A Rapid Screening Tool to Predict Optimal Feed Flow Sequence of A Multiple Effect Evaporator System Using Process Integration

Transcription

1 This Conerene Paper is arhive in A Rapi Sreening Tool to Preit Optimal Fee Flow Sequene o A Multiple Eet Evaporator System Using Proess Integration 9th National & 8th ISHMT-ASME Heat an Mass Transer Conerene January 3-5, 2008 JNTU Hyeraa, Inia

2 9 th National & 8 th ISHMT-ASME Heat an Mass Transer Conerene January 3-5, 2008 JNTU Hyeraa, Inia Paper No: TPH-4 A Rapi Sreening Tool to Preit Optimal Fee Flow Sequene o A Multiple Eet Evaporator System Using Proess Integration S. Khanam Department o Chemial Engineering National Institute o Tehnology Rourkela Rourkela shainahai@gmail.om, skhanam@nitrkl.a.in B. Mohanty Department o Chemial Engineering Inian Institute o Tehnology Roorkee Roorkee mohanty@iitr.ernet.in Astrat A simple mathematial moel ase on priniples o Proess Integration (PI has een evelope to sreen the optimal ee low sequene (OFFS o a multiple eet evaporators (MEE system whih will oer est steam eonomy. The moel assumes resh ee to e ompose o streams o prout an ierent onensate streams. It also takes in to aount temperature paths ollowe y eah stream an internal heat exhange etween hot an ol parts o a stream along with variale physial properties o steam/vapor an onensates. A septuple eet lat alling ilm evaporator (SEFFFE system with steam splitting an ee, prout an onensate lashing, use to onentrate weak lak liquor, is onsiere or simulation. The set o linear algerai equations o the moel is solve simultaneously using Gaussian elimination metho with partial pivoting. Bakwar ee low sequene is oun to e the optimum or the system. The results o the present moel are also ompare with other moels an oun to agree well as ar as seletion o OFFS is onerne. Key wors: Multiple eet evaporator, Rapi sreening tool, Optimal ee low sequene, Linear moel. Nomenlature C PP Speii heat apaity o prout, kj/kg/k C Speii heat apaity o onensate, kj/kg/ C F Fee low rate, kg/h h Enthalpy o onensate, kj/kg H Enthalpy o vapor, kj/kg n Numer o eets P Flow rate o prout stream, kg/h T Vapor oy temperature, C V Vapor low rate, kg/h x Mass ration Greek letters Dierene in values o a parameter at two points λ Heat o vaporization, kj/kg Susripts,2,3,4,5,6,7,k Seven eets F Fee 0 Live steam entering into irst eet L Liquor P Prout r Reerene V Vapor. Introution An energy auit shows that Multiple Eet Evaporator (MEE House o a Pulp an Paper inustry onsumes aout 24-30% o its total energy an thus has een a topi o investigation or last many eaes []. The main eorts are towars the evelopment o operating strategies whih shoul onsume minimum live steam an thus provie maximum steam eonomy. The operating strategies inlue seletion o est low sequenes o liquor an ee-, prout- & onensatelashing though it makes the system omplex. However, sreening o the est strategy, out o the easile ones, is time an resoure onsuming an i one experimentally eomes an aruous task. One o the reasonale way o oing it is through simulation. Harpor an Tsao [2] evelope a moel or the optimization o evaporation proess or a ew ee low sequene (FFS suh as orwar an akwar FFS. Nishitani an Kunugita [3] extene the work o Harpor an Tsao [2] to propose an algorithm or generating non-

3 inerior FFS amongst all possile FFSs o a MEE system. The non-inerior FFSs were ase on the onstraints o visosity o liqui an the ormation o sale or oam. The aove isusse moels are generally ase on set o non-linear equations an aommoate varying physial properties or vapor/steam an liquor. It either uses ixe overall heat transer oeiient (OHTC or variale OHTC ase on empirial equations or mathematial moels. Further, it has also een oserve that to aress ierent low sequenes the omplete set o equations nee to e hange an thus oers iiulty in hanling. To aress this prolem asae algorithm has een evelope in whih the moel o an evaporator oy is solve