Methanol synthesis from renewable H2 and captured CO2 from S-Graz cycle – Energy, exergy, exergoeconomic and exergoenvironmental (4E) analysis

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Methanol synthesis from renewable H2 and captured CO2 from S-Graz cycle e Energy, exergy, exergoeconomic and exergoenvironmental (4E) analysis Hossein Nami a,b, Faramarz Ranjbar c,*, Mortaza Yari c a

Department of Mechanical Engineering, Faculty of Engineering, University of Maragheh, P.O.Box 83111-55181, Maragheh, Iran b Department of Energy Technology, Aalborg University, Aalborg, Denmark c Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran

highlights
A zero emission system producing power, hydrogen and methanol is proposed.
A proposal to hydrogenate the captured CO2 from S-Graz cycle is suggested.
Exergoeconomic and environmental analysis of the system is done.

article info

abstract

Article history:

Thermodynamic, economic and environmental analyses of a combined CO2 capturing

Received 12 May 2019

system, including, geothermal driven dual fluid organic Rankine cycle (ORC), proton ex-

Received in revised form

change membrane electrolyzer (PEME), S-Graz cycle and methanol synthesis unit (MSU)

30 July 2019

were carried out. The presented zero emission system was designed based on the oxy-fuel

Accepted 11 August 2019

combustion carbon capturing to produce power, hydrogen and methanol, while released

Available online 5 September 2019

CO2 can be captured. Generated renewable power by the ORC was utilized by the PEME to produce renewable hydrogen. Part of the produced hydrogen is fed to the MSU, while the

Keywords:

rest was stored in hydrogen tanks. In fact, CO2 hydrogenation to produce methanol sug-

Carbon capturing

gested via direct methanol synthesis in order to utilize the captured CO2 from the S-Graz

CO2 hydrogenation

cycle. Exergy efficiency of the system defined to analyze the system thermodynamically,

Methanol production

while SPECO method utilized to evaluate system economically. Results revealed that the

Exergoeconomic

most important part of the system is the S-Graz cycle, from the viewpoint of capital in-

Zero emission

vestment. Also, the average product unit cost of 24.88 $/GJ obtained for the whole system.

Renewable hydrogen

© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction Fossil fuels have generally been the world’s main source of energy, which will continue to govern the fuel market in the

next years. Fossil fuels combustion results in carbon dioxide (CO2) emissions and other kind of atmospheric pollution, like thermal pollution [1,2]. Among all the emitted pollutants, the major contributor to global warming is CO2, which highly relates to human activities. For example, about 35 percent of

* Corresponding author. E-mail addresses: [email protected] (H. Nami), [email protected] (F. Ranjbar). https://doi.org/10.1016/j.ijhydene.2019.08.079 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

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produced CO2 by the human activities comes from power producing sectors. Released CO2 as the main greenhouse gas increases the world’s average temperature and causes irreversible climate change. However, it seems that the carbon dioxide capturing can be presented to alleviate this problem. Currently, three different technologies have been investigated to capture CO2 from power plants, namely pre combustion, post combustion and oxy-fuel combustion. In precombustion capture, the CO2 is removed prior to combustion. Accordingly, the approach is not feasible in conventional steam power plants, but is used in Integrated Gasification Combined Cycle (IGCC) plants. These power plants are based on gasification of fuel, gas clean-up and utilization of the resulting gas in a combined cycle [3]; post combustion option has only a minor impact on the power conversion process, and CO2 is usually removed by proven washing processes based on amine solvents [4] and oxy-fuel combustion approach is the technology in which the fuel is combusted with pure oxygen [5]. All these promising technologies have their own advantages with certain drawbacks preventing their industrial large scale applications [2]. The first one, pre-combustion CO2 capturing, is an appropriate option for Integrated Gasification Combined Cycles (IGCC), due to high CO2 concentration in the gasification gas. Since IGCCs are based on gasification of fuel, gas clean-up and use of the resulting gas, higher CO2 concentration leads to efficient de-carbonization of the fuel [6]. But it should be noted that, IGCCs have relatively higher investment costs. The second one, post-combustion CO2 capturing, involves CO2 removal from exhaust gases in conventional power plants, which has only a minor impact on the power conversion process from the structural point of view. Employing this technology leads to CO2 capture by proving washing procedures based on amine solvents. Again, it is worth mentioning that post-combustion is less efficient due to the high value of solvent regeneration energy and low concentration of CO2 in the flue gas. As mentioned above, the combustion process in the oxy-fuel cycles is with pure oxygen instead of air, which results in high proportions of CO2 and H2O in the flue gas. Therefore, the produced CO2 can be recovered by condensing the water fraction. For the case of oxy-fuel combustion technology, cooled flue gas recycling is required to limit the combustion temperature. However, the approach has a higher impression on the power plant procedure. This study focuses on the S-Graz cycle [7] as an example of oxy-fuel combustion system. In addition to this, the next problem is the captured CO2 from carbon capturing systems [8]. Thus, specialists are concentrating on the finding an economic method to utilize or store this captured CO2. Considering the heavy amount of CO2 producing, not only from power plants but also from other industries like cement industry, clarifies the necessity of finding an applied approach to use the separated CO2 in large scales [9]. It seems that, altering the captured CO2 to valuable liquid fuels like methanol can be considered as one of the most operative solutions [10]. Methanol can be introduced as a potential fuel for the coming industries or even automotive engines [11]. But, still it should be noted that CO2 hydrogenation and methanol production needs a reliable hydrogen source.

