Thermo-economic environmental optimization of Organic Rankine Cycle for diesel waste heat recovery

Thermo-economic environmental optimization of Organic Rankine Cycle for diesel waste heat recovery

Energy 63 (2013) 142e151 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Thermo-economic environm...

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Energy 63 (2013) 142e151

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Thermo-economic environmental optimization of Organic Rankine Cycle for diesel waste heat recovery Zahra Hajabdollahi a, Farzaneh Hajabdollahi b, Mahdi Tehrani c, Hassan Hajabdollahi d, * a

Mechanical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran Mechanical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran c Mechanical Engineering Department, Iran University of Science and Technology, Tehran, Iran d Mechanical Engineering Department, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 February 2013 Received in revised form 22 August 2013 Accepted 17 October 2013 Available online 14 November 2013

An Organic Rankine Cycle for diesel engine waste heat recovery is modeled and optimized. The design parameters are nominal capacity of diesel engine, diesel operating partial load, evaporator pressure, condenser pressure and refrigerant mass flow rate. In addition four refrigerants including R123, R134a, R245fa and R22 are selected and studied as working fluids. Then, the fast and elitist NSGA-II (Nondominated Sorting Genetic Algorithm) is applied to maximize the thermal efficiency and minimize the total annual cost (sum of investment cost, fuel cost and environmental cost) simultaneously. The results of the optimal design are a set of multiple optimum solutions, called Pareto optimal solutions. The optimization results show that the best working fluid is R123 in both of economical and thermo dynamical view point for a specified value of output power. R245fa, R134a and R22 are placed in the next ranking, respectively. The optimum result of R123 shows the 0.01%, 4.39%, and 4.49% improvement for the total annual cost in comparison with R245fa, R22, and R134a, respectively. The above values for efficiency are obtained 1.01%, 12.79% and 10.57%, respectively. Furthermore R123 needs the highest investment cost while the environmental and fuel costs are the lowest. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Organic Rankine Cycle Diesel engine Working fluid Total annual cost Thermal efficiency NSGA-II

1. Introduction ORC (Organic Rankine Cycle) enable efficient power generation unit from low-grade heat sources by replacing water with organic working fluids such as refrigerants or hydrocarbons. Najjar and Radehwan recovered waste heat by combining a heat-exchanger gas turbine cycle with closed Organic Rankine Cycle [1]. Some authors investigate the effect of working fluids on Organic Rankine Cycle for waste heat recovery [2e7]. Mago et al. presented an analysis of regenerative Organic Rankine Cycles using dry organic fluids to convert waste energy to power from lowgrade heat sources [8]. Dai et al. described the Rankine cycles for low grade waste heat recovery with different working fluids [9]. Papadopoulos et al. presented the first approach to the systematic design and selection of optimal working fluids for ORCs (Organic Rankine Cycles) based on CAMD (computer aided molecular design) and process optimization techniques [10]. The results were compared in the regions when net power outputs

* Corresponding author. Tel.: þ98 913 2924318; fax: þ98 391 4221764. E-mail addresses: [email protected], [email protected] (H. Hajabdollahi). 0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.10.046

were fixed at 10 kW. The outcomes indicated that R11, R141b, R113 and R123 manifested slightly higher thermodynamic performances than the others. Some authors investigated the performance of a low-temperature solar Rankine cycle system using various working fluids [11e19]. Shengjun et al. presented an investigation on the parameter optimization and performance comparison of the fluids in subcritical ORC and transcritical power cycle in low-temperature binary geothermal power system [20]. A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power was proposed and analyzed by Chen et al. [21]. Unlike a conventional Organic Rankine Cycle, a supercritical Rankine cycle does not go through the two-phase region during the heating process. By adopting zeotropic mixtures as the working fluids, the condensation process also happens non-isothermally. Both of these features create a potential for reducing the irreversibilities and improving the system efficiency. Alessandro Franco analyzed and discussed the exploitation of low temperature, water-dominated geothermal fields with a specific attention to regenerative Organic Rankine Cycles [22]. Yamada et al. proposed a new pump less Rankine-type cycle for power generation from low-temperature heat sources [23]. The new cycle mainly consists of an expander, two heat exchangers, and switching valves for the expander and heat

