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THERMAL SCIENCE: Year 2023, Vol. 27, No. 5A, pp. 3579-3589 3579
THERMOECONOMIC ANALYSIS OF A MICROCOGENERATION SYSTEM USING THE THEORY OF EXERGETIC COST
by
_Adriano da Silva MARQUES a, Yipsy Roque BENITO b, Alvaro Antonio OCHOA c, and Monica CARVALHO a_* a (^) Department of Renewable Energy Engineering, Federal University of Paraiba, Joao Pessoa, Brazil b (^) Department of Production and Mechanical Engineering, Federal University of Juiz de Fora, Juiz de Fora, Brazil c (^) Federal Institute of Technology of Pernambuco, Recife, Brazil Original scientific paper https://doi.org/10.2298/TSCI220806023M
Cogeneration and trigeneration systems have been broadly employed as part of
the strategies oriented toward rational energy use. The assessment of these systems
must include simultaneous considerations of costs, irreversibility, energy losses,
and their causes. This work presents a step-by-step thermoeconomic analysis of
a microcogeneration unit, composed of an internal combustion engine and an
NH 3 -water single-effect absorption refrigeration chiller. The research employed
the Theory of Exergetic Cost method to determine monetary and energy costs and
the exergy efficiency of equipment. It is therefore , possible to identify which pieces
of equipment present the highest impact and focus on these to improve the overall
performance of the energy system. Although not part of the Theory of Exergetic
cost, exergoeconomic parameters can be calculated to expand the assessment fur-
ther. The highest specific exergy cost is associated with the endothermic reaction
inside the absorber (282 $/GJ), while the lowest specific exergy cost is due to elec-
tricity consumed by the pump of the refrigeration system (2.16 $/GJ). The highest
exergy efficiency was identified at the condenser (almost 90%, while values under
40% were obtained for the engine, pump, and absorber. The combined analysis of
exergoeconomic results indicates that the lowest performances are related to the
generator, the absorber, the evaporator, and the regenerator.
Key words: absorption refrigeration, cogeneration, exergoeconomics,
cost allocation, thermoeconomics
Introduction
Combined energy systems can be employed as alternatives to energy supply issues, producing multiple energy services with higher performance than separate production [1]. Technical and financial feasibility assessments usually follow the First and Second Laws of Thermodynamics and economic indices. The performance of thermal systems can be improved using energy management concepts and exergy parameters [2]. The Theory of Exergetic Cost (TEC) presented by Lozano and Valero [3] combines energy and exergy flows with economics to verify the performance of energy systems. The objective of TEC is to identify the compo- nents that have higher exergy destruction and the costs associated with exergy flows in each sub-component of the system.
- (^) Corresponding author, e-mail: monica@cear.ufpb.br
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There is a deep relationship between irreversibilities, cost, and cause, to the point that Valero et al. [4] highlighted an Aristotelic analogy between thermoeconomic concepts and cause. Because TEC considers exergy destruction and carries out calculations from this view- point, the actual production cost is not separate from the cost of its exergy destruction [5]. Thermoeconomics has been used to check the viability of thermal energy systems [6] and even as an optimization technique to improve the overall energy system [7], taking into account ex- ergy and monetary costs [8]. Advanced exergy analysis can also be associated with thermoeco- nomics and has been applied to vapor absorption systems. Yu et al. [9] evaluated a cascade lithium bromide (LiBr) system and demonstrated that system optimization could reduce exergy destruction by 25%, the cost rate of exergy destruction by 24%, and capital costs by 18%. Other types of refrigeration systems can also benefit from thermoeconomic assessments, such as the case presented by Yildiz [10], who evaluated a diffusion absorption refrigerator. The energy ef- ficiency of the system increased by 3.90% (from 39.30-43.2%), and exergy efficiency increased by 0.59% (from 10.08-10.67%) after substituting the electric switching system with liquefied petroleum gas – however, the specific cost of exergy increased by 64%. The TEC is a crucial instrument to determine the economic costs of internal flows and products of energy systems, even those with intricate internal interactions. The work of Misra et al. [11] presented a TEC-based method for thermoeconomic optimization, applied to a single-effect LiBr-water absorption refrigeration system. The results showed that small changes in the configuration of the system led to a significant reduction in all costs. Rangel-Hernandez et al. [12] also applied TEC to a hybrid system constituted by a fuel cell and an absorption refrigerator, and