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Today, hydrogen as an alternative environmentally friend fuel plays an important role in fuel cell based modern industries. Moreover, hydrogen generation is a relatively mature technology that attracts investigator’s attention [12]. Most of hydrogen used in the world is produced by steam reforming processes, corresponding to the production of 96% of onpurpose hydrogen. Natural gas, which is mainly composed of methane and ethane, is the most widely utilized hydrogen source in the steam reforming process because of its abundance [13]. On the other hand, the drawbacks of hydrogen use are high carbon emissions intensity when produced from natural gas (hydrocarbon gas mixture consisting primarily of methane, but commonly including varying amounts of other higher alkanes) [14]. Water splitting can be accounted the next way of hydrogen producing. Hydrogen coming from the water splitting is the most expensive (in comparison with other method like methane reforming) since the energy input consumed for water splitting is higher than the energy achievable from the generated hydrogen. But, due to their use of water, a readily accessible resource, water-splitting approaches have attracted the interest of the researchers. However, it should be considered that, if fossil fuels are supplied to produce the electrolyzer required power, then the generated hydrogen cannot be characterized as the zero emission fuel due to the pollution released from the fossil fuel burning [15]. Thus, it should be paid more attention to provide a sustainable hydrogen economy in order to deal with the environmental problems, which the world faces today. Providing the utilized power by the electrolyzer from renewable energy sources is the one that has been recommended by the large number of researchers. In this way, it can be claimed that the captured CO2 from the oxy-fuel combustion cycle plus produced hydrogen from renewable energy sources lead to green methanol, which is a valuable byproduct, as mentioned above. Following literature review is the most recently published studies on the methanol production via hydrogenation of captured CO2. A methanol production system is proposed by Migrand et al. [10] using captured CO2 and renewable energy sources. Their modeling was based on mass and energy conservation equations. They concentrated on the utilization of different waste heat sources to improve the system efficiency. They conducted that, while the electricity generation efficiency from the renewable energy sources is almost about 59%, about 3.6% of total input energy should be supplied from the fossil fuels. The opportunity to recycle the CO2 produced burning fossil fuels with oxy-fuel combustion using renewable hydrogen as the second feed-stock is considered by Boretti [16]. He focused on the methanol own privilege as a liquid transportation fuel, even in comparison with the hydrogen. He noticed that, compared with gasoline, methanol allows much better fuel conversion efficiencies mainly due to the larger heat of vaporization. Furthermore, he stated that the methanol can be the best selection for high power concentration, small, directly injected and turbocharged engines due to its large resistance to knock. Methanol synthesis from the flue gas plus hydrogen generated from the wind energy is investigated by Sayah et al. [17] regarding to Iran economic condition. CO2 emission reduction from the flue gas was the main aim of their concept.

