Thermoeconomic and environmental assessments of a combined cycle for the small scale LNG cold utilization

Applied Energy xxx (2017) xxx–xxx

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Thermoeconomic and environmental assessments of a combined cycle for the small scale LNG cold utilization Baris Burak Kanbur a,b, Liming Xiang c, Swapnil Dubey a, Fook Hoong Choo a, Fei Duan b,⇑ a

Energy Research Institute @ NTU, Interdisciplinary Graduate School, Nanyang Technological University, 637141, Singapore School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798, Singapore c School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Singapore b

h i g h l i g h t s
A combined cycle is proposed for the LNG cold energy applications.
An exergy-cost matrix is produced for the proposed combined cycle.
7% higher power generation was provided in the combined cycle.
Emission reduction is observed as 7.8% at the pressure ratio of 3.64.
The levelized product cost is 25% higher in the proposed combined cycle.

a r t i c l e

i n f o

Article history: Received 1 December 2016 Received in revised form 11 January 2017 Accepted 26 January 2017 Available online xxxx Keywords: Thermoeconomic analysis Environmental analysis Exergy analysis Stirling engine Gas turbine LNG cold energy

a b s t r a c t Liquefied natural gas (LNG) cold utilized micro-cogeneration systems can be used as a part of small scale LNG regasification processes. The study proposes a LNG cold utilized micro-cogeneration system which combines a Stirling engine and a micro gas turbine. The combined system is compared to a conventional micro-cogeneration system the point of thermodynamic, environmental and thermoeconomic views. Parametric studies are conducted in the ranges of 288.15–313.15 K for the ambient air temperature and 3–4 for the compressor pressure ratio, respectively. Thermodynamic efficiencies and power generation rates are studied in thermodynamic analyses while carbon dioxide emission rates and the relevant emission reductions are observed in environmental analyses. An original exergy-cost matrix is produced for the combined system and thermoeconomic comparison is performed between the combined system and the conventional micro-cogeneration system. It is found that the combined system provides 7.8% higher power generation rates whereas it has 1% and 2.4% higher energetic and exergetic efficiencies, respectively at the actual pressure ratio of the micro gas turbine. Emission reductions are observed as 3.9%, 7.8% or 8% at individual pressure ratio of 3, 3.64 or 4. The unit fuel costs are calculated for the system components and it is deduced that the combined system has higher unit fuel costs at the lower pressure ratios. It is found that the single system has roundly 25% less levelized product cost than the combined system at the actual pressure ratio. A simple graphic-based thermoeconomic optimization study demonstrates that the minimum relative cost differences are at different locations for the combined cycle. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Liquefied natural gas (LNG) is one of the ways for the natural gas transportation and it is non-corrosive, non-toxic cryogenic liquid (162 °C) [1,2] at the atmospheric conditions. It is the only feasible, mature and commercial natural gas transportation method

⇑ Corresponding author.

for the distances for roundly 3500 km and above from the producing country to the consuming country [1]. Japan, South Korea, Taiwan, UK, Turkey and Spain are some of these consumer countries and areas which have giant LNG imports according to International Gas Union data [3]. The LNG trade has four main steps which are: (i) exploration and production, (ii) liquefaction, (iii) transportation, and (iv) regasification. The cost of the LNG trade depends on the cost performances of these steps, and the regasification step is the most crucial step on the LNG cost chain for the consumer

E-mail address: [email protected] (F. Duan). http://dx.doi.org/10.1016/j.apenergy.2017.01.061 0306-2619/Ó 2017 Elsevier Ltd. All rights reserved.

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Nomenclature c C e ER E_ f F  h H_ L LHV M _ m n_ p r RV  R s PEC T _ W Q_ x y

unit cost, $/kJ cost, $ specific exergy, kJ/kmol emission reduction, % exergy, kJ/s exergoeconomic factor, % fuel flow rate of microturbine, kJ/s specific enthalpy, kJ/kmol energy, kJ/s heat loss ratio from combustion chamber, % lower heating value, kJ/kg molar mass, kg/kmol mass flow rate, kg/s molar flow rate, kmol/s pressure, bar relative cost difference, % reversibility factor universal gas constant, kJ/kmol K specific entropy, kJ/kmol K purchased equipment cost, $ temperature, K work, kJ/s heat, kJ/s molar fraction exergy ratio, %

Greek letters b power to heat ratio c constant for polytropic state  k fuel-air ratio f ratio of cold gas inlet to hot gas inlet
effectiveness g energetic efficiency e exergetic efficiency 1 carbon dioxide emission rate s annual operation time, h x heat exchanger effectiveness

CH M T p PH

chemical exergy mechanical component of physical exergy thermal component of physical exergy product physical exergy

Subscripts 0 dead state a air abs absolute C compressor CL combustion loss CC combustion chamber D destruction GT gas turbine gen generated HE heat exchanger f fuel L loss mec; st mechanical for Stirling engine O&M operation and maintenance p product pcy polytropic REC recuperator ref reference state tab tabular source th thermal energy Abbreviations CHE Cold Heat Exchanger HHE Hot Heat Exchanger LNG Liquefied Natural Gas MCHP Micro Combined Heat and Power NIST National Institute of Standards and Technology ORC Organic Rankine Cycle US United States PCM Phase Change Material TES Thermal Energy Storage

Superscripts a air

countries due to its high operation costs which corresponds 15– 25% of the total LNG trade cost. To decrease operation costs and increase thermal efficiencies of the LNG regasification processes, LNG cold utilization systems have been used for many years. LNG cold utilization is a way to use the LNG cryogenic energy in some facilities such as power generation [4–6], separation technology [7], carbon dioxide (CO2 ) capture [8], waste treatment [9], food storage [10], and desalination [11]. LNG cold utilization systems have been widely used in power generation sector from past to present. In Japan, there are 14 LNG cryogenic power plants which have been operated according to Rankine and/or direct expansion cycle principles [1,12]. Besides these principles, Brayton cycles were designed in many studies for LNG cold utilization purposes. Basic theoretical background and some of the crucial studies of the Rankine, Brayton and direct expansion based LNG cold utilization systems were presented in the review of Gomez et al. [12]. Stirling engines were also proposed for LNG cold utilization studies by Oshima et al. [13], Dong et al. [14], and Szczygiel et al. [15]. All these cycles can be operated as single cycles in LNG cold utilization systems but it is also possible to integrate them into each other.

One of the pioneer combined cycle study for the LNG cold utilization was conducted by Angelino [16] in the second half of 1970s. Various combined cycle configurations were studied and four different inert organic gases were investigated as working fluids. In 1990s, Najjar and Zaamout [17], Wong [18], Chiesa [19] and Hisazumi et al. [20] contributed to LNG cold utilization studies by designing various combined cycles. Najjar and Zaamout [17] used propane in an organic Rankine cycle (ORC) and the ORC was combined with the Brayton and direct expansion cycles which could totally produce 2000 MW power. Freon was firstly used by Hisazumi et al. [20] in the combined LNG cold utilization systems that had 240 MW capacity. Shi and his colleagues performed various studies on the combined LNG cold utilization systems [21–23]. Two different novel designs were proposed. In the first novel cycle [21], a heat recovery steam generator combined with Brayton and steam cycles. In addition, the LNG direct expansion cycle was also combined with those two cycles. Parametric studies were conducted by using various inlet and outlet temperatures of the direct expansion turbine, inlet temperature of the gas turbine and condenser pressure of the steam cycle. In the second novel design [23], application of inlet air cooling and intercooling processes

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increased the power output nearly by 15%. Gomez et al. [24,25] presented two combined cycles which consist of direct expansion, Brayton and steam cycles with an heat recovery steam generator that was used to produce thermal energy. Helium was selected as the working fluid and a higher thermal efficiency was obtained at the lower pressure ratio owing to regenerator performance in their first study [24]. Nitrogen and carbon dioxide (N2 —CO2 ) were operated as the working mediums in addition to the helium in their second study [25] and it was concluded that the proposed design has higher thermal efficiency when it is operated with helium-carbon dioxide (He—CO2 ) working medium instead of nitrogen-carbon dioxide (N2 —CO2 ). Tomkow and Cholewinski [26] compared four different cycle configurations which were Brayton cycle, absorption cycle, ORC and combined absorption/ ORC cycles, respectively. For the working mediums, Krypton and propane were used. Results showed that the highest generated power and efficiency values belong to the combined cycle. All the combined cycles which are mentioned briefly above were designed for large scale LNG regasification processes. However, thanks to technological developments in the regasification processes, small scale LNG regasification applications are also possible. International Gas Union [27] stated that the small scale LNG regasification systems has better environmental, economic and geopolitical aspects when they are compared to the large scale systems. Many countries such as China, Indonesia and Japan from Asia region, Turkey and Russia from Eurasia region, Portugal, Spain and Norway from Europe region have started to construct/operate small scale LNG regasification units according to the same report. Although these improvements in the small scale LNG regasification systems, there are very few investigations on the LNG cold utilization systems for the small scale LNG regasification systems. Small scale systems are especially crucial for the inland and stranded areas where LNG is the only feasible transportation method [1]. To increase the thermodynamic efficiency and the environmental performance of the LNG cold utilization systems in the small scale regasification processes, we presented a new combined cycle in this study. The combined cycle includes a micro gas turbine cogeneration system and a Stirling engine as power generation devices. Besides, phase change materials (PCMs) are also used as a thermal energy storage (TES) device to operate the hot heat exchanger of the Stirling engine by using the waste heat of the micro gas turbine system. A LNG pump and a LNG vaporizer are the components of the small scale regasification part. Nitrogen is used as a working medium between the LNG vaporizer and the cold heat exchanger of the Stirling engine. Proposed cycle is new and it has an original exergy-cost matrix, inherently. Thermodynamic, environmental and thermoeconomic analyses are performed for the combined cycle and results are compared with the natural gas fuelled micro-cogeneration system. Energetic efficiency, exergetic efficiency, power to heat ratio, exergy destruction ratio, power rate of the Stirling engine and power rate of the combined cycle are the observed parameters from the point of thermodynamics. Besides, CO2 emission rate and the achieved emission reduction are also investigated as parts of the environmental analyses. In thermoeconomic part, unit costs of the fuel and the product are calculated by using the exergy-cost matrix. In addition, destruction costs are analyzed with levelized component costs. The levelized product cost, which is a critical parameter for thermoeconomic assessment, is analyzed and compared to the conventional micro-cogeneration system. The relative unit fuel cost is also investigated according to operation parameters which their ranges are between 288.15–313.15 K and 3–4 for the ambient air temperature parameter and the compressor pressure ratio parameter, respectively. In this way, a simple graphic based optimization study is performed that is based on the minimization of relative cost difference of the generated electricity in the combined system.