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Nomenclature

h

a A C h i LHV _ m p Q_

Subscripts a actual D diesel i inlet o outlet evap evaporator T turbine s isentropic cond condenser LMTD logarithmic mean temperature difference CW cooling water p pump env environment inv investment f fuel nom nominal PL partial load (%) total total wj water jacket

U _ W y

annual cost coefficient (e) condenser heat transfer surface area (m2) investment cost ($) enthalpy (kJ/kg K) interest rate (e) fuel lower heating value (kJ/kg) mass flow rate (kg/s) pressure (kPa) rate of heat transfer (kW) overall heat transfer coefficient (W/m2 K) power (kW) depreciation time (year)

Greek abbreviation jem pollutant emission cost ($/kg) jf fuel cost ($/kg) s hours of operation per year (h) n specific volume (m3/kg) ε total cycle thermal efficiency (e)

exchangers. Chen et al. studied transcritical Rankine cycles using refrigerant R32 (CH2F2) and carbon dioxide (CO2) as the working fluids for the conversion of low-grade heat into mechanical power [24]. Wang et al. used waste heat from stationary and mobile engine cycles to generate cooling for structures and vehicles [25]. It combined an ORC (Organic Rankine Cycle) with a conventional vapor compression cycle. In order to maintain high system performance while reducing size and weight for portable applications, micro channel based heat transfer components and scroll based expansion and compression were used. Sun and Li presented a detailed analysis of an Organic Rankine Cycle heat recovery power plant using R134a as working fluid. Mathematical models for the expander, evaporator, air cooled condenser and pump were developed to evaluate and optimize the plant performance [26]. Wagar et al. developed a model of an ammoniae water Rankine heat engine and examined with the inclusion of a two-phase expansion process. A general model for the optimal cycle was developed based upon the maximum operating temperature and the operating concentration [27]. Jing Li et al. presented a quantitative study on the convection, radiation, and conduction heat transfer from a kW-scale expander. A mathematical model was built and validated [28]. Xu and He proposed a regenerative Organic Rankine Cycle that used a vapor injector as the regenerator [29]. The thermal performance of both the novel cycle and the basic ORC was calculated and compared by using R123 as the working fluid. Invernizzi et al. investigated the possibility of enhancing the performances of micro-gas turbines through the addition of a bottoming Organic Rankine Cycle [30]. They showed ORC cycles were particularly suitable for the recovery of heat from sources at variable temperatures. Quoilin and et al. developed a thermodynamic model of a waste heat recovery ORC in order to compare both the thermodynamic and the thermoeconomic performance of several typical working fluids for low to medium temperature-range ORCs [31]. In this paper after thermo-economic modeling of ORCD (Organic Rankine Cycle for Diesel) waste heat recovery, this equipment is optimized by maximizing the thermal efficiency as well as minimizing the total annual cost, simultaneously. nominal capacity of diesel engine, diesel operating partial load, evaporator pressure, condenser pressure and refrigerant mass flow rate are taken as five design parameters and fast and elitist NSGA-II (Non-dominated

143

efficiency (e)