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They observed that, methanol production leads to a decrease in the cost of renewable energy technology employment. Also, they showed that the methanol production based on the wind hydrogen reduces the amount of consumed natural gas about 0.11 ton per ton of methanol and avoids emitting 0.27 ton of CO2 per ton of methanol. A solar based integrated system is investigated by Esmaili et al. [18] to hydrogen and methanol production, applying energy and exergy principles. Through a comprehensive parametric study, they studied the effect of the methanol synthesis unit pressure on the produced methanol and effect of the electrolyzer current density and temperature on the rate of produced hydrogen. They concluded that the solar intensity highly affects the system energy and exergy efficiencies. For instance, if the solar intensity increases from 250 to 600 W/m2, the system efficiencies can be tripled. Leonzio et al. [19] developed an equilibrium analysis of a methanol reactor with pure CO2 and H2 in the feeding stream. They considered three novel reactor configurations at equilibrium conditions: once-through reactor, reactor with recycle of unconverted gases; reactor equipped with membrane permeable to water. They obtained that at equilibrium conditions the highest CO2 conversion of 69% is achievable using a reactor with the recycle of unconverted gases. Atsonios et al. [20] investigated various design and operating aspects for the valorization of industrially captured CO2 towards methanol production. They found that, in various Power-to-Fuel concepts, hydrogen cost is the most crucial factor. Rivarolo et al. [21] compared time dependent thermoeconomic analysis of methanol synthesis using CO2 hydrogenation in high pressure reactors considering different renewable energy sources. Hydrogen is produced by an alkaline pressurized electrolyzer (1 MW, 30 bar), in this study. They concluded that, despite the biogas configuration gives the best economic performances, the configuration with CO2 purchasing allows for a lower capital investment. Three different mixed oxides were prepared by a co-precipitation method and tested as catalysts by Wang et al. [22] for methanol synthesis via CO2 hydrogenation. They showed that the difference in methanol yield over the three catalysts can be attributed to the differences in their BET specific surface areas and adsorption capacities for CO2. On the other hand, the growing concerns about the effective use of available energy resources have urged researchers to develop an approach called exergoeconomic to cover the thermodynamic and economic aspects of energy converting systems [23]. In fact, the exergoeconomic technique is a combination of conventional exergy analysis with economic principles to disclose the cost construction in system components and establish the product unit cost [23]. Exergoeconomic methodology provides some useful exergy based economic information, which is not obtainable with exergy or economic analysis, separately. The mentioned technique can be used to evaluate cost of products in cogeneration and multi-generation systems. Considering presented literature review, efficient use of accessible renewable energy sources with the minimum environmental effects has been the focus of attention in the last decades. In this regard, researchers have proposed several integrated energy converting systems and analyzed

them in detail. Nevertheless, no standard configuration exists with which the most efficient way of altering captured CO2 from fossil fueled power plants to methanol using carbon free H2. In the present study, a novel integrated energy system, including geothermal driven dual fluid ORC, proton exchange membrane electrolyzer, S-Graz oxy-fuel cycle and methanol synthesis unit was proposed and analyzed in detail in order to produce zero emission hydrogen, power and methanol. In this study, utilizing the extracted CO2 from an oxy-fuel cycle to produce methanol via direct hydrogenation was suggested for the first time. In fact, the main aim was to find a way which utilizes the captured carbon (from fossil fueled power sectors) instead of storing and transferring. This is not the end of the story and as stated above, methanol synthesis from CO2 needs hydrogen sources. Therefore, employed expanders at the dual fluid ORC produce the renewable power, which was fed to the PEME to produce hydrogen. Part of the produced hydrogen was stored and the rest was used to hydrogenate the portion of captured CO2 from the S-Graz oxy-fuel cycle and produce methanol. The presented cogeneration system studied in detail from the viewpoints of exergy and exergoeconomic. Also, e-Sankey diagrams were presented to show the exergy streams and the most exergy destructive components, as well. The exergoeconomic factors related to different parts of the whole system were obtained to clarify the portion of the exergy destruction cost compared with the capital investment cost. Moreover, in order to give a clear image from the cost of products (in term of exergy), the average unit product cost defined for the whole system. It should be noted that, geothermal hot water was considered as the available renewable energy source, which can be found enough in the Sabalan region, Iran [24] as well as natural gas.

