Exergoeconomic Optimization of a Diesel-engine-powered

Energy & Fuels 2009, 23, 1977–1989

1977

Exergoeconomic Optimization of a Diesel-engine-powered Cogeneration Plant Aysegul Abusoglu and Mehmet Kanoglu* Department of Mechanical Engineering, UniVersity of Gaziantep, 27310 Gaziantep, Turkey

An iterative exergoeconomic optimization procedure is applied to an actual diesel-engine-powered cogeneration plant. The method is based on the cost-optimal exergetic efficiency that is obtained for a component isolated from the remaining system components. Objective functions that express the optimization criterion for each subcomponent of the cogeneration system are developed. Product exergy flow rates and specific fuel exergetic costs of each subcomponent are kept constant as constraints. In the iterative optimization procedure, the variables, relative cost difference, and exergetic efficiency with the corresponding optimal values are obtained. Exergoeconomically optimal values for total cost flow rate, cost of electricity, and cost of steam are determined to be US $2316/h, $0.0670/kW h, and $0.0450/kg, respectively, whereas the corresponding actual base case values are US $2932/h, $0.0890/kW h, and $0.0522/kg, respectively.

1. Introduction A thermodynamic optimization usually aims at determining and minimizing thermodynamic factors to maximize efficiencies. The objective of a thermoeconomic optimization, however, is to minimize costs resulting from these inefficiencies.1,2 Thermoeconomic optimization studies started in the 1970s with the papers of El-Sayed and Evans3 and Szargut.4 These were the pioneer works for exergy-based cost optimization studies in the literature. Many studies have been published since the late 1980s with the progressive development of analytical and numerical optimization techniques. A major fraction of these published works were performed using algebraic methods in exergoeconomic analysis and optimization of thermal systems.5-26 In these studies, SPECO (specific cost exergy costing method)18,25 and MOPSA (modified productive structure analysis method)15 * To whom correspondence should be addressed. Phone: +90-3423172508; fax: +90-342-3601104; e-mail: [email protected]. (1) Bejan, A., Tsatsaronis, G., Moran, M. Thermal Design and Optimization. , 1st ed.; Wiley: New York, 1996. ¨ ztu¨rk, A.; S¸enel, A.; Onbas¸ıoglu, S. U. Int. J. Energy Res. 2005, (2) O 29, 657–670. (3) El-Sayed, Y.; Evans, R. L. J. Eng. Power 1970, 92, 27–35. (4) Szargut, J. Brennstoff-Wa¨rme-Kraft 1971, 23, 516–519. (5) Tsatsaronis, G.; Lin, L.; Pisa, J. J. Energy Resour. Technol. 1993, 115, 9–16. (6) Tsatsaronis, G.; Ho-Park, M. Energy ConVers. Manage. 2002, 43, 1259–1270. (7) Tsatsaronis, G.; Winhold, M. Energy 1985, 10 (1), 69–94. (8) Lozano, M., A.; Valero, A. Energy 1993, 18 (9), 939–960. (9) Tsatsaronis, G.; Pisa, J. Energy 1994, 19 (3), 287–321. (10) Evans, R. B. Energy 1980, 5 (8-9), 805–822. (11) Valero, A., Torres, C. Thermoeconomic Analysis. Encyclopedia of Life Support Systems (EOLSS); UNESCO, Eolss Publishers: Oxford, UK, 2006; URL: http://www.eolss.net. (12) Rosen, M. A.; Dincer, I. Energy ConVers. Manage. 2003, 44, 1633– 1651. (13) Vieira, L. S.; Donatelli, J. L.; Cruz, M. E. Energy ConVers. Manage. 2004, 45, 2495–2523. (14) Vieira, L. S.; Donatelli, J. L.; Cruz, M. E. Engenharia Termica (Thermal Engineering) 2005, 4 (2), 163–172. (15) Kim, S. M.; Oh, S. D.; Kwon, Y. H.; Kwak, H. Y. Energy 1998, 23, 393–406. (16) Cerqueira, S.A.A.G.; Nebra, S. A. Energy ConVers. Manage. 1999, 40, 1587–1597. (17) Kwon, Y. H.; Kwak, H. Y.; Oh, S. D. Exergy, Int. J. 2001, 1, 31– 40.

approaches were applied to combined heat and power systems in order to reduce the subjectivity of fuel and product definitions and cost partitioning. This is done by the help of an iterative exergoeconomic performance improvement procedure based on exergoeconomic variables such as relative cost difference, exergoeconomic factor, and exergetic efficiency as introduced by Tsatsaronis.1,5-9 The exergoeconomic optimization approach9 uses an iterative design improvement procedure that does not aim at calculating the global optimum of a predetermined objective function, as the conventional optimization methods do, but tries to find a “good” solution for the overall system design. The basic idea lies in a commonly accepted concept from the cost viewpoint: At constant capacity for a well designed component, group of components, or total system, a higher investment cost should correspond to a more efficient component and vice versa. With this approach, the cost-optimal exergetic efficiency is obtained for a component isolated from the remaining system components. The iterative exergoeconomic optimization technique consists of the following steps;2 (i) evaluation of the detailed schematics and inputs of the existing system (including the actual plant data), (ii) a detailed thermoeconomic analysis and evaluations of the system and obtaining the decision variables that affect both the exergetic efficiency and the investment costs, (iii) modification of the cost rates of the components having significantly higher cost rates than the remaining components, to their corresponding cost-optimal exergetic efficiency, and (iv) calculation of the relative deviations of the actual values from (18) Lazzaretto, A., Tsatsaronis G. Comparison between SPECO and functional exergoeconomic approaches. Proceedings of the ASME International Mechanical Engineering Congress and Exposition s IMECE/AES23656; New York, November 2001; pp 11-16. (19) Cziesla, F.; Tsatsaronis, G. Energy ConVers. Manage. 2002, 43, 1537–1548. (20) Kwak, H. Y.; Byun, G. T.; Kwon, Y. H.; Yang, H. Int. J. Energy Res. 2004, 28, 1145–1158. (21) Colpan, C. O.; Yesin, T. Int. J. Energy Res. 2006, 30, 875–894. ¨ zgener, L.; Hepbas¸lı, A.; Dinc¸er, I˙.; Rosen, M. A. Appl. Therm. (22) O Eng. 2007, 27, 1303–1310. (23) Abusoglu, A.; Kanoglu, M. Appl. Therm. Eng. 2009, 29, 234–241. (24) Abusoglu, A.; Kanoglu, M. Appl. Therm. Eng. 2009, 29, 242–249. (25) Lazzaretto, A.; Tsatsaronis, G. Energy 2006, 31, 1257–1289. (26) Abusoglu, A.; Kanoglu, M. Energy ConVers. Manage. 2008, 49, 2026–2031.

