Shell-and-Tube Heat Exchangers. R. Shankar Subramanian

Transcription

1 Shell-and-Tube Heat Exchangers R. Shankar Subramanian Shell-and-tube heat exchangers are used widely in the chemical prcess industries, especially in refineries, because f the numerus advantages they ffer ver ther types f heat exchangers. A lt f infrmatin is available regarding their design and cnstructin. The present ntes are intended nly t serve as a brief intrductin. Fr detailed infrmatin abut analyzing and designing shell-and-tube heat exchangers, cnsult The Chemical Engineers Handbk ( ) (Chapter 11) r any f a variety f surces n heat exchanger design. Mechanical standards fr shell-and-tube heat exchangers are set by TEMA (Tubular Exchangers Manufacturers Assciatin) and these supplement the ASME cde fr such heat exchangers. API (American Petrleum Institute) Standard 660 supplements bth f these standards, and chemical and petrleum cmpanies als have their wn internal standards in additin. Advantages Here are the main advantages f shell-and-tube heat exchangers (Thanks t Prfessr Rss Taylr fr this list). 1. Cndensatin r biling heat transfer can be accmmdated in either the tubes r the shell, and the rientatin can be hrizntal r vertical. Yu may want t check ut the rientatin f the heat exchanger in ur labratry. Of curse, single phases can be handled as well.. The pressures and pressure drps can be varied ver a wide range. 3. Thermal stresses can be accmmdated inexpensively. 4. There is substantial flexibility regarding materials f cnstructin t accmmdate crrsin and ther cncerns. The shell and the tubes can be made f different materials. 5. Extended heat transfer surfaces (fins) can be used t enhance heat transfer. 6. Cleaning and repair are relatively straightfrward, because the equipment can be dismantled fr this purpse. Basic cnsideratins The tube side is used fr the fluid that is mre likely t ful the walls, r mre crrsive, r fr the fluid with the higher pressure (less cstly). Cleaning f the inside f the tubes is easier than cleaning the utside. When a gas r vapr is used as a heat exchange fluid, it is typically intrduced n the shell side. Als, high viscsity liquids, fr which the pressure drp fr flw thrugh the tubes might be prhibitively large, can be intrduced n the shell side. 1

2 The mst cmmn material f cnstructin is carbn steel. Other materials such as stainless steel r cpper are used when needed, and the chice is dictated by crrsin cncerns as well as mechanical strength requirements. Expansin jints are used t accmmdate differential thermal expansin f dissimilar materials. Heat transfer aspects The starting pint f any heat transfer calculatin is the verall energy balance and the rate equatin. Assuming nly sensible heat is transferred, we can write the heat duty Q as fllws. ( ) ( ) Q m C T T m C T T ht p, ht ht, in ht, ut cld p, cld cld, ut cld, in Q UA F T lm The varius symbls in these equatins have their usual meanings. The new symbl F stands fr a crrectin factr that must be used with the lg mean temperature difference fr a cuntercurrent heat exchanger t accmmdate the fact that the flw f the tw streams here is mre cmplicated than simple cuntercurrent r ccurrent flw. Cnsider the simplest pssible shell-and-tube heat exchanger, called 1-1, which means that there is a single shell pass and a single tube pass. The sketch schematically illustrates this cncept in plan view. Nte that the cntact is nt really cuntercurrent, because the shell fluid flws acrss the bank f tubes, and there are baffles n the shell side t assure that the fluid des nt bypass the tube bank. The entire bundle f tubes (typically in the hundreds) is illustrated by a single line in the sketch. The baffle cuts are aligned vertically t permit dirt particles settling ut f the shell side fluid t be washed away. Baffle T 1 t1 t T