3

2. System descriptions The natural gas fuelled conventional micro-cogeneration system and the proposed combined system are shown in Fig. 1a and b, respectively. The conventional micro-cogeneration system consists of a microturbine, a compressor, a combustion chamber, a recuperator, and a heat exchanger, respectively. In this study, the system is called as a single system. The proposed combined cycle includes the micro gas turbine cogeneration system and the Stirling engine which are combined with the LNG cold utilization system as shown in Fig. 1b. In the combined cycle, LNG cold utilization components are integrated into the micro-cogeneration system. The LNG pump and the LNG vaporizer are the main parts of the LNG cold utilization system. The operation of the combined system starts from the LNG tank which stores LNG at the atmospheric conditions [1] (162 °C, 1 atm). LNG (stream 1) is firstly pumped by the LNG pump and then it (stream 2) is vaporized in the LNG vaporizer before entering the combustion chamber of the micro gas turbine cogeneration system (stream 3). During the LNG vaporization process, the required thermal energy is received by nitrogen gas (stream 16) which is a working medium between the LNG vaporizer and the cold heat exchanger of the Stirling engine. The vaporized natural gas (stream 3) is burnt with the compressed air (stream 6) in the combustion chamber and produced combustion gas (stream 7) is sent to the gas turbine to generate power. Exhausted gas of the micro gas turbine system (stream 9) firstly enters to the PCMs and then it enters to the heat exchanger for thermal energy production (stream 10). Melting temperature of the PCMs (T PCM ) is 493.15 K and outlet temperature of the PCMs is assumed constant as 498.15 K (stream 10) which means there is a 5 K temperature difference between melting temperature of the PCMs and the outlet temperature. Due to the this assumption, thermal energy production behaviors of the single system and the combined system are different. That is to say, the outlet temperature of the recuperator (stream 9) is equal to the inlet temperature of the heat exchanger so that the inlet temperature of the heat

Fig. 1. Schematic of the single (a) and combined (b) micro-cogeneration systems.

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exchanger is varied according to operation parameters such as various ambient air temperatures and compressor pressure ratios in the single system in Fig. 1a. For the combined system, the inlet temperature of the heat exchanger is equal to the outlet temperature of the PCMs (stream 10) as it is mentioned above which means the operation parameters do not have any impact on the inlet temperature of the heat exchanger as shown in Fig. 1b. With reference to case studies of the Capstone C30 micro gas turbine cogeneration system [28,29], the thermal production capacity of the heat exchanger is assumed as 50 kW at 298.15 K. In both systems, the micro gas turbine system is considered as the Capstone C30 microturbine system which has 3.64 compressor pressure ratio in the real life engineering applications [30,31]. The stored energy in the PCMs is equal to energy rate difference between stream 9 and stream 10 in the combined system. This stored energy is directly sent to the hot heat exchanger of the Stirling engine by using XCELTHERM MK1 heat transfer fluid [32]. Use of the heat transfer fluid is preferred owing to its high calorific thermal properties which can be seen from the Refs. [33,34]. Thus, temperature difference between stream 12 and 13 is small and it provides a higher mean wall temperature in the hot heat exchanger of the Stirling engine which is a crucial parameter for the numerical [35–37] and experimental studies of the Stirling engines [38–43]. In the Stirling engine modeling, the Pseudo Stirling engine calculations [44] are used in the study. Temperature of the vaporized natural gas is 298.15 K and it is constant in all parametric studies. Also, the outlet of the LNG vaporizer (stream 3) does not include any multiphase flows that means natural gas is 100% gas and it is assumed 100% methane. Lastly, city water (stream 14) enters to the heat exchanger at constant 298.15 K and outlet of the heat exchanger (stream 15) is hot water. That is to say, hot water production is occurred instead of steam generation in both systems.

kCH4 þ ½xa þ xa þ xa þ xa  N2 O2 CO2 H2 O ! ½1 þ k½xpN2 þ xpO2 þ xpCO2 þ xpH2 O 

ð1Þ

where xa and xp are molar fractions of the chemical components in the air and the combustion products respectively, and  k is the fuel air ratio of both systems. More details for the combustion case can be found in the work of Bejan et al. [45]. To investigate the thermoeconomic and thermodynamic feasibility of the combined system, parametric studies are conducted. Ambient air temperature and compressor pressure ratio are two main parameters to analyze the performance of combined system in different operating conditions. Parametric studies are performed in ranges between 288.15–313.15 K and 3–4 for the ambient air temperature and the compressor pressure ratio, respectively. Moreover, relative humidity of the air is assumed constant at 60%. Both cycles are not ideal cycles so that the isentropic efficiency values of the compression and expansion devices are required. The other assumptions which are required for the thermodynamic modeling are given in Table 2. The assumptions for the micro gas turbine and the Stirling engine are received from the manufacturer data of microturbine [31] and Rokni et al. [46], respectively. The first and second law calculations are used in the thermodynamic modelings of both systems. Specific enthalpy values of the streams are used to investigate the first law performances of micro-cogeneration systems while additional specific entropy calculations are required to observe the second law performances. Eqs. (2) and (3) define the specific enthalpy and entropy, respectively [45,47].

 pÞ ¼ h  þ ½hðT;  pÞ þ hðT  hðT; f ref ; pref Þ tab sðT; pÞ ¼ sabs ðT; pref Þ  R ln

ð2Þ

p pref

ð3Þ

 pÞ and sðT; pÞ are the specific enthalpy and the specific where hðT;  entropy values of the substance in Eqs. (2) and (3) respectively, h f and sabs ðT; pref Þ show the enthalpy of formation and the absolute  pÞ is the enthalpy of substance with refentropy respectively, hðT;

3. Modeling 3.1. Thermodynamic modeling

tab

To find the molar flow rate of the required fuel (n_ f ) and air (n_ a ), respectively, the molar flow rate of the product gas (n_ p ) can be cal_ p ) which can culated by using the mass flow rate of product gas (m be read from technical datasheet of the Capstone C30 model [30]. _ p ) and Difference between mass flow rates of the product gas (m _ f ) denotes the mass flow rate of the air (m _ a ) and then the fuel (m molar flow rate of the air (n_ a ) can be calculated by using molar fractions of the chemical contents in the ambient air. In calculations, all gases are assumed as ideal gases and the chemical contents of the air are assumed nitrogen, oxygen, carbon dioxide, and water vapor [45], respectively. Similar to the ambient air, chemical contents of the product gas can also be calculated by the same way. The relationship between the chemical contents of the air and the product gas can be seen in the combustion equation that is occurred in the combustion chamber as shown in Eq. (1). Molar fractions of the chemical contents in the ambient air and the product gas are given in Table 1.

 erence to related temperature and pressure whereas hðT ref ; pref Þ states the enthalpy of substance at the reference temperature and the reference pressure, and R denotes the universal gas constant in Eq. (3). All properties can be read from thermodynamic tables. In this study, the specific enthalpy and entropy values of methane, nitrogen, and oxygen are drawn from Setzmann and Wagner [48], Span et al. [49], and Schmidt and Wagner [50], respectively. For CO2 and H2 O, the data are received from Cengel and Boles [47]. All the absolute entropy values are read from the NIST-JANAF thermochemical tables [51]. By using these properties, the specific enthalpy and entropy values can be calculated. LNG and vaporized natural gas are assumed 100% methane (CH4 ) which means only methane properties are used in thermodynamic calculations of the LNG and vaporized natural gas. For the air and the product gas, specific enthalpies of the chemical contents are multiplied by their corresponding molar fractions and summation of these multiplications is equal to the specific enthalpy of gas mixture. Similarly,

Table 1 Molar fractions of chemical compounds in the air (xa ) and combustion products (xp ). Temperature (K)

288.15 298.15 303.15 308.15 313.15

N2

O2

CO2

H2 O

Ambient air

Product gas

Ambient air

Product gas

Ambient air

Product gas

Ambient air

Product gas

0.78278 0.77366 0.76910 0.76454 0.75998

0.78278 0.77366 0.76910 0.76454 0.75998

0.20802 0.20560 0.20438 0.20317 0.20196

0.17938 0.17768 0.17700 0.17644 0.17600

0.000303 0.000300 0.000298 0.000296 0.000294

0.014623 0.014256 0.013988 0.013662 0.013273

0.00890 0.02045 0.02622 0.03199 0.03777

0.03754 0.04836 0.05360 0.05873 0.06373

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Parameter

Value

Isentropic efficiency of the LNG pump Isentropic efficiency of the compressor Isentropic efficiency of the turbine

75% 79% [31] 84.3% [31] 92% [31] 96% [31] 5% 1.667 [46] 1.44 [46] 98% [46] 5K

due to fact that they do not have any heat losses to the environment. In addition, the exergy rate of the exhausted gases from the system to the atmosphere are assumed as exergy losses. That is to say, the exergy values of streams 10 and 11 are assumed as exergy losses in the single system and the combined system, respectively. The total exergy losses for the single system and the combined system are the summation of the exergy loss from the combustion chamber and the exergy rate of exhausted gas. The total heat input rate is significant parameter to calculate the energetic and exergetic performances. The fuel is burnt with the compressed air and the chemical reaction is occurred in the combustion chamber. This process is called as combustion and the total heat input rate can be calculated in the combustion chamber as shown in Eq. (9),

10 K

Q_ in ¼ n_ f  LHV NG  ð1  LÞ

Table 2 Assumptions for the thermodynamic modeling.