obtained the unit exergy cost associated with electricity, refrigeration, and the losses of the system. The TEC has also been applied to combined cooling, heating, and power (CCHP) systems, such as the study case presented Yang et al. [13]. The objective was to achieve high efficiency and low costs within a biomass gasification system in different opera- tion modes. Sensitivity assessments were carried out by varying the operation hours of equip- ment, interest rates, lifetime of equipment, and unit cost of biomass. The TEC has been applied to cogeneration systems with different fuels, and the ther- moeconomic cost of the produced work varied significantly with the complexity of the systems and the type of fuel [14]. Recently, Torres and Valero [15] presented an updated review of the fundamentals of TEC. They mention that the cost formation process of residues is given main- ly from a thermodynamic perspective instead of a mostly-economic approach. It is proposed to consider residues as external irreversibilities within industrial processes. A new concept is introduced ( irreversibility carrier ) to help identify the origin, transfer, partial recovery, and destination of residues. There are other thermoeconomic methods, such as the specific exergy cost (SPECO) [16]. This method was applied to verify the financial behavior and feasibility of a solar system integrated into a Rankine cycle-based power generation facility [17] and also to demonstrate the economic feasibility of a diesel-biodiesel internal combustion system [18]. Environmental considerations can also be added to thermoeconomic models, such as in Santos et al. [19], who allocated carbon emissions to the final cost of each energy product. The simultaneous association of thermodynamic, economic, and environmental evaluations is also referred to as exergoeconoenvironmental [20]. Trindade [21] used this concept to compare different cost allocation methods in life cycle assessment studies in a combined energy system. The study presented herein presents a detailed thermoeconomic analysis for a mi- crocogeneration system. The evaluation uses the concepts of thermodynamics and the TEC to show results of monetary and exergy-related costs, exergy efficiency, and relative costs of com-
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Point – 3 (mixture of air and fuel) and point – 18 (electricity consumption from the pump) are classified as fuels. Point – 15 (chilled water) and point – 19 (power) are classified as products, and points – 16 and – 17 (cooling air from heat exchangers) are the losses.
Thermodynamic analysis
All components were individually evaluated, except for the valves that were incor- porated into the following equipment. Mass, m , energy, E , entropy, S , and exergy, Ex balances were used to this end, eqs. (1)-(4), respectively. The following assumptions were considered:
- Steady-state conditions and internally reversible processes.
- Ideal gas mixtures are considered for combustion air and exhaust gases.
- Compression and expansion processes were considered adiabatic.
- Effects of kinetic and potential energy and load losses were negligible.
- Expansion valves were considered isoenthalpic.
- The exhaust gases from the steam generator were excluded from the analysis.
cv in out
m m m
t
∑^ ∑
(^) (1)
in out
cv cv cv
W mh
E
Q mh
t
=^ −^ +^ −
∂ ∑^ ∑
(^) (2)
( ) ( ) cv^ gen
cv (^) in out
S Q
ms ms S
t T
∂ ∑ ^ ∑ ^ ∑
(^) (3)
in out dest
Ex Ex Ex Ex
t
cv
(4)
where ṁ is the mass-flow rate, Q̇ (^) cv and Ẇcv are the rate flows of heat and the work through the control volumes, and h is the enthalpy. The subscripts in and out indicate the inlet and outlet of the streams, s refers to entropy, T is the temperature, and Ṡ ge n is the entropy generated, while Ex is the exergy, and the subscript dest expresses the share of exergy destroyed. The terms on the left (variations of mass, energy, entropy, and exergy in control volumes) were disregarded due to the steady-state analysis. The thermodynamic analysis was first developed for the engine, then for each cooling system component. The thermodynamic and thermoeconomic models were built within the engineering equation solver (EES) platform.
Internal combustion engine
The engine is a 16 valve I4 Ford with 16 valves, four cylinders, and a 10:1 compres- sion rate [23]. Considering gasoline (C 8 H 18 ), this equation provides the stoichiometric balance for the complete combustion:
C 8 H 18 + exc × a ( O 2 + 3.76N 2 )→ b CO 2 + c H O 2 + d N 2 + e O 2 (5)
where exc expresses the amount of excess air, and a , b , c , d , and e are the parameters that bal- ance out the equation. O 2 , N 2 , CO 2 , and H 2 O are oxygen, nitrogen, carbon dioxide and water, respectively.
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For the engine, the air-fuel ratio was then determined, followed by the air-fuel com- bustion energy. Solution of the thermodynamic equations yielded the energy of exhaust gases and exergy of combustion products.