repeately [4] & [5]. With the hange in low sequene the sequene o the solution o the moel an also the input ata to this moel hanges. Though this moel remove the aove sai weaknesses o the general simulation moels it exhiits onvergene an staility prolem uring solution [6]. Uner the aove akrop the present investigation has een planne to evelop a simpliie mathematial moel ase on priniples o Proess Integration, stream analysis, temperature path an internal heat exhange oneptualize y Westererg an Hillenran [7]. The present moel has een improve to aress all operating onigurations like steam splitting, ee-, prout- an onensate- lash. 2. Prolem Statement The MEE system shown in Fig. - a Septuple Eet Flat Falling Film Evaporator (SEFFFE system operating in a neary paper mill with akwar FFS is use or onentrating weak lak liquor. The irst two eets o it are inishing evaporators an use iret live steam. This system employs ee an prout lashing along with primary an seonary onensate lashing to generate vapor, whih are use in vapor oies to improve overall steam eonomy o the system. The seventh eet is attahe to a vauum unit. The operating parameters or this system are given in Tale an easile FFS are shown in Tale 2 whih are stuie in orer to otain the OFFS that yiels highest possile steam eonomy. Tale Operating parameters or the SEFFFE system Parameter(s Value Parameter(s Value Total numer o eets 7 Blak liquor ee low rate kg/h Numer o eets eing supplie live steam 2 Last eet vapor temperature 52 C Live steam temperature Eet 40 C Fee low sequene Bakwar Eet 2 47 C Fee lash tank position As iniate Blak liquor inlet onentration 0.8 Prout lash tank position in the Fig. Blak liquor outlet onentration 0.54 Liquor inlet temperature 64.7 o C Primary an seonary onensate lash tank position Live Steam Vapor rom Last eet P L PF PF2 PF3 F V F L PFT P V Prout SF SF2 SE3 Steam Vapor Conensate Blak Liquor FFT : Fee Flash Tank PFT: Prout Flash Tank PF PF3: Primary onensate lash tanks SF SF4: Seonary onensate lash tanks SF4 Conensates FFT Fee Fig. Shemati iagram o a SEFFFE system with akwar ee low sequene

4 Tale 2 Feasile liquor low sequenes in a SEFFFE system FFS Liqui Flow Sequene FFS Liqui Flow Sequene S S S S S S Moel Development A simpliie moel, ase on the priniples o PI an ase on the onepts o Westererg an Hillenran [7], is evelope or a SEFFFE system with akwar FFS. The moel uses some assumptions to ut own the omplexity. These are: riving ore or the transer o heat rom steam/vapor to oiling liquor is onstant or eah eet, vapor oy temperatures o eets are ixe or all FFS, oiling point rise, heat losses rom all eets an heat o mixing etween ierent streams o ee are also negligile. 3.. Desription o the System A simple system ase on Fig. is onsiere or the evelopment o the moel. In this system live steam o amount, Ws, enters into the steam hest o the irst eet at temperature T 0 an exits it as a onensate stream Cs (where, Ws = CS ater supplying latent heat or vaporization to the irst eet. The vapor generate in the irst eet, as a result o evaporation o liquor, is move to the vapor hest o the seon eet an aets evaporation in this eet. This sequene is repeate up to last eet. Fee irst enters into eet 7 an then ollows the akwar sequene. For this moel the ee is hypothetially onsiere to e ompose o eight ierent streams, whih or the purpose o omputation move separately through the system without any intererene rom other streams. The etails o aove sai eight streams are as ollows: one prout stream, P, an seven onensate streams esignate as, C, C 2, C 3, C 4, C 5, C 6 an C 7, shown in Fig. 2. Movements o these streams is etaile elow: Initially the ee whih is the omination o prout, P, an seven onensate streams, C to C 7, are at ee temperature, T F, an enter to the seventh eet. From this eet onensate stream C 7 whih is the onensate stream erive rom vapor stream V 7 omes out. Thus, the remaining streams o liquor are P an C to C 