Maximum limit for the recuperator effectiveness Isentropic efficiency of the generator Pressure drop (for all the system subunits) Constant value for the polytropic efficiency calculations of the Stirling Engine Reversibility factor Heat exchanger effectiveness of the Stirling Engine Temperature difference in the heat exchangers Temperature difference in the LNG vaporizer

specific entropy of gas mixtures can be calculated by the same way that means the specific entropy data is used instead of specific enthalpy data. Calculations of the specific enthalpy and entropy values of the gas mixtures were shown in detailed in the Ref. [45]. In the calculations, the specific enthalpy and entropy data of the ambi a ; sa ; h p , and sp , ent air and the product gas are denoted as h respectively. Energy rate of the stream is equal to enthalpy rate of the stream which can be obtained by the multiplication of the specific enthalpy with the molar flow rate with respect to the first law of thermodynamics. The exergy rate consists of irreversibilities and it is calculated by the product of the specific exergy value and the molar flow rate. Energy and exergy rates are shown as H_ and _ respectively. Specific exergy calculation is based on the second E, law of thermodynamics and it is divided into two parts as physical exergy and chemical exergy [45]. The physical and chemical exergy definitions are shown in Eqs. (4) and (5), respectively,

eCH ¼

X

xk eCH k þ RT 0

X

xk ln xk

 pÞ  hðT  0 ; p Þ  T 0 ½sðT; pÞ  sðT 0 ; p Þ ePH ¼ hðT; 0 0

ð4Þ ð5Þ

where eCH and ePH are the specific chemical and physical exergy respectively, and xk denotes the molar fraction of the chemical compound in gas mixture (air or product gas) in Eq. (4), and T 0 shows the dead state temperature that is equal to the ambient air temperature. Due to phase change of the natural gas from its cryogenic form to gaseous form, it is also required to calculate thermal and mechanical (pressure) components of the specific physical exergy which are shown in Eqs. (6) and (7),

 pÞ  hðT  0 ; pÞ  T 0 ½sðT; pÞ  sðT 0 ; pÞ eT ¼ hðT;

ð6Þ

eM ¼ ePH  eT

ð7Þ

where eT and eM are thermal and mechanical components of the specific physical exergy respectively. More details about the thermal and mechanical components of the physical exergy can be found in the studies of Morosuk and Tsatsaronis [52–54]. To calculate the exergetic performance of any thermal subsystem, it is required to know the exergetic balance equations which include the fuel, product, loss, and destruction exergy terms as denoted in Eq. (8),

E_ F ¼ E_ P þ E_ D þ E_ L

ð8Þ

where E_ L ; E_ D ; E_ F and E_ P show the loss, destruction, fuel, and product exergy terms respectively. In the mentioned systems, the combustion chamber is the only component that has heat loss which means exergy losses for the other components are assumed as zero

ð9Þ

where n_ f and LHV NG are the molar flow rate and the lower heating value of natural gas respectively, and the heat loss ratio is shown with L and it is related to the combustion efficiency [45]. To analyze the energetic performance of the thermal system, the energetic efficiency definition is used, denoted as g. The energetic efficiency is also known as the thermal efficiency or the first law efficiency. Ratio of the net obtained energy to the input fuel energy figures energetic efficiency of the cogeneration systems and the energetic efficiency for the single system and the combined system are shown in Eqs. (10) and (11), respectively,

gsingle ¼

  _ C þ Q_ HE _ T W W single

gcombined ¼

ð10Þ

Q_ in   _ T þW _ ST  W _ LNGPump  W _ C þ Q_ HE W combined Q_ in

ð11Þ

_ T and W _ C are gas work rates of the turbine/generator couwhere W ple and the compressor which belong to the micro gas turbine part of the LNG cold utilized systems. To pressurize the LNG from dead state to the stream 2, the LNG pump work is required and it is _ LNGPump . In the combined system, the Stirling engine denoted as W _ gen ) is equal _ ST . The net generated work (W work is shown with W to result of the parentheses that is in the numerator part of both equations. The generated thermal energy rates from the heat exchanger are shown as Q_ HE and Q_ HE for the single system single

combined

and the combined system, respectively. It is important to remind that, Q_ HEsingle and Q_ HEcombined will have different trends due to reason that is mentioned in Section 2 in detailed. To measure the feasibility of the second law analysis, exergetic efficiency (e) is defined that is equal to ratio of the product exergy to the fuel exergy. By using Eq. (8), exergy efficiency definitions can also be written as shown in Eqs. (12) and (13) for the single system and the combined system, respectively,

esingle ¼ 1 

E_ Dsingle þ E_ Lsingle E_ F

ecombined ¼ 1 

E_ Dcombined þ E_ Lcombined E_ F

ð12Þ

ð13Þ

The combined system consists of the micro gas turbine system and the Stirling engine which can generate electricity. Energetic and exergetic calculations for the micro gas turbine system are the same for the single and combined systems. However, thermodynamic analyses of the Stirling engine are also required to investigate the Stirling engine performance for various operating conditions. In the combined system, the required thermal energy

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for the LNG vaporizer is calculated by the enthalpy rate difference between streams 2 and 3. This difference is also equal to the enthalpy rate difference between streams 16 and 17. That is to say, the required thermal energy rate can be shown in Eq. (14),

Q_ LNGVap ¼ H_ 3  H_ 2 ¼ H_ 16  H_ 17

ð14Þ

where Q_ LNGVap is the required thermal energy rate for the LNG vaporizer from nitrogen gas to natural gas, H_ 2 and H_ 3 are the

enthalpy rates of the streams 2 and 3 whereas H_ 16 and H_ 17 are the enthalpy rates of streams 16 and 17, respectively. In the combined system, Q_ LNGVap is equal to the thermal energy rate of the cold heat exchanger of the Stirling engine (Q_ CHE ) which means the required thermal energy rate of the LNG vaporizer is drawn from the cold heat exchanger of the Stirling engine. Furthermore, it is known from the system schematic in Fig. 1b, the required thermal energy rate of the hot heat exchanger (Q_ HHE ) is directly provided by the PCMs which are mentioned in Section 2 in detailed. Eq. (15) denotes the required thermal energy rate of the hot heat exchanger, briefly.

Q_ HHE ¼ Q_ PCM ¼ H_ 9  H_ 10

ð15Þ

where Q_ HHE and Q_ PCM show thermal energy rates of the hot heat exchanger of the Stirling engine and the PCMs, respectively; mechanical efficiency of the Stirling engine can be calculated by using Q_ CHE and Q_ HHE owing to definition in Rokni’s study [46] as it can be seen in Eq. (16),

Q_

gmec;st ¼ 1  _ CHE Q HHE

ð16Þ

where gmec;st is the mechanical efficiency of the Stirling engine. Generated work rate of the Stirling engine is related to the difference between Q_ HHE and Q_ CHE . However, the polytropic efficiency is also crucial to calculate the generated work. Eq. (17) presents the generated work formula from the Stirling engine [46].

  _ _ _ ST ¼ g W pcy Q HHE  Q CHE

ð17Þ

where gpcy is the polytropic efficiency of the Stirling engine. The polytropic efficiency definition of the Stirling engine is drawn by Rokni [46] that is originally published by Reader [44]. The definition is shown in Eq. (18),

gpcy

   3 2  1  RV 1c  f RV c1  1 5  ¼ 4 1  RV 1c þ ð1  fÞð1  xST Þ

exchanger effectiveness of the Stirling engine, f is the ratio of the cold gas inlet to hot gas inlet which is equal to proportion of the stream 17 to the stream 13 in this study. Besides the mechanical efficiency, it is also required to calculate the exergetic efficiency of the Stirling engine from the point of second law and thermoeconomic analyses. Generated work from the Stirling engine is product of the exergetic balance equation while difference between the hot and cold heat exchanger exergy rates is the fuel of the balance equation. Energetic and exergetic balance equations for the system components which are used in the single and combined systems are shown in Table 3. Exergetic efficiency of the Stirling engine is defined in Eq. (19),

"

#

E_

eST ¼ 1  _ DST _ EHHE  ECHE

ð19Þ

where eST is the exergetic efficiency of the Stirling engine. In addition, E_ DST denotes the exergy destruction of the Stirling engine. E_ HHE and E_ CHE are exergy rates of the hot and cold heat exchangers which are shown in Eqs. (20) and (21), respectively,

" # T0 E_ HHE ¼ 1  T þT  Q_ HHE 13 12

ð20Þ

2

" # T0 E_ CHE ¼ 1  T þT  Q_ CHE 16

ð21Þ

17

2

Eqs. (20) and (21) show that temperatures of the inlet and outlet streams have important effect to calculate the exergetic efficiency. In the cold and hot heat exchangers, the heat transfer is assumed linear from the hot fluid to the cold fluid so that the average temperature is found by the calculation of arithmetic mean of the inlet and outlet streams. In thermodynamic analyses of the cogeneration systems, power to heat ratio is also crucial parameter to see the rate of the generated electricity to the thermal energy. As mentioned in the calculations, generated Stirling engine work rate depends on the thermal energy rates of the hot and cold heat exchanger which means generated work from the Stirling engine will have different values under various operating conditions. Power to heat ratio is defined for both cycles in Eqs. (22) and (23), respectively; to see the impact of the Stirling engine work on the overall generated work.