Sorting Genetic Algorithm) is applied to provide a set of Pareto multiple optimum solutions. As a summary, the followings are the contribution of this paper into the subject: Applying four simultaneous system analysis including energy, efficiency, economic and environment (4E analysis) for equipment selection. Selecting the nominal capacity of diesel engine, diesel operating partial load, evaporator pressure, condenser pressure as well as refrigerant mass flow rate as design parameters (not selected as a group of variables in other available literature). Performing the multi objective optimization of ORCD with efficiency and the total annual cost as two objectives (not selected in other available literature). Applying the optimization for four working fluids including R123, R134a, R245fa and R22. Sensitivity analysis of change in total annual cost when the price of diesel fuel varies. 2. Thermal modeling Schematic diagram of an ORCD (Organic Rankine Cycle for Diesel) waste heat recovery is shown in Fig. 1. It mainly consists of diesel engine and Rankine cycle including turbine, condenser, pump and evaporator (heat exchanger). Refrigerant enters the evaporator at a given pressure and temperature (state 4), where it is vaporized by the absorbed heat energy from waste heat recovery in diesel engine. The refrigerant exits the evaporator as superheated vapor (state 1), and then passes through the expander (turbine). The high quality refrigerant (state 2) enters the condenser and transfers heat to the cooling tower. The condensed liquid refrigerant (state 3) is next pumped to the evaporating pressure and enters directly to the evaporator (state 4). There are two sources of power generation here, including the net power from diesel engine and Rankine cycle. In order to do the thermal modeling, mass and energy balances on the system are required to determine the flow rates and energy transfer rates at the control surface. Appling the first law of thermodynamic in the steady state, one can find the formula for mass and energy balance as follow [32]:

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Fig. 1. Schematic diagram of Organic Rankine Cycle for diesel waste heat recovery.

Mass balance equation:

X

X

_i ¼ m

_ W

_o m

(1)

Energy balance equation:

_ ¼ Q_  W

X

_ o ho  m

X

_ i hi m

(2)

where subscripts i and o refer to streams entering and leaving the control volume, respectively. The energy balance equations for the various parts of the turbine cycle as shown in Fig. 1 are as follow: Evaporator:

_ i ðho  hi Þ Q_ evap ¼ m

(3)

Turbine:

_ W

h h

o;a hT ¼ _ T;a ¼ i hi  ho;s W T;s

_ T;a ¼ W

X

_ i hi  m

X

(4)

_ o ho m

hp ¼ _ p;s ¼ W p;a

ni ðPo  Pi Þ ho  hi

(9)

Diesel engine: A part of input energy into the diesel engine is converted to the power and remains transformed to the heat in exhaust, water jacket, lube oil and radiation. Just the heat in exhaust and water jacket are recoverable and useful. On the other hand, diesel engine characteristics such as thermal efficiency or recoverable heat rate are a function of partial load (part load) which is defined as the percentage of nominal load. By increasing the partial load, both power and recoverable heat rate increases but fuel mass flow rate increases too. As a result, the optimum value of partial load should be determined in optimization process and consequently the engine specifications as a function of partial load is needed too. The graphical data of power and heat rate produced by diesel engine in various partial loads is shown in Fig. 2 [33]. The following relations are curve fitted to obtain the mathematical formulation

(5)

Condenser:

Q_ cond ¼

X

_ i hi  m

X

_ o ho ¼ UAcond DTLMTD m

(6)

where U, Acond and DTLMTD are overall heat transfer coefficient, condenser heat transfer surface area and logarithmic mean temperature difference defined as follow:



 



T TCW;o  T3 TCW;i DT1  DT2 2   DTLMTD;c ¼ ¼ logðDT1 =DT2 Þ log T2 TCW;o T3 TCW;i

(7)

where CW (cooling water) indicates the cooling water recirculation in condenser. The pressure drop in condenser/evaporator is assumed to be Dp and as a result:

po =pi ¼ ð1  DpÞ Pump:

(8) Fig. 2. Power and heat produced by diesel engine versus partial load (points indicate the actual data and lines indicate the curve fitting).

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for power and heat rate as a function of partial load using data presented in Fig. 2: Power as a function of partial load:

_ D;PL W ¼ 1:07 expð0:0005736ðPLÞÞ _ f;PL LHVf m  1:259 expð0:05367ðPLÞÞhD;nom

(10)

recoverable energy from the water jacket and exhaust gas enthalpy as a function of partial load:

Q_ wj;PL ¼ 24:01 expð0:0248ðPLÞÞ _ f;PL $LHVf m þ 15:35 expð0:002822ðPLÞÞ Q_ o;PL ¼ 0:001016ðPLÞ2  0:1423ðPLÞ þ 31:72 _ f;PL $LHVf m

(11)

(12)

un-recoverable energy from oil and radiation (and etc) as a function of partial load:

