Computer Aided Design (CAD) of a Multi-component Condenser

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1 S. BANDYOPADHYAY et al., Cputer Aded Desgn (CAD) f a Mult-cpnent, Che. Bche. Eng. Q. 21 (2) (2007) 97 Cputer Aded Desgn (CAD) f a Mult-cpnent Cndenser S. Bandypadhyay, M. S. Ala, V. K. Agrawal, and K. L. Wasewar* Checal Engneerng Departent, Indan Insttute f Technlgy, Rrkee Inda, Tel.: , Fax: , Eal: klw73fch@tr.ernet.n, k_wasewar@redffal.c Orgnal scentfc paper Receved: June 6, 2006 Accepted: Nveber 27, 2006 In the case f ult-cpnent cndensatn the cndensng vapur cntans a xture f cpnents havng dfferent blng pnts, whch cndense ver a wde teperature range, ether n presence f r absence f nn-cndensng ateral. In ths wrk, a desgn algrth fr the cndensatn f a ult-cpnent vapur xture n shell sde f a shell and tube vertcal cndenser has been develped usng Bell and Ghaly s ethd. Based n ths algrth, an n-huse cputer cde has been develped. Ths cde was used fr the desgn f the cndenser fr the cndensatn f a hydrcarbn vapur xture cntanng prpane, butane, hexane, heptane and ctane n the le cpstn f 0.15, 0.25, 0.05, 0.30 and 0.25, respectvely. A cde was als develped fr the Kern s ethd fr the cndenser desgn. It was fund that Kern s ethd prvdes a lesser heat transfer area because Kern s ethd des nt cnsder the ass transfer resstance, nr des t take care f handlng the sensble heat transfer durng cndensatn. These facts have been ncrprated n Bell and Ghaly s ethd by takng the ne-phase heat transfer ceffcent durng vapur sensble heat transfer. The effects f peratng varables vz. vapur flw rate, clant flw rate, vapur nlet teperature, and clant nlet teperature n the verall heat transfer ceffcent, and shell sde pressure drp have been studed fr the wde range f paraeters. The results are useful fr the desgn f ult-cpnent cndensatn. Key wrds: CAD, ult-cpnent cndensatn, desgn Intrductn *Crrespndng authr A cndenser s a devce n whch the heat reved n the prcess f cnvertng a vapur t lqud s transferred t a clant. An ndrect r surface cndenser has a thn wall separatng the clant fr the vapur and ts cndensate; the heat passes thrugh ths wall. The surface used n ndrect cndensers ay be plates r tubes and these surfaces can be plan, extended wth fns, enhanced by passve r actve augentatn technques. The physcal arrangeent f the surfaces can take any frs and affects the tw-phase flw patterns f the vapur-cndensate xture and the flw pattern f the clant, thus nfluencng the heat transfer rates. The shell sde cndensatn plays an prtant rle n a varety f engneerng applcatns ncludng electrc pwer, refrgeratn, and checal prcess ndustres. Nwadays, sgnfcant nsght has been ganed nt the tw-phase flw pattern and heat transfer phenenn that ccurs n the shell sde f a surface cndenser. In the case f ult-cpnent cndensatn, the cndensng vapur cntans a xture f cpnents havng dfferent blng pnts, whch cndense ver a wde teperature range, ether n presence r absence f nn-cndensng ateral. The three wrds ult-cpnent vapur xture cver a wde range f stuatns. One lt f ths range s ne n whch all cpnents have blng pnts abve axu clant teperature; n ths case the xture can be ttally cndensed. The ther lt s a xture n whch at least ne cpnent n the ntal vapur strea has a blng pnt lwer than the nu clant teperature and, als s neglgbly sluble n the lqud cndensate fred fr the ther cpnents and hence cannt be cndensed at all. An nteredate case s typfed by a xture f lght hydrcarbns n whch the lghtest ebers ften cannt be cndensed as pure cpnents at the teperature encuntered n the cndenser, but nstead wll dsslve n the heaver cpnents. In each f these cases, the vapur xture ay fr partally r cpletely scble cndensate. Exstng ethds fr desgnng heat exchangers t cndense ult-cpnent xtures can bradly be classfed nt tw basc ethds: equlbru ethds, such as thse prpsed by Kern, 1 and Bell and Ghaly 2 and the dfferental r nn-equlbru ethds that have been develped fllwng the wrk f Clburn and Drew. 3 Clburn and Hugen 4