bsingle ¼

_ gen W single Q_ HE

ð22Þ

single

ð18Þ

where RV is the reversibility factor of the Stirling engine, c is the constant for the polytropic state calculations, xST is the heat

bcombined ¼

_ gen W combined Q_ HE

ð23Þ

combined

Table 3 Energetic and exergetic balance equations for the system components of the proposed combined system. System components

Energy balance

Fuel exergy balance

Product exergy balance

LNG Pump

_ ðLNGPumpÞ ¼ H_ 2  H_ 1 W Q_ ðLNGVapÞ ¼ H_ 3  H_ 2 ¼ H_ 10  H_ 11 La H_ 3 þ H_ 6 ¼ H_ 7 þ Q_

_ ðLNGPumpÞ þ ðE_ T  E_ T Þ W 1 2 _M _M _M ðE_ T10 þ E_ T2 Þ þ ðE_ M 10  E11 Þ þ ðE2  E3 Þ _E3

_M E_ M 2  E1 E_ T þ E_ T

Q_ HE ¼ H_ 10  H_ 11 ¼ H_ 15  H_ 14   _ _ _ ST ¼ g W pcy Q HHE  Q CHE

E_ 10  E_ 11 E_ HHE  E_ CHE

Q_ PCM ¼ H_ 8  H_ 9

E_ 8  E_ 9

LNG Vaporizer Combustion Chamber Compressor Recuperator Gas Turbine Heat Exchanger Stirling Engine PCM a

comb

_ C þ H_ 4 H_ 5 ¼ W H_ 5 þ H_ 8 ¼ H_ 6 þ H_ 9 _ GT ¼ H_ 7  H_ 8 W

_ C W E_ 8  E_ 9 E_ 7  E_ 8

3

11

E_ 7  E_ 6 E_ 5  E_ 4 E_ 6  E_ 5

_ GT W E_ 15  E_ 14 _ ST W   _EPCM ¼ 1  T 0 Q_ PCM T PCM

L denotes the heat loss ratio from the combustion chamber to the atmosphere.

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3.2. Environmental modeling Environmental modeling is performed to see the emission difference between the single and combined LNG cold utilized systems. CO2 emission rates for both cycles are calculated and the difference between both CO2 emission rates are called as emission reduction rate. In the calculations, CO2 is considered single pollutant in the gas mixture which means there is no NOx and SOx emissions to the atmosphere as it can be seen from Table 1. The CO2 emission rate and emission reduction calculations are shown in Eqs. (24)–(26) respectively. Emission reduction calculation is based on the study of Arsalis and Alexandrou [55].

1single ¼

xpCO2 n_ p MCO2 _ gen W

ð24Þ

single

xp n_ p MCO2

2 1combined ¼ CO _ gen W

ð25Þ

combined

ER ¼

1

1combined 1single

! ð26Þ

where 1single and 1combined are the CO2 emission rates for the single and combined systems, respectively, MCO2 is the molar mass of carbon dioxide which is 44.01 kg/kmol [47], and ER denotes the emission reduction as a result of comparison between the single system and the combined system. In this study, CO2 emission rates are calculated with respect to the net generated electricity from the systems as it can be seen in Eqs. (24) and (25). However, it is also possible to add the thermal energy production rate (Q_ HE ) to the denominator in the formulas. 3.3. Thermoeconomic modeling To see the impact of the economic and thermodynamic parameters on thermal systems, thermoeconomic studies are conducted. Cost of the products is one of the significant decision criteria in thermoeconomics. Cost of the product is also known as the levelized product cost. Due to fact that thermoeconomics includes both economic and thermodynamic aspects, the levelized product cost is occurred by two components: the levelized fuel cost and the levelized components costs. General thermoeconomic equation to calculate the levelized product cost is shown in Eq. (27) [45],

C_P ¼ C_F þ Z_k

ð27Þ

where C_P and C_F are the levelized product and fuel costs respectively, and Z_k denotes the levelized component cost. This equation can be written individually for each subunits of the overall system whereas it is also possible to write this equation for the overall sys-

Table 4 Assumptions for the thermoeconomic modeling. Parameter

Value

System lifetime Interest rate PEC of the microturbine PEC of the LNG pump PEC of the LNG vaporizer PEC of the Stirling engine PEC of the PCM Operation and Maintenance Cost Annual operation time NG cost

20 years 1.8% 1130 $/kW 700 $/kW 2000 $ 2200 $/kW [46] 3600 $ 1:092  PEC [56] 8000 h

LNG cost

6:98175  106 $/kJ [61]

6:49524  106 $/kJ [60]

tem. The Z_ term focuses on the economic aspect of the thermal systems which includes equipment costs, interest rates, system life time, etc. as it can be seen Eq. (28) [56],

ðCRF  C O&M Þ  PEC Z_k ¼

ð28Þ

s

where PEC is the purchased equipment cost of the components, and CRF is Capital Recovery Factor whereas operation and maintenance cost is denoted by C O&M ; s is annual operation time. Table 4 presents the values of these parameters for thermoeconomic calculations. More details on the calculations about the CRF and the other economic aspects were stated by Bejan et al. [45]. The levelized fuel cost is related to the fuel exergy rates of component. It is obtained by the multiplication of the unit fuel cost and the fuel exergy rate for each system component as presented in Eq. (29) [45],

C_ k ¼ cE_ k

ð29Þ

where c; C_ k and E_ k figures the unit cost, levelized cost and total exergy of stream, respectively. Thermoeconomic calculations of system components or overall system are based on this equation. To find the levelized costs, the unit cost calculation is required for each stream. Unit costs are found by using exergy-cost matrix. Each original cycle has its own exergy-cost matrix which means there is no common exergy-cost matrix structure for thermal systems. The exergy-cost matrix of the conventional micro-cogeneration system is well known exergy cost matrix and it was generated in many studies before [45,56–59]. The exergy-cost matrix of the single system is shown in Eq. (30),

2 _ E5 6 _ 6 E5 6 6 6 0 6 6 6 0 6 4 0 2

0 _E6 E_ 6 0 0



0



_C W

0

3

7 0 0 7 7 7 E_ 7 0 0 7 7     7 _C _ T þW W 0 7 E_ 8  E_ 7 7 5   _ _E10  E_ 9 0 E12 3 E_ 9  E_ 8

Z_ C 7 6 Z_ REC 7 6  7 6 6 Z_ þ c E_ 7 ¼ 6 CC NG 3 7 7 6 7 6 5 4 Z_ GT Z_ HE

2 3 x 6 7 6y7 6 7 6z7 6 7 6 7 4t5 k

ð30Þ

where x; y; z; t, and k are the unit costs of the streams in the single system. The unit cost of the ambient air (c4 ) and the unit cost of the water inlet (c11 ) are equal to zero. The unit cost of the compressed air (stream 5) is pointed out with x whereas y denotes unit cost of the stream 6. Unit costs of the streams 7, 8, 9, and 10 are equal to each other and they are presented as z. Unit cost of the generated electricity is shown with t which means streams 13 and 14 have the same unit costs. The water outlet of the heat exchanger (stream 12) is denoted by k. Unit cost of the stream 3 is equal to the natural gas price (6:49524  106 $/kJ) which is received from the U.S. Energy Information Administration [60]. The levelized component costs of the gas turbine, combustion chamber, compressor, recuperator and heat exchanger are pointed out with Z_ GT , Z_ CC ; Z_ C ; Z_ REC , and Z_ HE , respectively. More details on the exergy-cost matrix of the single system can be found in Bejan et al. [45]. For the combined system, an original exergy-cost matrix must be produced due to fact that the proposed cycle combines the Stirling engine and the micro gas turbine together which have not been studied before in the LNG cold energy applications from the point of thermoeconomics. The new exergy-cost matrix for the combined cycle is presented in Eq. (31),

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2

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E_ M E_ 2 2 E_ PH

0

0

0

0

0 

6 2    6 M 6 E_ 3 E_ 3 E_ M2 E_ 2 E_ T17 E_ 17 E_ T3 E_ 3 6 _ PH  _ PH 0 0 0 0 þ E2 E_ PH E_ PH 6 E3 17 3 6 6 E_ M E_ E_ T E_ 6 E_ 7  E_3PH3  E_3PH3 0 E_ 6 0 6 3 3 6 6 6 0 0 0 0 E_ 8  E_ 7 0 6 6 _5 0 0 0 0 0 E 6 6 _ _ _ _ 6 0 0 E5 E6 E9  E8 0 6 6 0 0 0 0 E_ 10  E_ 9 0 6 6 4 0 0 0 0 0 0 0 0 0 0 E_ 11  E_ 10 E_ 15

