Thermo-economic optimization of synthesis, design and operation of a marine organic Rankine cycle system

Size: px
Start display at page:

Download "Thermo-economic optimization of synthesis, design and operation of a marine organic Rankine cycle system"

Transcription

1 Original Article Thermo-economic optimization of ynthei, deign and operation of a marine organic Rankine cycle ytem Proc IMechE Part M: J Engineering for the Maritime Environment 2017, Vol. 231(1) Ó IMechE 2016 Reprint and permiion: agepub.co.uk/journalpermiion.nav DOI: / journal.agepub.com/home/pim Miltiadi Kalikatzaraki and Chrito A Frangopoulo Abtract The recovery of high temperature thermal energy releaed by propulion engine in order to cover thermal load i commonplace in contemporary hip. However, the medium- and low-temperature thermal energy i only partially exploited or not exploited at all. In the preent work, an organic Rankine cycle ytem driving an electric generator i conidered, in addition to the exhaut ga boiler, in order to recover available heat and produce electrical energy. The pecification of the ytem are determined by an optimization procedure taking economic criteria into conideration, apart from the technical criteria uually ued in thi kind of tudie. More pecifically, with the net preent value a the objective function and by application of optimization algorithm, the optimal ynthei, deign and operation of the organic Rankine cycle ytem are determined. For the particular veel conidered, the intallation of the organic Rankine cycle i technically feaible and economically profitable, with a dynamic payback period of 4 year. The olution of the optimization problem i upplemented with a enitivity analyi with repect to important parameter. Keyword Marine propulion, heat recovery, organic Rankine cycle, energy ytem optimization Date received: 6 July 2015; accepted: 11 December 2015 Introduction Recent economic development, international rie of fuel oil price and environmental concern with more and more tringent regulation gave the impetu for reearch on new technologie for more efficient, environmentally friendly and cot-effective hipping tranportation. In thi context, everal path are under invetigation, in order to reduce energy demand on board hip. One viable olution i the recovery of the main engine wate heat. A comprehenive review of the variou technologie for thi purpoe appear in Shu et al. 1 Wate heat boiler covering thermal load are commonplace on mot hip. Flah evaporator exploiting low-temperature wate heat for ea water dealination are alo frequently ued. With further exploitation of wate heat from the exhaut gae and the cooling circuit of the engine, it i poible and in many cae economically feaible to produce additional mechanical or electrical power for propulion and/or electrical load. The mot common technique for thi purpoe conit of a water-team Rankine cycle. 2 5 Kalina cycle alo ha been invetigated at leat theoretically. 6 Recently, the direct converion of wate heat to electricity by thermoelectric device gained attention for marine application. 1,7 10 The aforementioned technique, except of ea water dealination with flah evaporator, recover wate heat of more or le high temperature, uch a the heat in exhaut gae. However, there i till an important quantity of low-temperature heat that i till rejected to the environment. Recent reearch ha indicated a potential of 10% improvement in fuel economy uing organic Rankine cycle (ORC) ytem driving electric generator, which are capable of converting lowtemperature wate heat into electricity, in order to cover on-board demand Several work in the literature deal with coupling of ORC with internal combution engine. In general, School of Naval Architecture and Marine Engineering, National Technical Univerity of Athen, Zografou, Greece Correponding author: Chrito A Frangopoulo, National Technical Univerity of Athen School of Naval Architecture and Marine Engineering, Heroon Polytechniou 9, Zografou, Greece. caf@naval.ntua.gr