2 98 S. BANDYOPADHYAY et al., Cputer Aded Desgn (CAD) f a Mult-cpnent, Che. Bche. Eng. Q. 21 (2) (2007) and later Clburn and Edsn 5 frulated n farly rgrus fr the equatns and desgn prcedure fr cndensatn f a pure cpnent fr a cpletely nsluble gas n ether c-current r cunter-current flw. Kern 1 prpsed a general-purpse desgn ethd based n the equlbru del. He suggested hw t eply the nnlnear cndensatn teperature curve nstead f the lg ean teperature dfference but dd nt dscuss hw t handle a ultpass clant quanttatvely. Bell and Ghaly 2 prpsed an apprxate generalzed desgn ethd based n the equlbru ethd fr ult-cpnent partal cndensers. They cpensated the errr ntrduced by neglectng the ass transfer resstance by verestatng the heat transfer resstance. After Bell and Ghaly 2 a lttle wrk has been dne n the equlbru del. T desgn a cndenser usng fl thery ethds requres calculatns f the lcal heat and ass transfer rates and ntegratng these lcal rates ver the cndenser length usng dfferental ass and energy balances. Ths was prpsed by Krshna and Panchal. 6 In ths paper, an n-huse CAD algrth f a ult-cpnent cndenser based n the equlbru del has been develped t nvestgate the effects f peratng varables vz. vapur flw rate, clant flw rate, vapur nlet teperature and clant nlet teperature n the weghted ean teperature dfference, the heat transfer area, verall heat transfer ceffcent, and shell sde pressure drp f cndenser. Mult-cpnent cndenser desgn T desgn a ult-cpnent cndenser, ne requres a sutable ethd t evaluate the verall heat transfer ceffcent, whch s useful fr deternng the heat transfer area. Evaluatn f the verall heat transfer ceffcent needs sutable equatns t predct the heat transfer rates. e. heat transfer ceffcents. In ths paper, the equlbru ethd prpsed by Bell and Ghaly 2 was cnsdered fr predctng the surface area requred fr heat transfer because f ts rbustness, speed, and relablty. Cndensatn at shell sde, n a vertcal shell and tube heat exchanger was cnsdered because f ts large ndustral practces and sutablty twards the equlbru ethd. Fr the tube arrangeent, square, trangular and rtated square layuts were cnsdered. Mult-cpnent cndensatn takes place ver a wde teperature range fr dew t bubble pnt. Therefre, t s necessary t deterne the dew and bubble pnts befre startng desgn calculatns. Assuptns The desgn ethd s based n the fllwng assuptns: 1. The lqud and vapur cpstns are n equlbru at the vapur bulk teperature. 2. Lqud and vapur enthalpes are thse f the equlbru phases at the vapur bulk teperature. 3. The sensble heat f the vapur s transferred fr the bulk vapur t the vapur-lqud nterface by a cnvectve heat transfer prcess. The heat transfer ceffcent s calculated fr a crrelatn fr the geetry nvlved, assung nly the vapur phase s present and usng physcal prpertes f vapur and lcal vapur flw rate. 4. The ttal latent heat f cndensatn and sensble heat f the clng cndensate are transferred thrugh the entre thckness f the lqud fl. Dew and bubble pnt teperature The dew pnt f vapur crrespnds wth the nset f cndensatn and the bubble pnt wll crrespnd wth ttal cndensatn. At any teperature nteredate t the dew and bubble pnt, the cpstns f the equlbru lqud x and y can be deterned by vapur lqud equlbru cnsderatn. At dew pnt At bubble pnt n x 1 1 (1) n y 1 1 (2) At any nteredate teperature, the vapur fractn ust satsfy the fllwng equatn: ZF, y( 1 ) x (3) where Z F,I s the vapur feed cpstn. Fr eq. (3) the fllwng equatns are btaned fr calculatng the vapur and lqud xture s cpstn. and x x ZF, 1 ( K 1) KZ F, 1 ( K 1) (4) (5)

