HEAT EXCHANGER NETWORK SYNTHESIS CONSIDERING CHANGING PHASE STREAMS

Transcription

1 HEAT EXCHANGER NETWORK SYNTHESIS CONSIDERING CHANGING PHASE STREAMS F. S. Liporace a, F. L. P. Pessoa b, and E. M. Queiroz b, a PETROBRAS/CENPES/EB/SAP Cidade Universitária - Iha do Fundão , Rio de Janeiro, RJ, Brasi (21) iporace@petrobras.com.br b DEQ/Escoa de Química/UFRJ Cidade Universitária Iha do Fundão Boco E mach@eq.ufrj.br Rio de Janeiro, RJ, Brasi (21) ABSTRACT The Pinch Design Method was deveoped considering one-phase streams, with constant specific heats (Cp) throughout streams temperature ranges. Its first stage, the determination of utiities targets and pinch point (PP), is rued by the number of streams, their temperatures and MCp. But, for changing phase streams, the usua description of the Cp behavior by a constant vaue can ead to errors in this stage and, hence, in the synthesis one. This work proposes a procedure to dea with these streams and discusses its resuts through an exampe invoving muticomponent streams. First, bubbe (BP) and dew (DP) points of the streams are estimated. Then, changing phase streams are spit into sub-streams, using BP and DP as bounds. For each one, an effective Cp is estimated as the division of the enthapy change by the respective temperature difference. Resuts obtained show significant changes on the PP, utiities targets and network proposed structure. Keywords: pinch design method, muticomponent streams, infuence of phase change. NOMENCLATURE A heat transfer area, m 2 BP bubbe point temperature, ºC Cp specific heat, kj/kg ºC cu cod utiity D inner diameter, cm DP dew point temperature, ºC G mass fux, kg/s m 2 H mass enthapy, J/g h oca heat transfer coefficient, W/m 2 ºC h v atent heat of vaporization, J/kg, h m mean heat transfer coefficient, W/m 2 ºC hu hot utiity ITC inet temperature of cod stream, ºC ITH inet temperature of hot stream, ºC +v iquid + vapor M mass fowrate, kg/s MCp heat capacity fowrate, kw/ºc MTDminimum temperature difference, ºC OTC outet temperature of cod stream, ºC OTH outet temperature of hot stream, ºC P stream pressure, N/m 2 PP pinch point, ºC Pr Prandt number Pr Prandt number for the iquid Q heat oad, MW s saturated iquid sv saturated vapor T temperature, ºC TAC tota annua cost, $/year T i inet temperature, ºC T o outet temperature, ºC v mean fuid fow veocity, m/s x vaporized mass fraction Greek symbos σ iquid superficia tension, N/m H enthapy change, kw H mass enthapy change, J/g ρ iquid density, kg/m 3 κ iquid therma conductivity, W/m ºC µ iquid viscosity, N s/m 2 P pressure difference, N/m 2 T w superheat degree, ºC ρ v vapor density, kg/m 3 µ v vapor viscosity, N s/m 2 INTRODUCTION The area of heat exchanger network (HEN) synthesis has evoved a ot since the 80 s. Nowadays, there are two kind of approaches to sove synthesis probems: the mathematica programming approach, which uses MINLP programming and soves the probem in an automatic way, and the thermodynamic approach, in which the Pinch Design Method, PDM (Linnhoff and Hindmarsh, 1983) can be highighted. Athough the PDM presents a soid thermodynamic basis, a the exampes so far used considered ony Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