2 138 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) high thermal efficiency and optimum utilization of the available heat ource can be achieved by appropriate election of the working fluid and correct configuration of the ORC ytem. Wang et al. 17 gave a review regarding the effect of different ytem configuration, working fluid and component on the overall efficiency of the ytem. The BMW Group imulation, 18 which wa conducted in order to determine the potential of ORC uage on vehicle, demontrated that if the exhaut ga i the only available heat ource, water i the preferable working fluid, while if both exhaut ga and coolant can be exploited, then ethanol i more promiing. It i noted that the temperature level of vehicle exhaut gae i higher than that of the hip invetigated in the preent work. Hung et al. 19 analyed efficiencie of ORC and reached the concluion that ientropic fluid are the mot uitable for recovering low-grade wate heat. Wang et al. 20 tudied the effect of working fluid on the performance of ORC under different working temperature and uggeted the bet fluid for each temperature. The concluion wa that the election of working fluid i baed primarily on the available heat ource. Apart from the working fluid, different ORC configuration have an impact on the overall performance of the wate heat recovery ytem. Among everal olution, Smolen 21 tudied the performance of a twotage ORC ytem exploiting heat from the exhaut ga and coolant of an internal combution engine. Shu et al. 22 uggeted a imilar dual-loop configuration, with water a the working fluid for the high temperature (HT) loop, and variou organic fluid for the low temperature (LT) loop. Fewer work preented a comparion between imulation data and experimental value or evaluation of an ORC ytem from an economic tandpoint. 26 A common characteritic of the aforementioned tudie i the heat exchanger network (HEN) of the ORC ytem. More pecifically, the HEN of the ytem itelf i fixed. Thi approach ha the advantage of implifying the analyi of the ytem by reducing the available degree of freedom. However, the configuration obtained may not be the truly optimal one. A different approach baed on pinch analyi 27 and the HEATSEP method 28 i ued in thi work. Exploiting the available heat ource of an exiting containerhip, the HEN of the ORC ytem i kept entirely independent of the deign of the ret of the ytem. The temperature at the boundarie of the part of the ytem are conidered a deciion variable in the deign optimization procedure. Then, the deign of the HEN i performed uing the information provided by the compoite curve, reulting in the bet poible matching between the available hot tream (heat ource) and the ORC ytem. A formal mathematical optimization i performed, which take into conideration economic criteria, in addition to technical criteria uually ued in thi type of tudie. Energy ytem The 13,600 Twenty feet Equivalent Unit (TEU) containerhip that i tudied i powered by a two-troke marine Dieel engine with a maximum continuou rating (MCR) of 72,240 kw. It i alo equipped with five Dieel generator (including the emergency generator) with a nominal electric power output of 2700 kw each, which cover the electrical power need of the veel. Main engine layout Figure 1 depict the main engine and heat recovery ytem. An exhaut ga boiler (EGB) cover the thermal energy need in the form of hot water and team. In addition, dealinated water i produced by a freh water generator (FWG) operating with hot water coming from the cooling circuit of the main engine. The cooling ytem i compoed of the high and low-temperature circuit. The water flow from the high temperature circuit (w1) cool the cylinder jacket and head of the main engine (tate w2) and the combution air in the firt charge air cooler (AC1). Moreover, the flow of tate w2 i then fed to the FWG, which produce 40 ton of water per day. The low-temperature circuit cool the lubricating oil (from tate lo1 to tate lo2) and the combution air in the econd air cooler (AC2). Finally, the EGB recover heat form the main engine exhaut gae at the turbocharger outlet (g2), producing a total of 1500 kg of team hourly. The energy demand and operating profile of the main engine are given in Table 1. It i noted that the energy demand at variou operating mode were derived by tatitical analyi of operational data for hip of imilar ize at the ame trading route (Aia US Wet coat trading pattern). The propulion demand take into conideration different loading condition (mode in Table 1) at the variou miion tage. Moreover, the electricity demand take into account the number of reefer container tranported by the veel at different miion tage. It can be een that the hip ha elevated need in electricity in mot of it operating mode. 29 Poibility of wate heat recovery In addition to the heat recovery already taking place in the EGB, thermal energy available in the cooling circuit of the main engine can alo be exploited, intead of dicharging it to the environment. In order to analye and evaluate the available option, certain operating characteritic of the intalled power ytem are eential. The partial load performance in term of temperature and releaed thermal energie are given in Figure 2 4, baed on heat balance calculation. A can be een in Figure 4, coniderable amount of heat i rejected by the two air cooler. Epecially, at

3 Kalikatzaraki and Frangopoulo 139 Figure 1. Main engine cooling ytem layout. Table 1. Operating profile and energy demand. Mode Dt (h/a) _W pr, D (MW) N pr (r/min) _W el, D (MW) _m t, D (kg/h) A B C D Figure 2. Temperature level of air, exhaut ga and lubricating oil. Figure 3. Temperature level of the HT and LT cooling circuit.

4 140 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) Table 2. Propective working fluid. Fluid T crit. ( C) p crit. (bar) GWP 100 ODP Cot (e/kg) R-134a R-152a R-227ea R-236fa R-236ea R-245fa R-245ca ODP: ozone depletion potential. Figure 4. Releaed thermal energie of the marine propulion ytem. relatively high load, the available heat of the two air cooler combined urpae 20 MW. Apart from the charge air, propective heat ource are the lubricating oil and the cooling water of the main engine. The two heat flow amount to more than 6 and 8 MW, repectively, for load above 56% of the MCR. Finally, a relatively high temperature heat ource i the exhaut ga leaving the boiler. An analyi of the veel team demand (1500 kg/h a mentioned in the previou ection) indicated that the heat in the exhaut gae i only partially recovered. From Figure 2, it can be een that the exhaut ga at the exit of the EGB (tate g3) i till exploitable, ince it temperature i higher than 200 C at every operating load. ORC ytem modelling In thi ection, the modelling and optimization procedure of the ORC ytem are preented, along with the method ued in order to optimize the configuration, deign characteritic and operation of the ytem. Working fluid election More than 75 fluid have been propoed in the literature a working fluid for ORC ytem. 30 Taking into conideration the regulation a tated in the revied MARPOL Annex VI 31 regarding application of ozone depleting ubtance, only the fluid in Table 2 are tudied in thi work. Figure 5. Baic ORC ytem layout. HEATSEP method and pinch point analyi The HEATSEP method, originally introduced by Lazzaretto and Toffolo, 28 coniderably implifie the ynthei problem of the ytem by identifying and eparating it into it baic component, which in our cae are the expander and pump of the ORC ytem. The core idea i to cut thermal link between thee baic component, o that the inlet and outlet temperature at each component (i.e. expander or pump) are etablihed independently of each other a deciion variable of the optimization procedure, in which all the other deign parameter of the ytem are involved a well. In doing o, the HEN (appearing a a black-box in Figure 5, which include the hot and cold tream) i deigned independently with a parametric procedure at the black-box boundarie uing pinch point analyi and the econd law of thermodynamic. 28 ORC layout Several ORC configuration can collect the low-grade wate heat of the main engine. For example, the exiting tate of cooling ytem layout could directly provide the heat to the ORC ytem, by feeding it with all the hot