    Q_ oil ¼ 1:329  107 PL4  4:35  105 PL3 _ f;PL $LHVf m þ 0:005631 PL2  0:3471 PL þ 11:81

(15)

(16)

_ _ _ W ORC ¼ W T;a  W p;a

(17)

In addition the total thermal efficiency of the cycle is computed from:

_ W total _ f $LHV m

(18)

_ where W total is total output net power estimated as follow:

X

_ Dþ W

X

Cinv ¼ Cinv;D þCinv;T þCinv;cond þCinv;P  d  d  d4 d3 _ D 1 þb W _ T 2 þb ðA _ ¼ b1 W 2 3 cond Þ þb4 W p

(21)

_ f  jf  s Cf ¼ 3600  m

(22)

Cenv ¼ mtotal;CO2  jem

(23)

here jf, jem and 4 are the fuel cost, pollutant emission cost and maintenance factor, respectively. The constant values of b and d coefficients are obtained based on the regional price of the equipment. s and mtotal;CO2 are number of system operating hour in a year and total CO2 produced by fuel in a year. In addition a is the annual cost coefficient defined as:

i 1  ð1 þ iÞy

(24)

p1 > p2

(25)

T2 > 40

(26)

the constraint, T2 > 40, is applied for keeping the condenser temperature above the ambient temperature for condensing procedure.

x2 > 0:95

(27)

this constraint is applied to avoid the turbine vane corrosion.

_ W D hD;nom LHVf

Total cycle (ORC and diesel engine): _ Moreover, W ORC is total output net power in ORC (turbine cycle) estimated as follow:

_ W total ¼

(20)

(14)

_ f;nom is nominal diesel fuel consumption computed as: where, m

ε ¼

Ctotal ¼ afCinv þ Cf þ Cenv

where i and y are interest rate and depreciation time, respectively. In this study, nominal capacity of diesel engine, diesel operating partial load, evaporator pressure, condenser pressure and refrigerant mass flow rate are considered as design parameters. The following constraints are introduced for the optimization procedure:

_ f;PL m ¼ 0:02836 expð0:03254ðPLÞÞ _ mf;nom

_ f;nom ¼ m

In this study, the total cycle efficiency and total annual cost are considered as two objective functions. The efficiency is defined in Equation (18) and the total annual cost includes investment cost (capital cost of diesel and ORC), cost of diesel fuel as well as environmental cost (regarding the CO2 emission) is computed from:

a ¼

_ f and LHV (fuel lower heating value) are diesel where hD,nom,m nominal efficiency, fuel mass flow rate entered to diesel engine and fuel lower heating value, respectively. Furthermore, the fuel mass flow rate of prime movers is also assumed to be a function of partial load as bellow [33]:

þ 0:2556 expð0:01912ðPLÞÞ

3. Objective functions, design parameters and constraints

(13)

  Q_ etc ¼ 3:258  106 PL3 þ 0:001364 PL2 _ f;PL $LHVf m  0:1068 PL þ 15:64

145

_ W ORC

(19)

T1 < Te;D

(28)

this is necessary for heat transfer from waste heat recovery to the refrigerant where Te,D is the diesel engine exhaust temperature. It is also assumed that the stack temperature is not lower than 148.8  C for diesel engine to avoid stack corrosion [33]. 4. Genetic algorithm for multi-objective optimization 4.1. Definition of multi-objective optimization A multi-objective optimization problem requires the simultaneous satisfaction of a number of different and often conflicting objectives. It is required to mention that no combination of decision variables can optimize all objectives, simultaneously. Multiobjective optimization problems generally show a possibly uncountable set of solutions, whose evaluated vectors represent the best possible trade-offs in the objective function space. Pareto

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optimality is the key concept to establish a hierarchy among the solutions of a multi-objective optimization problem, in order to determine whether a solution is really one of the best possible trades-off [34]. A multi-objective problem consists of optimizing (i.e., minimizing or maximizing) several objectives, simultaneously with a number of inequality or equality constraints. The problem can be formally written as follows: Find x ¼ (xi)ci ¼ 1, 2 ,., Nparam such as fi(x) is a minimum (respectively maximum) ci ¼ 1, 2,., Nobj Subject to:

gj ðxÞ ¼ 0

cj ¼ 1; 2; .; M;