6. These streams exit seventh eet at a temperature T 7 an enter eet No. 6. The liquor is evaporate in it an in turn vapor stream V 6 is proue whih is sent to eet No.7 as heating meia. Ater giving its heat to eet No.7 this stream onverts it sel in to onensate stream C 6 an exits rom the vapor hest o eet No.7. In at, in this eet two onensate streams C 7 & C 6 are separate whih is unommon in other eets. Exit liquor rom sixth eet at temperature T 6, whih is the omination o prout stream P an onensate streams C 5 to C, enters the eet No.5. In the similar manner, onensate streams C 5 to C get separate one y one rom the vapor hests o eets No. 6 to 2, respetively. Finally, the prout stream P omes out rom eet No.. The aove at is shematially presente in Fig.2. To trae the level o temperatures a partiular stream aquires while it traverses rom entry eet to exit eet (sequene o entry an exit epens on low sequene the onept o temperature path is use. It is eine as a Path ollowe y the temperatures o a stream when it passes through an eet or a network o it. It shoul e note that onept o temperature path is only vali or streams having sensile heat. It plays a vital role in the evelopment o moel equations. For present ase, the temperature paths o all eight onstituent streams o ee are shown in Fig. 3 in whih T, T 2, T 3, T 4, T 5, T 6 an T 7 are vapor oy temperatures o st, 2 n, 3 r, 4 th, 5 th, 6 th an 7 th eets, respetively. The temperature paths are plotte to emonstrate another important onept alle internal heat exhange. This onept works on one o the asi priniples o PI, alle maximum energy reovery. It allows ierent streams or their part to exhange heat with eah other in orer to know the maximum amount o heat that an e reovere through internal exhange an thus provies a mean to reue the amount o live steam require y the system. To emonstrate the onept o internal heat exhange let us onsier the temperature path o P, shown in Fig. 3, whih irst moves ownwar in temperature rom point a to through point an hene ehaves as a hot stream. However, the same stream rom point to through e works as a ol stream as its temperature rises in this temperature path. When the prout stream is working as a hot stream it an provie heat to a ompatile ol stream. In the same manner when it is working as a ol stream it an take heat rom a ompatile hot stream.

5 Con. rom 7 th at T 7 Con. rom 7 th at T 6 Con. rom 6 th at T 5 Con. rom 5 th at T 4 Con. rom 4 th at T 3 Con. rom 3 th at T 2 Con. rom 2 th at T C 7 C 6 C 5 C 4 C 3 C 2 C Fee, at T F C 7 C 6 C5 C4 C3 C2 C P Con.: Conensate Prout, P, oming out rom irst eet Fig. 2 Movement o prout, P, an seven onensate streams, C to C 7, through the SEFFFE system P C C 2 C 3 C 4 C 5 C 6 C 7 T T, t T 2 T, s =T 2, t T 3 T 2, s =T 3, t T 4 T 3, s =T 4, t T 5 T F T 6 a a a a a a a a e e e e e e T 4, s =T 5, t T 7, s T 5, s T 7 T 7, s T 7, t Fig. 3 Temperature paths o ierent streams o ee or a SEFFFE system or akwar FFS In at, when two streams exhange heat there exist a minimum temperature ierene, T. As a irst guess it an e taken as 0 C. As the prout stream P ehaves as hot stream in some part o the temperature path an as ol stream in remaining path while traversing the omplete temperature path its hot stream part an exhange heat with its ol stream part sujete to the T min onstraint. The hot stream part o P, enote y a to through, irst ools own rom point a to y exhanging its heat with ol stream part o it. In turn the temperature o ol stream rises rom point to e. In at the aove reerre hot stream temperature an not rop elow point whih is equal to T 7 + T min, while exhanging heat with the orresponing ol stream as it will violate T min riterion. In this ase, the prout stream P enters into the seventh eet at point where it is oole own an reah at point eore gets evaporate. Thereore, in this ase, or stream, P, maximum possile internal heat exhange is equal to [P*C PP *(T F -T 7 - T min ] kw.