10.1021/ef800893q CCC: $40.75  2009 American Chemical Society Published on Web 02/27/2009

1978 Energy & Fuels, Vol. 23, 2009

Abusoglu and Kanoglu

Figure 1. The schematic of DEPC plant. C: compressor, T: turbine, WHB: waste heat boiler, DeSOx: desulphurization, AWR: air-water radiator, IC: intercooler, WH: water heater, LOC: lubrication oil cooler, LOT: lubrication oil tank, SD: steam drum, FWT: feed water tank, FDT: fuel oil day tank, CON: condenser, FFM: fuel forwarding module, P: pump.

the cost-optimal values for the exergetic efficiency and relative cost difference. In literature, with the objective of “a unified methodology for exergybasedanalysesandoptimization”,differentmethods7,8,12,13,15-17 have been proposed and developed. Combined heat and power systems (i.e., cogeneration) have some large-scale problems due to their complicated nonlinear characteristics. Methodologies developed for exergoeconomic optimization have been applied to relatively simple systems.12 To overcome major difficulties for optimizing complex thermal systems, the computational power of some professional process simulators were used. The proposed integrated approaches13 deal with the decision variables only, whereas the thermodynamic requirements are completely realized by the simulator. With this approach, user interference through optimization problem has been successfully avoided.14 The exergoeconomic optimization methodology in this study is integrated from thermoeconomic isolation method introduced by R. Evans10 and the iterative exergoeconomic optimization approach that is derivated from the game theory introduced originally by von Neuman and Nash.27,28 This integrated methodology is applied for the subcomponents of a dieselengine-powered cogeneration system where all subcomponents in the system act as players in a cooperative game. According to the game theory which states that;29 “an individual’s success in making choices depends on the choices of others”, the players (i.e., subcomponents) operate simultaneously and influence each (27) Roth, A. E. J. Hist. Econ. Thought 1993, 15, 184–209. (28) Rubinstein, A.; Safra, Z.; Thomson, W. Econometrica 1992, 60, 1171–1186. (29) Nash, J. F.; Kuhn, H.; Harsanyi, J.; Selten, R.; Weibull, J.; Van Damme, E.; Hammerstein, P.) Duke Math. J. 1995, 81, 1–29.

other. Each player has its own objective function, which also depends on parameters of the other players. The main objective of the game (i.e., the thermoeconomical optimization of a dieselengine-powered cogeneration (DEPC) system for this work) is to obtain values for the parameters, satisfying the objective functions of the players, which makes multiobjective optimization criteria possible. The advantage of the model proposed in this paper is that malfunction of each component in the system due to the both exergy destruction rate and the corresponding cost rate change of product can be predicted. This paper searches the best operational range (i.e., optimum condition) for the system by taking only major components (i.e., power producer and steam generator) into account. The exergoeconomic optimization methodologies proposed and developed in literature have established a well built background for future studies. However, all the scientists and researchers in the field of exergy-based analyses and optimization of thermal systems can be considered as players who will have their strategies (i.e., methodologies), pure or mixed, for their own studies. A pure methodology in this manner may be defined as a player’s action in a game under given circumstances. Exergoeconomic analysis and optimization is applied to both simple and complex systems, and different methodologies are used. With a well developed process simulator based on the methodology, the model developed can be successfully applied to complex energy systems. The methodology with a large number of components would not be practical if a computerized solution is not available. In this paper, the iterative exergoeconomic optimization method integrated from thermoeconomic isolation method10 and game theory29 is applied for the optimization of an existing

Optimization of a Diesel-powered Cogeneration Plant

Energy & Fuels, Vol. 23, 2009 1979

Table 1. Plant Data, Thermodynamic Properties, and Exergies in the Plant with Respect to the State Points in Figure 1a state

fluid

pressure, P (bar)

temperature, T (°C)

mass flow rate, m ˙ (kg/s)

enthalpy, h (kJ/kg)

entropy, s (kJ/kg°C)

specific exergy, ψ (kJ/kg)

exergy rate, E˙ (kW)

0 0 0 0 1 2 3 4′ 4 5 6 7 8 9 10 11 12 13 14′ 14′′ 14 15 16 17 18 19 20 21 22 22′ 23 24 25 25′ 26 27 28 29 30 31 32

air water fuel oil lub oil air air air fuel oil fuel oil fuel oil exhaust exhaust exhaust exhaust water water water water water water water water water water water water HT water HT water HT water HT water LT water LT water LT water LT water lub oil lub oil lub oil air air air air

1.00 1.00 1.00 1.00 1.00 2.90 2.80 1.90 4.30 5.10 2.40 0.80 0.75 1.190 2.40 8.00 8.00 8.00 4.90 8.00 8.00 8.00 7.80 8.00 4.70 4.60 3.10 3.00 2.80 2.70 3.10 3.00 2.90 2.70 4.20 3.00 2.90 1.00 0.99 1.00 0.90

30.0 30.0 30.0 30.0 30.0 172 53.7 81.0 81.0 137.5 451 302 247 53.7 88.0 88.0 95.0 170 170 170 170 170 70.0 170 60.0 50.0 71.7 81.0 88.0 71.7 38.4 44.9 50.3 38.4 63.0 78.3 59.7 30.0 51.0 30.0 47.0

18.4 18.4 18.4 0.46 0.46 0.46 17.0 17.0 17.0 17.0 0.75 0.75 0.75 0.75 0.75 0.75 0.55 0.05 0.05 0.15 0.15 0.15 30.0 30.0 30.0 30.0 47.2 47.2 47.2 47.2 20.0 20.0 20.0 0.30 0.30 267.0 267.0

303.5 125.1 303.5 446.9 313.7 87.2 103.5 231.5 739.2 580.9 523.8 327.3 326.1 326.5 397.9 718.6 698.0 718.6 718.6 718.6 293.0 718.6 250.9 209.1 299.7 338.7 368.1 299.7 160.5 187.6 210.2 160.4 65.7 97.7 58.9 303.5 324.6 303.5 320.0

5.712 0.434 5.712 5.794 5.492 0.254 0.316 0.654 6.357 6.428 6.342 5.738 1.050 1.049 1.248 2.041 1.980 2.041 2.041 2.041 0.953 2.041 0.829 0.702 0.974 1.085 1.167 0.974 0.549 0.635 0.706 0.550 0.206 0.299 0.186 5.712 5.781 5.712 5.765

0.0 0.0 0.0 0.0 0.0 118.40 76.80 5.87 7.75 33.34 240.20 60.42 29.33 16.02 14.55 15.11 26.31 106.80 88.80 106.80 106.80 106.80 10.84 106.80 6.20 3.01 11.21 16.37 21.02 11.17 0.69 1.68 2.20 0.65 3.33 7.05 2.71 0 0.26 0 0.41

0.0 2179 1413.1 2.70 3.57 15.34 4083.4 1027.1 499 272.3 11.0 11.3 20.0 80.1 66.6 80.1 58.7 5.4 0.6 16.0 1.0 0.5 336.3 491.1 630.7 335.1 32.5 79.5 104.0 30.7 66.6 141.0 54.2 0.0 0.1 0.0 110.7

a

Values are for one engine set only24.

diesel-engine-powered cogeneration system. To the best knowledge of the authors, this is the first application of exergoeconomic optimization on a diesel-engine-powered cogeneration plant. The use of this optimization approach requires exergetic and exergoeconomic analysis results of the plant, which are taken from the previous papers by the authors.23,24,26 In the next section, the exergoeconomic optimization procedure of the DEPC plant is described. The procedure is used for obtaining cost-optimal exergetic efficiencies and related performance parameters for a component isolated from the remaining system components. The objective functions of the DEPC system components are expressed for the optimization criterion as a function of dependent and independent variables. 2. Exergoeconomic Optimization of Diesel-engine-powered Cogeneration (DEPC) System The objective function expresses the optimization criterion as a function of dependent and independent variables. For the DEPC system, the objective function can be written as ˙ OM minimize C˙P,total ) C˙F,total + Z˙CI total + Ztotal

(1)

˙ F,total, the total cost The variablessthe total cost rate of fuel C CI ˙ rate of capital investment Ztotal, and the total cost rate of

operation and maintenance (OM) costs Z˙OM totalsare functions of decision variables. In this study, we minimize the total cost rate associated with the product C˙P,total instead of the cost per unit of product exergy cP. The cost optimal exergetic efficiency approach is used for an isolated system component, and the following constraints are used for the existing DEPC system: The net power produced by the DEPC system is 25.32 MW, and the steam generated is 8.1 tons/h (2.25 kg/s) at 8 bar. The electricity is generated by three diesel-engine-actuated generator sets, each having two turbochargers. The schematic diagram of this plant for one engine set is shown in Figure 1, where only one turbocharger is shown.23,24,26 The engine is a four-stroke, compression ignition engine with 18 cylinders in a V configuration. Heavy fuel oil is used as fuel for the engines.23,24,26 Specifically, for every system component we must use following equations as constraints that is for a kth component to be optimized E˙P,k ) constant

(2)

cF,k ) constant

(3)

Also, for each component of the DEPC plant we must calculate1,5-7,9,23



Table 2. Exergy Flow Rates, Cost Flow Rates, and Unit Exergy Costs Associated with Each Stream of the Planta

a

state No.