(29)

hk ðxÞ  0

ck ¼ 1; 2; .; K;

(30)

where x is a vector containing the Nparam design parameters, (fi)i¼1,.,Nobj the objective functions and Nobj the number of objectives. The objective function (fi)i¼1,.,Nobj returns a vector containing the set of Nobj values associated with the elementary objectives to be optimized simultaneously. The first multiobjective GA (Genetic Algorithm), called vector evaluated GA (or VEGA), was proposed by Schaffer [35]. An algorithm based on non-dominated sorting was proposed by Srinivas and Deb [36] and called NSGA (Non-dominated Sorting Genetic-Algorithm)). This was later modified by Deb et al. [37] which eliminated higher computational complexity, lack of elitism and the need for specifying the sharing parameter. This algorithm is called NSGA-II which is coupled with the objective functions developed in this study for optimization. 4.2. Non-dominated sorting and Pareto front

Sq ¼ S

1  c q1 c ; 1  cw

(32)

To form a parent search population, Ptþ1 (t denotes the generation), of size S, where 0 < c < 1 and w is the total number of ranked non-dominated. 4.5. Crowding distance The crowding distance metric proposed by Deb [38] is utilized, where the crowding distance of an individual is the perimeter of the rectangle with its nearest neighbors at diagonally opposite corners. So, if individual X(a) and individual X(b) have same rank, each one has a larger crowding distance is better. 4.6. Crossover and mutation Uniform crossover and random uniform mutation are employed to obtain the offspring population,Qtþ1. The integer-based uniform crossover operator takes two distinct parent individuals and interchanges each corresponding binary bits with a probability, 0 < pc  1. Following crossover, the mutation operator changes each of the binary bits with a mutation probability, 0 < pm < 0.5. 4.7. Historical archive The NSGA-II algorithm has been modified to include an archive of the historically non-dominated individuals, Ht. Archive is used to update the data at each iteration. 5. Case study

(a)

As defined by Deb [38], an individual X is said to constraindominate an individual X(b), if any of the following conditions are true: (1) X(a) and X(b) are feasible, with (a) X(a) is no worse than X(b) in all objective, and (b) X(a) is strictly better than X(b) in at least one objective. (2) X(a) is feasible while individual X(b) is not. (3) X(a) and X(b) are both infeasible, but X(a) has a smaller constraint violation. Here, the constraint violation [(X) of an individual X is defined to be equal to the sum of the violated constraint function values [39],

[ðXÞ ¼

B  X



g gj ðXÞ gj ðXÞ;

(31)

j¼1

where g is the Heaviside step function. A set of non-dominated individuals is used to form a Pareto-optimal fronts. 4.3. Tournament selection Each individual competes in exactly two tournaments with randomly selected individuals, a procedure which imitates survival of the fittest in nature. 4.4. Controlled elitism sorting To preserve diversity, the influence of elitism is controlled by choosing the number of individuals from each subpopulation, according to the geometric distribution [39]:

In this study, four working fluids including R123, R134a, R245fa and R22 are selected and an ORCD system is optimized for each of them, separately. For this purpose, MATLAB and Refprop soft wares are used to evaluate the thermo dynamical properties of the refrigerants. To minimize the total annual cost value and maximize the total cycle efficiency, five design parameters including nominal capacity of diesel engine, diesel operating partial load, evaporator pressure, condenser pressure, and refrigerant mass flow rate are selected. Design parameters and the range of their variations are listed in Table 1. The ORCD system should deliver 200 kW output net power operate at s ¼ 6000 hours in a year. System is optimized for depreciation time y ¼ 20 years, interest rate i ¼ 0.12, jem ¼ 0.02086 $/kg for CO2 pollutant emission cost and hD,nom ¼ 0.35 for nominal efficiency of diesel engine by considering 5% pressure drop in evaporator, 0.9 as both turbine and pump isentropic efficiency and 0.168 $/kg as diesel fuel cost [40]. Moreover, the constants of investment cost in relation (21) are taken b ¼ [1763 4750 150 3500] and d ¼ [0.95 0.75 0.8 0.47] and 4 ¼ 1.05 is considered for the maintenance factor. In addition, evaporator (heat recovery heat exchanger) is a part of diesel engine and cost of it is considered with investment cost of diesel engine.