Cooling system
Figure 2 illustrates a scheme of the absorption chiller, which includes a generator with a vapor rectifier, a condenser, an absorber, one evaporator, an intermediate heat exchanger (IHX), a pump, and two expansion valves.
Figure 2. Scheme of the absorption refrigeration chiller [24] For the cooling system, the condenser temperature is considered as ambient tempera- ture plus 10 °C [24], evaporator temperature 5 °C [25], refrigerant concentration at the vapor rectifier is 0.999634 [24], and the concentrations of strong and weak ammonia solutions are, respectively, 0.368 and 0.268 [24].
Thermoecoonomics: Theory of exergetic cost
The TEC [3] introduced the exergy cost concept to the thermoeconomic field for the first time, and was initially formulated to solve cost allocation problems and optimization in thermal systems. The methodology is based on the concepts of product, P , (exergy that contains the benefits obtained), fuel, F , (exergy provided through the resources), and unit exergy cost, which refers to the external exergy required to make an exergy stream available within a spe- cific production process. The difference between fuel and product within a process equals its irreversibility, which is always equal or higher than zero. The unit exergy cost of any product is always equal to or higher than one. The TEC follows four propositions [3]:
- the P #1 – the exergy cost of a flow B , fuel F , or product P , is the amount of exergy required for its productions,
- the P #2 – in the absence of an external assessment, the exergy cost of flows entering the system equals their exergy,
- the P #3 – all costs generated by the productive process must be present in the cost of final products, and
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The exergy cost balances for each control volume of the microcogeneration unit con- sidering the propositions (P#) of Lozano and Valero [3] are shown in tab. 1, where NA is non-applicable. Columns P#1, P#2, and P#5 of tab. 1 refer to the propositions of the TEC method, and the columns cost and auxiliary refer to the cost equations of the TEC method. Propositions 3 and 4 did not apply to all equipment. The term Pc [$ per hour] represents the monetary cost of the exergy flow. Proposition #3 of Lozano and Valero [3] applies only to the generator, eq. (7), while proposition #4 is not applicable herein as no losses to the external environment are considered:
B B
Ex Ex = (7)
The monetary cost of each piece of equipment, Ż , is given by eq. (8) [27], which de- pends on the capital recovery factor, CRF, [27], in eq. (9):
( CRF )
Z C
n
(^) = (8)
( ) ( )
n n
i i
CRF
i
= ^
(9)
The CRF accounts for the interest rate, i , and the lifetime of the equipment, n , and C represents the purchase cost of each piece of equipment within the unit. The capital cost of the cooling unit was split into its components, according to their importance to the unit [22]: generator 25%, absorber 25%, evaporator 20%, condenser 14%, regenerator 14%, and pump 2%. Although not part of TEC, two other parameters are calculated based on SPECO [16]: the relative difference cost, rk , and exergoeconomic factor, fk. The former is the difference be- tween the specific cost of the product, cP,k , and the fuel, c F,k , and the latter relates the portion of non-exergy-related costs (capital costs plus operation and maintenance) to the overall costs of the component, as shown, respectively [16]:
, , ,
P k F k k F k
c c
r
c
= (^) (10)
, (^ dest, , )
k k k F k k L k
Z
f
Z c Ex Ex
(11)
where Żk is the monetary costs of equipment, and Ex Dest, k and ExL,k refer to the destruction of exergy and exergy associated with losses, respectively.
Results and discussion
The results of the TEC method are presented in tab. 2, which includes exergy flows, B , exergy cost flows, B *, unit exergy costs, k , monetary costs, Pc , and monetary costs per exergy unit, c *. The results of Pc were obtained from the simultaneous resolution of the equations presented in tab. 1. The results of c *^ were obtained from the solution of the system of linear equations of the SPECO method as presented in [22].