6 The Moel-M, or the simple SEFFFE system has een evelope with the help o Temperature Paths, shown in Fig. 3. To evelop equation or an eet the temperatures at whih liquor enters (supply temperature, T s an exits (target temperature, T t rom the eet shoul e known. These temperatures an e otaine rom the Fig. 3. For example, to evelop equation or the irst eet supply an target temperatures are taken as T 2 an T, respetively. Further, it an e seen rom Fig. 3 that only streams, P an C, enter into irst eet. Due to evaporation, C amount o vapor is proue in this eet at T. Thus, energy alane aroun irst eet at steay state provies ollowing equations: Latent heat Sensile heat o Latent heat supplie y live + entering streams P = availale with the steam at T 0 & C at T,s stream, C at T,t Sensile heat o + exiting streams, ( P & C at T,t Latent heat supplie y live steam at T 0 = Ws * λ s (2 Sensile heat o streams, P an C, whih enters the irst eet at T,s is: P * CPP * ( T, s Tr + C *[T,s * C (T,s (3 - Tr * C (Tr ] where, C PP = 4.87 * ( *x P C an T r are speii heat apaity o onensate an reerene temperature, respetively. Latent heat availale with the exit vapor stream o amount C at T,t = C * λ (4 Sensile heat o exiting streams rom irst eet at T,t is: P * CPP * ( T, t Tr + C *[T,t *C (T,t (5 - Tr * C (Tr ] When Eqs. 2, 3, 4 an 5 are sustitute in Eq. with T,s & T,t equal to T 2 & T an rearranging it, one gets ollowing equation or irst eet: λs Ws + C λ PC + λ ( T2 λ T = 0 Where, = [T2 *C (T2 - T *C (T ] Similarly, equation or six other eets an e evelope. Overall mass alane aroun the SEFFFE system provies: C + C 2 + C 3 + C 4 + C 5 + C 6 + C 7 = F P ( Inution o Conensate Flashing in the Moel Moel-M is urther evelope y inuting the provisions o primary an seonary onensate lash as shown in Fig.. This moel is alle Moel-M2. The onensate exits rom steam/vapor hest o an eet ontains suiient amount o sensile heat whih an e PP (6 extrate y means o lashing to proue low pressure vapor an an e use as heating meium. For Moel-M2 steam splitting an ee an prout lashing are not onsiere. For this ase live steam is use only in irst eet an its onensate, CS, exits rom irst eet an enters into lash tank, PF. The vapor stream, V, enters into vapor hest o seon eet an onensate o it, C, exits this eet an re-enters to lash tank, SF. Fee iretly enters into eet 7 at T F an prout, P, omes out rom irst eet at T. For this system, live steam o amount, Ws, enters to the steam hest o irst eet at temperature, T 0 an exits it as a onensate, CS (where, Ws = CS at the same temperature, T 0. It shoul e kept in min that onensate o live steam is alle primary onensate whereas; onensate o other vapor stream is reerre as seonary onensate. In at when a onensate stream at a high pressure (thus temperature is lashe (say irst lash at a lower pressure a part o it is vaporize y taking heat rom remaining liqui an thus a mixture o low temperature liqui an vapor is proue. Hene, or theoretial interpretation the onensate stream CS an e thought o as two streams one liqui an the other vapor stream at one temperature whih is lower than the initial temperature o CS. This proess an e repeate with the resiual onensate o stream CS whih is otaine ater irst lashing. When the aove onensate stream is lashe (say seon lash it will also proue two stream one liqui an other vapor at a temperature whih will e lower than the initial temperature o resiual onensate stream. The vapor stream whih was otaine rom the irst stream will provie heat to an eet an will susequently onvert into a onensate stream. This stream now an also e lashe (say thir lash to get