5 Kalikatzaraki and Frangopoulo 141 Figure 6. Propective ORC heat ource. water tream, before they are dicharged to the central water cooler (tream w3 and w5 w7 in Figure 1). However, in thi work, a new arrangement i conidered, o that the ORC ytem will exploit the available wate heat at the highet poible temperature level. The propective heat ource conidered for the ORC ytem are given in Figure 6. Thermodynamic model Each component of the ORC i modelled in the MATLAB environment, wherea the fluid propertie are calculated uing NIST Refprop 8.0 oftware. Heat exchanger. The heat exchanger are ignificant component of the heat recovery ytem, ince in mot cae they account for more than half of the total invetment cot. 11 Thu, a detailed model i ued in thi work, in order to evaluate the heat exchanging area and the total cot of the heat exchanger accurately. Shell and tube heat exchanger are aumed for the ORC ytem HEN. The ORC fluid i conidered flowing through the tube, while the variou heating fluid flow on the hell ide. The urface area of each heat exchanger i calculated by equation (1) A = Q UDT lm F ð1þ where Q i the heat load, U i the overall heat tranfer coefficient, DT lm i the logarithmic mean temperature difference, and F i the correction factor. Heat tranfer within the heat exchanger and the overall heat tranfer coefficient are given by equation (2) and (3), repectively _Q = _m c p, ðt in, T out, Þ= _m t c p, t ðt out, t T in, t Þ ð2þ

6 142 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) Table 3. Coefficient K 1 and n 1 of equation (18) for triangular and quare pitche. 37 No. of tube pae Triangle tube pitch Square tube pitch K 1 n 1 K 1 n 1 Figure 7. Triangular and quare tube pitch arrangement. 37 U = 1 + R f, + d o R f, t ð3þ h d i h t where d i =0:8 d o ð4þ The heat tranfer coefficient for the hell ide i given by Kern formulation 35 h =0:36 k Re 0:55 Pr 0:33 m 0:14 ð5þ D e m w where D e i the hydraulic hell diameter, calculated by equation (6a) and (6b) for quare and triangular pitch, repectively 36,37 ( 4 P 2 t 0:25pd2 o ð6aþ D e = pd o 0:4 pd o 0:43P 2 t 0:5pd2 o 4 ð6bþ The triangular and quare tube pitche, P t, are hown in Figure 7. The Prantdl and Reynold number for the hell ide are given by equation (7) and (8) Pr = m c p, k Re = r u D e m ð7þ ð8þ where u i the velocity of the fluid of the hell ide, 36,37 given by the equation u = _m a r ð9þ In equation (9), a i the cro-ectional area normal to the flow, given by equation (10) a = D ebp ð t d o Þ r ð10þ The tube ide heat tranfer coefficient depend on the flow type and i given by the following equation: 36,37 For Re t h t =3:657 k t + k t 0:0677 d Re t Pr 1:33 i t L d i d i d 1+0:1Pr t Re i 0:3 ð11þ t For 2300 \ Re t \ 10,000 L h t = Pr t f t 8 For Re t. 10,000 k ðre t 1000Þ 1+ d i 0:67 t L qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð12þ d i f 1+12:7 t 8 ð Pr t 0:66 1Þ h t =0:027 k t Re 0:8 0:33 m 0:14 t Prt t t ð13þ d i m w The Darcy friction factor i calculated by equation (14) 1 f t = ð1:82 logðre t Þ 1:64Þ 2 ð14þ The Prandtl and Reynold number for the tube ide are given by equation (15) and (16) Pr t = m tc p, t k t Re t = r tu t d i m t and the tube ide flow velocity i given by 36 u t = _m t n pd 2 i 4 r N t t ð15þ ð16þ ð17þ where n i the number of tube pae and N t i the number of tube that can be calculated by equation (18) 36,37 D n1 N t = K 1 ð18þ d o K 1 and n 1 are coefficient that are function of flow arrangement and number of pae. The value for variou flow arrangement are given in Table The length of the tube i given by equation (19) L = A pd o N t ð19þ The logarithmic mean temperature difference i computed by equation (20) ð DT lm = T, in T t, out Þ ðt, out T t, in Þ ð20þ ln T, in T t, out T, out T t, in