System description and assumptions Generally, the presented system in this study was the combination of a geothermal driven dual fluid organic Rankine cycle (ORC), proton exchange membrane electrolyzer (PEME), S-Graz oxy-fuel cycle and methanol synthesis unit (MSU). In fact, produced power by the ORC is fed to the PEME to generate renewable hydrogen via separating water into pure hydrogen and oxygen. Then, it can be claimed that the produced hydrogen is completely renewable. Also, produced oxygen by the PEME is sent to the S-Graz cycle. The S-Graz cycle is a zeroemission power producing system, which uses oxy-fuel combustion chamber. So, part of the utilized oxygen in the S-Graz cycle was provided by the PEME. Since, the combustion process in the S-Graz cycle occurs with pure oxygen (instead of air), the flue gas is a combination of water and high concentrated CO2, which can be separated in the water condensation procedure. In this way, part of the extracted CO2 (depends on the produced hydrogen) supposed to be forwarded to the MSU in order to produce methanol. A schematic diagram of the whole system is indicated in Fig. 1. More details about different parts of the system are addressed in the coming subsections.

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Fig. 1 e Schematic diagram of the proposed cogeneration system.

Geothermal driven organic Rankine cycle (ORC)

S-Graz oxy-fuel cycle

The employed ORC in this system was a kind of dual fluid, which has its own advantages in comparison with the simple ORC, based on Shokati et al. [25]. Fig. 2 depicts a schematic diagram of the dual fluid ORC. As the figure shows, this cycle was integrated from a high pressure ORC (top cycle) and a low pressure ORC (bottom cycle) operating in such a condition that the low pressure one recovers the wasted heat from the high pressure one. At the top cycle, the preheated organic fluid evaporated in the high pressure evaporator (HPE) by the geothermal water before passing the high pressure turbine (HPT) and producing power. Then, the HPT exiting flow was cooled down in the low pressure evaporator (LPE) before entering the high pressure feed pump (HPFP). Finally, pressurized fluid preheated in the high pressure preheater (HPPH) before entering HPE and completes the cycle. Evaporated organic fluid at the bottom cycle expanded in the low pressure turbine (LPT) to produce power before cooling down in the condenser. Then, having passed the low pressure feed pump (LPFP) and low pressure preheater (LPPH), pressurized working fluid entered the LPE to turn into evaporated flow.

The basic principle of the S-Graz cycle (so-called Graz cycle) has presented and published by Jericha in 1985 [26]. His main aim was introducing a power producing system based on the internal combustion with pure oxygen. The schematic diagram of the methane fired version of the S-Graz cycle is shown in Fig. 3. As the figure indicates, this cycle is a combination of high temperature Brayton cycle and low temperature Rankine cycle. Pure methane is entered the combustion chamber with a near stoichiometric flow rate of oxygen. The considered chemical reaction in the combustion chamber was as follows: CH4 þ 2O2 /CO2 þ 2H2 O; DH ¼ 800kJ=mol CH4

(1)

Due to absence of nitrogen, combustion products are a mixture of steam (74% in mass) and carbon dioxide (26% in mass), which enters high temperature turbine (HTT) at mean temperature of 1673 K [5]. 13.7% of the HTT inlet mass flow rate comes from the high pressure turbine (HPT) to cool the HTT and increase the steam content up to 77% at the exit flow. Exiting gas was fed to the heat recovery steam generator (HRSG) to vaporize and superheat steam for high pressure

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Fig. 2 e Schematic diagram of the geothermal driven ORC.

Fig. 3 e Schematic diagram of the S-Graz cycle.

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turbine (HPT). Having passed the HRSG, part of the cooled gas was compressed up to combustion chamber pressure to cool the burners and the liner. Remain cooled gases supplied to the low pressure turbine (LPT) to further expansion and produce more power before entering the condenser. Separation of CO2 from a mixture of non-condensable (CO2) and a condensable gas (steam) was occurred in the condensation process. Extracted CO2 was compressed to the required pressure for the next usage. From there on, the pure water was supplied to the pumps before entering HRSG.