_ gen W _ W LNGPump _ gen þW _ W ST

0

0 

E_ M E_ 17 17  E_ 16 E_ PH





3 _ W _ W ST LNGPump _ gen þW _ W ST

0

17

0

0

0

_ T þW _C W _C W 0

0 0 0

0 0 0

0 0

E_ PCM _ECHE  E_ HHE

0 _ ST W

0

0

0

   2 3 E_ T2 E_ 2 _ 2 3 E  þ Z_ LNGPump c LNG 1 PH 7 x _ E 6 7 2 7 7   76 7 6 7 76 y 7 6 E_ T2 E_ 2 6 7 _ 76 7 6 c þ Z 7 LNG E_ PH LNGVap: 76 z 7 6 7 2 76 7 6 7 76 7 6 7 _ CC 76 t 7 6 Z 7 76 7 6 7 76 7 6 _ 7 Z GT 76 k 7¼6 7 76 7 6 7 _ 7 6m7 6 ZC 7 76 7 6 7 76 7 6 7 Z_ REC 76n7 6 7 76 7 6 7 _ PCM 74 a5 6 Z 7 7 6 7 7 4 5 Z_ ST 5 b _Z HE ð31Þ

where x; y; z; t; k; m; n; a, and y are the unknowns which denote the unit fuel costs of the streams in the combined system. To find the unknowns which figure the unit costs of the streams, it is required to use thermoeconomic balance equations [45] which are similar to the second law balance equations. Table 5 presents the thermoeconomic balance equations for the combined system. In the calculations, the system has some constant unit costs such as units costs of fuel (c1 ), ambient air (c4 ) and inlet water stream of heat exchanger (c14 ). Unit costs of the ambient air and the inlet water for the heat exchanger are assumed 0 $/kJ [45]. The combined system is LNG fuelled that means unit cost of stream 1 is equal to the unit cost of LNG which is 6:98175  106 $/kJ with reference to the U.S. Energy Information Administration data [61]. The other unit costs are calculated by using the exergy-cost matrix. In the thermoeconomic assessment, the levelized destruction and unit fuel costs are also investigated for each component. The unit fuel and levelized destruction costs can be calculated by the thermoeconomic balance equations. In addition to these evaluation parameters, relative cost difference and exergoeconomic factors are the other significant evaluation parameters and they are generally preferred in the optimization studies [45,56]. They are defined in Eqs. (32) and (33), respectively,

rk ¼

cP;k  cF;k cF;k

ð32Þ

fk ¼

Z_ k  Z_ k þ cF;k E_ D;k þ E_ L;k

ð33Þ

where r k and f k denote the relative cost difference and the exergoeconomic factor, respectively. The unit product cost (cP;k ) and the unit fuel cost (cF;k ) are used in the calculation of the relative cost difference. The relative cost difference is also used in the graphic based optimization study which is one of the purposes of this study. By calculating the relative cost difference between the maximum and minimum points for various operating parameters, optimum points are found. f k is the rate of the levelized component cost to the summation of levelized component and destruction costs as it can be understood from the definition in Eq. (33). The summation of levelized component and destruction costs are called as the summarized levelized cost in this study. Impact of the levelized destruction costs on the summarized levelized cost are analyzed by using exergoeconomic factor term. 4. Results and discussion 4.1. Thermodynamic analyses The first and second law analyses are conducted in the thermodynamic analyses. Fig. 2 represents the results of the energetic or the first law analysis. In Fig. 2a, the thermal efficiency trends are

Table 5 Thermoeconomic balance equations for the system components of the combined system. Component

Balance equations

Auxiliary equations

LNG Pump

C_ 1 þ C_ 21 þ Z_ LNGPump ¼ C_ 2

T cLNG ¼ c1 ¼ cT1 ¼ cM 1 ¼ c2

LNG Vaporizer

C_ 2 þ C_ 16 þ Z_ LNGVap: ¼ C_ 3 þ C_ 17

Combustion Chamber

C_ 3 þ C_ 6 þ Z_ CC ¼ C_ 7 C_ 7 þ Z_ GT ¼ C_ 8 þ C_ 18 þ C_ 19 C_ 4 þ C_ 18 þ Z_ C ¼ C_ 5 C_ 5 þ C_ 8 þ Z_ REC ¼ C_ 9 þ C_ 6

cM 2 ¼ x; c 21 ¼

Gas Turbine Compressor Recuperator Heat Exchanger PCM Stirling Engine System Product System Fuel System Destruction System Loss

C_ 10 þ C_ 14 þ Z_ HE ¼ C_ 11 þ C_ 15 C_ 9 þ Z_ PCM ¼ C_ 10 þ C_ PCM C_ HHE þ Z_ ST ¼ C_ CHE þ C_ 20 C_ P ¼ C_ F þ Z_ TOT

_ gen c20 W _ ST c19 W _ ST _ gen þW W

M c10 ¼ cT16 ¼ cM 16 ¼ c 17 T T ¼ x; c ¼ c ¼ y cM 3 3 17

¼a

c6 ¼ t; c7 ¼ k c18 ¼ c19 ¼ n; c8 ¼ k c4 ¼ 0; c5 ¼ z c8 ¼ c9 ¼ k c14 ¼ 0; c15 ¼ m c9 ¼ c10 ¼ k; cPCM ¼ c13 ¼ c12 ¼ a cHHE ¼ cCHE ¼ a; c20 ¼ b

C_ F ¼ cF E_ F C_ D ¼ cF E_ D C_ L ¼ cF E_ L

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9

and the combined system. For the combined system, the highest thermal efficiency is 77% at the lowest compressor ratio and the highest ambient air temperature. When the impact of the ambient air temperature on thermal efficiency is investigated, it is seen that higher temperatures have higher thermal efficiencies for the combined system. Fig. 2b shows the net generated work in the single and combined systems. At the pressure ratio 3, generated power of the both systems are very close to each other. For instance, the combined system has just 4% higher power rate than the single system at the pressure ratio 3 while the generated work of the combined system is 8.7% higher than the single system at the pressure ratio 4. These results point that the Stirling engine performance depends on the compressor pressure ratio. Both systems have decreasing power generation trends with respect to the ambient air temperature. At compressor pressure ratio of 3.64, net generated work is found 27.87 kW that is an average value between 288.15 K and 313.15 K. As mentioned in Section 3.1, power to heat ratio (b) is a significant criterion for cogeneration systems to measure how much energy are produced in the power generation and thermal energy generation parts. Power to heat ratio for the single system and the combined system are presented in Fig. 2c. It is seen that b is 0.53 and 0.58 for the single system and the combined system, respectively. Like in the thermal efficiency (Fig. 2a), different trends of the generated thermal energy from the heat exchanger for both cycles is one of the important reasons that are why the single system has higher b values at the low pressure ratios and ambient air temperatures. Another reason is the Stirling engine has low power generation rates at the low pressures. Exergetic analyses of the overall systems are investigated and shown in Fig. 3. Both systems show increasing trends by the rising of the pressure ratio while the ambient air temperature drops from the point of exergetic efficiency. At the compressor pressure ratio of 3.64, the exergetic efficiency is 26.3% for the combined system. That is, there is no significant difference between the single and combined system from the point of exergetic efficiency at the actual pressure ratio of the MCHP for real applications. At the pressure ratio of 4 that is the highest pressure ratio value in the concept of this study, the combined system has 1.64% less exergetic efficiency than the single system. When the low pressure ratios are investigated, for instance at pressure ratio of 3, the exergetic efficiency of the combined system is 26% greater than the single system. It suggests that exergetic efficiency of the both systems are close to each other at the actual pressure ratio and higher ratios.

Fig. 2. Energetic performance of the micro-cogeneration systems: thermal efficiency (a), net generated work (b) and power to heat ratio (c).

illustrated for the single system and the combined system, respectively. The combined system and the single system have opposite trends according to the pressure ratio which means the thermal efficiency of the combined system decreases by the rising of the compressor pressure ratio while energetic efficiency of the single system increases. At the compressor pressure ratio of 3.64, the combined cycle has roundly 1% higher thermal efficiency. Different trends of the produced thermal energy from the heat exchanger that were mentioned in detailed in Section 2 are the main reasons for opposite trends of the thermal efficiencies in the single system

Fig. 3. Exergetic efficiency of the micro-cogeneration systems.

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Performance of the Stirling engine has crucial impact on the overall system performance as shown in Figs. 2 and 3. Its thermodynamic performance is illustrated in Fig. 4 from the point of energetic and exergetic views. Fig. 4a represents the generated electricity rate of the Stirling engine in the various ambient air temperatures and pressure ratios. It is seen that the highest work rate is 2.95 kW at the highest pressure ratio of 4 and the ambient air temperature of 313.15 K while the lowest generated power rate is 0.33 kW at the lowest pressure ratio of 3 and the ambient air temperature of 288.15 K. Besides the pressure ratio, the ambient air temperature has also important effect on the power generation rate of the Stirling engine. At compressor pressure ratio 3.64, there is 0.58 kW generated power rate difference between 288.15 K and 313.15 K. The mean generated power is 2 kW at the pressure ratio of 3.64. In Fig. 4b, the exergetic and mechanical efficiency results are examined, and it is seen that the highest pressure ratio has the highest exergetic and mechanical efficiency values. As an average value between 288.15 K and 313.15 K, exergetic and mechanical efficiencies have 38.55% and 34.2% higher values at pressure ratio of 4 when they are compared to their values at pressure ratio of 3, respectively. At compressor pressure ratio of 3.64, the Stirling engine has 34.9% and 87% exergetic and mechanical efficiencies, respectively. Moreover, it is also important to know that the ambient air temperature parameter is a significant factor for both efficiency types. For instance, the exergetic efficiency increases by

Fig. 5. Environmental analyses of the micro-cogeneration systems: CO2 emission rate (a) and emission reduction (b).

21.2% whereas the mechanical efficiency rises by 6.4% from 288.15 K to 313.15 K. 4.2. Environmental analyses

Fig. 4. Thermodynamic performance of the Stirling engine: net generated work (a) and exertegic/mechanical efficiencies (b).

Environmental impacts are represented in Fig. 5. CO2 emission rate (1) is shown in Fig. 5a for the single and combined systems, respectively. When the results are investigated, it is seen that the combined system decreases 1 value by 4%, 7.3%, and 8% at the pressure ratios of 3, 3.64, and 4, respectively. Moreover, it can be said that the lowest pressure has the highest CO2 emission rate which means the 1 value at pressure ratio of 3 is averagely two times higher than the 1 value at pressure ratio of 4. The combined system has lower CO2 emission rates due to fact that the generated power is higher than the single system while the emitted CO2 is the same for both systems as it can be understood from Eqs. (24) and (25). The difference between the CO2 emission rates of the single and combined systems is called as emission reduction in Eq. (26) and the trend of emission reduction is shown in Fig. 5b with respect to the different air temperatures and pressure ratios. It is seen that the emission reduction has the highest value at the highest ambient air temperature and the highest pressure ratio value while the lowest emission reduction is at the lowest air temperature and the lowest pressure ratio. At the actual operation pressure ratio (3.64), the emission reduction is averagely 7.2%. Furthermore, emission reduction difference is by 3.2% between the lowest and the highest ambient air temperatures at the pressure ratio of 3.64.