2 F. S. Liporace et a. Heat Exchanger Network... one-phase streams. In this particuar case, the use of a constant specific heat (Cp) vaue throughout the stream temperature range is the common procedure. In the context of the PDM, the determination of the utiities targets and of the pinch point (PP), which guide the synthesis of the initia HEN with minima consumption of utiities and its structura evoution, is strongy inked to the number of process streams, their inet and target temperatures and heat capacity fowrates (MCp). When process streams undergo a phase change, the use of the traditiona PDM procedure can ead to errors in the targeting and synthesis stages, due to the fact that the use of a constant Cp vaue throughout the temperature range of these kind of process stream no onger represents, correcty, their therma behavior. Westphaen and Wof Macie (1999) presented an aternative procedure to take into account these changing phase process streams, during ony the supertargeting stage. When performing the energy targets estimation, using the Temperature Interva Method, for each temperature interva and for each stream in the interva, the enthapy is cacuated at the initia and fina temperatures of the interva, as we as a mean vaue between these two enthapies. This ast resut is compared to the enthapy evauated at the mean temperature of the interva and, if both are different according to a specified toerance, the temperature interva is spit using the mean temperature as bound. After the convergence of this procedure, the utiities target estimation is conducted taking into account the great number of temperature intervas generated. This procedure may be suitabe for the supertargeting stage, but there are no comments about the synthesis stage in this new context with a great number of temperature intervas, and hence, of process streams. This work aims to go beyond the supertargeting stage and, by presenting a HEN synthesis Case Study invoving muticomponent process streams undergoing phase change, it intends to show their infuence on the fina resuts, i.e., fina HEN structure. First of a, bubbe (BP) and dew (DP) points temperatures of a streams are estimated using the Equation of State of Peng- Robinson. Then, stream by stream, it is verified if it changes phase competey or not, and then, when there is a phase change, it is spit into two or three sub-streams, using the BP and DP as bounds. For each sub-stream, an effective mean Cp is estimated as the division of the enthapy change by the respective temperature difference. This approach is beer than the traditiona one in the thermodynamic sense and makes easier units design, since the desuperheating, subcooing and phase change wi occur in different units. An exampe is used to show the strong infuence of the phase change, incuding modification on the PP, utiities targets and streams distribution aong the PP, hence on the HEN synthesis, which was not accompished by Westphaen and Wof Macie (1999). EXAMPLE, EQUATIONS AND RESULTS This exampe is reported in Ha et a. (1990). Tabe 1 presents the origina set of process streams. Tabe 1. Origina set of process streams Probem Tabe - Minimum Temperature Difference (MTD) = 20.0ºC Stream T i T o MCp H , , , , , , , , ,000.0 cu hu Assuming that a streams present the same moar fraction composition and tota pressure, as shown in Tabe 2, and using the Equation of State of Peng-Robinson, the bubbe and dew points temperatures (BP and DP) can be cacuated and are aso presented in Tabe 2. Tabe 3 presents the enthapy and the vaporized mass fraction of a stream, with the specified composition, for a the inet and target temperatures of Tabe 1, as we as for the BP and DP, which were cacuated using the software Petrox, from Petrobras. 88 Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

3 F. S. Liporace et a. Heat Exchanger Network... Tabe 2. Moar composition, pressure, BP and DP Tabe 4. Mass fowrates and effective mean Cp for the origina set of process streams With the data presented in Tabes 1 and 3, the mass fowrate and an effective mean specific heat for each stream can be cacuated. For instance, consider the origina hot stream 1. From Tabe 1, H = 2,750.0 kw; from Tabe 3, H = H (120.0ºC) - H (65.0ºC) = J/g; hence M = 12.7 kg/s; and since MCp) 1 = 50.0 kw/ºc, then Cp) 1 = 3.94 kj/kg ºC. Of course, this mean Cp vaue does not take into account the phase change that is occurring since the whoe temperature range was considered. Tabe 4 summarizes the resuts for the other streams. Using the traditiona procedure of the PDM and based on the data presented in Tabe 4, Figures 1 and 2 show the Composite Curves and the Grand Composite Curve, whie Tabe 5 presents the PP temperature and the utiities targets for the Case Study here presented. These resuts are in agreement with the ones reported in Ha et a. (1990), as it is expected, because they aso use the traditiona procedure. Tabe 3. Vaporized mass fraction and enthapy As mentioned before, due to the assumed streams composition and pressure, amost a streams of the origina set are changing phase, some of them competey, for instance, streams 4, 7 and 8, and others ony partiay (streams 1, 3, 5 and 9). Then, if a constant Cp vaue is taken for a the temperature range, there is a distance from reaity since the energy is not inear distributed aong that range. A beer thermodynamic approach is spit the stream according to the number of present phases and cacuate an effective mean Cp vaue for each sub-range. The BP and DP are used as bounds for this spit. For instance, the origina hot stream 4 goes from superheated vapor to subcooing iquid. According to the proposed procedure, this hot stream is repaced by 3 new hot streams: the first stream with T i = 220.0ºC and T o = 141.4ºC (desuperheating condition); the second stream with T i = 141.4ºC and T o = 110.0ºC (phase change condition); and the ast one with T i = 110.0ºC and T o = 95.0ºC (subcooing condition). Tabe 5. PP temperature and utiities targets - origina set of process streams Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