3 The cnventin in shell-and-tube heat exchangers is as fllws: T : 1 inlet temperature f the shell-side (r ht) fluid T exit temperature f the shell-side (r ht) fluid : t inlet temperature f the tube-side (r cld) fluid 1 : t : exit temperature f the tube-side (r cld) fluid Thus, ( T1 t) ( T t1) Tlm T1 t ln T t 1 The fractin f the circular area that is pen in a baffle is identified by a percentage cut and we refer t the types f baffles shwn as segmented baffles. Fr the shell side, in evaluating the Reynlds number, we must find the crss-flw velcity acrss a bundle f tubes that ccurs between a pair f baffles, and determine the value f this velcity where the space fr the flw f the fluid is the smallest (maximum velcity). Fr the length scale, the tube utside diameter is emplyed. Mst shell-and-tube heat exchangers have multiple passes t enhance the heat transfer. Here is an example f a 1- (1 shell pass and tube passes) heat exchanger. Baffle T 1 t 1 t T As yu can see, in a 1- heat exchanger, the tube-side fluid flws the entire length f the shell, turns arund and flws all the way back. It is pssible t have mre than tw tube passes. Multiple shell passes als are pssible, but invlve fabricatin that is mre cmplex and is usually avided, if pssible. Crrectin factrs t be used in the rate equatin have been wrked ut by analysis, subject t a set f simplifying assumptins, fr a variety f situatins. In the lden days, the frmulae fr 3

4 them were cnsidered t cumbersme t use. Therefre graphs were prepared pltting t t1 T1 T F( PR, ), where P and R are parameters n which F depends. Figures C4.ad in Appendix C f the textbk by Mills display such graphs. Nwadays, ne can cmpute these T 1 t 1 t t1 factrs quickly with a pcket calculatr. Given next are the tw cmmn factrs. F 1 F 4 R P ln R 1 1 PR A+ R + 1 ln A R + 1 R P ln ( R 1) 1 PR A+ B+ R + 1 ln A+ B R + 1 P P where A 1 R, B ( 1 P)( 1 PR) The first and secnd subscripts n the factr F crrespnd t the number f shell and tube passes, respectively. The simplifying assumptins mentined in the previus paragraph, given in Perry s Handbk, are as fllws. 1. The heat exchanger is at steady state.. The specific heat f each stream remains cnstant thrughut the exchanger. 3. The verall heat transfer cefficient U is cnstant. 4. All elements f a given fluid stream experience the same thermal histry as they pass thrugh the heat exchanger (see ftnte in Perry fr a discussin regarding the vilatin f this assumptin in shell-and-tube heat exchangers). 5. Heat lsses are negligible. The frmula given abve fr F1 als applies fr ne shell pass and, 4, (r any multiple f ) tube passes. Likewise, the frmula fr F 4als applies fr tw shell passes and 4, 8, (r any multiple f 4) tube passes. In designing heat exchangers, ne shuld avid the steep prtin f the curves f F versus P, because small errrs in estimating P can cause large changes in the value f F. A misleading rule f thumb is that F 0.8, but the crrect idea is that the regin f steep fall-ff in the curves shuld be avided. 4