7 Kalikatzaraki and Frangopoulo 143 The correction factor ued in equation (1) i given by equation (21) pffiffiffiffiffiffiffiffiffiffiffiffiffiffi S F = 2 +1 ln 1 P 1 PS pffiffiffiffiffiffiffiffiffiffi ð21þ S 1 2 PðS+1 S ln ffiffiffiffiffiffiffiffiffiffi 2 +1Þ p 2+PðS+1 S 2 +1Þ where P and S are efficiency and correction factor that depend on the configuration of the flow. They are calculated by equation (22) and (23) P = T t, out T t, in T, in T t, in S = T, in T, out T t, out T t, in ð22þ ð23þ The total cot of a heat exchanger conit of the capital cot and the operating cot due to the energy required in order to overcome the preure drop of the fluid. For a contant heat load in a pecified heat exchanger, a the fluid velocity increae, the heat tranfer coefficient rie, and a a reult, the required heat exchanging urface area and the invetment cot decreae. However, increae in fluid velocitie reult in higher preure drop, which in turn increae the operation cot. For thi reaon, the ucceful deign of the heat exchanger i the reult of a balanced trade-off between the heat exchanging area and the preure drop. 37 The tube ide preure drop i compoed of major and minor loe given by equation (24) Dp t = Dp major + Dp minor = r tu 2 t 2 L +2:5 n d i ð24þ The hell ide preure drop i calculated by equation (25) r Dp = f u 2 L D ð25þ 2 B D e where f i a friction factor, given by equation (26) f =1:44Re 0:15 ð26þ Finally, the additional pumping power required due to the preure drop i computed by equation (27) _W pump = 1 _m t Dp t + _m Dp ð27þ h P r t r In off-deign condition, the overall heat tranfer coefficient varie mainly due to the variation in flow rate. The following correlation i ued to calculate thi coefficient in the actual condition 38 _m 0:65 U = U nom ð28þ _m nom At thi point, it i noted that the conideration of a global mean logarithmic temperature difference between the input and output of the fluid in the heat exchanger reult in inaccurate calculation, in particular when at leat one of the fluid change phae in the heat exchanger. Epecially, under upercritical condition, the thermal propertie of the working fluid are trongly dependent on temperature, epecially in the peudo-critical temperature range. The calculation procedure of the overall heat tranfer coefficient (U) i alo temperature dependent, a it include thoe propertie. A a reult, U cannot be conidered contant throughout the whole heat tranfer procedure, becaue calculation error are unacceptably high. 39,40 Taking the aforementioned into conideration, the overall heat tranfer coefficient i calculated with the following procedure. The heat exchanger i divided into elementary ection, which are treated a individual heat exchanger. The partitioning of the heat exchanger i performed auming that the ame thermal energy i tranferred through each ection. All the calculation preented in thi work are made having divided the heat exchanger into 500 elementary ection, a partitioning which can achieve a calculation error in the order of 0.01%. 39 The calculation procedure for the heat exchanger i given in Figure 8. For each elementary ection, the heat load i calculated firt, along with the temperature of the fluid at the ection inlet and outlet. Then, the overall heat tranfer coefficient and the required heat exchanging area of the ection are calculated. The total heat exchanging area i the um of the area of the elementary ection. Expander. Each volumetric expander (croll, crew, reciprocating) i characterized by an internal, built-in volume ratio correponding to the ratio between the inlet pocket volume and outlet pocket volume. Underexpanion occur when the internal preure ratio impoed by the expander i lower than the ytem preure ratio. In that cae, the preure in the expanion chamber at the end of the expanion proce i higher than the preure in the dicharge line. Over-expanion occur when the internal preure ratio impoed by the expander i higher than the ytem preure ratio. Under- and over-expanion can be modelled by plitting the expanion into two conecutive tep, in accordance with Figure 9. 41,42 Non ientropic expanion w 1 = h 1 h 2 = h 1 ðh 1 h 0 2Þh, T ð29þ where h 0 2 pecific enthalpy that the fluid would have at point 2, if the expanion were ientropic, and h, T ientropic efficiency of the expander. Contant volume expanion w 2 = v 2 (p 2 p 3 ) ð30þ The total expander work i given by equation (31), in which the mechanical efficiency account for all internal leakage loe, friction and upply preure drop

8 144 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) Figure 8. Heat exchanger calculation procedure. Several performance indicator are calculated, uch a the following. Net electrical power output _W net = X _W T _W P ð35þ ORC cycle efficiency Figure 9. Volumetric expander model. _W T = _m ORC ðw 1 + w 2 Þh m, T ð31þ It i noted that w 2 can be either poitive or negative in the cae of under-expanion or over-expanion, repectively. Pump. The working fluid pump are modelled by their ientropic efficiency, defined by equation (32) h, P = Dh Dh = v inðp out p in Þ h out h in ð32þ where p in and h in are preure and pecific enthalpy of the fluid at the pump inlet, and p out and h out are preure and pecific enthalpy of the fluid at the pump outlet. The pumping power required i given by equation (33) _W P = _m ORC Dh=h m, P ð33þ Finally, the partial load behaviour of the pump i modelled by an ientropic efficiency correlation given by equation (34) 43,44 h, p =2h, p(nom) _m _m 2 h _m, pðnomþ ð34þ nom _m nom Cycle model. The integration of the individual component model give the global ORC ytem model. h ORC = _ W net _Q ORC where _Q ORC i the heat recovered by the ORC ytem. Heat recovery efficiency h HR = _ Q ORC _Q av ð36þ ð37þ where _Q av i the available heat provided by the heat ource. Total ytem efficiency h overall = Economic evaluation _ W net _Q av = h ORC h HR ð38þ The cot correlation ued in thi work have been previouly validated with real cot data. 45 The economic analyi i performed according to the module coting technique (MCT), which i primarily ued for preliminary cot etimate of chemical plan. 45,46 The cot of each component i calculated by equation (39) log 10 C 0 p = K 1 + K 2 log 10 z + K 3 ðlog 10 zþ 2 ð39þ where z i the ize parameter of the component and K i = 1, 2, 3 contant depending on the component. Specific operating condition (ytem preure, equipment material, etc.) are handled by appropriate multiplying factor. The preure factor (F P ) i calculated with equation (40) and the material factor (F M )