4 F. S. Liporace et a. Heat Exchanger Network... Figure 1. Composite curves - origina set of process streams - Ha et a. (1990) Tabe 6 presents the new set of process streams obtained by the proposed procedure. Now, the cacuus routine is different from the one used to buid Tabe 4. For instance, consider the new hot stream 1 (first temperature interva of origina hot stream 1). From Tabe 3, H = H (120.0ºC) - H (110.0ºC) = 98.7 J/g; hence H = 1,250.0 kw, MCp = kw/ºc and Cp = 9.85 kj/kg ºC. Using data from Tabe 6, the utiities targets, as we as the PP temperature, are determined for this new set of process streams, and are shown in Tabe 7. It can be noted that there are differences among the targets of both sets due to the beer energy distribution throughout the temperature range in the new set of process streams. Figures 3 and 4 present the Composite Curves and the Grand Composite Curve for the new set. It can be seen in Figure 4 the possibiity of owpressure vapor generation beow the PP, which was not visuaized before (refer to Figure 2), represented by a considerabe heat source around 100.0ºC. Tabe 7. PP temperature and utiities targets - new and origina set of process streams Figure 2. Grand composite curve - origina set of process streams - Ha et a. (1990) For each condition, an effective mean Cp vaue is estimated as the division of the enthapy change by the respective temperature variation, according to the traditiona procedure. The advantage, now, is that the energy distribution is no onger considered inear throughout the whoe temperature range, but inear distributed in each temperature interva, which at east for the desuperheating and subcooing conditions is a good approximation. The difference on the PP temperature and the increase on the number of process streams, wi affect the HEN synthesis since there is a modification on the streams distribution above and beow the PP, as shown in Tabe 8. Tabe 6. New set of process streams Figure 3. Composite curves - new set of process streams 90 Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

5 F. S. Liporace et a. Heat Exchanger Network... h D 0.15 Pr Re = κ F Re t (2) G ( 1 x) D = (3) µ x ρ v µ = x (4) ρ µ v (5) Figure 4. Grand composite curve - new set of process streams Tabe 8. Streams distribution aong the PP - new and origina set of process streams In order to show how the fina HEN structures wi be infuenced by the proposed procedure, the capita and operationa costs, as we as the heat transfer coefficients for each process streams must be known. The heat transfer coefficients are estimated, according to the stream s condition, using the reported correations from the iterature. In order to use these correations, it is assumed an inner tube diameter of cm (1 1/4 ) and the oca mean fuid fow veocity in each stream is cacuated as a function of its mass fux G, which is estimated for one temperature (density) and is kept constant for a the temperature range, no maer if the stream changes phase or not. - for one-phase stream, the we-known Dius- Boeter, Eq. (1): 0.8 n Nu d = Re d Pr (1) where n = 0.3 for cooing and n = 0.4 for heating; Re d is the Reynods number, Nu d is the Nusset number and Pr is the Prandt number. - convective condensation (Traviss et a., 1973), Eqs. (2) to (5): where h is the oca heat transfer coefficient, D is the tube inner diameter (assumed cm), κ is the iquid therma conductivity, Pr is the Prandt number for the iquid, Re is the Reynods number for the iquid, x is the vaporized mass fraction, G is the mass fux, is the Martinei parameter for the turbuent-turbuent fow, ρ is the iquid density, ρ v is the vapor density, µ is the iquid viscosity, µ v is the vapor viscosity and F t is a parameter. - convective boiing (Chen, 1987), Eqs. (6) to (14): F F h = h mac + h mic (6) h = h F( ) Pr (7) h mac κ D = Re Pr (8) Re G ( 1 x) D = (9) µ x ρ v µ = x (10) ρ µ v ( ) ( ) = = > 0.1 (11) Re = Re [ F( )] (12) tp ( ) ( Re ) 1 S Re h mic tp = (13) 0.24 ( T T ( P )) P ( T ) w κ = σ sat tp Cp ρ µ hv ρv 0.75 ( P ) S( Re ) sat w tp (14) where h is the oca heat transfer coefficient, h mac is the macroscopic (convection) Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