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4.3. Thermoeconomic analyses The new combined system includes LNG cold utilization part so that the unit fuel costs of the micro gas turbine is not directly equal to the unit cost of LNG (cLNG ). Due to the thermoeconomic balance equations, the combined system has different unit fuel costs (c3 ) according to various operating parameters. The unit fuel cost affects the overall unit product cost and the levelized product cost, inherently. Fig. 6a illustrates the unit fuel cost trends for the combined system with respect to the various ambient air temperatures and pressure ratios. The unit fuel cost decreases by the rising of compressor pressure ratio and the lowest unit fuel costs are at different ambient air temperatures for different pressure ratios. These results show that the pressure ratio dramatically changes the unit fuel cost trends. The unit electricity cost of the LNG pump in the combined system (c21 ) is a combination of unit electricity cost of the micro gas turbine (c19 ) and the Stirling engine (c20 ) so that the unit fuel cost is affected by these two devices in the combined system. The minimum unit fuel costs are at 288.15 K, 298.15 K and 308.15 K for the pressure ratios of 4, 3.64, and 3, respectively. As mentioned above, the unit electricity cost of the LNG pump has significant impact on the unit fuel cost. Fig. 7 illustrates the unit electricity cost trends at the different ambient air temperatures and pressure ratios. In the combined system, the unit electricity cost of the LNG pump depends on both Stirling engine and micro gas turbine so that the unit electricity cost shows different

11

trends at different pressure ratios. For instance, the unit electricity cost of the LNG pump at pressure ratio of 3 is the lowest unit cost at 288.15 K while it is the highest unit cost at 313.15 K in the range of pressure ratios between 3 and 4. At the pressure ratio of 3.64, the mean unit cost is 78.3 $/GJ for the combined system. That means there is no exact relationship between the pressure ratio and the unit electricity cost of the LNG pump. The exergoeconomic factor (f) and the relative cost difference of the generated electricity of both systems are shown in Fig. 8a and b, respectively. It is deduced that the single system has higher f values than the combined system. However, it is also seen that the difference between the single system and the combined system decreases by the rising of the compressor pressure ratio. For instance, the exergoeconomic factor of the combined system is 18.17% lower than the exergoeconomic factor of the single system at the pressure ratio of 3 while it is 2.5% or 0.27% lower than the single system at the pressure ratios of 3.64 or 4. These trends can be seen in Fig. 8a. That is to say, the levelized cost of destructions and losses have more dominant impact in the combined system. It is also seen that the ambient air temperature values do not have significant impacts on the exergeconomic factor at the actual pressure ratio. The relative cost difference of the generated electricity trends are presented with respect to ambient air temperature for various pressure ratios in Fig. 8b. Due to fact that the unit electricity cost is a combination of the Stirling engine and the micro gas turbine, the relative cost difference of the generated electricity has different trends in the combined system when it is compared to the single system. The highest relative product cost is at the pressure ratio of 3.64 for the combined system while the single system has the highest relative cost difference at the pressure ratio of 3. In all pressure ratios, the single system has higher relative cost difference. For example, the combined system has 65.83%, 38.87%, and 33.07% less relative cost differences than the single system at the pressure ratios of 3, 3.64, and 4, respectively. As it is known from the approach which was presented in Bejan et al. [45], less relative cost differences are more beneficial so that it is seen that the combined system provides less relative cost differences. These trends for the combined system are the main reasons of trends of the unit cost of the LNG pump that is mentioned in Fig. 7 with the detailed expressions. _ of both systems are shown in The levelized component costs (Z) Fig. 9a. The combined system increases the Z_ value by 34%, 20.4%, and 19.2% for the pressure ratios of 3, 3.64 and 4, respectively which means the increment of the levelized component cost differ-

Fig. 6. Unit fuel costs (c3 ) of the combined system.

Fig. 7. Unit electricity costs of the LNG pump.

Fig. 8. Exergoeconomic factor (a) and relative unit product cost difference of electricity (b) for both systems.

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(a)

i i g

i

g

h

g

e

f

f

e

d

f

f

d

c b

h

g

f

e d

c

d

c

b b

c a

a b c d e f g h i k

a

Fig. 10. Total levelized product costs of both systems.

(b)

h h f f c c

b

a a

g e e

b b b

a

a

a

a

a

a a

g

e

b b

a

g

b

a b c d e f g h i k

a

_ (a), summarized levelized costs (C_ D þ Z) _ (b) of Fig. 9. Component levelized costs (Z) both systems.

ence between the single system and the combined system is higher at compressor pressure ratio of 3. Moreover, Z_ value decreases by 13.2%. 16.6% and 10.99% for the combined system from 288.15 K to 313.15 K at pressure ratios of 3, 3.64, and 4, respectively. The summarized levelized costs are pointed out in Fig. 9b. When the results are investigated, it is deduced that the summarized levelized costs of the combined system are 93.3%, 59.6%, and 54.2% higher than the single system at pressure ratios of 3, 3.64, and 4, respectively. These results deduce that the levelized destruction cost significantly affects the summarized levelized cost. At the actual pressure ratio, the summarized levelized cost is 5.65 and 9.02 $/s for the single system and the combined system, respectively. The levelized product costs of the single and combined systems are presented in Fig. 10. The single system has roundly 43.64%, 26.3%, and 22.89% less levelized product costs than the combined system at pressure ratios of 3, 3.64, and 4, respectively, that means the difference between levelized product costs of the single and combined systems decreases by the rising of the compressor pressure ratio. The main reason is unit fuel costs of the microcogeneration systems. In the combined system, unit fuel costs are affected by the LNG cold utilization components as they are mentioned in Fig. 6. However, the unit fuel cost of the single system is always constant due to fact that the single system is the vaporized natural gas fuelled whereas the LNG vaporization is required for the combined system. Moreover, the levelized product cost drops by 22%, 11.98% and 11% for the combined system from

288.15 K to 313.15 K at the pressure ratios of 3, 3.64, and 4, respectively. The mean levelized costs at pressure ratio of 3.64 is 13.35 $/ s for the combined system. To find the best operation parameters, a simple graphic based optimization study is conducted in the determined ranges which are between 288.15–313.15 K and 3–4 for the ambient air temperature and pressure ratios, respectively. Relative cost difference of the unit product cost (electricity) is selected as the single objective of the study. It is investigated according to ðE_ D þ E_ L Þ=E_ P value which was used in the thermoeconomic optimization studies by Bejan et al. [45] before. The graphic based optimization is conducted for the combined system. The minimum relative cost difference of the unit product costs for all the ambient air temperatures is achieved at the lowest pressure ratio when only the gas turbine is investigated in the combined cycle in Fig. 11a. Furthermore, 313 K air temperature has the lowest unit product cost in the range of 288.15–313.15 K. It is deduced that the lowest pressure ratio and the highest ambient air temperature provide the minimum relative cost difference of the unit product cost for the gas turbine system in the combined cycle. Combination of the Stirling engine and gas turbine gives different unit product costs for the produced electricity so that the relative cost difference trends are dissimilar when they are compared to relative cost difference of the only gas turbine case. Fig. 11b represents the relative cost difference of generate power for combination of the Stirling engine and gas turbine in the combined system. When the results are investigated it is seen that the lowest relative cost differences are at the lowest pressure ratio of 3 for 288.15 K and 298.15 K ambient air temperature. For 303.15 K, 308.15 K and 313.15 K ambient air temperatures, the lowest relative cost differences are at the highest pressure ratio of 4. These results deduce that the minimum relative cost differences are at different ambient air temperatures and pressure ratios due to application of the Stirling engine. It is seen that the LNG fuelled combined system increased the power generation rate, thermal efficiency and environmental performance. However, thermoeconomic study includes opposite trends when the exergoeconomic factor, relative cost differences and the levelized costs are compared. These trends can be explained step by step. First of all, the combined system achieves less relative cost differences which will be more beneficial for the future optimization strategies. When the exergoeconomic factor is observed, it is seen that the combined system decreases the impacts of the levelized component costs on the thermoeconomic performance that means the external parameters such as the purchased equipment costs, and operation and maintenance costs.