Table 1 The design parameters and their range of variation for the optimization procedure. Case studies

From

To

Capacity of diesel engine (kW) Partial load (%) Evaporator pressure (kPa) Condenser pressure (kPa) Refrigerant mass flow rate (kg/s)

10 20 300 10 0.1

200 100 2000 2000 5

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6. Results and discussion 6.1. The procedure of thermo-economic and environment analysis By evaluating the nominal capacity of diesel engine and partial load as design parameters, the power and recoverable heat from diesel is specified. The turbine power, condenser required heat as well as pump power is also computed by using the recovered heat from diesel and other design parameters including evaporator pressure, condenser pressure and refrigerant mass flow rate. By knowing the diesel power, turbine power, pump power as well as condenser heat transfer surface area (using Equation (6)), the investment cost of equipments are computed using relation (21). The fuel consumption is also computed from relation (16) and consequently the fuel and environmental cost (relations (22) and (23)) are determined. Considering the power generated by diesel engine and net power output from ORC cycle, the total cycle efficiency is also computed from Equation (18).

147

Table 2 The critical temperature and pressure of studied working fluids. Working fluid

R22

R123

R134a

R245fa

Critical temperature (K) Critical pressure (kPa)

369 4989

457 3668

374 4059

427 3639

next Ranking. The critical temperature and pressure of four studied working fluids are listed in Table 2. It is worth mentioning that higher ORC efficiency due to the higher working fluid critical temperature was previously investigated by Aljundi [3]. Nevertheless, the effect of critical points has been not reported in thermo-economic viewpoint. Comparing the optimum results with critical points listed in Table 2 reveal that a working fluid with higher critical temperature and lower critical pressure leads to the better thermo-economic and environmental result. The distribution of variables for the optimal points on Pareto front (Fig. 3) is shown in Fig. 4aee. The lower and upper bounds of the variables are shown by dotted lines. The following points for the optimal variables in Fig. 4 could be deduced:

6.2. Optimization The Genetic Algorithm Optimization is performed for 1000 generations, using a search population size of M ¼ 150 individuals, crossover probability of pc ¼ 0.9, gene mutation probability of pm ¼ 0.035 and controlled elitism value c ¼ 0.55, separately for four working fluids including R123, R134a, R245fa and R22. The results of optimum efficiency and total annual cost for four refrigerants are depicted in Fig. 3. As it shown, the Pareto fronts suffer from diversity and lower number of optimum points compared with Pareto fronts presented in some other works reported in Refs. [41e44]. Actually the diversity and number of points in the final Pareto front is highly depended on searching area which is highly limited by five constraints presented in Section 3. Moreover to preserve the number of optimum points in evolution of algorithm, the historical archive (Section 4.7) as well as high number of generation (1000) were used which guaranteed the optimum results. The Pareto optimum results reveal the conflict between two objectives, the efficiency and the total annual cost. Any change that increases the efficiency, leads to an increase in the total annual cost and vice versa. It is observed that the best refrigerant for this case study is R123. Their results are totally dominated over the other refrigerants in both efficiency and total annual cost. The refrigerants R245fa, R134a and R22 are respectively in the

Fig. 3. Pareto optimal front for four working fluids including R22, R123, R134a and R245fa.