E˙ (kW)

C˙ ($/h)

c ($/GJ)

1 2 3 4′ 4 5 6 7 8 9 10 11 12 13 14 14′ 14′′ 15 16 17 18 19 20 21 22 22′ 23 24 25 25′ 26 27 28 29 30 31 32 ˙ compressor W ˙ turbine W ˙ pump W ˙ plant W

0.0 6537 4239.3 62,768 62,768 62,803 12,250 3081.3 1497 817.0 33.0 34.0 60.0 240.3 176.1 199.8 240.3 16.2 1.8 48.0 3.0 1.5 1008.9 1473.3 1892.1 1005.3 97.5 238.5 312.0 92.1 200.0 424.0 163.0 0.0 0.3 0.0 332.7 6540 9168 1.26 25,320

0.0 1706.2 1109.0 1821.0 1821.0 1933.3 723.0 182.0 47.20 0.0 12.01 12.05 21.85 87.51 64.13 72.76 87.51 6.41 0.71 19.0 1.20 0.60 9.80 14.31 18.40 9.78 5.25 12.84 16.80 4.96 4.25 9.0 3.46 0.0 0.03 0.0 123.2 1626.0 2277.3 4.80 2820.0

0.0 24.20 24.22 2.70 2.70 2.85 5.50 5.50 3.0 0.0 33.71 33.71 33.71 33.71 33.71 33.71 33.71 36.64 36.52 36.70 37.03 37.03 2.70 2.70 2.70 2.70 17.50 5.0 5.0 5.0 5.90 2.0 2.0 0.0 24.20 0.0 24.20 23.02 23.02 353.0 10.31

nk ) and Fk )

compressor 23.02 intercooler 17.50 lubrication oil cooler 5.00 air-water radiator 5.00 diesel engine 2.85 turbine 5.50 waste heat boiler 5.50 fuel oil day tank 36.52 fuel forwarding module 36.70 condenser 37.03 pumps 353.0 3.0 DeSOx

24.22 24.20 2.00 2.70 10.31 23.02 33.71 2.85 2.85 24.20 33.71 -

r (%)

f (%)

4.95 27.70 60.00 46.00 72.40 76.10 83.70 92.20 92.20 34.65 90.45 -

41.30 35.20 73.60 55.60 63.30 79.00 50.45 95.20 98.60 96.70 81.00 25.40

˙D D ($/h)

1 - εk Z˙kCI + Z˙kOM + εk cF,kE˙P,k

cF,k(E˙D,k + E˙L,k)OPT Z˙OPT k

(

(β + γk)Bknk

∆rk )

1-mk τcF,kE˙P,k

)

(6)

1/(nk+1)

(7)

rk - rOPT k rOPT k

× 100

(8)

• An optimum value of the exergetic efficiency εOPT can be k written as ) εOPT k

1 (1 + Fk)

(9)

• An estimate of the costs of the electricity and steam based on the given total costs of the heavy fuel oil and the calculated costs of the DEPC plant components. That is, ˙ W ,DE ) C˙3 + C˙5 + (C˙21 - C˙22) + (C˙26 minimize C net C˙27) - C˙6 + Z˙DE (10) minimize C˙13 ) (C˙7 - C˙8) + C˙12 + Z˙WHB

Z˙T ($/h)

120.22 80.30 106.70 28.30 3.37 9.40 95.46 28.30 296.0 510.20 21.62 80.30 27.80 28.30 47.33 9.40 1.27 94.40 0.16 4.80 1.14 4.80 138.82 47.20

• An optimum value of the relative cost difference rOPT (the k actual value of rk is always greater than rOPT k ), which is given as rk )

(5)

Here, cF,k is the cost per exergy unit of fuel, τ is the annual number of hours of system operation, β is the capital recovery factor, γk is the fixed OM cost factor, and nk is the cost exponent. In the exergoeconomic analysis of the DEPC system, actual vendor quotations were used.24 Relative cost difference relation between the actual base case and the optimal value is

Table 3. Unit Exergetic Costs of Fuels and Products, Relative Exergetic Cost Difference, Exergoeconomic Factor, Cost Rate of Exergy Destruction, and Total Investment Cost Rate for the Plant Components24 cf,k cp,k ($/GJ) ($/GJ)

nk + 1 Fk nk

where

State numbers refer to Figure 1.24

component

) rOPT k

(4)

(11)

˙ D,total, and its • The cost of the total plant exergy losses D OPT and for a kth system component D ˙ D,total ˙ D is optimal value D expressed as ˙ D,k ) cf,kE˙D,k D

(12)

For an existing system such as the DEPC plant of this study, performance evaluation and optimization procedure are parallel to what may be considered as “performance improvement” and “searching a good solution” for the overall system rather than to find a global optimum.1 Moreover, for such a system, total capital investment costs and operating and maintaining costs are taken as sunk costs that may not be included in the exergetic cost rate balances. However, by using the SPECO method appropriately,23,24 thermoeconomic analysis and optimization include all investment data for each components of the cogeneration system neglecting any simplification in such a manner. In Table 1, the DEPC plant data, thermodynamic properties, and exergies in the plant with respect to state points in Figure 1 are given.24,26 Exergy flow rates, cost flow rates, and unit exergy costs associated with each stream of actual DEPC plant with 25.32 MW electricity and 8.1 tons/h steam production are given in Table 2.24 In Table 3, unit exergetic costs of fuels and products, relative exergetic cost differences, exergoeconomic factors, cost rate of exergy destructions, and total investment cost rates for the system components are presented.24 In Table



Table 4. Objective Functions of Major Plant Components and Corresponding Constraint Equations objective functions for major components of DEPC minimize cp,2E˙2 ) c1E˙1 + cf,COMPE˙W,COMP + Z˙COMP

component compressor

constraints ˙E2 ) constant cf,COMP ) constant E˙P,IC-1 ) constant

minimize c3E˙3 ) (c20E˙20 - c21E˙21) + (c23E˙23 - c24E˙24) + c2E˙2 + Z˙IC

intercooler (sections 1 and 2)

turbine

minimize cWTURBINEE˙WTURBINE ) c6E˙6 - c7E˙7 + Z˙TURBINE

waste heat boiler

minimize c13E˙13 ) (c7E˙7 - c8E˙8) + c12E˙12 + Z˙WHB

lubrication oil cooler

minimize c28E˙28 ) c27E˙27 + (c24E˙24 - c25E˙25) + Z˙LOC

airswater radiator

minimize c32E˙32 ) (c25′E˙25′ - c25E˙25) + (c22′E˙22′ - c22E˙22) + c31E˙31 + Z˙AWR

E˙P,IC-2 ) constant cf,IC-1 ) constant cf,IC-2 ) constant E˙P,Turb ) constant cf,Turb ) constant E˙P,WHB ) constant cf,WHB ) constant E˙P,LOC ) constant cf,LOC ) constant E˙P,AWR-1 ) constant cf,AWR-1 ) constant E˙P,AWR-2 ) constant cf,AWR-2 ) constant

Table 5. Dependent Variables Obtained during the Searching Procedure of the Appropriate Thermoeconomical Optimal Range of the Compressor case 1

case 2

case 3

case 4

case 5

case 6

P2/P1

variable

1.10

1.50

1.75

2.00

2.25

2.50

2.90 (base case)

cf,comp ($/GJ) E˙P,comp (kW)