Proton exchange membrane electrolyzer (PEME) Fig. 4 is represented a simplified schematic diagram of the PEME, while each real electrolyzer include power electronics, control system, stack, drying unit, gas separation and water circulation [27]. Although, almost all of the electrolyzers are based on the water splitting into hydrogen and oxygen, usually they have classified into two main types, namely, Alkaline Water Electrolyzer (AWE) and Proton Exchange Membrane Electrolyzer (PEME). AWE is relatively mature technology, which utilizes liquid electrolyte, while solid polymer electrolyte is employed in the PEME. In fact, the selection of electrolyzer is a function of some decision parameters, i.e. current, power density, durability of stack, energy and Faradaic efficiency, capacity of plant and the cost of electrolyzer [28]. Though the AWE is much matured technology than the PEME, the current density and efficiency of AWE is much lower than those of the PEME (2e6 kA/m2 in comparison with 10e20 kA/m2) [29]. Therefore, it is decided to employ the PEME in the presented cogeneration system. The schematic diagram of the PEME for H2 production is shown in Fig. 1. During electrolysis, the required electricity and heat are both supplied to the electrolyzer to drive the electrochemical reactions. As it is shown in the figure, the theoretical energy of hydrogen production consumed by the electrolyzer was produced by the ORC. Considered equation for water splitting is as follows:

3H2 O / 1:5O2 þ 3H2 ; DH ¼ þ286kJ=mol H2

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(2)

Leaving the cathode, the H2 produced dissipates heat to the environment and cools to the reference environment temperature. The oxygen gas produced at the anode is separated from the water and oxygen mixture and then cooled to the reference environment temperature. The theoretical required energy by the PEME (without any losses) in term of J/mol H2 can be written as follows [30]: DG ¼ DH þ TDS

(3)

The molar flow rate of produced hydrogen and oxygen is a function of current density (J) and Faraday constant (F), as follows: J ¼ 2  N_ O2 N_ H2 ¼ 2F

(4)

Moreover, the utilized electrical energy by the PEME is determined by: Eelectric ¼ J  V

(5)

here, V is the electrolyzer voltage and is calculated using the following equation: V ¼ V0 þ Vact;a þ Vact;c þ Vohm

(6)

where, V0, Vact,c, Vact,a and Vohm are the reversible potential which can be obtained from the Nernst equation, the activation overpotential of the anode, the activation overpotential of the cathode and the ohmic overpotential of the electrolyte, respectively. Table 1 is listed different terms of electrolyzer voltage [30]. The constant values, which are used as input for PEME modeling is reported in the assumptions section.

Methanol synthesis unit (MSU) Generally, methanol production from CO2 hydrogenation has categorized in two methods. The first method includes direct synthesis of methanol from CO2 flue. The reactants, a mixture

Fig. 4 e Schematic diagram of the PEME.

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Table 1 e Electrochemical equations for the PEME [31e33]. V0 ¼ 1:229  8:5  104 ðTPEME  298Þ Eact;a
 RT J ref 1 sinh ; J0;a ¼ Ja e RT Vact;a ¼ F 2J0;a Eact;c
 RT J ref 1 sinh ; J0;c ¼ Jc e RT Vact;c ¼ F 2J0;c Z D dx sPEME ½lðxÞ ¼ ½0:5139lðxÞ  Vohm ¼ J  RPEME ; RPEME ¼ 0 sPEME ½lðxÞ
 1 1  1268 303 TPEME lðxÞ ¼ la  lc x þ l 0:326e c D

Nernst equation Anode overpotential equation

Cathode overpotential equation

Ohmic overpotential equation

of carbon dioxide and hydrogen at a ratio of 1:3, are directly led to the reactor for methanol synthesis. This is while, indirect method has two steps. During the first step, CO2 alters into CO via reverse water gas shift (RWGS) reaction, then methanol is formed through the second step. However, it should be considered that, RWGS reaction needs to be occurred in higher temperature ranges like 1073 K to ensure the optimal conversion of CO2 [34]. As reported by Anicic et al. [35], direct methanol synthesis has higher efficiency and economic benefits compared with indirect method. Following equation describes the governing equation in the methanol synthesis unit: CO2 þ 3H2 /CH3 OH þ H2 O; DH ¼ 49:51 kJ=mol CH3 OH

