The Thermo Economical Cost Minimization of Heat Exchangers

Transcription

1 he hermo Economical ost Minimization of Heat Exchangers Dr Möylemez Deartment of Mechanical Engineering, niversity of Gaziante, 7310 bstract- thermo economic otimization analysis is resented yielding simle algebraic formula for estimating the otimum oerating temeratures for three different tyes of heat exchangers which are alied in industrial alications n economic analysis method is used in the resent study, together with the thermal analyses of heat exchangers, for thermo economic otimization of all of the three different tyes of heat exchanger he validity of the otimization formulations was checked Keywords-hermo economics; Heat exchanger; ost otimization I IRODIO Economics of heat exchanger oeration is vitally significant o, otimum oerating temeratures for three different tyes of heat exchanger as shown in Fig 1 is extremely imortant in order to have imum overall life cycle cost for these systems he otimum values of imum oerating temeratures must be calculated at which imum cost occurs for four heat exchangers that can be alied for industrial alications for that reason here exist many arameters for otimizing such heat exchangers in a thermo economical manner Fixing, and so eliating all of these thermal and economical arameters deending on the certainty of oerating characteristics of alications and the most efficient oerating condition of the heat exchangers can detere the otimum oerating temeratures for heat exchangers It is known that the effectiveness of the heat exchanger is directly related to its size together with its initial cost thermo economic feasibility study is necessary before installing the heat exchanging systems he basic toic of the resent work deends uon this idea new thermo economic otimization technique is realized and resented for this urose Original formulae are develoed for calculating the otimum oerating temeratures at which the imal total life cycle cost occur thorough search of the current literature showed that there was no revious study on imizing the life cycle cost of a heat exchanger in detail well known and ractical method, 1 - method, which is offered by Duffie and eckman (1980, is used for otimizing the size and oerating conditions of heat exchanger, and original interesting results are resented Variable arameters used in formulating the otimization roblem are listed as technical life of the heat exchanger, first cost of the heat exchanger er unit heat transfer area, annual interest rate, resent net rice of energy, annual energy rice escalation rate, annual average oerating time, ratio of imum heat caacity rate into imum heat caacity rate, design values of imum and imum temeratures of hot and cold fluids for single fluid heat exchanger, overall heat transfer coefficient of the heat exchanger, resale value and the ratio of annual maintenance and oeration cost to the first original cost Otimum steam temerature for single fluid heat exchanger and otimum value of imum temerature difference for counter current and arallel flow heat exchangers can be calculated easily in a few utes with the hel of ractical formulae thorough search of the resent literature showed that there were several studies about the heat exchangers (Vojtech et al 011, hung et al 00, Grazzini and Rinaldi 001, ornelissen and Hirs 1999, Georgiadis 1998, Şahin 1997, Edwards and Matavosian 198 ll of these studies are not directly related to the resent work Original formulae are develoed and resented finally II MHEMIL FORMLIO ingle Fluid ( 0 Heat Exchangers (team Heater he total cost of single fluid heat exchanger as shown in Fig 1 can be calculated by using the cost data (urmeister 1998 as: Fig 1 chematic Figure of lternative Heat Exchangers + 1 m H t (1 he area of heat transfer for single fluid heat exchanger can be calculated by the following m ln(1 ε ( E Vol o 1, wwwij-eeorg World cademic ublishing I (rint I (online

2 Where the effectiveness of the heat exchanger is defined by: ε (3 he total cost of the single fluid tye of heat exchanger er unit heat caacity rate can be estimated by means of the following function where and ln(1 + 1 E m H t ln + ( (5 1 H t (6 he cost of energy in the form of steam as a function of steam temerature in dollars er joule can be aroximated (toecker1989 as in the following form nd also: 1 1 E (7 ε (8 he first derivative of the total cost function with resect to steam temerature can be obtained for otimization urose by the following equality /( m ] ( ( Eq (9 can be simlified to form Eq (10 as: + 0 (9 ( (10 he otimum oerating steam temerature can be calculated by the hel of Eq (11, ot + ± ( + ( / (11 he second derivative of the total cost function is always ositive which indicates a local imum certainly m, ot + [ / ( ] [ ( ] > 0 (1 ( ( ince:, ot, ot, ot ( + > / (13 ounter urrent ( 1 Heat Exchangers he same rocedure can be alied for the counter and arallel flow heat exchangers and the following equations can be obtained he cost of energy is aroximated due to the imum oerating temerature difference, in $/J (toecker1989 also as in Eq (1 E (1 /( m m ε ε ( [ /( m ] (1 ε ε + 1 E m (1 ε / H t + 1 / (16 (17 1 H t (18 ε (19 /( m ] ( ot + 0 (0 + 0 (1 ( ( ( / ± + / ( Vol o 1, wwwij-eeorg World cademic ublishing I (rint I (online