23.02 6536

23.02 6536

Fixed Parameters 23.02 23.02 6536 6536

23.02 6536

23.02 6536

23.02 6536

εcomp cp,comp ($/GJ) ∆rcomp (%) E˙D,comp (kW) ˙ D,comp ($/h) D

0.2385 10.08 –61.20 6036 500.22

0.4264 15.33 –38.36 4547.4 251.0

Dependent Variables 0.5198 0.6007 17.95 20.21 –26.97 –17.16 3807.6 3166 246.0 230.3

0.6720 22.20 –8.51 2601 207.9

0.7358 23.98 –0.78 2095 173.6

0.8260 24.22 0.00 1380 120.22

variable P2/P1

case 7

case 8

case 9

case 10

case 11

case 12

case 13

case 14

3.00

3.25

3.50

3.60

3.70

3.80

3.85

23.02 6536

23.02 6536

23.02 6536

0.9734 30.63 28.11 204.0 16.91

0.9895 31.08 30.1 78.0 6.46

0.9974 31.30 31.02 18.0 1.50

cf,comp ($/GJ) E˙P,comp (kW)

23.02 6536

23.02 6536



0.8463 27.07 12.64 1212 100.44

0.8948 28.43 18.60 828.0 68.62

Dependent Variables 0.9397 0.9568 29.69 30.16 24.02 26.10 474.0 336.0 39.30 27.84

4, objective functions of major plant components that have an effect on optimizing the DEPC plant, exergy destruction cost

rates, cost of electricity and steam, and the corresponding constraint equations are given. 3. Results and Discussion Exergoeconomic optimization of various components in the plant as well as the entire plant is performed, and the results are given below.

Figure 2. Variation of product cost values of compressor with respect to different pressure ratios and corresponding calculated exergetic efficiencies.

Figure 3. Variation of destruction cost rate of the compressor with respect to different pressure ratios and corresponding calculated exergetic efficiencies.



Table 6. Dependent Variables Obtained during the Iterations of the Pressure Ratio for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Compressora case 6 f

1st iteration

2nd iteration

2nd iteration

1st iteration

case 10 r

2.50

3.045

3.118

3.118

3.160

3.50

E˙P,comp ($/GJ) cf,comp (kW)

23.02 6536

Fixed Parameters 23.02 23.02 23.02 6536 6536 6536

23.02 6536

23.02 6536


0.7358 23.98 –0.78 2095 173.6

Dependent Variables 0.8553 0.8697 0.8697 27.33 27.73 27.73 18.7 20.5 20.5 1146 1032 1032 95.0 85.5 85.5

0.8778 27.96 21.5 968.0 80.2

0.9397 29.69 24.02 474.0 39.30

variable P2/P1

a The arrows in Tables 6-13 indicate that iterations go forward and backward due to thermodynamic and economic constraints.

Figure 6. Variation of destruction cost rate of the intercooler (first section) with respect to the iterated HT water inlet temperatures and corresponding calculated exergetic efficiencies of the intercooler.

Figure 4. Variation of destruction cost rate of the compressor with respect to the iterated pressure ratios and corresponding calculated exergetic efficiencies.

Figure 5. Variation of relative cost difference and product cost with respect to the corresponding exergetic efficiencies of the compressor.

3.1. Compressor. The compressor pressure ratio P2/P1 is taken as the decision variable, and it is required to be given in the range 1.10 e P2/P1 e 3.85 for the operational restrictions of the turbocharger unit. Also, for cost reasons, the maximum

value of the compressor isentropic efficiency is less than 0.9 (it is 0.8 for this study). In Table 5, dependent variables are given during the searching process for the thermoeconomically optimal range of the compressor. The base case value (i.e., 2.90, see Table 1) is the actual pressure ratio of the system at full load. In this study, not only the estimated convergent range but also all possible variations of cost structure of the subsystems and corresponding exergetic efficiencies and destruction cost rates are taken into account. As shown in Table 5, in the first seven cases, up to the base case value, the exergetic efficiency increases considerably with a decrease in exergy destruction. This, as expected, makes the product cost value higher but the exergetic destruction cost rate lower than the previous case. Because the exergetic efficiency term has the higher weighing factor in the definition of relative cost difference relation (see eqs 4-8), pressure ratios less than 2.90 have negative effects on the destruction cost. The total investment cost of the components in the system including compressor may be considered as constant. In the remaining seven cases, more attention must be paid to exergetic destruction rates and corresponding cost rates, which seem to be far from the optimum range. On the other hand, relative cost difference is positively affected when we take the components destruction cost into account. In Figure 2, product cost values are given with respect to variations of pressure ratios and corresponding results of the exergetic efficiencies. As shown in Figure 2 together with Table 5, optimum thermoeconomic range lies between 2.50 and 3.50 for the pressure ratio. Optimum value for the destruction cost of the component must be searched in this range even when the product cost value is higher with respect to the base case. In Figure 3, destruction cost rate values are given with respect to selected pressure ratios and corre-

Table 7. Dependent Variables Obtained during the Iterations of the HT Water Inlet Temperature for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Intercooler - 1 f

1st iteration

2nd iteration

3rd iteration

3rd iteration

2nd iteration

1st iteration

r

P2/P1 T20 (°C)

variable

3.118 71.7 (min)

3.118 73.05

3.118 73.43

3.118 76.53

3.118 76.53

3.118 78.44

3.118 80.85

3.118 86.5 (max)

cf,IC-1 ($/GJ) E˙P,IC-1 (kW)

2.70 1817

2.70 1817

2.70 1817

εIC-1 cp,IC-1 ($/GJ) ∆rIC-1 (%) E˙D,IC-1 (kW) ˙ D,IC-1 ($/h) D

0.4571 2.55 -5.55 986.4 9.60

0.4442 2.63 -2.60 1009 9.82

0.4404 2.67 -1.11 1017 9.90

Fixed Parameters 2.70 1817

2.70 1817

Dependent Variables 0.4035 0.4035 3.10 3.10 14.8 14.8 1084 1084 10.54 10.54

2.70 1817

2.70 1817

2.70 1817

0.3618 3.34 23.4 1160 11.30

0.2865 4.28 58.5 1296 12.60

0.1654 5.23 93.7 1516 14.74



Table 8. Dependent Variables Obtained during the Iterations of the LT Water Inlet Temperature for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Intercooler - 2 f

1st iteration

2nd iteration

3rd iteration

4th iteration

5th iteration

P2/P1 T20 (°C) T23 (°C)

variable

3.118 76.53 50.72

3.118 76.53 44.0

3.118 76.53 47.3

3.118 76.53 49.1

3.118 76.53 50.0

3.118 76.53 50.5

cf,IC-2 ($/GJ) E˙P,IC-2(kW)

17.50 2422.4

17.50 2422.4

17.50 2422.4

εIC-2 cp,IC-2 ($/GJ) ∆rIC-2(%) E˙D,IC-2 (kW) ˙ D,IC-2 ($/h) D

0.1269 16.57 -5.31 2115.0 76.14

0.1772 18.43 5.32 1993.1 71.8


variable P2/P1 T20 (°C) T23 (°C)

Fixed Parameters 17.50 2422.4

6th iteration 3.118 76.53 50.72

17.50 2422.4

17.50 2422.4

17.50 2422.4

0.2292 21.65 23.71 1867.2 67.2

0.2334 22.44 28.23 1857.0 66.9

0.2353 23.21 32.63 1852.4 66.7

6th iteration

5th iteration

4th iteration

3rd iteration

2nd iteration

1st iteration

r

3.118 76.53 50.72

3.118 76.53 51.2

3.118 76.53 51.5

3.118 76.53 52.2

3.118 76.53 53.5

3.118 76.53 56.1

3.118 76.53 61.5 (max)

cf,IC-2 ($/GJ) E˙P,IC-2 (kW)