3 S. BANDYOPADHYAY et al., Cputer Aded Desgn (CAD) f a Mult-cpnent, Che. Bche. Eng. Q. 21 (2) (2007) 99 The shell-sde heat-transfer ceffcent was btaned fr the crrelatn taken fr the Heat Exchanger Desgn Handbk 7 whle the pressure drp was btaned fr the Martnell equatn. 8 The tube-sde heat-transfer ceffcent was btaned fr the crrelatn gven by Kutaleladze and Brshansk 9 and pressure drp fr the crrelatn taken fr Culsn and Rchardsn. 10 Heat transfer area The basc equatn fr calculatn f the heat transfer area s U A T (6) T where, U s the ean verall heat transfer ceffcent, A s the ttal heat exchanger area, and T s the ean teperature dfference between the ht and the cld flud strea. The nature f the heat release curve n ult-cpnent cndensatn s nt lnear. Therefre, t s unrealstc t take the ean teperature dfference and ean verall heat-transfer ceffcent ver the whle exchanger. Here, the calculatn was carred ut at each pnt and then the results were ntegrated t btan the ttal exchanger area. Durng cndensatn, there are three types f heat lads t be accunted fr ttal heat lad. These are latent heat lad, lqud sensble heat lad, and vapur sensble heat lad. where, U d d d T sv da da da h da p U ( T T ) (7) p c 1 da x w Rd A k A R 1 d d d h where subscrpt and stand fr the nsde and utsde f the tube, respectvely. The heat flux fr the sensble heat reval fr the vapur t the vapur-lqud nterface s gven as fllws: d da sw w sw v l h ( T T ) (8) Substtutn f T l fr eq. (8) nt eq. (7) gves: d T U ( T T ) v c 1 da ZU h (9) where, Z d sv d T Integratn yelds the fllwng equatn: ZU A 1 T hsv da d T 0 0 U TvT (10) ( ) The verall heat transfer ceffcent fr ult-cpnent cndensatn U c s calculated by the fllwng equatn: 1 1 U Z U h (11) c sv If the assuptns are taken that U and h sv depend nly upn the lcal vapur sde cndtn, the generalzed desgn equatn fr the ultpass can be wrtten as fllws where, T A ZU 1 T hsv d U TvT T T 0 ( ) ( ) N tp k1 T N k c tp (12) The ter ( TT ) wthn the ntegratn lt s the ean teperature between the ht vapur and the clant at any pstn. The ntegratn s carred ut nuercally and the znes are nsuffcently sall, hence the lgarthc teperature dfference at each nterval was taken. Results and dscussn The upper and lwer lts f the peratng varables used are gven n Tab. 1. The value f a set f peratng and geetrcal varables and utput varables are gven n Tab. 2. A lgcal structure and flw chart based n the algrth used fr the desgn f the cndenser are shwn n Fg. 1(a) and 1(b). The surface area f the cndenser calculated fr varus cuulatve heat lad fr cndensatn f hydrcarbn vapurs usng Kern s and Bell and Ghay s Table 1 Range f varables Varable Vapur flw rate q /kg s 1 Vapur nlet teperature T /K Clant flw rate q /kg s 1 Clant nlet teperature T c /K range