3 [ /( m arallel Flow Heat Exchangers ] ( ot 3 > 0 (3 ot > ( m ln[1 ε (1 ] (5 + (1 + ln E m (1 + (1 + H t ln /( m E (6 (7 1 H t (8 ] (9 ε (30 (1 + ( (31 ( 1+ 0 (3 (1 + ± (1 + + ( / ot (33 ot + [ / ( m ] [ (1 ] > 0 (3 ( (1 + ot ot > ( 1+ / (35 ot D ounter urrent ( # 1 Heat Exchangers ε 1 e 1 e ( 1 ( 1 m 1 ε ln (1 1 ε (36 1 ε ln + 1 E m (1 1 ε (1 + H t ln /( m ] ( E (37 (38 1 H t (39 (0 ε (1 ( + 0 ( ( (3 (1 + ± (1 + [ ( / ] ot ( [ /( m ] [ ot (1 + ] ( ( ot ot > 0 (5 > ( 1+ / (6 ot he economic arameters 1 and are defined as in following equations (Duffie and eckman 1980 If I is equal to d: nd for i # d: nd 1 1+ i 1 1+ i 1 1 ( d i 1+ d 1 M RV (1 + d (7 (8 (9 Vol o 1, wwwij-eeorg World cademic ublishing I (rint I (online - 1 -

4 III REL D DIIO For a tyical heat exchanger roblem, it is assumed that i d 008, 500 W/(m K, H 000 hr/yr, 0 yr, 00 K for counter and arallel flow heat exchangers, 50 for single fluid heat exchanger, 50, 100 $/m, M s 0, R v 0 he values of total costs for this secific examle are deicted in Figs to 5 here exist secific local imum cost oints in each figure he best imum steam temerature is calculated for single fluid heat exchanger as 53 degrees by using Eqn (11 whereas otimum imum temerature difference values are calculated by using Eqns (, (33 and ( as, 03 and 06 degrees resectively for counter flow 1, arallel flow 1 and counter flow # 1 heat exchangers he values of otimum temeratures with corresonding effectiveness and heat transfer area values are resented in able 1 he same data was used for all of the four alternative heat exchangers is selected as unity for arallel flow heat exchanger and 05 as an examle for counter flow heat exchanger for # 1 case as illustrated in concerning figures here exist so many design tools such as comuter codes for designing the heat exchangers hese codes are helful for seedy estimation of heat exchangers and they are used in industry hese comuter codes select the standardized heat exchanger due to redesigned oerating temerature levels by using thermo-hydraulic data without considering economics /(m, $/(W/K otal cost versus imum steam temerature 6 for single fluid, imum steam temerature (degrees Fig otal ost versus team emerature for ingle Fluid Heat Exchangers /(m, $/(W/K otal cost versus imum temerature difference for counter flow, imum temerature difference (degrees Fig 3 otal ost versus Maximum emerature for ounter urrent Heat Exchangers 1 /(m, $/(W/K otal cost versus imum temerature difference for arallel flow, imum temerature difference (degrees Fig otal ost versus Maximum emerature for arallel Flow Heat Exchangers 1 /(m, $/(W/K otal cost versus imum temerature difference for counter flow, # imum temerature difference (degrees Fig 5 otal ost versus Maximum emerature for ounter urrent Heat Exchangers # 1 LE 1 HERMO EOOMI ERFORME VLE FOR FOR HE EXHGER ye of heat exchanger ingle fluid, 0 ounter, 1 arallel, 1 ounter, # 1,ot or,ot ( Otimum effectiveness /(m (m K/W /(m [$/(W/K] IV OLIO It can be deduced that there exists always a local imum value in heat exchanger alications for three alternative configurations Excessive steam temerature or imum temerature difference will not be cost effective beyond the otimum values in site of a greater heat transfer recovery otential he imum oerating temerature of heat exchanging fluid has doant effect on the amount of total life cycle cost It is clear that there exist good thermal erformance at the otimum oint for each alternative heat exchanger hese tyes of systems must be designed close to this otimum oint he resent formulae may seem to be helful for heat exchanger designers and manufacturers Vol o 1, wwwij-eeorg World cademic ublishing I (rint I (online