5 Heat Transfer Cefficients The evaluatin f the verall heat transfer cefficient is an imprtant part f the thermal design and analysis f a heat exchanger. Yu ll find several tables f typical verall heat transfer cefficients in shell-and-tube heat exchangers in Chapter 11 f Perry s Handbk. The fllwing generic result can be written fr the verall heat transfer cefficient U based n the utside surface area f the tubes, which is the heat transfer surface. 1 1 r A 1 A R + R U h k Alm hi Ai f,0 f, i In the abve equatin, h is the heat transfer cefficient fr the fluid flwing in the shell, h i is the heat transfer cefficient fr the fluid flwing thrugh the tubes, A i and A are the inside and utside surface areas f a tube, respectively, and A lm is their lg mean. The fuling resistances n a unit area basis are R f,0 fr the shell side, and R f, i fr the tube side. Accumulated infrmatin n fuling resistances can be fund in the Standards published by TEMA. The inside heat transfer cefficient h i can be evaluated using the standard apprach fr predicting heat transfer in flw thrugh tubes, including applying a viscsity crrectin where pssible. Typically, turbulent flw can be expected, and a gd design wuld aim t arrange fr turbulent flw, because f the substantial enhancement in heat transfer prvided by eddy transprt. Predicting the shell-side heat transfer cefficient h is mre invlved, because the flw passage is nt simple, even in the absence f baffles. The presence f baffles needs t be taken int accunt in calculating the fluid velcity acrss the tube bank. Heat transfer crrelatins fr flw thrugh tube banks are used, such as thse given in the bk by Hlman (1). These crrelatins assume flw nrmal t the lng axes f a set f tubes placed in a gemetrical array. The crrelatin given in Hlman s bk is Nu hd k C n 1/3 Re Pr DV maxρ The Reynlds number Re, where D is the utside diameter f a tube. V max is the µ maximum velcity f the fluid thrugh the tube bank. T find it, first, the crss-flw area clearance must be evaluated. This is given as Crss flw area Shell ID Baffle spacing pitch where the clearance l and pitch S n (nrmal t the flw directin) are illustrated in the sketch n the next page fr tubes in a square pitch. 5

6 Flw directin pitch S p clearance l pitch S n D Tube OD The clearance l Sn D. When the vlumetric flw rate f the shell-side fluid is divided by the crss-flw area defined here, it yields the maximum velcity thrugh the tube bank, V max. The symbls k, ρ, and µ represent the thermal cnductivity, density, and viscsity f the shellside fluid, respectively, and all the prperties shuld be evaluated at the arithmetic average temperature f that fluid between the tw end temperatures. The symbl Pr stands fr the Prandtl number f the shell-side fluid. The expnent n and the multiplicative cnstant C depend n the pitch t tube OD rati, and are given in a table prvided in Hlman s bk. An excerpt frm the table fr tubes n a rectangular pitch (in-line tube rws) is given belw. Values f the cnstant C Sn / D Sp / D

7 Values f the cnstant n Sn / D Sp / D As an alternative, ne can use the prcedure utlined in Sectin f the bk by Mills. Fr the shell-side heat transfer cefficient, the Nusselt number calculated frm crrelatins using prperties at the arithmetic average f the inlet and exit temperatures is usually sufficient. The actual flw patterns are mre invlved, because the flw entering the shell has t distribute itself int the space in which the tubes are lcated, and then the flw has t turn arund each baffle. At the exit, the flw again has t cnverge tward the exit pipe frm the shell. In additin, crrectins need t be applied fr leakage arund the baffles, fr by-pass f tube bundles, and ther less imprtant nn-idealities. As a rugh rule f thumb, because f these varius crrectins, the ideal heat transfer cefficient h fr flw acrss the tube bank calculated using a suitable crrelatin is multiplied by a cnservative crrectin factr f 0.6 in the end. Pressure Drp Tube-Side Pressure Drp In designing heat exchangers, pressure drp cnsideratins are usually quite imprtant. Typically, a design cnstraint might be P N psi, where the number N is specified, and such cnstraints may apply n bth the tube side and the shell side. Calculatin f the tube-side pressure drp is made by first estimating the (Darcy) frictin factr fr flw thrugh the tubes frm the value f the Reynlds number and the relative rughness, and applying the viscsity crrectin we discussed in class. Then, this frictin factr is used t evaluate the pressure drp fr flw thrugh the tubes frm L 1 P f V D crrected ρ Number f tube passes where L is the length f the tubes, D is the ID f the tubes, ρ is the density f the tube-side fluid, and V is the average flw velcity thrugh a single tube. T this, we must add Pr, the return pressure lss. This accunts fr the pressure drp assciated with fluid entry int the tube bundle, fluid leaving the bundle, and fluid flwing arund bends. 7