4 100 S. BANDYOPADHYAY et al., Cputer Aded Desgn (CAD) f a Mult-cpnent, Che. Bche. Eng. Q. 21 (2) (2007) Table 2 Set values f peratng, geetrcal, and utput varables fr the cndensatn f hydrcarbn vapur xture Varable Value Operatng varables: clant flw rate, q a /kg s vapur nlet teperature, T,v /K vapur utlet teperature, T,v /K clant nlet teperature, T c /K clant flw rate, q c /kg s pressure, p/kpa Geetrcal varables: tube uter daeter, d / 25.4 tube nsde daeter, d / length f tube, l/ ptch arrangeent Equlateral trangular ptch ptch 1.25d nuber f tubes, N 2 baffle type 25% cut Segental baffle baffle spacng, D s /5 tube sheet thckness, / 54 tube rughness, theral cnductvty f tube wall ateral, h/w 2 K fulng resstance, R/ 2 KW Output varables: dew pnt f the vapur xture, T d /K bubble pnt f the vapur xture, k ttal heat lad, l /kw weghted ean teperature dfference, T/K 77.0 verall heat transfer ceffcent, U/W 2 K heat transfer surface area, A/ ttal nuber f tubes, N t 752 tube sde pressure drp, p/pa shell sde pressure drp, p/pa ethds are shwn n Fg. 2. Fg. 2 reveals that Kern s ethd under desgn the ult-cpnent cndenser. Bth the ethds gve the sae area fr superheatng and subclng zne but dffer durng cndensatn. Ths s because durng ult-cpnent cndensatn nt nly s there heat transfer Fg. 1a Basc lgcal structure fr prcess desgn f cndenser Fg. 1b Flw chart fr the desgn f ult-cpnent cndenser

5 S. BANDYOPADHYAY et al., Cputer Aded Desgn (CAD) f a Mult-cpnent, Che. Bche. Eng. Q. 21 (2) (2007) 101 Fg. 2 Heat-transfer surface area fr varus cuulatve head lads fr cndensatn f hydrcarbn vapurs fr bth the lqud and vapur phases t the clant but als transfer f vapur lecules fr the vapur phase t the lqud phase. Therefre, there s dffusnal ass transfer resstance alng wth heat transfer resstance durng ult-cpnent cndensatn. In Kern s ethd, the effect f ass transfer s nt cnsdered. Hence, Bell and Ghay s ethd s re relable and used fr the desgn. Effect f the vapur flw rate Fg. 3 shws the varatn f the verall heat transfer ceffcent wth the vapur flw rate fr sngle and tw tube pass cndensers. As t can be seen fr Fg. 3, the verall heat transfer ceffcent decreases wth the ncrease n vapur flw rate, rrespectve f the tube pass. Typcally, f the flw ncreases, the heat transfer ceffcent als ncreases due t hgher turbulence. Hwever, n ths nvestgatn the case s dfferent. In the case f a vertcal cndensatn, the heat-transfer ceffcent decreases wth the ncrease n Reynlds nuber up t 2000, and then ncreases wth the Reynlds nuber. 10 Reynlds nuber n ths nvestgatn was calculated n every pssble cbnatn f teperatures and cndensate flw rates, and the values f Reynlds nubers were well belw Ths justfes the results btaned by the Fg. 4 Effect f vapur flw rate n shell-sde pressure drp fr sngle and tw-tube pass cndensers del. Als, the hgher the vapur flw rate, the hgher the heat lad f the cndenser, thereby the hgher the requred surface area. Therefre, the verall heat transfer ceffcent decreases. Fr any gven flw rate, the tw-tube pass cndenser gves a hgher verall heat transfer ceffcent. Fg. 4 represents the varatn f the shell-sde pressure drp wth the vapur flw rate fr a sngle and tw-tube pass cndenser. A clse exanatn f Fg. 4 depcts that the shell-sde pressure drp ncreases wth the ncrease n vapur flw rate, rrespectve f the tube pass arrangeent. Besdes, fr a gven value f vapur flw rate the tw-tube pass cndenser gves a lesser pressure drp than the sngle-tube pass. The abve features are bvus because the ncrease n flw rate ncreases the pressure drp. In any gven geetry, t btan re flw thrugh a restrctn (cndenser s a restrctn t vapur flw), ne ust have re pressure upstrea f the restrctn,. e. pressure drp n the cndenser ncreases. Effect f vapur nlet teperature Fg. 5 shws the varatn n the verall heat transfer ceffcent fr a sngle and tw-tube pass cndenser. A clse exanatn reveals that ncrease n vapur nlet teperature decreases the verall heat Fg. 3 Effect f vapur flw rate n verall heat transfer ceffcent fr sngle and tw-tube pass cndensers Fg. 5 Effect f vapur nlet teperature n verall heat transfer ceffcent fr sngle and tw-tube pass cndensers

