Manipulation of Cooling Water Flow Rates in a Cooling Water Heat Exchangers Network
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1 HWAHAK KONGHAK Vol. 41, No. 2, April, 2003, pp * * ( , ) 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 , Korea *Department of Chemial Engineering, Pukyung University, San 100, Yongang-ong, Nam-gu, Busan , Korea (Reeive 5 September 2002; aepte 15 February 2003)!" #$% & ' () # *+,-. / !" 6 &7 89, 6 :; '< 01 => *+6 3B 45 C :; 'D EF< 7G 23. H I J 45 :; '< KL MN> '< OPM Q '$ C 01 RS TU< VWX3. YI YI '< Z[L\ RS *+,-.6! => ]^_ RS 4`< Za$%, 4` RS /6 I => RS b Cef GAMS/ MINOS6 X3. Abstrat In a large, omplex ooling water heat s network, ooling water flow rates are manipulate by ajusting the valves loate at the rear of eah heat. Sine the heat s are onnete to a network, the manipulation of the ooling water flow rate in a heat by ajusting the valve results in the hanges of the ooling water flow rates in the other heat s. Therefore, the manipulation tehniques of ooling water flow rates in a ooling water heat s network are require in orer to operate the ooling water networks effiiently. This paper presents the analysis an the manipulation metho of the ooling water flow rates in all heat s in a network simultaneously. A nonlinear programming(nlp) formulation is propose to etermine the optimal ajustment of the valves for the require flow rates of the ooling water in the heat s. Solution of this formulation is obtaine with a ommerial NLP solver (GAMS/MINOS). Key wors: GAMS/MINOS, Optimization, Exhanger Network Cooling Water Flow Rates 1.!" #$%&' ( ) %* +) #$, -./ 0 (ooling water network)1 2),3. 4 5(6 / 5) 78 9 %&': /3. ;< => %-?@ A9% BC, 01 DE % To whom orresponene shoul be aresse. bslee@khu.a.kr 4 5F GH I 5 J K),3. </ BC JK 51 L M N OP 9 0 #$%& ( 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
2 168 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 !" 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 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 { (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 year-ol, unline 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 #$%H I noe j.m 0,3. Õ ]Ö/ Hazen-Williams { noe ˆ1 JK 51 Ô_ } xy,3. n noe 2& 0 noe i r H{ { (1)1 { (2). 3Ø { (3) & 3. n j = C H D H j H i ji Q 6.819L ji + ext, i = 0 ( = i, 1, n) E H j H i noe j i n(6 e) * ; Ê noe Ù Ú /3. D ji L ji noe j i #$!" ŠBF Å3. n noe./ ³ µ #Û Ü{ O >² Lk{, => JK / Ýx LM%&: /3. ;< O / 5F O m \q, 5F U~ ± N,3. { (4) #4 «, O Å3. Q ji ( ji, ) S Minimize (4) (2) (3)
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 / #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 ), 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 % lose 0% lose Ï ƒ 3. Q ji ( ji, ) S Minimize (5) n 2.63 Subjet to C H D H j H i ji Q (6) 6.819L ji ext, i = 0 ( = i, 1, n) j = C H D H j H i ji = 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 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 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 ) 4 (7) (8) Fig. 1. The heat s network for example 1. HWAHAK KONGHAK Vol. 41, No. 2, April, 2003
4 170 / œ 9 Table 2 ye œ 4 ç 4% 51 G œ $ƒ ), L M./ => xy Ô> 3Ø ]Ö Fig. 1F Ï #$%& ( À» 5ò ó xy, ô»3. Table 1 m Hazen-Williams { -È \ 1201 xy /3. "(noe 1) DE 0 % 5 Q ext,1 = m 3 /s *, 9 % 1 noe 40 n õb H 40 =103 m9 H,3. )t œ9 Žš%& 3. ö b œ 25% lose 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) B(noe 13-14) C(noe 15-16) D(noe 17-18) E(noe 19-20) F(noe 21-22) G(noe 23-24) H(noe 25-26) I(noe 27-28) J(noe 29-30) F 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 ) 4/ œ 9 Table 2 ye 4/ œ % x H I BC m %!" ŠB1 ºE m 3 4 Üý1 xy 3.!" ºE œ 9 l[ 25-75% x On QþH ÿ m 4 ç 4% 51 LMƒ œ $ƒ ) %Ì3. ; $F Table 5 Ì3. Table 6 º,!" ŠBF $, œ 7S DF \q, 5F 9 4 5F ~ Ì3. O 4/ \q, 5 4 5F ~9 ) ±/ N1  3. Table 5!" ŠB º BC 0 #$, 10.E JK 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 % lose % lose *0.0889* % lose % lose % lose % lose *0.0254* % lose % lose % lose *0.0381* % 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 B 25% lose C 25% lose D 25% lose E 25% lose F 25% lose G 25% lose H 25% lose I 25% lose J 25% lose 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 B C D E F G H I J
5 171 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] H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H Ô> 2 Fig. 2 ùe ø Ï 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 , 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 1 Q, JK 51 Table 10 Ì3. Table 10 $ F ù JK \q, 5F 4 5 HWAHAK KONGHAK Vol. 41, No. 2, April, 2003
6 172 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  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% þ@ 2& -./ 0 R Ô P 0 ³m ) v3. Ô > & 3± ˆÆ/ 0 m 4 ç & 5 4 5F - ^ Ê(Table 6)1 1 Ì3. 3V Table 5 œ Ê1 ù 70% b œ 9 10 ¼ 5 ~H } => œ Ï F ) 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± ÿ/ 4L Calulate flow rate Q [m 3 /s] Error [%] H1 25% lose H2 25% lose H3 25% lose H4 25% lose H5 25% lose H6 25% lose H7 25% lose H8 25% lose H9 25% lose H10 25% lose H11 25% lose H12 25% lose H13 25% lose H14 25% lose H15 25% lose H16 25% lose H17 25% lose H18 25% lose H19 25% lose H20 25% lose H21 25% lose H22 25% lose H23 25% lose H24 25% lose H25 25% lose H26 25% lose H27 25% lose H28 25% lose H29 25% lose H30 25% lose Table 9. The egrees of valve losing after ajustment for example 2 Noe Change iameter from to D L e L v Valve ajustment % lose % lose % lose % lose % lose % lose % lose % lose % lose % lose % lose % lose % lose * % lose % lose % lose % lose * % lose % lose % lose % lose % lose % lose % lose % lose % lose % lose % lose % lose * % lose *Diameter hange for the optimization Ô> 2 l ù3 9!) 60% /H l m 4 4 5F LM, 5F U~ On 10% 3ØF Ï Lk{1 A < 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)
7 173 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 [%] H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H 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: ) 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), (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
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