 4 lm { (9) &H 5 U~ $y l #% ) 9am 3. 3V R> m 4 lm \q ˆ w &9),3. => xy% -./ 0 BC( =100 ) 5 LMÊ1 4 5F `F 10% U~ l GA lm m 4 l/ '( \q ˆ ) ±,3. R xy, 5F e á =z{[ Hazen-Williams { )º9 Ç U~ O m 4 E 5 U~ [m 5 à ) %H I1 N3. */ 5 LM / BC R > Üý $y U~ l 51 LM => Lë +,, (9)
173 Table 10. The optimize results for example 2 Desire flow rate Q [m 3 /s] Lë)9 Žš, 5\(6 - \) ù *) 51 LME: ƒ N3. 5. Real flow rate after ajustment Q [m 3 /s] Error [%] H1 20.0 20.0 0 H2 13.0 13.8 6.2 H3 16.0 15.8 1.3 H4 18.0 18.0 0 H5 10.0 10.0 0 H6 16.0 15.9 0.6 H7 85.0 89.8 5.6 H8 1975.0 1987.5 0.6 H9 166.0 175.7 5.8 H10 10.0 10.0 0 H11 8.0 8.0 0 H12 15.0 14.0 6.7 H13 15.0 13.7 8.4 H14 1975.0 2014.0 2 H15 24.0 24.0 0 H16 13.0 12.0 7.7 H17 13.0 12.0 7.7 H18 15.0 15.0 0 H19 13.0 12.0 7.7 H20 12.0 12.0 0 H21 13.0 13.1 0.8 H22 15.0 15.7 4.7 H23 310.0 309.8 0.1 H24 2100.0 2128.4 1.4 H25 2450.0 2450.9 0 H26 170.0 183.2 7.8 H27 240.0 240.5 0.2 H28 651.0 664.0 2 H29 915.0 876.1 4.3 H30 556.0 567.2 2 R 01 JK 51 LM l/ Üý1 «3. lm 01 4À!" #$ H 1 DF 5./ r H{1 *C!" JK 5F!" ŠB, ;p e á»/»\{ Hazen-Williams =z{1 xy 3. Œ / š%& œ Øç JK 51 LM). O 1 VÌ3. 01 O m 4 ç $ %& 9 DE œ $ƒ Ì, +) $%& œ E n Ô> ùe ø Ï V /<@ U~ l 5 LM%Ì3. #4 $F => xy% -./ 0.m y 9a* 51 fg JK 51 LM } y) yî 1 N.,3. R /¹FÉÆ(F>iÐ: 1999-1-307-002-3) Žf[ É H0 E 1%Ì x"û23. C H D H L Q Q S : roughness oeffiient in Hazen-Williams equation : pipe iameter : heas : pipe length : esire ooling water flow rates for heat [m 3 /s] : alulate ooling water flow rates for heat [m 3 /s] : set of noe onnetions whih enotes heat s e : equivalent v : valve n : number of noes in network i : any noe j : any noe onnete to noe i ext : external flow rate into(or from) the noe 1. Brooke, A., Kenrik, D. an Meeraus, A., GAMS: A User's Guie, Release 2.25, The Sientifi Press, Massahusetts(1992). 2. Carnahan, B., Luther, H. A. an Wilkes, J. O., Applie Numerial Methos, John Wiley & Sons, New York, NY(1969). 3. Foust, A. S., Wenzel, L. A., Clump, C. W., Maus, L. an Anersen, L. B., Priniples of Unit Operations, John Wiley & Sons, New York, NY(1980). 4. Hammer an Mark, J., Water an Wastewater Tehnology, John Wiley & Sons, New York, NY(1986). 5. Lee, H., Lee, B. an Lee, I. B., Anaysis an Operation of Cooling Water Flows in a Exhanger Network, Korean J. Chem. Eng., 14(4), 257-262(1997). 6. Lee, I. B., Lee, E. S., Chung, C., Yi, G., Lee, B. an Shin, D., Chemial Proess Optimization, A-Jin, Seoul(1999). 7. King, H. W., Wisler, O. W. an Wooburn, G. W., Hyraulis, Robert E. Krieger, Floria(1980). 8. Luwig, E. E., Applie Proess Design for Chemial an Petrohemial Plants, Gulf Publishing Co., Texas(1977). 9. Male, J. W. an Walski, T. M., Water Distribution Systems: A Troubleshooting Manual, Lewis Publishers, Chelsea, Mih.(1990). 10. Mays, L. W. an Tung, Y. K, Hyrosystems Engineering an Management, MGraw-Hill, New York, NY(1992). 11. Simon, A. L., Hyraulis, John Wiley & Sons, New York, NY(1986). HWAHAK KONGHAK Vol. 41, No. 2, April, 2003