How to Figure True Temperature Difference in Shell-and-Tube ...

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e different. For example, one difference will be T 1 - t 1 , and the Pattern for one-shell pass; two-tube pass other will be T 2 - t2' t 2This type 'Of flDW pattern is sel f r- ...., i T1dDm used. It is not very effiCfentand therefore -will not cDol a givenfluid as. much as the CDuntercurrentflDW will. The hot 'Outlet temperaturecan 'Only approach the cold'Outlet; it cannot crDSS it.But use can be made of this inabilitytD cross temperatures. Forexample, in wax and. asphaltic cDolers,coeUITent flow is' used tD makesure that the sDlidificatiDn point willnDt be reached. If CDuntercurrentflow were used, there would be danger'Of cooling below design whenthe exchanger is clean..9.8.7.5[;1" I I I, ,,! I+T 1 -t 1 t 2 -t 1~~IC?.~ C!C! C!1C!:Jt c .. \LC~tt~~~~~oo...o LnRood', ~tl('l'\LIllI •.t 2-t T -T1 1 2X=--.· R=-T1 = Inlet temperature shell sideT2::: Outlet temperature shell sidet1 = Inlet temperature tube sidet2::: Outlet temperature tube side;a.t 1and errDr, but a much faster chartmethod is cDmmDnly used. Thischart method is based on applyingaCDrrectiDn factDr tD the log-me antemperaturedifference. Then, thetrue temperature difference for thisflDW pattern will be:LlTc = LMTD (F) (3)Where LMTD is defined byEquatiDn 2F = cDrrectiDn factDrIf there is. CDnstant temperature'On either side; F will be 1.0.Fig. 4 is the LMTD cDrrectionfactDr fDr a 'One-shell pass, two-ormoretube-pass exchanger. SeveralpublicatiDns I 2 3 give cDrr~ctiDn-factDrcurves fDr one tD six shells inseries. and even number of tubepasses.TD use the correctiDn curves it is_i\~_ ..Q~c:i~~ --'••••\ • ......-.~ .~\..... ~~-~~~~~r...::..,T2 + Fig. 3necessary tD calculate two dimensiDnlessparameters. The parameter'On the curves is called R and isequal to:T 1 -T 2 WCR = Dr -- (4)t2 -t 1weWhere:wc = heat capacity of tube fluid,Btu/OF.we = heat capacity 'Of shell fluid,Btu/OF.The variable 'On the abscissa iscalled X and is defined by:t2 -t1x = -----"-'-''---'-- (5)T 2 -t 1As shown in Fig. 4, at high valuesof R it is difficult tD read F accurately.TD 'Overcome this prDblem,the parameters 'Of R and X can beredefined:b,~'5:.f).~'l,. '1,\,MTD correction factors 1 shell pass 2 or more tube passes '"" Fig. 4.1 .2 .3 .4 .5 .6xTHE OIL AND GAS JOURNAL • SEPTEMBER 14, 1964.7 .8 .9 1.0109
o-:,)smallest temperature rangeWhen R = 1, Equations 6 and 7 break down, and Equations 6a andR= ~~ 7 a should be used:greatest temperature rangeXgreatest temperature range X n - 2n = (6a)X =(Sa)Tl~hIt follows that R will always beX n - 2ny'2 (----'----1 or less, and that the curves will 1 - X n - 2nalways have a relatively flat slope. F n - 2n = (7a)For example, when the shell fluid (2/Xn-2n~ - 1 - R + y'R2 + 1cools from 190 0 to 90 0 and the In [----------tube-side fluid heats from 80 0 to (2/X n - 2n) ....,. 1 - R - y'R2 + 190 0 • Using Equations 4 and 5:Where n = number of shell passes.Whenever there is a temperature190 - 90 cross in one exchanger, the thermalR = = 10 Use Equation 6 to calculate Xdesign should be checked very care90 - 80 for the desired number of shells infully. (This occurs at a correctionseries. Then use this value in Equafactorof approximately 0.8, or90 - 80 tion 7 to obtain F.when the correction factor is lessX == = 0.091 Suppose it is desired to find the190 - 80 than 0.8 with shell passes in series.)MTD correction factor for the folThis should be done for two realowingtemperature conditions:A slight misreading of X cansons:make an appreciable difference inHot' Cold 1. It may be more economical toF. But by using Equations 4a anduse more shells in series, especially410Sa we find:404 i if the units are made of an expen1400 204 Isive alloy.90 - 80 2. 'The exchanger may not work10 200R = = 0.1 as well as it was designed for. At190 - 90 R = 10/200 = 0.05 close temperature. approaches theMTD correction factors tend to190 - 90 X =200/206 = 0.971 break down at low values of F.X = = 0.91 Very seldom are three tube passes190 - 80Using Equation 6 and three shellsin series as an example, (or a larger odd number) used.Now, the correct value of 0.826 is easily read from Fig. 4. '1 - 0.05 X 0.9711 - ( )1/Equations 4a and Sa should only31 - 0.971be used with the normal one-shellX 3-6 = = 0.70pass and even number of tube passes. 1- 0.05 x 0.971They are inadequate for divided 0.05 - ( )1 /3flow or split flow. In this latter type 1 - 0.971of flow pattern the relationship R =we/We is violated.Then, from Equation 7,Sometimes R will be outside thenormal range of chart values, andy'(0.05)2 + 1 1 - 0.70more than six shell passes in seriesIn (-----0.05 - 1 1 - 0.05 x 0.70will be needed. In these cases useF 3-6 = = 0.988the follOwing equations, based on(2/0.70) - 1 - 0.05 + y'(0.05)2 + 1work by Bowman: 4 In [1-RX(2/0.70) - 1 - 0.05 - y'(0.05)2 + 11- ( - - ) l/n "Manufacturing difficulties m a k eI-XTo calculate the corrected MTDevery type but a fixed-tube-sheetX n - 2n =(6) by computer, block diagraming inunitundesirable.corporating Equations 6 and 7 canFischer6 derived a trial-and-errorR-( be found. 5I-Xsolution for a one-sheIl-pass". threetUbe-passunit. One tube pass is iny'R2+1 1 - X n - 2n cocurrent flow and the other twoIn (-----are in countercurrent flow. SinceR-1 1 - R X n - 2n more than one-half of the tubeFn- 2n = (7) passes are in countercurrent flow,(2/X n - 2n) - 1 - R + y'IP + 1 the correction factor is higher than~[ ] in an even-tube-pass unit. A correc(2/Xn- 2n) - 1 - R - y'R2 + 1 . tion-factor chart for one shell is110 THE OIL AND GAS JOURNAL • SEPTEMBER 14, 1964
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How to Figure True Temperature Difference in Shell-and-Tube ...

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