6 F. S. Liporace et a. Heat Exchanger Network... contribution, h mic is the microscopic (nuceate boiing) contribution, h is the heat transfer coefficient for the iquid, Re is the Reynods number for the iquid, x is the vaporized mass fraction, G is the mass fux, is the Martinei parameter for the turbuent-turbuent fow, ρ is the iquid density, ρ v is the vapor density, µ is the iquid viscosity, µ v is the vapor viscosity, Re tp is the Reynods number for both phases, S is the suppression factor, D is tube inner diameter (assumed cm), κ is the iquid therma conductivity, Pr is the Prandt number for the iquid, σ is the iquid superficia tension, h v is the atent heat of vaporization (assumption: h v = H (BP) - H (DP)), T w is the wa temperature (assumption: superheating of 10.0ºC), P is the stream pressure, P sat (T w ) is the saturation pressure at T w (assumption: it is the pressure where, at T w, the vaporized mass fraction is the same as the one for the condition [P, stream temperature]). These two ast correations were originay deveoped for pure fuid changing phase, but they wi be used for muticomponent streams as a first approximation due to the ack of reported correations for this specia case. Tabe 9 presents the estimated heat transfer coefficients for the one-phase process streams. The reported vaues are the mean ones between the oca heat transfer coefficient at the inet and outet temperature conditions (oca heat transfer coefficient), whie Tabe 10 shows the heat transfer coefficients for the changing phase process streams, Tabe 9. Heat transfer coefficients for the new set of process streams (one phase) 92 Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

7 F. S. Liporace et a. Heat Exchanger Network... Tabe 10. Heat transfer coefficients for the new set of process streams (changing phase) which are mean vaues cacuated by h m = ( x x ) f 1 i xf xi h ( x) dx, where the integra in numericay evauated (Gauss-Legendre), and h(x) is represented by the appropriated expressions (Eqs. (2) or (6)). The heat transfer coefficients for the origina set of process streams (traditiona procedure) are presented in Tabe 11 and are obtained as foows. Origina hot stream 1 is spied into new hot streams 1 and 2; from Tabes 9 and 10, h 1 = 8,022.0 W/m 2 ºC and h 2 = 2,164.0 W/m 2 ºC; from Tabe 6, H 1 = 1,250.0 kw and H 2 = 1,500.0 kw, hence the origina h 1 is 5,072 W/m 2 ºC. Tabe 12. Data on costs and heat transfer coefficients for the utiities Tabe 11. Heat transfer coefficients for the origina set of process streams Figure 5. Fina HEN for the origina set of process streams - TAC: $2.74 x 10 6 /year Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