1. A plant with higher value of efficiency needs a lower capacity of diesel engine. 2. All the diesel engines should operate in the range of 90e100% of their nominal capacity. 3. The turbine outlet pressure in the all plants is higher than 145 kPa. The corresponding value of this parameter in the common steam cycle power plant is in the range of 10e20 kPa. The higher selected turbine outlet pressure is due to the constraint mentioned in the Section 3 (relation (26)). The percent of power produced by ORC to total power generated by ORCD for all the optimum points in the Pareto front are obtained and depicted in Fig. 5. The power produced by ORC is about 31.5% of total power generated by ORCD for R123 which has the maximum efficiency, too. This value is approximately 30.8%, 23.2% and 21.5% for R245fa, R134a and R22, respectively. Actually, the ratio of ORC to ORCD power generation is corresponding with the total cycle efficiency which is presented in Pareto fronts. 6.3. Final optimum solution The selection of a single optimum point from existing points on the Pareto front (boundary of infeasible region and feasible but nonoptimum region) needs a process of decision-making. In fact, this process is mostly carried out based on engineering experiences and importance of each objective for decision makers. The process of final decision-making is usually performed with the aid of a hypothetical point named as ideal point. If two objective functions would be optimized individually, i.e. disregarding another objective function, the composition of these values represents the ideal point or ideal objective point [45]. The typical Pareto front as well as ideal point in maximizing the first objective and minimizing the second objective is shown in Fig. 6. It is clear that it is impossible to have both objectives at their optimum point, simultaneously. Since the ideal point is not a solution located on the Pareto frontier, closest point of Pareto frontier to the ideal point might be selected as final optimum solution. Before it, the objectives should be non-dimensionalized. In this paper, LINMAP (Linear programming techniques for multidimensional analysis of preferences) method is used to nondimensionalize the objectives using the following relation [41]:

Fij Fijn ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi 2 Pm  F i¼1 ij

(33)

148

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Fig. 4. Distribution of optimum values of design parameters for points in Pareto front. a. Diesel capacity, b. diesel partial load, c. turbine inlet pressure, d. turbine outlet pressure, e. refrigerant mass flow rate.

where i is the index for each point on Pareto front, j is the index for each objective and m denotes the number of points on the Pareto front. Then the distance of each point on Pareto front from the ideal point is obtained:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2  2 uX n Fijn  Fideal;j di ¼ t j¼1

(34)

where ideal is the index of ideal objective functions. Then the value of distance for each point on the Pareto frontier is computed using the above relation and optimum point which leads to the minimum d is selected as final optimum solution. The final value of optimum objective functions, investment cost, fuel cost and environmental cost along with corresponding design parameters using the above procedure are obtained and listed in Table 3. It is observed that the best refrigerant in economical view point is R123 with total annual cost of 86,253 $/year. The refrigerants

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149

Table 3 The final optimum values of design parameters and objective functions for four refrigerants. Case studies

Fig. 5. Percent of ORC net power to total ORCD net power for optimum results presented in Pareto front.

R245fa, R22, and R134a are in the next Rankine, respectively that the total annul cost for them are 86,261 $/year, 90,039 $/year and 90,127 $/year, respectively. The optimum result of R123 is improved 0.01%, 4.39%, and 4.49% in comparison with R245fa, R22, and R134a refrigerants, respectively. On the other hand the best refrigerant in thermo dynamical efficiency view point is R123 with efficiency of 0.5127. The refrigerants R245fa, R134a and R22 are in the next Rankine, respectively with efficiency of 0.5075, 0.4585 and 0.4471, respectively. The optimum result of R123 is improved 1.01%, 10.57% and 12.79% in comparison with R245fa, R134a and R22, respectively. Furthermore, the plant with refrigerant R123 needs the lower diesel capacity, diesel partial load, and refrigerant mass flow rate in comparison with the plants with other studied refrigerants. Moreover, plant with refrigerant R22 needs the lowest refrigerant mass flow but higher partial load and diesel capacity in comparison with the plants with the other refrigerants. It is also observed from Table 3 that the R123 needs the highest investment cost while lowest environmental and fuel costs.

Fig. 6. Concept of ideal point in the Pareto frontier for maximizing the objective 1 and minimizing the objective 2.