6 102 S. BANDYOPADHYAY et al., Cputer Aded Desgn (CAD) f a Mult-cpnent, Che. Bche. Eng. Q. 21 (2) (2007) transfer ceffcent, rrespectve f the nuber f tube passes. Als, fr a gven vapur nlet teperature, the tw-tube pass cndenser prvdes a hgher verall heat transfer ceffcent. In general, the cndensatn verall heat transfer ceffcent depends upn factrs such as cndenser type, layut, surface geetry, heat lad and ther-physcal prpertes f the cndensng vapur. Snce the change n nlet vapur teperature alters the ther-physcal prpertes f vapur, as we knw the behavur f vapur densty and vapur dynac vscsty wth change n teperature fr the fundaentals f nterlecular frces and cllsn phenenn. Wth an ncrease n vapur teperature, the densty f vapur decreases and dynac vscsty ncreases. Wth a clse exanatn f Nusselt del equatn, t s clear that an ncrease n nlet vapur wll adversely affect the heat transfer ceffcent. 10 Als, the abve features can be explaned by the fact that an ncrease n vapur nlet teperature ncreases the de-superheat zne heat lad, therefre decreases the verall heat transfer ceffcent. Fg. 6 depcts a plt between the tube-sde pressure drp fr a sngle and tw-tube pass cndenser. Ths fgure reveals that an ncrease n vapur nlet teperature decreases the tube-sde pressure drp. Ths s because the ncrease n vapur nlet teperature ncreases the heat-transfer surface area, and thereby the tube-sde pressure drp. Fg. 7 Effect f clant flw rate n verall heat transfer ceffcent fr sngle and tw-tube pass cndensers rate decreases the heat transfer area and thereby ncreases the verall heat transfer ceffcent. Fg. 8 s a plt between the heat transfer area fr the clant flw rate fr sngle and tw-tube pass cndensers. Ths fgure reveals that the ncrease n clant flw rate decreases the heat-transfer surface area rrespectve f tube pass arrangeent. Ths s due t the fact that the ncrease n clant flw rate decreases the heat transfer ceffcent and thereby the surface area f the cndenser. Fg. 8 Effect f clant flw rate n heat-transfer surface area fr sngle and tw-tube pass cndensers Fg. 6 Effect f vapur nlet teperature n tube-sde pressure drp fr sngle and tw-tube pass cndensers Effect f the clant flw rate Fg. 7 shws the varatn f the verall heat transfer ceffcent wth the clant flw rate fr a sngle and tw-tube pass cndenser. It can be seen fr the fgure that the ncrease n clant flw rate enhances the verall heat transfer ceffcent rrespectve f tube pass arrangeent. Als, fr a gven clant flw rate, the tw-tube pass cndenser ffers hgher verall heat transfer ceffcents. The abve features are due t the fact that the ncrease n flw Effect f clant nlet teperature Fg. 9shws the varatn f the verall heat transfer ceffcent wth the clant nlet teperature fr sngle and tw-tube pass cndensers. Ths fgure shws that the ncrease n clant nlet teperature decreases the verall transfer ceffcent rrespectve f the tube pass. Ths s because the ncrease n clant nlet teperature reduces the weghted ean teperature dfference and ncreases the heat transfer area, thereby reducng the verall heat transfer ceffcent. The cndensatn verall heat-transfer ceffcent depends upn factrs such as cndenser type, layut, surface geetry, heat lad and ther-physcal prpertes f the cndensng vapur. The change n clant nlet teperature wll change the vapur