8 F. S. Liporace et a. Heat Exchanger Network... Tabe 12 shows the data on capita and operationa costs used in this work and aso presents the heat transfer coefficients for hot and cod utiities. The fina HEN for the origina set of process streams (traditiona procedure) is shown in Figure 5 and Tabe 13 whie the fina HEN for the new set of process streams (proposed procedure) is presented in Figure 6. Those structures were obtained using the software AtHENS (Automatic Heat Exchanger Network Synthesis), deveoped at Escoa de Química of Universidade Federa do Rio de Janeiro. This software uses a modified PDM rue to perform the synthesis near to the PP and a heuristic rue to synthesize the network away from the PP. After the synthesis of the initia HEN that accompishes the minima consumption of utiities, the HEN is evoved in order to decrease the HEN TAC. This evoutionary optimization is performed with the hep of the Simuation Matrix in order to restore the MTD and the stream s target temperature when they are vioated by the oop-breaking procedure (Liporace et a., 1999). As the process streams are not, in fact, spit, the HEN structure presented in Figure 6 must be rearranged in order to show the matches of the origina streams (Figure 7 and Tabe 14), so as a comparison between the fina HENs obtained by the traditiona and proposed procedures can be performed. Figure 6. Fina HEN for the new set of process streams - TAC: $3.50 x 10 6 /year It must be noted the different matches, spits, number of units and, of course, utiities consumption and TACs between both structures (Figures 5 and 7). Figure 7. Rearrangement of the HEN structure from Figure 6 Tabe 14. Data on the HEN presented in Figure 7 Tabe 13. Data on the HEN presented in Figure 5 94 Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p

9 F. S. Liporace et a. Heat Exchanger Network... These are due to different PP temperature and streams distribution through both above and beow the PP regions, showing the great infuence of a beer approach to the energy distribution aong the temperature range when there are changing phase process streams. The great number of spits in both HEN is a consequence of the modified PDM rue used to perform the synthesis near to the PP. Another fact that shoud be mentioned is that, when the HEN of Figure 6 was rearranged, some new oops appeared. As mentioned earier, spiing a stream using the DP and BP as bounds makes easier the unit design since the desuperheating, subcooing and phase change occur in different units. If these new oops are broken, these phenomena may occur in the same unit, which may increase the difficuties to perform its design. So, in our point of view, they shoud not be broken. Athough the probem size may increase a ot due to the spit of some of the process streams, it took AtHENS ess than 15 seconds of average computing time (Pentium 166 MHz and 16 MB RAM) to synthesize an initia HEN with minima consumption of utiities and evove it, for each of the resuts of the Case Study here discussed. CONCLUSIONS REFERENCES Chen,S.L., Gerner,F.M. and Tien,C.L., 1987, Genera fim condensation correations, Exp. Heat Transfer 1, pp Ha,S.G., Ahmad,S. and Smith,R., 1990, Capita Cost Targets for Heat Exchanger Networks Comprising Mixed Materias of Construction, Pressure Ratings and Exchanger Types, Comp.Chem.Eng., 14 (3), pp Linnhoff,B. and Hindmarsh,E., 1983, The Pinch Design Method for Heat Exchanger Networks, Chem. Eng. Sci., 38 (5), pp Liporace,F.S., Pessoa,F.L.P. and Queiroz,E.M., 1999, Automatic Evoution of Heat Exchanger Networks with Simutaneous Heat Exchanger Design, Braziian Journa of Chemica Engineering, 16 (1), pp Traviss,D.P., Rohsenow,W.M. and Baron,A.B., 1973, Forced Convection Condensation in Tubes: A Heat Transfer Correation for Condenser Design, ASHRAE Trans. 79, Part I, pp Westphaen,D.L. and Wof Macie,M.R., 1999, Pinch Anaysis based on Rigorous Physica Properties, Braziian Journa of Chemica Engineering, 16 (3), pp In this work, it is shown how changing phase process streams can significanty interfere on the energy targets and PP estimation and, aso, on the fina HEN structures in HEN synthesis probems. A procedure to account for these aspects in the supertargeting and synthesis stage is proposed, which is based on the spit of the changing phase process streams using the BP and DP as bounds. This approach is beer than the traditiona one in the thermodynamic sense, due to the beer energy distribution aong the temperature range, and makes easier the unit design, since the desuperheating, subcooing and phase change wi occur in different units. ACKNOWLEDGEMENTS The authors woud ike to acknowedge the financia support from CAPES and FAPERJ. Engenharia Térmica (Therma Engineering), Vo. 3 No. 2 December 2004 p