vapor an liqui streams. Ater three onseutive lashing the original primary onensate stream CS an e assume to e ompose o our streams. Thus, theoretially, a onensate stream an e assume to e ompose o a numer o vapor an liqui streams whih an e assume to e physially separate. This onept is use elow uring the evelopment Moel-M2. The primary onensate stream CS enters into lash tank (PF an lashe at T 3 to proue vapor stream, CS V, an liqui stream, CS L. The stream, CS V, enters the vapor hest o ourth eet with stream V 3. Both the streams are treate separately to ompute their hil streams generate out o lashing in ierent lash units or ease o moeling. In the SEFFFE system primary onensate streams are lashe in lash units, PF to PF3, an seonary onensates are lashe in lash units, SF to SF4. The seonary onensate stream, CS V enters the lash unit (SF2 operating at temperature T 4 to generate vapor stream CS VV an liqui stream CS VL. The vapor stream CS VV enters into the vapor hest o ith eet along with vapor generate in ourth eet, V 4. The liqui stream CS VL along with onensate streams CS VV enter into lash unit (SF3 operating at temperature T 5. As a result o it, two vapor streams as

7 CS VLV an CS VVV an two liqui streams as CS VLL an CS VVL are generate here. These streams are onsiere as separate streams. The same is also true or liqui stream oming out rom SF3. Vapor streams CS VLV an CS VVV along with vapor generate in ith eet, V 5, enter into the vapor hest o sixth eet. Following the same pattern, as shown in Fig. 4, the onensate streams are lashe in lash units SF4 an vapor proue in these units enter in to eet 7. From SF4, the onensate streams, whih an not e lashe urther, ome out at temperature T 6. The omplete tree o CS V whih shows the lashing sequenes using lash units SF2 to SF4 are shown in Fig. 4. Similarly, the onensate tree o CS L an e rawn. The list o ierent vapor streams generate ue to lashing o onensate, CS, an then enter into vapor hests o ourth-, ith-, sixth- an seventh- eets to work as a heating meium, are provie in Tale 3. The expressions require to quantiy these streams are evelope an shown in Appenix A. Now the primary onensate stream CS an e thought o as a omination o 7 vapor as well as 8 liqui streams. The other lash streams, whih are speiially generate rom CS, an enter into ourth to sixth eet are omination o some o the streams out o the aove 5 (7+8 streams. For example the lash vapor stream Cs VVV whih enters into sixth eet is a omination o vapor stream Cs VVVV an liqui stream Cs VVVL. It shoul e note that the present isussion relates to only onensate stream, CS, an not the streams C to C 5. Base on the logi, isusse aove, lashing o seonary onensate streams C, C 2, C 3, C 4 an C 5 are also treate. For the present ase, ee is assume to e a ompose o eight ierent streams. The temperature paths o these streams are also shown in Fig. 3. The governing equations or Moel-M2 an e erive in the similar manner as o Eq. 6 or Moel-M. The only hange require is to inlue the amount o lash vapor as a heating meium in appropriate eets. Likewise the provisions o ee an prout lashing an e inorporate in the SEFFFE system Inution o Live Steam Splitting in the Moel In some o the Pulp an Paper plants, irst two eets o a SEFFFE system are use as inishing eets in whih live steam is e. I total steam onsumption in irst two eets in the system is Ws, then it an e assume that ration, s, o it enters into the irst eet at T 0 whereas, (-sws enters into the seon eet at T 02. The hange in live steam temperatures in irst two eets is ue to the ierene in saturation pressures o the steam