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Fig. 11. Relative unit product cost difference of electricity generation in the gas turbine (a) and combined gas turbine/Stirling (b) power generation devices in the combined system.

have less effects on the thermoeconomic performance when the combined system is compared to the single (natural gas fuelled) system. Thanks to combined thermoeconomic and thermodynamic approaches, the possible improvable points are shown to decrease the exergy destruction that means the levelized destruction costs can be decreased by the thermodynamic improvements in the future studies. However, the levelized costs have opposite trends with the exergoeconomic factor and the relative cost differences. It is seen that the combined system has higher levelized costs than the single system. The contrasts show that the LNG cold utilization components significantly affect the levelized cost performance of the microturbine components. As a result of the discussion, the combined system can be proposed for the small scale LNG regasification applications. Moreover, thermoeconomic approach shows that the proposed combined cycle has still gaps to improve its thermodynamic and thermoeconomic performances. Thanks to thermoeconomic analyses, the thermoeconomic performances of the all streams and subunits are observed and the possible improvement methodologies are considered such as the detailed exergoenvironmental analyses which also add the environmental data in the matrix, or the multiobjective optimization strategies to obtain the best operation parameters. The discussed two systems have some uncertainties and limitations. First of all, the performed systems includes 30 kW microturbine model so that all the analyses are conducted according to related manufacturer data of the 30 kW microturbine model. There are also other LNG cold utilized combined system possibilities in the micro-cogeneration applications for 65, 200 kW, etc. power generation rates, and their thermodynamic, environmental and thermoeconomic approaches can show different trends during

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the comparison of the natural gas fuelled and LNG fuelled microcogeneration systems. The comparison between the various microturbine types can be conducted with respect to thermodynamics, thermoeconomics and environmental aspects as future study. Also, the combined system includes the Stirling engine which is operated between the LNG vaporizer and the TES device. The performance of the Stirling engine depends on these two subunits. In the real cases, the operation of Stirling engine has some uncertainties such as the mean temperature values in the hot and cold heat exchangers, the heat loss in the regenerative part of the Stirling engine, and effectiveness of the heat exchangers during the Stirling operation. These issues are not considered in the study and some proved assumptions [46] are carried out during the steady state simulations. However, the dynamic operation of the Stirling engine can affect thermoeconomic performance of the combined system, and it can be a possible future study of this combined system. Another uncertainty is about the LNG vaporizer. The vaporized natural gas is assumed in 100% gas phase that means there is no multiphase flow. However, in the real applications, the outlet stream (stream 3) can consists of multiphase flow so that additional processes are required to provide the single phase flow before entering the combustion chamber. Thus, it is also possible to investigate the additional processes in the combined system from the point of thermodynamics and thermoeconomics in the future studies when the outlet stream will be assumed as multiphase flow, because it is known that multiphase flow will also affect both the Stirling engine and microturbine components. Besides these uncertainties and limitations, it must be highlighted that the developed exergy-cost matrix for the proposed combined system is valid for all the power generation rates in the micro-cogeneration applications. Based on these uncertainties and limitations, some improvements can also be applied for the combined system. For instance, various PCMs with different melting temperatures can be simulated for the combined system and the outputs can be compared according to thermodynamic, environmental and thermoeconomic aspects. It is known that the mean temperature of the hot heat exchanger and the inlet temperature of the heat exchanger for hot water production are directly related to melting temperature of the PCMs. Therefore, thermodynamic outputs will show different results when various PCMs are performed. Moreover, it is known that the different PCMs have different unit costs so that the investigation of different PCMs will present different unit cost of the all system components.

5. Conclusions The new combined system was proposed for the LNG cold utilization in the small scale applications and the designed cycle was compared to the natural gas fuelled conventional microcogeneration system from the point of thermodynamics, environmental and thermoeconomic views. The Stirling engine was combined with the micro gas turbine for power generation whereas the heat exchanger was embedded to the system to produce hot water. Also, the PCMs were applied to the combined cycle as a TES device to achieve better thermal performance for the hot heat exchanger part of the Stirling engine. The parametric study was conducted in the ranges between 288.15–313.15 K and 3–4 for the ambient air temperature and the compressor pressure ratio, respectively. From the point of thermodynamics, the combined system produced nearly 7.8% more power than the single system at the actual pressure ratio of the micro gas turbine whereas the energetic and exergetic efficiency values were approximately 1% and 2.4% higher in the combined system, respectively. It was found that the Stirling engine performance was really low at low pressure ratios while it significantly affected the overall thermal perfor-

Please cite this article in press as: Kanbur BB et al. Thermoeconomic and environmental assessments of a combined cycle for the small scale LNG cold utilization. Appl Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.01.061

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mance of the combined cycle at the high pressure ratios. Environmental analyses showed that the combined system had a lower CO2 emission rate than the single system due to fact that it produced higher power rate while both systems had the same emitted CO2 to the atmosphere. Thus, the combined system provided 7.3% emission reduction as an average value between 288.15 K and 313.15 K. Thermoeconomic studies were mainly based on the unit fuel and product costs to determine the levelized product cost. At the actual pressure ratio, the single system had roundly 25% less levelized cost than the combined system. To find the best operation parameters for the combined system, a simple graphic based optimization study was also performed which was based on the relative cost difference of the generated electricity. It was found that the relative cost difference had their minimum points at different locations for various ambient air temperatures in the combined system. As a result, the combined system was proposed for the small scale LNG regasification plants thanks to its high thermal and environmental performance in the all ambient air temperature values. It is highlighted that combined system requires future studies to better understand the thermoeconomic behavior of the system under the difference LNG prices, and also future comparative studies are required between these two systems under the various natural gas and LNG prices. Furthermore, multiobjective optimization studies are required to find the best operation parameters for the combined system due to fact that thermodynamic, environmental and thermoeconomic analyses show different trends in the study. Also, environmental parameters can be enclosed in the thermoeconomic calculations by using the exergoenvironmental aspects. Furthermore, various working mediums can be operated between the LNG vaporizer and the cold heat exchanger of Stirling engine to obtain less levelized product costs for the LNG cold utilization part. Lastly, various PCMs can be operated in the combined system as TES devices with their reliable economic and thermal properties. Acknowledgments The work was funded under the Energy Innovation Research Programme (EIRP, Award No. NRF2013EWT-EIRP001-017), administrated by the Energy Market Authority (EMA). The EIRP is a competitive grant call initiative driven by the Energy Innovation Programme Office, and funded by the National Research Foundation (NRF), Singapore. In addition, we gratefully thank to Dr. Kai Wang, Dr. Lu Qiu, Dr. Chenzhen Ji and Mr. Zhen Qin for their helps on this original study. References [1] Mokhatab S, Mak JY, Valappil JV, Wood DA. Handbook of liquefied natural gas. Burlington (MA): Elsevier Science; 2013. http://dx.doi.org/10.1016/B9780-12-404585-9.00001-5. [2] Kumar S, Kwon HT, Choi KH, Lim W, Cho JH, Tak K, et al. LNG: an eco-friendly cryogenic fuel for sustainable development. Appl Energy 2011;88:4264–73. http://dx.doi.org/10.1016/j.apenergy.2011.06.035. [3] International Gas Union. World LNG report 2016; 2016. [4] Kaneko K, Ohtani K, Tsujikawa Y, Fujii S. Utilization of the cryogenic exergy of LNG by a mirror gas-turbine. Appl Energy 2004;79:355–69. http://dx.doi.org/ 10.1016/j.apenergy.2004.02.007. [5] Zhang G, Zheng J, Yang Y, Liu W. A novel LNG cryogenic energy utilization method for inlet air cooling to improve the performance of combined cycle. Appl Energy 2016;179:638–49. http://dx.doi.org/10.1016/j. apenergy.2016.07.035. [6] Querol E, Gonzalez-Regueral B, Garcia-Torrent J, Ramos A. Available power generation cycles to be coupled with the liquid natural gas (LNG) vaporization process in a Spanish LNG terminal. Appl Energy 2011;88:2382–90. http://dx. doi.org/10.1016/j.apenergy.2011.01.023. [7] Mehrpooya M, Kalhorzadeh M, Chahartaghi M. Investigation of novel integrated air separation processes, cold energy recovery of liquefied natural gas and carbon dioxide power cycle. J Clean Prod 2016;113:411–25. http://dx. doi.org/10.1016/j.jclepro.2015.12.058.