17.50 2422.4

17.50 2422.4

Fixed Parameters 17.50 17.50 2422.4 2422.4

17.50 2422.4

17.50 2422.4

17.50 2422.4

εIC-2 cp,IC-2 ($/GJ) ∆rIC-2 (%) E˙D,IC-2 (kW) ˙ D,IC-2 ($/h) D

0.2353 23.21 32.63 1852.4 66.7

0.2394 24.01 37.20 1842.5 66.3


0.2586 25.97 48.40 1796.0 64.6

0.2800 27.32 56.11 1744.1 63.0

0.3232 31.44 79.65 1639.5 59.0

sponding exergetic efficiencies. Note that the investment costs, operating and maintenance (OM) costs, costs of fuel, and other costs are originally given in US dollars. Therefore, no currency conversion was needed. The optimum pressure ratio is determined to be 3.12. Keeping the cost rate of the fuel and product exergy value of the compressor constant we calculate the optimal values of the exergetic efficiency and destruction cost rate of the component at this optimum pressure ratio value to be εOPT comp ) 0.8697 and ˙ OPT ) $85.5/h, respectively. Figure 4 shows the iterations D D,comp of the pressure ratio of the compressor in the range of case 6 through case 10 as given in Table 6, and the variation of destruction cost rates and the corresponding values of exergetic efficiencies through optimization process. The forward and backward arrows in the tables indicate that iterations go forward and backward between minimum and maximum values due to the thermodynamic and economic constraints of each subcomponent. Figure 5 shows the variation of relative cost difference and product cost with respect to the corresponding exergetic efficiencies of the compressor.

Figure 7. Variation of destruction cost rate of the intercooler (second section) with respect to the iterated LT water inlet temperatures and corresponding calculated exergetic efficiencies of the intercooler.

3.2. Intercooler. The intercooler of the DEPC plant is a heat exchanger network. On the basis of their different mass flow rates, high-temperature (HT) water and low-temperature (LT) water can be separated into two different heat exchanging processes by using weighing factors. Thus, the decision variables in this component are taken as the inlet temperatures of the two water streams from air-water radiator (AWR) unit, T20 and T23. The first process takes place between hot air from the compressor unit and the HT water from the AWR unit. The maximum temperature difference in the first process is 100.3 °C. Therefore, the hot air from the compressor cannot be cooled by more than 100.3 °C (to 71.7 °C). Taking the HT water inlet temperature to the intercooler as decision variable, the optimum range is determined in the range of 71.7 and 86.5 °C. In Table 7, exergetic efficiencies, destruction cost rates, and corresponding product costs calculated during the iterations in the first heat exchanging process are given for the intercooler at the optimum pressure ratio of the compressing process. As shown in Table 7, the optimum value of the HT water inlet temperature and the corresponding optimum values of exergetic efficiency and destruction cost rate of the first heat exchanging process in the OPT ) 0.4035 and D ˙ OPT ) intercooler are T20 ) 76.5 °C, εIC-1 D,IC-1 $10.54/h. The second heat exchanging process in the intercooler is between the air from the first section and the LT water. The maximum temperature difference in the second process is 103.6 °C. Therefore, the hot air from the first section of the intercooler unit cannot be cooled by more than 103.6 °C (to 38.4 °C). When we take the LT water inlet temperature to the intercooler as a decision variable, the optimum range becomes 38.4-61.5 °C. In Table 8, exergetic efficiencies, destruction cost rates and corresponding product costs calculated during the iterations in the second heat exchanging process are given for the intercooler at the optimum pressure ratio of the compressing process and the optimum inlet temperature of the HT water from the first heat exchanging process. Thus, in the intercooler network, optimum values of exergetic efficiency and destruction cost rate OPT ) 0.6388 and D ˙ OPT ) $77.24/h, are determined to be εIC D,IC-1



Table 9. Dependent Variables Obtained during the Iterations of the Exhaust Temperature at the Turbine Exit for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Turbine f

1st iteration

2nd iteration

3rd iteration

4th iteration

5th iteration

6th iteration

P2/P1 T20 (°C) T23 (°C) T7 (°C)

variable

3.118 76.53 50.72 267 (min)

3.118 76.53 50.72 277

3.118 76.53 50.72 284.3

3.118 76.53 50.72 290

3.118 76.53 50.72 298

3.118 76.53 50.72 300

3.118 76.53 50.72 303

cf,Turb ($/GJ) E˙P,Turb(kW)

5.50 8076

5.50 8076

5.50 8076

5.50 8076

5.50 8076

εTurb cp,Turb ($/GJ) ∆rTurb (%) E˙D,Turb (kW) ˙ D,Turb ($/h) D

0.9919 5.53 0.54 99.23 2.00

0.9616 5.30 -3.64 470.4 9.31

Dependent Variables 0.9388 0.9206 5.0 4.93 -9.10 -10.4 750.0 973.0 14.90 19.30

0.8944 4.78 -13.10 1294.0 25.62

0.8877 4.66 -15.30 1376.0 27.24

0.8775 4.60 -16.40 1500 29.70

6th iteration

5th iteration

4th iteration

3rd iteration

2nd iteration

1st iteration

r

3.118 76.53 50.72 303

3.118 76.53 50.72 305

3.118 76.53 50.72 307

3.118 76.53 50.72 311

3.118 76.53 50.72 314.3

3.118 76.53 50.72 320

3.118 76.53 50.72 327 (max)

5.50 8076

5.50 8076

5.50 8076

0.8381 4.25 -22.72 1983.3 39.30

0.8173 4.07 -26.0 2238.0 44.31

0.7910 3.85 -30.0 2560.3 50.7

variable P2/P1 T20 (°C) T23 (°C) T7 (°C)


Fixed Parameters cf,Turb ($/GJ) E˙P,Turb (kW)

5.50 8076

5.50 8076

5.50 8076

5.50 8076

εTurb cp,Turb ($/GJ) ∆rTurb (%) E˙D,Turb (kW) ˙ D,Turb ($/h) D

0.8775 4.60 -16.40 1500 29.70

0.8707 4.52 -17.82 1584.0 31.40

Dependent Variables 0.8638 0.8498 4.50 4.34 -18.20 -21.09 1668.5 1840.0 33.04 36.43

respectively, by using the optimal values determined through the iterations in Tables 7 and 8. Figures 6 and 7 show variations of destruction cost rates of the intercooler with respect to the HT and LT water stream temperatures, respectively, and the corresponding exergetic efficiencies of the intercooler network through optimization process. In Table 8, the second section of the intercooler in which heat exchange process exists between the hot air and the LT water is the component with the largest ∆r values. As the decision variable T23 is varied further, it becomes apparent that some limits have been reached that do not allow for further significant improvements in the intercooler network. In addition, any attempt to reduce the relative cost difference value for this component may result in an increase in the heat transfer area of the heat exchanger or an increase of the air-fuel ratio of the engine, which may cause incomplete combustion. 3.3. Turbine. The decision variable in the turbine is selected as the temperature of exhaust gases at the exit of the turbine T7. The base case value of this temperature is 302 °C. The iterations performed for the optimization of the turbine is given

in Table 9. The turbine has the smallest ∆r values in the plant. OPT ) 0.8775 and D ˙ OPT The optimum values determined are εTurb D,Turb ) $29.70/h. These values are obtained at T7 ) 303 °C, which is essentially the same value as in the base case. This means that the turbine is already performing well based on the decision variables selected. In Figures 8 and 9, the variations of destruction cost rates and product cost of the turbine with respect to the corresponding exergetic efficiencies of the turbine are given. 3.4. Waste Heat Boiler. The relative cost difference of the waste heat boiler (WHB) unit is among the higher ones in the system (see Table 3). This is because of the low mass flow rate of the saturated steam as compared to the exhaust gas in the unit. Because the product exergy value is a constraint in thermoeconomic optimization, we may increase the exergetic efficiency (thus reduce the relative cost difference) of the

Figure 8. Variation of destruction cost rate of the turbine with respect to iterated turbine exhaust exit temperatures and corresponding calculated exergetic efficiencies of the turbine.