hests o these eets. The onensates o oth the streams o live steam are lashe in lash unit PF (see Fig. an entere into the steam hest o thir eet along with V an V 2. CS ( shows the eet in whih vapor stream enters [ ] shows the lash tank in whih onensate stream lashes CS VV (5 [SF3] CS V (4 [SF2] [PF] CS L CS VL [SF3] CS VVV (6 CS VVL CS VLV (6 [SF4] [SF4] [SF4] CS VLL [SF4] CS VVVV (7 CS VVVL CS VVLV (7 CS VVLL CSVLVV (7 CS VLVL CS VLLV (7 CS VLLL Fig. 4 Conensate tree o stream CS V o primary onensate CS Tale 3 Total numer o vapor streams entering into eets 2 to 7 Eet No. o vapor Vapor streams streams Fourth n= CS V Fith n=2 CS VV, CS LV Sixth n=4 CS VVV, CS VLV, CS LVV, CS LLV Seventh n=7 CS VVVV, CS VVLV, CS VLVV, CS VLLV, CS LVVV, CS LVLV, CS LLVV

8 T =T 2 P V P C C 2 C 3 C 4 C 5 C 6 C 7 T, s = T, t =T 2, t T 3 T 2, s =T 3, t T 4 T 3, s =T 4, t T 5 T 4, s =T 5, t T 6 T 7, s = T 6, t = T 5, s T 6, s T 7 T 7, s T 7, t Fig. 5 Temperature paths o ierent streams o ee or a SEFFFE system, whih inlues steam splitting Temperature paths o ierent streams o ee suh as P, P V, C, C 2, C 3, C 4, C 5, C 6 an C 7 are shown in Fig. 5. In this igure onensate streams C an C 2 ollow same temperature paths as temperatures o irst two eets (rom where streams C an C 2 are exiting are onsiere to e equal. The moiie moel, Moel-M3, is evelope whih ontains ollowing equations or eets to 3. These equations are erive in a manner similar to Eq. 6. First eet: λs Ws* C λ Seon eet: λs2 Ws2 + C + C λ2 λ2 PCPP ( T3 T2 + = 0 where, λ2 Ws 2 = ( s Ws [T3C (T3 - T2C (T2 ] = Thir eet: = 0 Where Ws = s * Ws (8 2 PV + λ2 λ2 λ λ 2 + C C C3 λ3 λ3 λ3 PCPP( T4 T PV = 0 λ3 λ3 where, 2 = [T4 * C (T4 - T3 * C (T3 ] (9 (0 Likewise, or the k th eet ollowing equation is evelope: n λk λk + k [ kj ( Ws + kj ( Ws2 ] + B' + B'' + Ck j= λk λk ( (,, + + PC T T k PP k s k t Ck + A' + A'' + F' = 0 λk λk where, k = 4, 5,..7 an = T C ( T T * C ( T k k, s * k, s k, t k, t λk + k A ' = PV * or values o k equal to 5, 6 an 7, λk A = 0. p k kj( PV + PV * k j = λ A' ' = or the value o k equal to λk 4, A = 0. k 2 λk * k ( Ci + Ci * k B' = or the value o k i= λk equal to 5, 6 & 7, B = 0. m λ + 2 * ( * k k kj Ci Ci k j = B'' = or the value o k i= λk equal to 4, B = 0.

9 λk F ' = F V * or values o k equal to 4 to 6, F = λk 0. In Eq., n represents the total numer o vapor streams, proue rom lashing o onensates o live steam rom irst an seon eets as untions o Ws an Ws2, whih enter into vapor hest o k th eet. For the values o k equal to 4, 5, 6 an 7, the values o n are, 2, 4 an 7, respetively. The value o n an e otaine in a manner similar to the omputation o the values o n one in the ase o onensate, CS, as an e seen in Tale 3. Similarly, m in Eq. shows the total numer o vapor streams generate rom lashing o onensates C, C 2, C 3, C 4 an C 5 that enter into k th eet. These lashe streams are untions o C, C 2, C 3, C 4 an C 5. Likewise, p, represents the numer vapor streams proue rom P V (vapor stream generate rom prout lashing ue to lashing an enter into vapor hest o k th eet. Eq. an give rise to our ierent equations or values o k equal to 4, 5, 6 an 7, respetively. Overall mass alane aroun the SEFFFE system is given as: 7 i= C i + P V + F V = F P (2 Thus, Moel-M3 onsists o eight numers o governing equations. 