9 Kalikatzaraki and Frangopoulo 145 Table 4. Capital cot coefficient. Component z K i =1,2,3 B 1, B 2 F M C i =1,2,3 F BM Feed pump W (kw) , , , , , Expander W (kw) , , Heat exchanger A (m 2 ) , , , , , Piping D pipe,l pipe (m) ( D pipe )L pipe ha a contant value given in Table 4, along with the value of all coefficient log 10 F P = C 1 + C 2 log 10 p + C 3 ðlog 10 pþ 2 ð40þ In addition to the purchae cot, other cot (hipping and intallation cot, automated control cot) alo need to be conidered. In the MCT technique, a multiplication factor (F BM ) i ued to account for all direct and indirect cot, which i either given by equation (41), or ha a contant value given in Table 4, depending on the component F BM = B 1 + B 2 F P F M ð41þ The um of indirect and direct cot give the bare module cot (C BM ) of each component, according to equation (42) C BM = C 0 p F BM ð42þ Value of 15% and 3% of the bare module cot are conidered for contingency cot and fee. 45 Addition of thee to the bare module cot give the total capital cot for purchaing and intalling the complete heat recovery ytem, according to equation (43) C 0 =1:18 Xn i =1 C BM, i ð43þ The cot of the working fluid i etimated a follow: It i aumed that about 300 kg of fluid are needed for every 1 kg/ of it ma flow rate. Thi quantity i multiplied with the unit cot of each fluid, which i given in Table 2. The diameter of the piping network i calculated by limiting the peed of the working fluid to 1 m/. A total of 20 m of piping i aumed. The main operating and maintenance cot are alo included in the analyi, equal to c om = 0.01 $/kwh. 47 The fuel aving amount to the total cot of Dieel oil that would be needed by the Dieel generator in order to produce the ame electrical energy a the ORC ytem. The net preent value (NPV), dynamic payback period (DPB), and internal rate of return (IRR) are evaluated for the heat recovery ytem with equation (44) (46), uing the value of economic parameter given in Table 5 ( t 1 ) NPV = C 0 + XN C f 1+f f Com ð1+fþ t 1 ð44þ ð1+iþ t t =1 Table 5. Lower heating value of fuel and value of economic parameter. Parameter c f C 0 + C 0 + XN X Nmin = DPB t =0 t =0 ( t 1 ) C f 1+f f Com ð1+fþ t 1 ð1+iþ t 50 ð45þ ( t 1 ) C f 1+f f Com ð1+fþ t 1 ð1+irrþ t =0 ð46þ Optimization procedure Optimization algorithm The ORC ytem ynthei and operation will be optimized uing a hybrid cheme, involving a combination of genetic algorithm (GA) and equential quadratic programming (SQP) algorithm. The combination of thee algorithm i choen in order for the olution not to be trapped in local optima. Due to G, due to their nature, GA are capable of avoiding local optima and revealing the global optimum olution. However, convergence to the exact olution i a low proce, epecially in final generation, in which the objective function i very cloe to the optimal olution. Determinitic method on the other hand, uch a the SQP algorithm, lead to the optimum olution very fat, provided that they tart from a good initial point. In thi work, the GA i applied firt, in order to produce the proper tarting point, after which the procedure i continued with the SQP algorithm. 48 Mathematical tatement of the problem The optimization problem i tated a follow: Find ~x which maximize NPV(~x), ubject to Value 0.6 $/kg LHV 40,100 kj/kg SFOC 181 g/kwh f 3% f f 4% i 10% N 20 year 0.01 $/kwh c om LHV: lower heating value; SFOC: pecific fuel oil conumption.

10 146 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) Figure 10. NPV calculation procedure during the optimization. Table 6. Sytem contant. Parameter Value Table 7. Deciion variable and bound. Variable Lower bound Upper bound h,p 0.40 h,t 0.85 h m,p 0.90 h m,t 0.90 _W ORC j = A, B, C, D 4 _W mode j el, D j = A, B, C, D ; mode j Sytem contant, according to Table 6; DT pp 5 10 C; Vapour quality at expander outlet higher than 0.9 (in order to avoid problem caued by liquid droplet within the expander); Exhaut ga temperature at the boiler outlet higher than 180 C (in order to avoid corroion of the tube). In order to obtain a better undertanding of the overall calculation procedure, the objective function (NPV) calculation flow chart, along with the deciion variable, i hown in Figure 10. It i noted that within the main optimization procedure, a econd optimization i performed, in order to determine the optimum characteritic of each heat exchanger of the HEN. Thi i neceary in order to minimize the total heat exchanger cot. The deciion and HEx deign variable along with their upper and lower bound are given in Table 7 and 8. It i noted that the upper bound of the maximum cycle preure i conidered due to p min Fluid dependent 15 bar p max p min 20 bar _m kg/ ORC layout Binary Heat ource Binary ORC: organic Rankine cycle. Table 8. Deciion variable and bound HEx deign. Variable Lower bound Upper bound d o 0.01 m 0.1 m D e 0.1 m 2.5 m B 0.05 m 1 m Tube pae 1 8 regulatory precription in certain countrie, known a team boiler code. 49 The optimization procedure continue until one of the following topping criteria i met: The variation of the objective function i lower than the tolerance value, which i et equal to 1 $ in thi tudy. Number of iteration in the SQP algorithm exceed 500.