8 G t Pr 4 Number f tube passes ρ Here, Gt ρ V is the mass velcity and is defined as Mass flw rate m Gt Ttal flw area available per pass At and A t Ttal number f tubes Crss - sectinal area f a tube Number f passes Shell-Side Pressure Drp There are several ways t estimate the pressure drp fr the flw f the shell-side fluid in a shelland-tube heat exchanger. A reasnable estimate can be btained by the relatively simple apprach described belw, which is given in a bk by Peters, Timmerhaus, and West (). This bk als prvides much valuable infrmatin n the design f such heat exchangers, including mre sphisticated methds f estimating the pressure drp. The pressure drp n the shell-side is calculated using P shell fgd ( N + ) s s B ρd µ e µ s In this equatin, f is a Fanning frictin factr fr flw n the shell side given in Figure f reference (), G s is the mass velcity n the shell side, D s is the inside diameter f the shell, N B is the number f baffles, ρ is the density f the shell-side fluid, and D e is an equivalent diameter. The mass velcity Gs m/ Sm, where m is the mass flw rate f the fluid, and S m is the crssflw area measured clse t the central symmetry plane f the shell cntaining its axis. This area is defined as clearance Crss flw area Ds LB pitch where B L is the baffle spacing, and the clearance and pitch are defined in the ntes n shell-andtube heat exchangers. The equivalent diameter is defined as fllws. 8

9 D e π D 4 CS p 4 π D 0 n 0 Here, D 0 is the utside diameter f the tubes, and S n is the pitch (center-t-center distance) f the tube assembly. The cnstant C p 1 fr a square pitch, and C p 0.86 fr a triangular pitch. The frictin factr f is given in Figure f the bk as a functin f the Reynlds number based n the equivalent diameter (Nte the difference frm the Reynlds number that we use fr the heat transfer cefficient frm Hlman, which uses D 0 as the length scale). Fr the frictin factr graph, we must use the Reynlds number Re defined as DG µ e s Re where µ is the viscsity f the shell-side fluid. A scanned image f Figure frm Peters et al. () is available fr yur use at the curse web site. An alternative apprach t estimating the shell-side pressure drp is given n pages t frm Perry s Handbk; the ntatin is explained in pages 11-7 and But, it is recmmended that yu use the simple apprach given in Peters et al. (). Cst Cst is always an imprtant cnsideratin in designing any prcess equipment. Cst can be brken int tw principal cmpnents capital cst and perating cst. In additin, maintenance csts are incurred during peratin, but they tend t be mre r less independent f the size f the heat exchanger, s lng as the size is within a reasnable range. The capital cst fr heat exchangers increases with increase in the heat transfer area, and is evaluated by using values knwn frm , and applying a multiplicative factr knwn as the Cst Index. This index is published in each issue f Chemical Engineering, and uses 100 a the basis fr the cst in T find the cst fr the equipment in , cnsult the nmgram in Figure and Tables and frm Perry s Handbk. Operating cst is primarily pumping cst. The pumps must prvide wrk t vercme the pressure drp n the tube side and that n the shell side. The shaft wrk per unit mass f fluid is P / ρ, and this must be multiplied by the mass flw rate f the stream t btain the shaft wrk per unit time r shaft pwer. Then, this must be divided by the verall pump efficiency t btain the actual pwer needed. It is typical t cnservatively assume the verall pump efficiency t be 0.6. The yearly pumping pwer cst can be calculated if ne knws the cst per KWH (kilwatthur). Yu can assume peratin 4 hurs per day fr 350 days a year (the remaining days being nminal maintenance shutdwn days). 9

10 By writing ff the capital csts ver a certain length f time, the ttal cst per year can be wrked ut. This is then minimized by making a suitable chice f heat exchanger, a jb that requires examining several designs using sftware t perfrm the tedius cmputatins. References 1. J.P. Hlman, Heat Transfer, 9 th Editin, McGraw-Hill, 00.. Peters, M.S., Timmerhaus, K.D., and West, R.E., Plant Design and Ecnmics fr Chemical Engineers, McGraw-Hill, New Yrk,