4. Solution o the Moel The moel-m3 onsists o a set o linear algerai equations. The input variales o this moel are F, x F, x P, F V, P V, T 0, T 02, T F, T P, s, T, T 2, T 3, T 4, T 5, T 6 an T 7 whereas, output variales are ategorize as Ws, C, C 2, C 3, C 4, C 5, C 6 an C 7. It shoul e note that the ompliate mathematial moels use or sreening o OFFS or the SEFFFE system uner similar situation uses aout 23 non-linear algerai equations whih nee to e solve simultaneously or iteratively. During solution o these moels in general onvergene an osillation prolems are enountere. As the present moel uses a set o linear equations ar less in numer rom its ounterparts it oes not poses any onvergene or staility prolems. Thus the present moel oers ae avantages. The set o linear algerai equations are solve simultaneously using Gaussian elimination metho with partial pivoting. 5. Results an Disussions Moel-M3 is evelope to sreen the OFFS whih will provie est steam eonomy. The values o steam onsumptions (SC or ierent FFSs, given in Tale 2, are ompute using Moel-M3 an are shown in Fig. 6. It an e oserve rom this igure that the value o SC varies rom maximum to minimum in the ollowing orer o low sequenes: S5 > S6 > S4 > S3 > S2 > S. The steam onsumption or a low sequene mainly epens on two ators: sensile heating require or the entering liquor to ring it to the temperature o the eet an latent heat use or evaporation. In the present system as live steam is e to eet no. an 2 an so aove two ators are ompute or these eets or all easile low sequenes an are shown in Tale 4 whih. This tale learly shows why value o SC hanges with low sequenes. The steam eonomy (SE is eine as total amount o water evaporate ivie y the amount o live steam onsume in irst two eets. As or the present system the ee an prout onentrations an ee low rate remain same or all low sequenes an so the total water to e evaporate is equal in all ases. Thus, the value o SE varies inversely with SC as an e seen in Fig. 6. Tale 4 shows that low sequene, S, is the OFFS as it onsumes minimum amount o live steam an provies highest steam eonomy. 5.. Comparison o Preitions o Moel-M3 with Other Moels To hek the eetiveness an reliaility o the present moel its preitions have een ompare with the preitions o other simulation moels [8], [3] & [6]. For this purpose Moel-M3 is re-onigure to suit the operating onitions an onstraint o the aove moels. In at, the aove investigators have worke on ierent liquors suh as hemial solution an milk an hene, the physial property orrelations o these moels were use in Moel-M3 eore solving it or omparison. The omparison is shown in Tale5. Kern [8] onsiere a triple eet evaporator (TEE system or the onentration o hemial solution an preite the OFFS ase on minimum live steam onsumption. The moel was ase on mass an enthalpy alane equations an onsiere negligile BPR, onstant physial properties o solution an ierent OHTC or three eets. The preitions o Kern [8] are similar to that o Moel-M3. Both show that the live steam onsumption was minimum or akwar FFS ollowe y orwar FFS. Nishitani an Kunugita [3] have use a TEE system employe or onentrating milk. Their moel was ase on thermal analysis an operating onstraints as visosity o liqui an ormation o sale. Their riteria or seletion o a set o non-inerior (a set o low sequenes whih inlues OFFS as well as near OFFSs in orer o inreasing total annual ost (TAC low sequenes is ase on minimum heat transer area an live steam onsumption. The preitions o moels ue to Nishitani an Kunugita [3] an the present investigation are iential. Bhargava [6] onsiere the SEFFFE system, shown in Fig., an evelope a rigorous nonlinear mathematial moel or the simulation o aove system y taking in to aount the variation in -physial property, -BPR, -OHTC an -heat losses rom eets. The moel was valiate using the ata rom a neary paper mill. Both the moels, Moel-M3 an that o Bhargava [6], show akwar low sequenes as OFFS.