R22

R123

R134a

R245fa

158.438 152.500 158.438 152.557 Capacity of diesel engine (kW) Partial load (%) 99.710 90.625 96.875 90.647 Evaporator pressure 1847.893 771.182 1851.596 525.654 (kPa) Condenser pressure 887.280 146.480 1004.626 192.092 (kPa) Refrigerant mass flow 2.550 2.564 4.693 3.785 rate (kg/s) Thermal efficiency 0.4471 0.5127 0.4585 0.5075 () Total annual cost 90,039 86,253 90,127 86,261 ($/year) Total investment 307,320 323,260 315,410 320,050 cost ($) Environmental cost 12,911 11,323 12,563 11,330 ($/year) Cost of fuel ($/year) 34,147 29,948 33,228 29,966 14.305 13.058 13.939 13.131 Percent of Environmental to total cost (%)

6.4. Sensitivity analysis on diesel fuel price In this study the diesel fuel price was considered 0.168 $/kg based on local price of fuel [40]. However, the mentioned price is significantly varied in geographical zone. For this purpose the variation of total annual cost versus percent of variation in fuel price for different working fluid at final optimum point are shown in Fig. 7. The result demonstrates: for example by increase of 100% in diesel fuel price, the optimum value of total annual cost increases 38.16%, 34.37%, 36.92% and 34.82% respectively for R22, R123, R134a and R245fa. Furthermore, due to the higher investment cost for plants with lower total annual cost, the optimum value of total annual cost converged to a same point by decreasing the price of diesel fuel.

Fig. 7. Variation of AAB (total annual cost) versus percent of variation in diesel fuel price at final optimum point.

150

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by substituting the relations (10)e(14) into the above relation, the energy conservation error is obtained based on partial load which is depicted in Fig. 9. As it shown, the maximum deviation is in the range of 1.5% which is shown the accuracy of the applied relations for diesel engine. 7. Conclusions An ORCD was optimally designed using multi objective optimization technique by considering the thermo-economic and environmental aspects. The design parameters (decision variables) were nominal capacity of diesel engine, diesel operating partial load, evaporator pressure, condenser pressure and refrigerant mass flow rate. In the presented optimization problem, the efficiency and total annual cost were two objective functions (the efficiency was maximized and total annual cost was minimized). The above procedure was performed for four working fluids including R123, R134a, R245fa and R22. Based on the studied system the following conclusions can be inferred: _ T þ Q_ _ Fig. 8. Comparison of recovered heat from diesel engine and W cond  W p for optimum results presented in Pareto front.

6.5. Model verification Basically total recovered heat from diesel engine should be the _ T þ Q_ _ same with W cond  W p . These two values are obtained for all optimum points in Pareto front and shown in Fig. 8. As it shown, the maximum deviation is in the range of 2% which is acceptable for engineering problem. In addition, as it mentioned in thermal modeling section, the graphical data regarding the power and heat produced by different part of diesel engine in terms of partial load in the rang of 20e100% were used and curve fitted using relations (10)e(14). To verify the precision of applied relations and satisfying the first law of thermodynamic, the following error in terms of partial load is defined:

    _ _ _ _ _ _ f;PL LHVf  W m D;PL þ Q wj;PL þ Q o;PL þ Q oil;PL þ Q etc;PL   ErPL ð%Þ ¼ _ f;PL LHVf m 100

1. R123 is found to be the best working fluid while R22 is the worst. Beside the worst results, R22 has ozone depletion and high global warming potential which is not recommended as working fluid in our studied case. 2. R245fa has approximately the same results in comparison with R123 in both efficiency and total annual cost and it seems to be a good replacement for R123. 3. The optimum result of R123 was improved 0.01%, 4.39%, and 4.49% for total annual cost in comparison with R245fa, R22, and R134a refrigerants, respectively. The above values for efficiency were found to be 1.01%, 12.79% and 10.57%, respectively. 4. A plant with lower total annual cost needs the higher investment cost. 5. Selecting a working fluid with higher critical temperature and lower critical pressure leads to the better thermo-economic and environment result in this case. 6. By decreasing the diesel fuel price, the optimum value of total annual cost for different working fluid leads to the same result. References

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Fig. 9. Energy conservation error for curve fitted relations in various partial load.

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