5 REFEREE [1] urmeister L 1998 Equiment cost estimation In Elements of hermal-fluid ystem Design, rentice Hall: ew Jersey; [] hung K, Lee K, Kim W 00 Otimization of the design factors for thermal erformance of a arallel-flow heat exchanger, International Journal of Heat and Mass ransfer 5(, [3] ornellissen RL, Hirs GG 1999 hermodynamic otimization of a heat exchanger, International Journal of Heat and Mass ransfer (5, [] Duffie J, eckman W 1980 olar rocess economics In olar Engineering of hermal rocesses, Wiley: ew York; [5] Edwards DK, Matavosian R 198 hermoeconomically otimum counter flow heat exchanger effectiveness, Journal of Heat ransfer- ransactions of the ME 10(1, [6] Georgiadis M, Rotstein GE, and Macchietto 1998 Otimal design and oeration of heat exchangers under milk fouling, IhE Journal (9, [7] Grazzini G, Rinaldi R 001 hermodynamic otimal design of heat exchangers for an irreversible refrigerator, International Journal of hermal ciences 0(: [8] toecker WF 1989 Design of hermal ystems, 3 rd Edn, Mc Graw-Hill: ew York; 68 [9] Şahin Z 1997 hermodynamic design otimization of a heat recuerator, International ommunications in Heat and Mass ransfer (7, [10] Vojtech, etal 011 Otimum design of fluid distribution systems in heat exchangers, sia asific Journal of hemical Engineering 6(5, EDIX onstant deending on values of fixed oerating arameters as defined in Eqns (5, (17, (9, (0 rea of heat exchanger, (m onstant deending on values of fixed oerating arameters as defined in Eqns (6, (18, (8, (39 Ratio of imum to imum heat caacity rates of two streams in heat exchanger rea deendent first cost of the heat exchanger, ($/m E ost of energy deending on the imum temerature, ($/J E ost of energy in the form of steam, ($/J Higher heat caacity rate in heat exchanger, ( m, (W/K Lower heat caacity rate in heat exchanger, ( m, (W/K ecific heat of circulating fluid having imum heat caacity rate, [ J/ (kgk] d H i Market discount rate in fraction nnual time of oeration, (h/yr Energy rice escalation rate in fraction m Mass rate of flow of circulating fluid having imum heat caacity rate, (kg/s M s Ratio of annual maintenance and oeration cost into first original cost echnical life, (yr umber of transfer units 1 Ratio of the life cycle energy cost savings to the first year energy cost savings, (yr Ratio of the life cycle exenditures incurred because of the additional caital investment to the initial investment R v Ratio of resale value into the first original cost Maximum temerature of hot fluid at the inlet side of single fluid heat exchanger, ( Minimum temerature of cold fluid at the inlet side of single fluid heat exchanger, ( emerature of hase changing steam in single fluid heat exchanger, (,ot Otimum temerature of steam in single fluid heat exchanger, ( otal cost of the heat exchanger Overall heat transfer coefficient, [W/ (m K] t umber of seconds in an hour, ( 3600 Inlet-exit temerature difference for fluid having imum caacity rate in counter or arallel flow heat exchangers, ( Maximum temerature difference between hot and cold fluid inlet in counter or arallel flow heat exchangers, ( ot Otimal imum temerature difference between hot and cold fluid inlet in counter or arallel flow heat exchangers, ( ε Effectiveness of heat exchanger Dr M ait öylemez was born in Gaziante, urkey, in 196 He got his and M degrees in Mechanical Engineering in 1985 and in 1988; he obtained his M degree in Mechanical Engineering Deartment of the Middle East echnical niversity, urkey hen he continued his studies and got his h D Degree at the Mechanical Engineering Deartment of the niversity of Gaziante, in urkey, in 199 He has ublished over 50 research aers in the International Journals and conference roceedings He is currently working as Lecturer in the same university His major interests are heat transfer and energy economics Vol o 1, wwwij-eeorg World cademic ublishing I (rint I (online - 1 -