10 From the aove isussion it an e onlue that as ar as the seletion o OFFS is onerne there is no ierene in the preitions o present moel an that o other moels Steam onsumption Steam eonomy 5.50 Steam onsumption, kg/h Steam eonomy S S2 S3 S4 S5 S6 Flow sequenes Fig. 6 The values o SC or ierent FFSs 4.20 Tale 4 Computation o total heat supplie y steam or six low sequenes Flow sequene(s S S2 S3 S4 S5 S6 Eet No. Sensile heating insie the eet, kj/h Heat require or evaporation, kj/h Eet No. 2 Sensile heating insie the eet, kj/h Heat require or evaporation, kj/h Total heat supplie y live steam, kj/h Tale 5 Comparison o Moel-M3 with other moels Desription o moel Results Remarks No o eet liquor Prolem Moel-M3 Moel-X 3 Chemial solution F= kg/h, x F =0., x P =0.50, T F =37.7 C, T L =5.7 C, T 0 =63 C, low sequenes: OFFS: 32 OFFS: 32 X: Kern [8] 23, 32 3 Milk F=5000 l/h, x F =0., x P =0.4, T F =50 F, T L =07 F, T 0 =250.3 F, low sequenes: 23, 32, 23, 23, 32, 32 3 Milk F=5000 l/h, x F =0., x P =0.4, T F =40 F, T L =07 F, T 0 =250.3 F, low sequenes: 23, 32, 23, 23, 32, 32 NFS: 32, 32, 23 NFS: 32, 32, 23 X: Nishitani an Kunugita [3] NFS: Noninerior low sequene NFS: 23 NFS: 23 X: Nishitani an Kunugita [3] NFS: Noninerior low sequene

11 7 Blak liquor System is shown in Fig., operating parameters an low sequenes are given in Tale & 2, respetively. OFFS : Bakwar OFFS: Bakwar X: Bhargava [6] 6. Conlusions. The Moel-M3 an work as an eetive sreening tool or the seletion o OFFS. 2. Out o the ierent FFSs investigate or SEFFFE system, the akwar FFS was oun to e optimal leaing to highest value o steam eonomy. 3. The solution o the present moel is easy an oes not pose any instaility or osillation prolems as generally oserve in other simulation moels ase on sets o non-linear equations or ase on iterations. 7. Reerenes []. Rao, N. J. an Kumar, Ram, Energy Conservation Approahes in a Paper Mill with Speial Reerene to the Evaporator Plant, IPPTA International. Seminar on Energy Conservation in Pulp an Paper Inustry, New Delhi, pp: (985. [2]. Harper, J. M. an Tsao T. F. Evaporator strategy an optimization, In Computer Programs or Chemial Engineering Euation, Vol. VI Design, (E. R. Jelinek, pp: 7-45, Azte Pulishing, Austin, Texas (972. [3]. Nishitani, H. an Kunugita, E., The optimal low pattern o multiple eet evaporator systems, Computers an Chemial Engineering, Vol.3, pp: (979. [4]. Stewart, G. an Beverige, G.S.G, Steay state asae simulation in multiple eet evaporation, Computers an Chemial Engineering, Vol., No., pp: 3-9 (977. [5]. Ayangile, W.O., Okeke, E.O an Beverige, G.S.G, Generalize steay state asae simulation algorithm in multiple eet evaporation, Computers an Chemial Engineering, Vol.8, No.3/4, pp: (984. [6]. Bhargava, R., Simulation o lat alling ilm evaporator network, Ph.D. Thesis, Department o Chemial Engineering, Inian Institute o Tehnology Roorkee, Inia, (2004. [7]. Westererg, A.W. an Hillenran Jr. J. B. The synthesis o multiple eet evaporator systems using minimum utility insights-ii liqui low pattern seletion, Computers an Chemial Engg., Vol.2, No.7, pp: (988. [8]. Kern, D.Q., Proess Heat Transer, MGraw Hill ( Appenix A The lok iagram o primary onensate lash unit (PF is shown in Fig. A.. In this iagram, onensate stream CS enters in to PF at temperature, T 0, an is lashe at T. As a result o it, vapor stream, CS V, an liqui stream, CS L, are generate. The mathematial expressions o these streams an e erive as: Overall mass alane aroun PF CS = CS V + CS L (A. Energy alane aroun PF CS * h s = CS V * H + CS L * h (A.2 Using Eqs. A. an Eq. A.2 ollowing equation is otaine: CS *( hs h Ws * ( hs h CSV = = (A.3 ( H h ( H h Eqs. A. an A.3 are use to preit the expression o CS L as ( hs h an CS L = ( CS CSV = Ws (A.4 ( H h Following this pattern, the expressions o 5 streams as untion o Ws an e erive. Conensate CS, h s, T 0 PF at T CS V, H CS L, h Fig. A. Blok iagram o a primary onensate lash tank