Figure 9. Variation of product cost values of turbine with respect to iterated exhaust exit temperatures of the turbine and corresponding calculated exergetic efficiencies.



Table 10. Dependent Variables Obtained during Iterations of the Feed Water Temperature at the Inlet of the Waste Heat Boiler for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Waste Heat Boiler f

1st iteration

2nd iteration

3rd iteration

3rd iteration

2nd iteration

1st iteration

r

P2/P1 T20 (°C) T23 (°C) T7 (°C) T12 (°C)

variable

3.118 76.53 50.72 303 60 (min)

3.118 76.53 50.72 303 74

3.118 76.53 50.72 303 81.1

3.118 76.53 50.72 303 81.6

3.118 76.53 50.72 303 81.6

3.118 76.53 50.72 303 81.2

3.118 76.53 50.72 303 84.4

3.118 76.53 50.72 303 95 (max)

cf,WHB ($/GJ) E˙P,WHB (kW)

5.50 240.3

5.50 240.3

5.50 240.3


5.50 240.3

5.50 240.3

5.50 240.3

5.50 240.3

εWHB cp,WHB ($/GJ) ∆rWHB (%) E˙D,WHB (kW) ˙ D,WHB ($/h) D

0.1399 32.11 82.0 1325.1 26.10

0.1310 32.63 82.52 1339.0 26.62

0.1254 33.01 82.90 1347.5 27.0

Dependent Variables 0.1249 33.02 82.91 1348.2 27.01

0.1249 33.02 82.91 1348.2 27.01

0.1253 33.01 82.90 1347.6 27.0

0.1225 33.11 83.0 1352 27.10

0.1123 33.81 83.70 1367.7 27.80

component by decreasing the inlet temperature of feedwater or by decreasing the exit temperature of the exhaust. Because of the low mass flow rate of the steam, the second option provides no improvement on the exergetic efficiency of the component. Therefore, we must search the optimum solution for the WHB in the lower bounds of the inlet temperatures of the feedwater relative to the base case instead of changing the exhaust temperature. As shown in Table 10, optimal values for the exergetic efficiency and destruction cost rate of the WHB unit ˙ OPT are εOPT WHB ) 0.1249 and DD,WHB ) $27.01/h, respectively. These values are close to actual base case values. In Figures 10 and 11, variations of destruction cost rates and product cost of the WHB at the iterated values of the feedwater inlet temperature with respect to the corresponding exergetic efficiencies are given. 3.5. Lubrication Oil Cooler. In the base case, the temperature of the LT water at the inlet of the intercooler is 44.9 °C (see Table 1). In the optimization of the intercooler, the decision variable of the component is selected as the temperature of the LT water at the inlet of the intercooler. This changes temperature of the LT water (dependent variable) at the exit of the intercooler. This in turn changes the temperature of the LT water at the inlet of the lubrication oil cooler (LOC) unit, and thus the exergetic efficiency. The optimum temperature of the LT water at the exit of the LOC may be searched in the range of 61.5 and 65.4 °C at the corresponding exergetic efficiencies. As shown in Table 11, the optimal values of exergetic efficiency ˙ OPT ) $1.31/ and destruction cost rate are εOPT ) 0.6952 and D D,LOC LOC h, respectively. The optimal values for this component are outside of the actual base case range. This is because when we fix optimal values for other subcomponents through optimization process, the working conditions of the LOC unit do not satisfy the real range of the process, therefore it should be redesigned. The inlet and exit temperatures of the lubrication oil are kept constant. Possible increments of temperature at the inlet and

outlet of the LT water are considered based on the exergetic efficiency range of the component (i.e., 0.1-0.99). In Figures 12 and 13, variations of destruction cost rates and product cost of the LOC at the iterated values of the LT water temperatures with respect to the corresponding exergetic efficiencies are given. 3.6. Air s Water Radiator. On the basis of their different mass flow rates, high-temperature (HT) water and low-temperature (LT) water can be separated into two different heat exchanging processes in the air-water radiator (AWR) by using a weighing factor. Thus, the decision variables in this component are taken as the temperatures of LT and HT waters at the inlet of AWR, T25, and T22. First heat exchange process is between the ambient air and the HT water. The maximum temperature difference in this process is 58.8 °C. Therefore, the HT water cannot be cooled by more than 58.8 °C in the radiator. Taking the HT water exit temperature as the decision variable, the optimum range is determined in the range of 71.7 and 87.0 °C. In Table 12, exergetic efficiencies, destruction cost rates, and corresponding product costs calculated during the iterations in the first heat exchange process are given for the AWR at the optimum pressure ratio of the compressing process. As shown in Table 12, the optimum value of the HT water exit temperature and the corresponding optimum values of exergetic efficiency and destruction cost rate of the first heat exchanging process OPT ˙ OPT are T22′ ) 74.42 °C, εAWR-1 ) 0.6264, and D D,AWR-1 ) $6.12/ h, respectively. The second heat exchanging process in the AWR is between the air from the first section and the LT water coming from the intercooler. The maximum temperature difference in this process

Figure 10. Variation of destruction cost rate of the waste heat boiler with respect to iterated feedwater inlet temperatures and corresponding calculated exergetic efficiencies.

Figure 11. Variation of product cost values of waste heat boiler with respect to the iterated feedwater inlet temperatures of the WHB and corresponding calculated exergetic efficiencies.



Table 11. Dependent Variables Obtained during Iterations of the LT Water Exit Temperature for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Lubrication Oil Cooler f

1st iteration

2nd iteration

3rd iteration

4th iteration

P2/P1 T20 (°C) T23 (°C) T7 (°C) T12 (°C) T25(°C)

variable

3.118 76.53 50.72 303 81.6 61.5

3.118 76.53 50.72 303 81.6 63.1

3.118 76.53 50.72 303 81.6 63.7

3.118 76.53 50.72 303 81.6 64

3.118 76.53 50.72 303 81.6 64.1

cf,LOC ($/GJ) E˙P,LOC (kW)

5.0 163.0

5.0 163.0

5.0 163.0

5.0 163.0

εLOC cp,LOC ($/GJ) ∆rLOC (%) E˙D,LOC (kW) ˙ D,LOC ($/h) D

0.1506 3.43 -31.4 202.2 3.70

0.4811 5.32 6.4 123.5 2.22

Fixed Parameters

variable

5.0 163.0 Dependent Variables 0.6089 6.98 39.6 93.10 1.68

0.6736 7.43 48.6 77.7 1.40

0.6952 7.56 51.2 72.5 1.31

4th iteration

3rd iteration

2nd iteration

1st iteration

r

P2/P1 T20 (°C) T23 (°C) T7 (°C) T12 (°C) T25(°C)

3.118 76.53 50.72 303 81.6 64.1

3.118 76.53 50.72 303 81.6 64.2

3.118 76.53 50.72 303 81.6 64.3

3.118 76.53 50.72 303 81.6 64.6

3.118 76.53 50.72 303 81.6 65.4

cf,LOC ($/GJ) E˙P,LOC (kW)

5.0 163.0

5.0 163.0

5.0 163.0

5.0 163.0

5.0 163.0

Fixed Parameters

εLOC cp,LOC ($/GJ) ∆rLOC (%) E˙D,LOC (kW) ˙ D,LOC ($/h) D

0.6952 7.56 51.2 72.5 1.31

Dependent Variables 0.7170 8.07 61.4 67.35 1.21

is 103.6 °C. Therefore, the LT water from the intercooler unit cannot be cooled by more than 18.4 °C (to 38.4 °C). When we

0.7387 8.32 66.4 62.2 1.12

f

1st iteration

2nd iteration

3rd iteration

P2/P1 T22′ (°C)

3.118 71.7 (min)

3.118 72.34

3.118 73.65

3.118 74.42

cf,AWR-1 ($/GJ) E˙P,AWR-1 (kW)

2.70 1005.3

Fixed Parameters 2.70 2.70 1005.3 1005.3

εAWR-1 cp,AWR-1 ($/GJ) ∆rAWR-1 (%) E˙D,AWR-1 (kW) ˙ D,AWR-1 ($/h) D

0.8611 24.20 0.888 865.7 8.41


variable P2/P1 T22′ (°C) cf,AWR-1 ($/GJ) E˙P,AWR-1 (kW) εAWR-1 cp,AWR-1 ($/GJ) ∆rAWR-1 (%) E˙D,AWR-1 (kW) ˙ D,AWR-1 ($/h) D

Figure 13. Variation of product cost values of lubrication oil cooler with respect to iterated LT water exit temperatures of the LOC unit and corresponding calculated exergetic efficiencies.