7 S. BANDYOPADHYAY et al., Cputer Aded Desgn (CAD) f a Mult-cpnent, Che. Bche. Eng. Q. 21 (2) (2007) 103 pressure drp was fund t ncrease wth vapur flw rate where ther varables have nnal effects. Fg. 9 Effect f clant nlet teperature n verall heat-transfer ceffcent fr sngle and tw-tube pass cndensers teperature, whch alters the ther-physcal prpertes f vapur. Hence, t s clear that an ncrease n nlet clant teperature wll adversely affect the heat transfer ceffcent. Cnclusns The atheatcal desgn dels have been develped based n the equlbru ethd, and thereby a cputer aded desgn algrth fr the desgn f a ult-cpnent cndenser has been develped based n Bell and Ghaly s ethd. Based n the algrth, a cputer prgra has als been develped. Ths prgra was tested fr a wde range f peratng varables and fund satsfactry n gvng expected results. The desgn algrth based n Bell and Ghaly s ethd was cpared wth Kern s ethd. It has been fund that Kern s ethd underszes the cndenser because t ts the ass transfer resstance and des nt take enugh care t handle sensble heat transfer durng cndensatn. Ths fact has been ncrprated nt Bell and Ghaly s ethd by takng the vapur phase heat-transfer ceffcent durng vapur sensble heat transfer n the hpe that t wll apprxately verestate the ass transfer resstance. The undersze f the cndenser ay be severe by Kern s ethd f the cndensng range beces large. The effects f peratng varables vz. vapur flw rate, vapur nlet teperature, clant flw rate and ts nlet teperature n the utput varables vz. verall heat transfer ceffcent, heat transfer surface area were studed fr bth sngle and tw-tube pass cndensers. As a result, the verall heat transfer ceffcent was fund t ncrease wth clant flw rate and decrease wth an ncrease n clant nlet teperature, vapur nlet teperature, and vapur flw rate. Further, the pressure drp n the tube sde was fund t ncrease wth an ncrease n clant flw rate, and decrease wth an ncrease n vapur flw rate and clant nlet teperature. The shell-sde Nenclature A heat transfer area based n utsde tube area, 2 A heat transfer area based n nsde tube area, 2 h heat transfer ceffcent nsde the tube, W 2 K 1 h heat transfer ceffcent utsde the tube, W 2 K 1 h sv sensble heat transfer ceffcent, W 2 K 1 K vapur lqud equlbru cnstant W theral cnductvty f the wall, W 1 K 1 N nuber f cpnents q vapr ass flw rate, kg s 1 heat lad, kw l lqud phase heat lad, kw sv sensble heat lad fr vapur, kw T ttal heat lad, kw R d fulng resstance nsde the tube, 2 KW 1 R d fulng resstance utsde the tube, 2 KW 1 T teperature, K T l lqud phase teperature, K T ean teperature, K T ean teperature dfference between ht and cld flud streas, K T v vapur phase teperature, K T c clant teperature, K U ean verall desgn heat-transfer ceffcent, W 2 K 1 U c verall heat-transfer ceffcent fr ult-cpnent cndenser, W 2 K 1 x le fractn n lqud phase, 1 W tube wall thckness, y le fractn n vapur phase, 1 Z F feed lar cpstn vapur fractn lar bass References 1. Kern, D. Q., AIChE J. 17(5) (1971) Bell, K. J., Ghaly, M. A., AIChE Syp. Ser. 131(69) (1973) Clburn, A. P., Drew, T. B., Trans. A. Inst. Che. Engnrs. 33 (1937) Clburn, A. P., Hugen, O. A., Ind. Eng. Che. 26 (1934) Clburn, A. P., Edsn, A. G., Hydrcarbn Prcessng 33 (1941) Krshna, R., Panchal, C. B., Che. Eng. Sc. 32 (1977) Heat Exchanger Desgn Handbk, Hesphere. 1983, New Yrk 8. Lckhart, Q. W., Martnell, R. C., Che. Eng. Prg. 48 (1949) Kutaleladze, S. S., Brshansk, V. M., Cncse Encyclpeda f Heat Transfer, Pergan Press, Oxfrd, Snntt, R. K., Culsn & Rchardsn s Checal Engneerng Vl. 6, Butterwrth-Heneann, Lndn, 1996.

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