(7)

Therefore, the direct methanol synthesis based on the ICI technology (Imperial Chemical Industries, now Synetix) [36] was considered in this study. A simple flow diagram of the methanol synthesis unit is shown in Fig. 5. Based on the ICI, reaction between gas phase CO2 and H2, as raw materials, occurs over a Cu/ZnO/Al2O3 catalyst under the adiabatic process. As stated by Eq. (7), the molar ratio of CO2 to H2 is 1: 3 at the inlet stream of the reactor, which has the pressure and temperature of 50 bar and 500 K, respectively [37]. Moreover, the molar ratio of recycle per reactor output was considered to be 8:9, based on the Migrand et al. [10]. Consequently, CO2 to methanol conversion was just 20%. As the figure shows, different cooling processes were considered to cool the reactor

outlet flow and separate products from the unreacted stream. Due to a little pressure drop in the methanol reactor, the recycled gas was compressed to the feed pressure, before mixing with the fresh inlet flow. After the reactor, the second important component is a distillation tower, mainly because of products separation which is called purification process. Also, other compounds like CO2 and H2 can be removed from the products within this unit. In fact, distillation tower was considered to perform as a separator in the present simulation. Various operating parameters, i.e. number of column stages, reflux ratio and distillate rate should be considered in distillation column modeling. As reported by Farzi et al. [38,39], the pure methanol with desired purity of 99% is obtainable with lower stage numbers in a distillation tower.

Assumptions The most effective parameter on the system exergetic and economic performance was the produced hydrogen, which highly depends on the renewable power. In fact, hydrogen produced by the PEME, determines the mass flow rate of produced methanol as well as utilized CO2 [8]. Furthermore, in order to simplify the simulations, the following choices and assumptions were adopted in this study:
The whole system operated under the steady state condition.

Fig. 5 e Schematic diagram of the MSU.

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Table 2 e Input parameters used to model PEM electrolysis [30]. Parameters

Value

Parameters

Value

TPEM ð CÞ Eact;a ðkJ =molÞ Eact;c ðkJ =molÞ la

80 76 18 14

PO2 ¼ PH2 ðatmÞ DðmmÞ FðC =molÞ

1.0 50 96486 1.7  105

lc

10

Jc ðA =m2 Þ



ref

Ja ðA =m2 Þ ref

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Neglecting the Potential and Kinetic exergies, the specific exergy is divided into two parts, namely physical and chemical exergies. The specific physical (a.k.a. thermomechanical) exergy of a stream is a function of the ambient conditions as well as the stream temperature and pressure and can be written as [43]: ei ¼ eph;i þ ech;i

(9)

4.6  103

eph ¼ h  h0  T0 ðs  s0 Þ
The ambient temperature and pressure supposed to be 298.15 K and 101.3 kPa, respectively [40].
Heat losses from pipelines and components were neglected.
Isopentane and Isobutane were considered as working fluids of high and low pressure loops of employed ORC, respectively [25].
Geothermal water has the temperature, pressure and mass flow rate of 448 K, 7 MPa and 83 kg/s, respectively [25].
Employed heat exchangers in the ORC have the minimum temperature difference of 5 K [25].
Power consumption of extra oxygen from ASU (air separation unit), which is needed in the S-Graz cycle was considered 1225 kJ/kg of oxygen [7].
Supplied fuel to the S-Graz cycle was pure methane with the mass flow rate of 0.1 kg/s and lower heating value of 50015 kJ/kg [8].
The data used for modeling the PEME is listed in Table 2.

emix ch ¼

As mentioned before, the exergoeconomic is the combination of conventional exergy and economic analysis at the level of a component in different energy converting systems. In fact, the method was applied to the proposed cogeneration system in order to evaluate the cost of exergy products and destruction in term of dollar per unit of exergy. In the present study, the SPECO (specific exergy costing) method was utilized, which has developed by Tsatsaronis et al. [41] for the first time. Following subsections described the application of SPECO method in detail.