0.9821 9.85 97.0 4.26 0.08

Table 12. Dependent Variables Obtained during the Iterations of the HT Water Exit Temperature for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Air-Water Radiator - 1 variable

Figure 12. Variation of destruction cost rate of the lubrication oil cooler with respect to iterated LT water exit temperatures and corresponding calculated exergetic efficiencies.

0.8044 8.76 75.2 46.6 0.84

2.70 1005.3 0.6264 20.23 0.866 629.7 6.12

3rd iteration

2nd iteration

1st iteration

r

3.118 74.42

3.118 76.54

3.118 81.76

3.118 87.0 (max)

2.70 1005.3



2.70 1005.3 0.5088 16.93 0.841 511.5 4.97

2.70 1005.3 0.4409 14.40 0.813 443.2 4.31

take the LT water temperature at the exit of the AWR as the decision variable, the optimum range becomes 38.4-48.7 °C. In Table 13, exergetic efficiencies, destruction cost rates, and corresponding product costs calculated during the iterations in the second heat exchange process are given at the optimum pressure ratio of the compressing process and the optimum exit temperature of the HT water. In the AWR network, the optimum



Figure 14. Variation of destruction cost rate of the air-water radiator (first section) with respect to the iterated HT water exit temperatures and corresponding calculated exergetic efficiencies of the air-water radiator.

values of exergetic efficiency and destruction cost rate due to opt the second heat exchange process are determined to be εAWR-2 ˙ opt ) 0.4271 and D ) $1.69/h, respectively, by the iterations D,AWR-2 shown in Table 13. Figures 14 and 15 show variations of the destruction cost rates with respect to the temperatures of the HT and LT water streams, respectively, and corresponding exergetic efficiencies. 3.7. Overall Plant. In the optimization of the DEPC plant, two types of optimization are considered: thermodynamic and thermoeconomic. The objective of the thermodynamic optimization is to maximize the exergetic efficiency and thus to minimize the exergy destruction in the plant. In the thermoeconomic optimization, the objective is to minimize the destruction cost rate of the components, and by doing this we can optimize the product cost values of components in the plant (see Table 4).2 The thermodynamic optimization is based on the model explained in refs 23 and 26, which contain thermodynamic formulations for the subcomponents of the DEPC plant, whereas the thermoeconomic optimization employs both the thermodynamic model and the exergy-based economic model presented in refs 23 and 24. Table 14 gives the values of the decision variables and selected parameters for the thermodynamically optimal case

Figure 15. Variation of destruction cost rate of the air-water radiator (second section) with respect to the iterated LT water exit temperatures and corresponding calculated exergetic efficiencies.

(TO) and the thermoeconomically cost optimal case (CO). For comparison, values for the actual base working conditions are also presented. As expected, the thermodynamic optimum is obtained at the nearly maximum values of the decision variables such as the compressor pressure ratio, the isentropic efficiencies of the compressor and turbine, the temperatures of the LT water at the exit of the intercooler and lubrication oil cooler (states 23 and 25), the minimum values of the temperature of the exhaust gas at the exit of the turbine, and the temperature of feedwater at the inlet of the waste heat boiler unit. In Table 15, the values of three important exergy-related variables are listed for the DEPC plant and each of the system components: the rate of exergy destruction E˙D,k, exergy destruction ratio (E˙D,k)/(E˙F,total), and the exergetic efficiency εk. The overall exergetic efficiency for the TO case is determined to be 93.9% when the diesel engine is not taken into account. When the diesel engine is taken into consideration, the corresponding value is 48.0%. The exergy efficiencies for the base case and the CO case are 88.2 and 91.1%, respectively, when the diesel

Table 13. Dependent Variables Obtained during the Iterations of the LT Water Exit Temperature for the Optimization Procedure of Exergetic Efficiency and Corresponding Destruction Cost Rate of the Air-Water Radiator - 2 f

1st iteration

2nd iteration

3rd iteration

4th iteration

5th iteration

6th iteration

P2/P1 T22′ (°C) T25′ (°C)

variable

3.118 74.42 38.40

3.118 74.42 39.11

3.118 74.42 39.87

3.118 74.42 40.54

3.118 74.42 41.32

3.118 74.42 42.05

3.118 74.42 43.48

cf,AWR-2 ($/GJ) E˙P,AWR-2 (kW)

5.0 219.9

5.0 219.9

5.0 219.9

εAWR-2 cp,AWR-2 ($/GJ) ∆rAWR-2 (%) E˙D,AWR-2 (kW) ˙ D,AWR-2 ($/h) D

0.4850 20.23 0.753 106.7 1.92

0.4778 19.87 0.748 105.1 1.89


variable P2/P1 T22′ (°C) T25′ (°C) cf,AWR-2 ($/GJ) E˙P,AWR-2 (kW) εAWR-2 cp,AWR-2 ($/GJ) ∆rAWR-2 (%) E˙D,AWR-2 (kW) ˙ D,AWR-2 ($/h) D


5.0 219.9 0.4412 16.33 0.694 97.0 1.75

5.0 219.9 0.4366 15.70 0.682 96.0 1.73

0.4271 14.54 0.656 93.9 1.69 r

6th iteration

5th iteration

4th iteration

3rd iteration

2nd iteration

1st iteration

3.118 74.42 43.48

3.118 74.42 44.66

3.118 74.42 45.49

3.118 74.42 46.37

3.118 74.42 47.10

3.118 74.42 48.05

5.0 219.9 0.4271 14.54 0.656 93.9 1.69

5.0 219.9 0.4172 13.43 0.628 91.7 1.65

Fixed Parameters 5.0 5.0 219.9 219.9 Dependent Variables 0.4068 0.3961 12.79 11.69 0.609 0.572 89.5 87.1 1.61 1.57

5.0 219.9 0.3863 10.56 0.527 84.9 1.53

5.0 219.9

5.0 219.9 0.3776 9.54 0.476 83.0 1.49

3.118 74.42 48.7(max) 5.0 219.9 0.3680 8.88 0.437 80.9 1.46



Table 14. Values of the Decision Variables and Selected Parameters for the Actual Base Case, Thermodynamically Optimal Case, and Thermoeconomically Cost Optimal Case parameter

base case

thermodynamically optimal case

cost optimal case

P2/P1 T20 (°C) T22′ (°C) T23 (°C) T7 (°C) T12 (°C) T25 (°C) T25′ (°C) ηc ηt

2.90 71.7 71.7 38.4 302 95.0 50.3 38.4 0.80 0.85

3.50 72.0 76.5 61.5 277 60.0 65.4 44.6 0.88 0.90

3.12 76.5 74.4 50.7 303 81.6 64.1 43.5 0.82 0.85

Figure 16. Exergetic efficiencies of the subcomponents in the DEPC system with respect to the base, thermodynamically optimal, and cost optimal cases.