11 Kalikatzaraki and Frangopoulo 147 Table 9. Invetment cot. Component Cot ($) Heat exchanger 2,747,000 Feed pump 55,640 Expander 151,540 Piping 627 Working fluid 332,400 Micellaneou a 591,700 Total 3,878,900 Table 10. Optimal operating characteritic of the ORC ytem. HT cycle LT cycle Working fluid R-236fa R-134a p max (bar) p min (bar) 10 9 _m (kg/) _W T (kw) _W net (kw) a Contingency and intallation cot, fee, ORC control ytem. Number of generation in the GA exceed 300. Thi criterion i ued in order to terminate the optimization procedure in cae there i no convergence. The witch from GA to the SQP algorithm occur when the average change of value of the objective function between two conecutive generation in the GA i lower than 10 $. Finally, it i noted that the organic fluid i condened by mean of water of the central cooling ytem at 25 C (w 1 in Figure 1 and 6). Thi fact et the lower limit for the low preure of the cycle. Optimization reult Figure 11 depict the optimum ORC layout reulting from the optimization procedure. It can be een that a dual ORC ytem i the optimum, with the HT cycle recovering heat from the exhaut ga only, while the LT cycle recover heat from the HT cooling circuit (HEX2 in Figure 11), the HT cycle working fluid (HEX4) and the charge air (HEX3). The bet working fluid for the ORC ytem are R-236fa for the HT cycle and R-134a for the LT cycle. The net preent value of the ytem i 8,669,000 $, with a DPB of 4 year and a 32.45% IRR. It i noted that the econd-tage air cooler (AC2 in Figure 11) i till ued a a afety meaure, o a to enure that the air enter the main engine at the appropriate temperature. Heat recovery from the lubricating oil circuit i proven not cot-effective, due to the relatively low temperature (Figure 2 and 3). In Table 9, a detailed analyi of capital cot i preented. It can be een that the total invetment cot of the heat recovery ytem i about 3.9 M$, about 70% of which i due to the heat exchanger. Thi jutifie the detailed (and computationally time conuming) model ued for the heat exchanger, becaue mall variation in the required heat exchanger area or preure drop can reult in large variation in the total heat exchanger cot. The annual fuel aving are 1.22 M$, wherea the annual operation and maintenance cot are 112,440 $. The operating characteritic of the dual ORC ytem are preented in Table 10, while the deign parameter of the ORC HEN are preented in Table 11. Appendix Table 11. Deign characteritic of the ORC heat exchanger network. Hex 1 Hex 2 Hex 3 Hex 4 Hex 5 d o (m) D e (m) B (m) n N t L (m) lit all the temperature and ma flow rate at each point of the flow diagram of Figure 11 for each operating mode of the main engine. An off-deign performance evaluation of the ytem ha alo been performed with repect to operational parameter (working temperature and power output) for different load of the propulion ytem. The reult are given in Figure for the LT and HT cycle. It i noted that for engine load below 36,120 kw (50% MCR), the ORC ytem i not operated, becaue the available heat i not ufficient to enure that the vapour quality of the working fluid at the expander outlet i above 90%. The off-deign analyi howed that with the ORC ytem intalled, there i an overall efficiency improvement ranging between 3.1% and 1.98% for load of 50% 100% of the MCR. Senitivity analyi A enitivity analyi of the optimal ytem ha been performed with repect to the dieel oil price level and capital cot of the ORC ytem. The reult of the fuel cot enitivity analyi (cot varying between 0.3 and 1 $/kg) are hown in Figure 15. A expected, the ORC ytem become more attractive from an economic tandpoint with increaing cot of fuel: an increae of the Dieel oil price from 0.3 $/kg to 1 $/kg reult in increae of the NPV from 1.25 M$ to 18.5 M$. Additionally, the DPB range between 1.9 and 27.7 year depending on the oil price. For the capital cot enitivity analyi, capital cot are varied from 50% to 200% of their bae value. The enitivity analyi reult are hown in Figure 16. The

12 148 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) Figure 11. Optimized ORC ytem layout. Figure 12. Off-deign performance of the optimum HT-ORC ytem. Figure 13. Off-deign performance of the optimum LT-ORC ytem.

13 Kalikatzaraki and Frangopoulo 149 Figure 14. Off-deign performance of the optimum ORC ytem. preented. A ynthei, deign and operation optimization problem ha been formulated addreing technical and economic parameter concurrently. The reult have clearly indicated that the ORC technology i indeed promiing a a wate heat recovery ytem on hip. The optimum ORC ytem offer approximately 2% 3% of additional power to the baeline ytem, effectively reducing the operating load of the Dieel generator et. On the other hand, the ORC ytem offer ignificant annual aving, up to more than 1 M$ for large veel, a in the cae preented here. The enitivity analyi howed that the net preent value i relatively high for a wide range of fuel price and component cot. Moreover, depending on the operating profile of the main engine and the price of fuel, the ORC ytem can have a hort payback period. Acknowledgement The author expre their appreciation to Dr N. Kakali and Dr G. Dimopoulo of DNV-GL for the ueful information they provided. Figure 15. Senitivity analyi of the optimal olution with repect to Dieel oil price. Declaration of Conflicting Interet The author() declared no potential conflict of interet with repect to the reearch, authorhip and/or publication of thi article. Funding The author() received no financial upport for the reearch, authorhip and/or publication of thi article. Figure 16. Senitivity analyi of the optimal olution with repect to capital cot. NPV varie from 10.5 M$ to 4.94 M$ for variation of the capital cot from 50% to 200% of the initial value. The DPB i between 3.3 and 7 year. Concluion A thermodynamic and economic optimization of an ORC ytem operating on wate heat of the main engine of a 13,600 TEU cla containerhip, by mathematical modelling and imulation method, ha been Reference 1. Shu G, Liang Y and Wei H. A review of wate heat recovery on two-troke IC engine aboard hip. Renew Sut Energ Rev 2013; 19: Theotokato G and Livano G. Techno-economical analyi of ingle preure exhaut ga wate heat recovery ytem in marine propulion plant. Proc IMechE, Part M: J Engineering for the Maritime Environment 2013; 227(2): Dimopoulo G, Georgopoulou C and Kakali N. The introduction of exergy analyi to the thermo-economic modelling and optimiation of a marine combined cycle ytem. In: Proceeding of the 25th international conference on efficiency, cot, optimiation, imulation and environmental impact of energy ytem (ECOS), Perugia, June 2012, paper no Laren U, Sigthoron O and Haglind F. A comparion of advanced heat recovery power cycle in a combined cycle for large hip. Energy 2014; 74: Baldi F and Gabrielii C. A feaibility analyi of wate heat recovery ytem for marine application. Energy 2015; 80: Laren U, Nguyen T-V, Knuden T, et al. Sytem analyi and optimiation of a Kalina plit-cycle for wate heat recovery on large marine Dieel engine. Energy 2014; 64:

14 150 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) 7. Loupi M, Papanikolaou N and Proualidi J. Fuel conumption reduction in marine power ytem through thermoelectric energy recovery. In: Proceeding of the 2nd international MARINELIVE conference on All Electric Ship, Athen, February Zogogianni C, Vogliti D, Saridaki S, et al. Invetigation of a wate heat recovery ytem for a more electric hip. In: Proceeding of the 17th European conference on power electronic and application (EPE), Geneva, 8 10 September He W, Wang S, Zhang X, et al. Optimiation deign method of thermoelectric generator baed on exhaut ga parameter for recovery of engine wate heat. Energy 2015; 91: Tian H, Sun X, Jia Q, et al. Comparion and parameter optimiation of a egmented thermoelectric generator by uing the high temperature exhaut of a Dieel engine. Energy 2015; 84: Bonafin J, Pinamonti P, Reini M, et al. Performance improving of an internal combution engine for hip propulion with a bottom ORC. In: Proceeding of the 23rd international conference on efficiency, cot, optimiation, imulation, and environmental impact of energy ytem (ECOS), Lauanne, June Choi BC and Kim YM. Thermodynamic analyi of a dual loop heat recovery ytem with trilateral cycle applied to exhaut gae of internal combution engine for propulion of the 6800 TEU container hip. Energy 2013; 58: Laren U, Pierobon L, Haglind F, et al. Deign and optimiation of organic Rankine cycle for wate heat recovery in marine application uing the principle of natural election. Energy 2013; 55: Öhman H and Lundqvit P. Comparion and analyi of performance uing Low Temperature Power Cycle. Appl Therm Eng 2013; 52: Tchanche BF, Lambrino GR, Frangoudaki A, et al. Low-grade heat converion into power uing organic Rankine cycle a review of variou application. Renew Sut Energ Rev 2011; 15: Yang M and Yeh R. Analyzing the optimiation of an organic Rankine cycle ytem for recovering wate heat from a large marine engine containing a cooling water ytem. Energ Conver Manage 2014; 88: Wang T, Zhang Y, Peng Z, et al. A review of reearche on thermal exhaut heat recovery with Rankine cycle. Renew Sut Energ Rev 2011; 15: Ringler J, Seifert M, Guyotot V, et al. Rankine cycle for wate heat recovery of IC engine. SAE paper , Hung TC, Shai TY and Wang SK. A review of organic Rankine cycle (ORC) for the recovery of low-grade wate heat. Energy 1997; 22: Wang EH, Zhang HG, Zhao Y, et al. Performance analyi of a novel ytem combining a dual loop organic Rankine cycle (ORC) with a gaoline engine. Energy 2012; 43: Smolen S. Simulation and thermodynamic analyi of a two-tage organic Rankine cycle for utilization of wate heat at medium and low temperature level. Energ Sci Tech 2011; 1(1): Shu G, Liu L, Tian H, et al. Parametric and working fluid analyi of a dual-loop organic Rankine cycle (DORC) ued in engine wate heat recovery. Appl Energ 2014; 113: Zhang HG, Wang EH and Fan BY. A performance analyi of a novel ytem of a dual loop bottoming organic Rankine cycle (ORC) with a light-duty Dieel engine. Appl Energ 2013; 102: Manente G, Field R, DiPippo R, et al. Hybrid olargeothermal power generation to increae the energy production from a binary plant. In: Proceeding of IMECE, Denver, CO, November 2011, pp New York: ASME. 25. Pe G, Li J, Li Y, et al. Contruction and dynamic tet of a mall-cale organic Rankine cycle. Energy 2011; 36: Lazzaretto A, Toffolo A, Manente G, et al. Cot evaluation of organic Rankine cycle for low temperature geothermal ource. In: Proceeding of the 24th international conference on efficiency, cot, optimiation, imulation, and environmental impact of energy ytem (ECOS), Novi Sad, 4 7 July Niš, Serbia: Univerity of Niš. 27. Quoilin S, van Den Broek M, Declaye S, et al. Technoeconomic urvey of organic Rankine cycle (ORC) ytem. Renew Sut Energ Rev 2013; 22: Lazzaretto A and Toffolo A. A method to eparate the problem of heat tranfer interaction in the ynthei of thermal ytem. Energy 2008; 33: Kakali N, Dimopoulo G and Stefanato I. Model-baed techno-economic aement and optimiation of marine wate heat recovery option. In: Proceeding of the international council on combution engine (CIMAC), Shanghai, China, 3 December 2009, paper no Bao J and Zhao L. A review of working fluid and expander election for organic Rankine cycle. Renew Sut Energ Rev 2013; 24: MARPOL. Revied MARPOL Annex VI, regulation 12 ozone depleting ubtance, 1997, _image/ _revied_annex_vi_regulation_12_ Guidance_Note_formatted.pdf Kern DQ. Proce heat tranfer. New York: McGraw- Hill, Sinnot RK. Coulon and Richardon chemical engineering, Volume 6: chemical engineering deign. 4th ed. Oxford: Butterworth-Heinemann, Turgut OE, Turgut MS and Coban MT. Deign and economic invetigation of hell and tube heat exchanger uing Improved Intelligent Tuned Harmony Search algorithm. Ain Sham Eng J 2014; 5: Manente G, Toffolo A, Lazzaretto A, et al. An organic Rankine cycle off-deign model for the earch of the optimal control trategy. Energy 2013; 58: Karella S, Leontariti A-D and Panoui G. Chapter 10. Heat tranfer in Organic Rankine Cycle application. In: Minea AA (ed.) Advance in indutrial heat tranfer. Boca Raton, FL: CRC Pre, 2012, pp Karella S, Schuter A and Leontariti AD. Influence of upercritical ORC parameter on plate heat exchanger deign. Appl Therm Eng 2012; 33: Quoilin S, Declaye S, Bertrand FT, et al. Thermo-economic optimiation of wate heat recovery uing organic Rankine cycle. Appl Therm Eng 2011; 31:

15 Kalikatzaraki and Frangopoulo Lemort V, Quoilin S, Cueva C, et al. Teting and modeling a croll expander integrated into an Organic Rankine Cycle. Appl Therm Eng 2009; 29: Lecompte S, Huieune H, van Den Broek M, et al. Part load baed thermo-economic optimiation of the organic Rankine cycle (ORC) applied to a combined heat and power (CHP) ytem. Appl Energ 2013; 111: Lippke F. Simulation of the part load behaviour of a 30 MWe SEGS plant. Report no. SAND , June Albuquerque, NM: Sandia National Laboratorie. 45. Toffolo A, Lazzaretto A, Manente G, et al. A multicriteria approach for the optimal election of working fluid and deign parameter in organic Rankine cycle ytem. Appl Energ 2014; 121: Turton R, Bailie RC, Whiting WB, et al. Chapter 8. Etimation of manufacturing cot. In: Turton R and Bailie RC (ed) Analyi, ynthei and deign of chemical procee. 3rd ed. Boton, MA: Prentice Hall, pp David G, Michel F and Sanchez L. Wate heat recovery uing organic Rankine cycle technology example of bioga engine and teel mill application. In: Proceeding of the world engineer convention (WEC), Geneva, 4 9 September Manoornejad B, Motoufi N and Jalali FF. A hybrid GA SQP optimiation technique for determination of kinetic parameter of hydrogenation reaction. Comput Chem Eng 2008; 32: Lai NA, Wendland M and Ficher J. Working fluid for high temperature organic Rankine cycle. Energy 2011; 36: Appendix 1 Notation A heat exchanging area B baffle pacing c p pecific heat capacity at contant preure C cot d tube diameter D hydraulic diameter DPB dynamic payback period f friction factor F correction factor, equation (1) and (21) GWP global warming potential h heat tranfer coefficient h pecific enthalpy i market interet rate IRR internal rate of return k thermal conductivity L heat exchanger length LHV lower heating value _m ma flow rate n number of tube pae N revolution per minute NPV net preent value N t number of tube in the heat exchanger ODP ozone depletion potential p preure P efficiency factor, equation (21) and (22) Pr Prandtl number Q heat load R reitance R flow configuration efficiency correction factor Re Reynold number S correction factor, equation (21) and (23) SFOC pecific fuel oil conumption T temperature u velocity U overall heat tranfer coefficient v pecific volume w pecific power output _W power z ize parameter ued for cot correlation Greek ymbol a cro-ectional area Dh enthalpy difference Dp preure drop DT temperature difference Dt annual hour of operation h efficiency m dynamic vicoity r denity Subcript av available BM bare module crit. critical D demand e hydraulic el electricity f fouling f fuel HR heat recovery i inner in inlet lm mean logarithmic m mechanical M material max maximum min minimum nom nominal o outer om operation and maintenance ORC organic Rankine cycle out outlet p pump pp pinch point pr propulion hell ide ientropic t team t tube ide T turbine w wall

16 152 Proc IMechE Part M: J Engineering for the Maritime Environment 231(1) Appendix 2 Temperature and ma flow rate at each point of the flow diagram of Figure 11 for each operating mode of the main engine are given in Table 12. Table 12. Operating temperature and ma flow rate of the propulion ytem. Mode A B C D Temperature ( C) W W W W W W W a a a g g g g lo lo Ma flow rate (kg/) Air Fuel Exhaut ga Lubricating oil Steam Freh water ORC-HT ORC-LT