[8] Zhang N, Lior N. A novel near-zero CO2 emission thermal cycle with LNG cryogenic exergy utilization. Energy 2006;31:1666–79. http://dx.doi.org/ 10.1016/j.energy.2005.05.006. [9] Miyazaki T, Kang YT, Akisawa A, Kashiwagi T. A combined power cycle using refuse incineration and LNG cold energy. Energy 2000;25:639–55. http://dx. doi.org/10.1016/S0360-5442(00)00002-5. [10] Messineo A, Pann G. LNG cold energy use in agro-food industry:a case study in Sicily. J Nat Gas Sci Eng 2011;3:356–63. http://dx.doi.org/10.1016/j. jngse.2011.02.002. [11] Cravalho EG, McGrath JJ, Toscano WM. Thermodynamic analysis of the regasification of LNG for the desalination of sea water. Cyrogenics 1977;17:135–9. http://dx.doi.org/10.1016/0011-2275(77)90272-7. [12] Romero Gomez M, Ferreiro Garcia R, Romero Gomez J, Carbia Carril J. Review of thermal cycles exploiting the exergy of liquefied natural gas in the regasification process. Renew Sust Energy Rev 2014;38:781–95. http://dx. doi.org/10.1016/j.rser.2014.07.029. [13] Oshima K, Ishizaki Y, Kamiyama S, Akiyama M, Okuda M. The utilization of LH2 and LNG cold for generation of electric power by cryogenic type Stirling engine. Cryogenics 1978;18:617–20. http://dx.doi.org/10.1016/0011-2275(78) 90024-3. [14] Dong H, Zhao L, Zhang S, Wang A, Cai J. Using cryogenic exergy of liquefied natural gas for electricity production with the Stirling cycle. Energy 2013;63:10–8. http://dx.doi.org/10.1016/j.energy.2013.10.063. [15] Szczygiel I, Stanek W, Szargut J. Application of the stirling engine driven with cryogenic exergy of LNG (liquefied natural gas) for the production of electricity. Energy 2016;105:25–31. http://dx.doi.org/10.1016/j. energy.2015.08.112. [16] Angelino G. Use of liquid natural-gas as heat sink for power cycles. J Eng Power-T Asme 1978;100:169–77. http://dx.doi.org/10.1115/1.3446314. [17] Najjar YSH, Zaamout MS. Cryogenic power conversion with regasification of LNG in a gas-turbine plant. Energ Convers Manage 1993;34:273–80. http://dx. doi.org/10.1016/0196-8904(93)90111-M. [18] Wong W. Lng power recovery. P I Mech Eng A–J Pow 1994;208:3–12. http://dx. doi.org/10.1243/PIME_PROC_1994_208_003_02. [19] Chiesa P. LNG receiving terminal associated with gas cycle power plants. In: International gas turbine & aeroengine congress & exhibition. Orlando(FL); 1997 Jun 2–5. http://dx.doi.org/10.1115/97-GT-441. [20] Hisazumi Y, Yamasaki Y, Sugiyama S. Proposal for a high efficiency LNG powergeneration system utilizing waste heat from the combined cycle. Appl Energy 1998;60:169–82. http://dx.doi.org/10.1016/S0306-2619(98)00034-8. [21] Shi X, Agnew B, Che D. Analysis of a combined cycle power plant integrated with a liquid natural gas gasification and power generation system. P I Mech Eng A–J Pow 2010;1:1–11. http://dx.doi.org/10.1243/09576509JPE805. [22] Shi X, Che D. Thermodynamic analysis of an LNG fuelled combined cycle power plant with waste heat recovery and utilization system. Int J Energy Res 2007;31:975–98. http://dx.doi.org/10.1002/er.1293. [23] Shi X, Agnew B, Che D, Gao JM. Performance enhancement of conventional combined cycle power plant by inlet air cooling, inter-cooling and LNG cold energy utilization. Appl Therm Eng 2010;30:2003–10. http://dx.doi.org/ 10.1016/j.applthermaleng.2010.05.005. [24] Gomez MR, Garcia RF, Gomez JR, Carril JC. Thermodynamic analysis of a Brayton cycle and Rankine cycle arranged in series exploiting the cold exergy of LNG (liquefied natural gas). Energy 2014;66:927–37. http://dx.doi.org/ 10.1016/j.energy.2013.12.036. [25] Gomez MR, Garcia RF, Carril JC, Gomez JR. High efficiency power plant with liquefied natural gas cold energy utilization. J Energy Inst 2014;87:59–68. http://dx.doi.org/10.1016/j.joei.2014.02.007. [26] Tomkow L, Cholewinski M. Improvement of the LNG(liquid natural gas) regasification efficiency by utilizing the cold exergy with a coupled absorption-ORC(organic Rankine cycle). Energy 2015;87:645–53. http://dx. doi.org/10.1016/j.energy.2015.05.041. [27] Program Committee D3, International Gas Union. Small scale LNG-2012-2015 triennium work report. World Gas Conference, Paris; 2015. [28] Capstone Turbine Corporation. den Dulk Dairy case study; 2016. [accessed: 22.08.16]. [30] Capstone Turbine Corporation. Capstone model C30 technical reference; 2006. [31] Capstone Turbine Corporation. Advanced micro turbine system (AMTS). Final Report; 2008 March. Report No.:DE-FC26-00CH11058. [32] Radco Industries. XCELTHERMK MK1 heat transfer fluid safety data sheet; 2014. [33] The Dow Chemical Company. Dowtherm A heat transfer fluid: product technical data; 1997. [34] Moore RL. Implementation of DOWTHERM A properties into RELAP5-3D/ ATHENA. Idaho National Laboratory; 2010 April. Report No.: INL/EXT-1018651. [35] Wang K, Dubey S, Choo FH, Duan F. A transient one-dimensional numerical model for kinetic Stirling engine. Appl Energy 2016;183:775–90. http://dx.doi. org/10.1016/j.apenergy.2016.09.024. [36] Babaelahi M, Sayyaadi H. A new thermal model based on polytropic numerical simulation of Stirling engines. Appl Energy 2015;141:143–59. http://dx.doi. org/10.1016/j.apenergy.2014.12.033.

Please cite this article in press as: Kanbur BB et al. Thermoeconomic and environmental assessments of a combined cycle for the small scale LNG cold utilization. Appl Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.01.061

B.B. Kanbur et al. / Applied Energy xxx (2017) xxx–xxx [37] Valenti G, Silva P, Fergnani N, Campanari S, Ravida A, Di Marcoberardino G, et al. Experimental and numerical study of a micro-cogeneration Stirling unit under diverse conditions of the working fluid. Appl Energy 2015;160:920–9. http://dx.doi.org/10.1016/j.apenergy.2015.05.112. [38] Ni M, Shi B, Xiao G, Peng H, Sultan U, Wang S, et al. Improved simple analytical model and experimental study of a 100 W b-type stirling engine. Appl Energy 2016;169:768–87. http://dx.doi.org/10.1016/j.apenergy.2016.02.069. [39] Garcia D, Gonzalez MA, Prieto JI, Herrero S, Lopez S, Mesonero I, et al. Characterization of the power and efficiency of Stirling engine subsystems. Appl Energy 2014;121:51–63. http://dx.doi.org/10.1016/j. apenergy.2014.01.067. [40] Fenies G, Formosa F, Ramousse J, Badel A. Double acting Stirling engine: modeling, experiments and optimization. Appl Energy 2015;159:350–61. http://dx.doi.org/10.1016/j.apenergy.2015.08.128. [41] Cinar C, Yucesu S, Topgul T, Okur M. Beta-type Stirling engine operating at atmospheric pressure. Appl Energy 2005;81:351–7. http://dx.doi.org/10.1016/ j.apenergy.2004.08.004. [42] Karabulut H, Yucesu HS, Cinar C, Aksoy F. An experimental study on the development of a b-type Stirling engine for low and moderate temperature heat sources. Appl Energy 2009;86:68–73. http://dx.doi.org/10.1016/j. apenergy.2008.04.003. [43] Gheith R, Aloui F, Nasrallah SB. Determination of adequate regenerator for a Gamma-type Stirling engine. Appl Energy 2015;139:272–80. http://dx.doi.org/ 10.1016/j.apenergy.2014.11.011. [44] Reader GT. The pseudo stirling engine-a suitable performance criterion. In: Proceeding of 13th intersociety energy conversion engineering conference, vol. 3. San Diego, California; August 20–25, 1979. pp. 1763–70. [45] Bejan A, Tsatsaronis G, Moran MJ. Thermal design and optimization. NY: Wiley; 1996. [46] Rokni M. Thermodynamic and thermoeconomic analysis of a system with biomass gasification, solid oxide fuel cell (SOFC) and stirling engine. Energy 2014;76:19–31. http://dx.doi.org/10.1016/j.energy.2014.01.106. [47] Cengel YA, Boles MA. Thermodynamics: an engineering approach. 5th ed. Boston (MA): McGraw-Hill; 2006. [48] Setzmann U, Wagner W. A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 100 MPa. J Phys Chem Ref Data 1991;20:1061–155. http://dx. doi.org/10.1063/1.555898.

15

[49] Span R, Lemmon EW, Jacobsen RT, Wagner W, Yokozeki A. A reference equation of state for the thermodynamic properties of nitrogen for temperatures from 63.151 to 1000 K and pressures to 2200 MPa. J Phys Chem Ref Data 2000;29:1361–433. http://dx.doi.org/10.1063/1.1349047. [50] Schmidt R, Wagner W. A new form of the equation of state for pure substances and its application to oxygen. Fluid Phase Equilibr 1985;19:175–200. http:// dx.doi.org/10.1016/0378-3812(85)87016-3. [51] Chase MW. NIST-JANAF Thermochemical Tables. 4th ed. Monograph 9; 1998. [52] Morosuk T, Tsatsaronis G. Comparative evaluation of LNG – based cogeneration systems using advanced exergetic analysis. Energy 2011;36:3771–8. http://dx.doi.org/10.1016/j.energy.2010.07.035. [53] Morosuk T, Tsatsaronis G, Boyano A, Gantiva C. Advanced exergy-based analyses applied to a system including LNG regasification and electricity generation. Int J Energy Environ Eng 2012;3:1–9. http://dx.doi.org/10.1186/ 2251-6832-3-1. [54] Morosuk T, Tsatsaronis G. LNG-based cogeneration systems: evaluation using exergy-based analyses. In: Gupta SB, editor. Natural Gas – Extraction to End Use, EU: Intech; 2012. p. 235–66. http://dx.doi.org/10.5772/51477. [55] Arsalis A, Alexandrou A. Thermoeconomic modeling and exergy analysis of a decentralized liquefied natural gas-fueled combined-coolingheating-andpower plant. J Nat Gas Sci Eng 2014;21:209–20. http://dx.doi.org/10.1016/j. jngse.2014.08.009. [56] Tsatsaronis G, Pisa J. Exergoeconomic evaluation and optimization of energy systems – application to the CGAM Problem. Energy 1994;19:287–321. http:// dx.doi.org/10.1016/0360-5442(94)90113-9. [57] Valero A, Lozano MA, Serra L, Torres C. Application of the exergetic cost theory to the CGAM problem. Energy 1994;19:365–81. http://dx.doi.org/10.1016/ 0360-5442(94)90116-3. [58] Vonspakovsky MR. Application of engineering functional-analysis to the analysis and optimization of the CGAM problem. Energy 1994;19:343–64. http://dx.doi.org/10.1016/0360-5442(94)90115-5. [59] Lazzaretto A, Tsatsaronis G. SPECO: a systematic and general methodology for calculating efficiencies and costs in thermal systems. Energy 2006;31:1257–89. http://dx.doi.org/10.1016/j.energy.2005.03.011. [60] U.S. Energy Information Administration. Natural gas prices; 2016. https:// www.eia.gov/dnav/ng/ng_pri_sum_dcu_nus_m.htm [accessed: 22.08.16]. [61] U.S. Energy Information Administration. Price of U.S. natural gas LNG imports; 2016. [accessed: 22.08.16].

Please cite this article in press as: Kanbur BB et al. Thermoeconomic and environmental assessments of a combined cycle for the small scale LNG cold utilization. Appl Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.01.061