engine is not taken into account. Table 15 also shows that the component values for the exergy destruction rate and exergy destruction ratio are smaller in the TO case than in the base and CO cases. Also, exergy destruction parameters for the overall DEPC plant are lower in the TO case than those in the base and CO cases. The constraints on the values of the decision variables limit the maximum value of εtotal that can be obtained in practice. For example, when the thermodynamically optimal values are used for the remaining variables, the maximum value of εtotal would be obtained for P2/P1 to be greater than 3.50, which according to the thermodynamic model exceeds the maximum allowable value. Therefore, for this DEPC plant, the thermodynamic optimum is obtained at the boundary points not only with respect to the isentropic efficiencies of the compressor and turbine or the LT water temperatures but also with respect to the pressure ratio of the compressor, exhaust gas generated by the diesel engine, and power produced by the engine. Figure 16 shows the exergetic efficiencies of the subcomponents in the DEPC system with respect to the TO, CO, and base cases. In Table 16, the costs obtained in all three cases (TO, CO, and base cases) are given. The costs of the electricity and steam (i.e., products) in the base case are greater than those in the CO case. The differences are compensated by the reduced fuel cost corresponding to the reduced mass flow rate requirement of the fuel in the plant. This also indicates a reduction in the cost of exergy destruction in the CO case as compared to the base case. The results show that the total cost flow rate and the costs of electricity and steam are significantly higher in the TO case than in the CO case. Although the total exergy destruction in the plant is higher in the CO case (34747 kW) than that in the

Table 16. Calculated Costs for the Actual Base Case, Thermodynamically Optimal Case, and Cost Optimal Case parameter

base case

TO case

CO case

2932

7359

2316

total cost flow rate ($/h) cost of electricity ($0.01/kW h) cost of steam ($0.01/kg)

8.90

21.36

6.70

5.22

10.04

4.50

TO case (32840 kW) as shown in Table 15, the costs of electricity and steam in the TO case ($0.0670/kW h and $0.0450/ kg) are considerably greater than those in the TO case (0.021 36/ kWh and $0.010 04/kg). This is due to the fact that the reductions in the cost of exergy destruction rates in the TO case are accompanied by significant increases in the investment and operating and maintenance costs of the subcomponents. These additional costs are mainly due to the improvements of the turbocharger unit, air-water radiator, intercooler, and lubrication oil cooler. In the optimization studies of cogeneration systems, the total cost associated with the thermodynamically optimal cases, as in the present study, are sometimes significantly higher. Accordingly, studies focusing only on the thermodynamically optimal performance of a system can lead to gross misevaluations and skewed decision making.1,5-7,9 The results obtained from thermodynamic analysis may help the designer/system manager to figure out the working range for the improvement for the overall exergetic efficiency up to maximum possible value. However, the researcher is interested in cost-optimal design through thermoeconomic optimization

Table 15. Exergy Destruction, Exergy Destruction Ratio, and Exergetic Efficiency for the kth Component of the DEPC Plant for the Actual Base Working Condition, Thermodynamically Optimal and Thermoeconomically Cost Optimal Cases

component

E˙D,k (kW)

base case ˙ (ED,k)/(E˙F,total) (%)

compressor intercooler lubrication oil cooler air-water radiator turbine waste heat boiler fuel oil day tank fuel forwarding module condenser pumps DeSOx total plant comp. diesel engine total DEPC

1380 1693 187.0 775.0 1092 1404 3.60 3.20 1.20 79.47 817.0 7435.5 28,830 36267

2.20 2.70 0.30 1.23 1.74 2.24 0.006 0.002 0.001 0.0013 0.010 10.43 45.94 56.37

thermodynamically optimal case (TO) (E˙D,k)/(E˙F,total) (%) (kW)

εk (%)

E˙D,k

82.60 26.30 63.0 30.0 88.1 11.4 79.1 87.4 16.6 62.1

474.0 243.2 4.26 661.8 470.4 1325.1 3.60 3.20 1.20 6.40 817.0 4010.2 28,830 32840

88.15 40.4 42.21

0.756 0.400 0.0007 0.475 0.75 2.11 0.006 0.002 0.001 0.0001 0.010 4.51 45.94 50.45

thermoeconomically cost optimal case (CO) (E˙D,k)/(E˙F,total) (%) εk (%) (kW)

εk (%)

E˙D,k

93.90 78.03 98.21 52.46 96.16 14.0 79.1 87.4 16.6 95.0

1032 400 72.5 723.6 1500 1348 3.60 3.20 1.20 15.37 817.0 5916.5 28,830 34747

95.5 40.4 49.6

1.64 0.64 0.12 0.505 2.40 2.15 0.006 0.002 0.001 0.0002 0.010 7.47 45.94 53.41

86.90 63.88 69.52 49.54 87.75 12.49 79.1 87.4 16.6 88.0 92.6 40.4 46.6


which, in general, has a lower thermodynamic efficiency than thermodynamically optimal design. 4. Conclusions In this paper, the iterative exergoeconomic optimization method is applied for the optimization of an existing diesel engine powered cogeneration system. The methodology used in this paper aims to evaluate real economic impacts of each subcomponent of the cogeneration system by interpreting the effects of malfunctions due to the exergy destruction rate and corresponding cost rate change through optimization stages, and it appears to be a useful and powerful tool in the optimization of complex energy systems such as the DEPC system of this paper. As emphasized in the previous works in literature,1-9,18-20,25 an exact type of optimization of complex energy systems is rather difficult. The optimization implies the improvement of the existing cogeneration system rather than calculation of a global optimum. In the iterative optimization procedure we used the relative cost difference and exergetic efficiency with the corresponding optimal values obtained through the optimization procedure. The effects of changes in the decision variables on the relative cost difference, exergetic efficiency, and destruction cost rate can provide suggestions for the design changes that need to be considered in the next optimization step. Acknowledgment. The authors thank the plant management for providing the data for the plant.

Nomenclature c ) cost per unit of exergy ($/GJ) C˙ ) cost rate associated with exergy ($/h) E ) the amount of emission based on energy content (g/kWh) E˙ ) exergy rate (kW) f ) exergoeconomic factor (%) m ˙ ) mass flow rate (kg/s) r ) relative cost difference (%) T ) temperature (K) ˙ ) power (kW) W ydest,k ) component exergy destruction over total exergy input y*dest,k ) component exergy destruction over total exergy destruction Z˙ ) cost rate associated with the sum of capital investment and operation and maintenance ($/h) Z˙CL ) cost rate associated with capital investment ($/h) Z˙OM ) cost rate associated with operation and maintenance ($/h)

Energy & Fuels, Vol. 23, 2009 1989 AbbreViations AWR ) air-water radiator C ) compressor CON ) condenser DEPC ) diesel engine powered cogeneration DeSOx ) desulphurization FDT ) fuel oil day tank FFM ) fuel forwarding module FWT ) feedwater tank IC ) intercooler LOC ) lubrication oil cooler LOT ) lubrication oil tank MOPSA ) modified productive structure analysis method P ) pump SD ) steam drum SPECO ) specific cost exergy costing method T ) turbine WH ) water heater WHB ) waste heat boiler Subscripts CI ) capital investment D ) destruction DE ) diesel engine F ) fuel k ) any component m ) year OM ) operating and maintanence P ) product D ) destruction Superscripts OPT ) optimum Greek Letters η ) energy efficiency ηturb ) turbine isentropic efficiency ηcomp ) compressor isentropic efficiency ε ) exergy efficiency τ ) total annual operating hours of system at full load (h) β ) capital recovery factor γ ) fixed operating and maintenance factor n ) cost exponent EF800893Q

Exergoeconomic Optimization of a Diesel-engine-powered

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