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Table 2. Results of thermoeconomic evaluation Flow Description B [kW] B *^ [kW] k [kWkW–1] Pc [$h–1] c *^ [$/GJ–1] 3 Fuel 138.50 138.50 1.00 9.33 18. 4 ICE gases 25.08 92.98 3.71 3.31 36. 5 Refrigerant 7.76 67.95 8.76 2.42 86. 6 Refrigerant 6.88 34.17 4.97 2.16 87. 7 Refrigerant 2.98 14.78 4.97 0.93 87. 8 Strong solution 0.53 5.39 10.25 0.24 126. 9 Strong solution 0.81 7.08 8.76 0.25 86. 10 Strong solution 5.66 49.58 8.76 1.77 86. 11 Weak solution 8.52 74.61 8.76 2.66 86. 12 Weak solution 1.60 32.11 20.08 1.14 198. 14 Inlet water 1.44 1.44 1.00 0.01 2. 15 Outlet water 2.80 20.83 7.45 1.24 122. 16 Condenser heat 0.80 33.78 42.01 0.26 90. 17 Absorber heat 1.81 41.49 22.94 1.84 282. 18 Electricity: pump 1.69 1.69 1.00 0.01 2. 19 ICE power 45.55 45.55 1.00 6.01 36. Point #15 represents the product of this cogeneration unit, chilled water for the refrig- eration process. Losses are represented by currents #16 and #17, which correspond to the heat exchanges in dissipative components (condenser and absorber). The fuels of the cogeneration system are points #3, #14, and #18, which are the entries of fuel, water, and the work consumed by the re-circulation pump, respectively. The cost of producing chilled water is 0.28 $ per ton, so selling this energy service for any value above this cost results in economic benefits for the unit. Heat losses in dissipative components are high: 0.26 $ per hour in the condenser and 1.84 $ per hour in the absorber, and the cost of fuel is 9.33 $ per hour. According to Lozano and Valero [3], there are challenges as- sociated with applying TEC when losses (residues) originate in dissipative components, such as condensers in vapor-driven absorption chillers. These results were expected once the TEC ap- proach provides higher monetary and exergy unit costs in these components that dissipate heat. Figure 3 shows the monetary unit costs of the cogeneration system. The highest mon- etary unit cost is associated with flow #3, which corresponds to the natural gas inlet. The cost of flow #11 is 2.66 $ per hour, associated with the pre-heating of the strong solution, pumped from the absorber to the generator. This is necessary to ensure the operation of the system. The engine’s mechanical power (flow #19), one of the products of the system, is evaluated at 6.01 $ per hour. Figure 4 presents the specific exergy costs of the cogeneration system evaluated. The highest specific exergy cost is identified at the heat loss (flow #17) due to the endothermic re- action between water and ammonia inside the absorber (282 $/GJ), followed by flow #12 with a specific exergy cost of 199 $/GJ. This weak solution flows from the generator to the absorber, losing heat in the regenerator to pre-heat the strong solution that is pumped back into the gen- erator. It must be highlighted that the lowest specific exergy costs are present in the inputs of the microcogeneration system: natural gas (flow #3, with 18.70 $/GJ), the minimal amount of
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Conclusions
The TEC was applied to a microcogeneration system to determine the exergy efficien- cy of each component, along with the monetary cost rates and exergy destruction costs associat- ed with each internal flow and final product. This work presented a step-by-step application of TEC as a valuable tool for the thermoeconomic assessment of energy systems. The results of the exergy assessment indicate that energy optimization efforts should be directed to the generator and absorber of the refrigeration system. The monetary evaluation of the exergy flows demonstrated that the highest cost rates are associated with the flows of the generator due to the need to pre-heat the solution pumped by the absorber. The generator, engine, solution pump, and absorber presented exergy efficien- cy values under 40% – this suggests that further studies are required to propose improvements in these components and achieve increases in exergy efficiency. The analysis of exergoeconom- ic parameters (although not part of TEC, these can be calculated) pinpointed that the generator, absorber, and regenerator must be prioritized regarding monetary investment aimed at improv- ing processes and mitigating thermoeconomic impacts. Although the relative cost difference and exergoeconomic factor are characteristic pa- rameters of SPECO-based assessments, these can be quantified from thermodynamic and exer- gy-related TEC data, providing a hybrid model for thermoeconomic assessment. The combined evaluation of both parameters pointed to the generator, absorber, evaporator, and regenerator as the thermoeconomic villains of the energy system. Particular attention should be given to these components regarding the design, thermal insulation, heat exchange area, and refrigerant fluid, especially when vapor absorption systems are coupled with an energy generation unit. From this study, specific computational tools are being developed for the thermoeco- nomic diagnosis of energy systems within the industrial and tertiary sectors. The latter includes shopping centers, hotels, hospitals, and supermarkets. The results of the exergy assessments can be employed as inputs in the exergoenvironmental analysis, which also includes the life cycle assessment of the equipment and energy flows of the microcogeneration system.
Funding
National Council for Scientific and Technological Development (Brazil): Pro- ductivity grants 309452/2021-0 and 309154/2019-7. FACEPE/CNPq: Research project APQ-0965-3.05/21.
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Paper submitted: August 6, 2022 Paper revised: October 22, 2022 Paper accepted: December 5, 2022
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