Calculating thermodynamic properties and exergy values of each state point of the system Energy and mass conservation equations as well as the exergy balance equations applied to each system component to compute the thermodynamic properties and exergy values at the level of different state points [42]. Exergy balance equation can be written as: E_Q þ

X

m_ i ei ¼ E_W þ

X

m_ e ee þ E_D

(8)

where, subscripts i and e symbolize the component inlet and outlet, respectively, while E_Q , E_W , and E_D are the exergy rate related to heat transfer, the exergy rate of mechanical power and the exergy destruction rate, respectively.

xi echi þ RT0

i¼1

n X

Xi lnðxi Þ

(11)

i¼1

here, T0 ,R and xi are the ambient temperature, the universal gas constant and the molar fraction of a mixture component, respectively. Then, the exergy rate in each state can be written as: E_i ¼ m_ i ei

(12)

Fuel and product definition for each system component All system components were considered as a control volume to define the fuel and product from the viewpoint of exergy. Definition of fuel and product for each unit was presented in Appendix section. Finally, the total exergetic efficiency for the proposed cogeneration system can be written as follows: εtotal ¼

Thermodynamic, exergoeconomic and exergoenvironmental principles

n X

(10)

E_P;total E_in;total

(13)

Product exergy for the whole system was the exergy associated with the produced power and methanol as well as the stored hydrogen, while the fuel exergy was the exergy related to the geothermal hot water along with consumed fuel in the S-Graz cycle.

Cost and cost balance equations associated with each component In order to list the applied cost equations for each component in a particular size or capacity, Table A-2 in Appendix section was presented. Using Capital Recovery Factor (CRF) definition, it is possible to change the capital cost investment of each component in a time based costs, which can be used in cost balance equations, as follows [23]: Z_K ¼ CRF  ZK 

f 3600N

(14)

n

CRF ¼

i  ð1 þ iÞ n ð1 þ iÞ  1

(15)

In the equations above N, f, i and n are the annually operating hours (7446), maintenance factor (1.06), interest rate (10%) and expected life cycle (20 years), respectively [23]. Table 3 outlins the cost balance and related auxiliary equations adopted for each component. The cost balance equation for the kth component expresses that sum of the cost rates related to all exiting exergy streams is balanced with

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Table 3 e Cost balance and auxiliary equations applied to the proposed system components. Main unit

Component

Dual Fluid ORC

HPT LPT HPE LPE HPFP LPFP COND HPPH LPPH

S- Graz cycle

CC HTT HPT LPT HRSG FP CP COND 3SC CO2 COMP

PEME

Total

MSU

COMP HE1 HE2 MR

Cost balance equations c1 ¼ c2

C_ 5 þ C_ 1gw þ Z_ HPE ¼ C_ 1 þ C_ 2gw C_ 2 þ C_ 10 þ Z_ LPE ¼ C_ 3 þ C_ 6

c1gw ¼ c2gw

C_ 3 þ C_ W;HPFP þ Z_ HPFP ¼ C_ 4 C_ 8 þ C_ W;LPFP þ Z_ LPFP ¼ C_ 9

e

C_ 7 þ C_ CW1 þ Z_ COND ¼ C_ 8 þ C_ CW2 C_ 4 þ C_ 2gw þ Z_ HPPH ¼ C_ 5 þ C_ 3gw

c7 ¼ c8 cCW1 ¼ 0

C_ 9 þ C_ 3gw þ Z_ LPPH ¼ C_ 10 þ C_ 4gw C_ 11 þ C_ 12 þ C_ 26 þ C_ 28 þ Z_ CC ¼ C_ 13

c3gw ¼ c4gw

C_ 13 þ C_ 25 þ Z_ CC ¼ C_ 14 þ C_ W;HTT C_ 24 þ Z_ HPT ¼ C_ 25 þ C_ 26 þ C_ W;HPT C_ 16 þ Z_ LPT ¼ C_ 17 þ C_ W;LPT

c13 ¼ c14

C_ 14 þ C_ 23 þ Z_ HRSG ¼ C_ 15 þ C_ 24 C_ 22 þ C_ W;FP þ Z_ FP ¼ C_ 23 C_ 18 þ C_ W;CP þ Z_ CP ¼ C_ 20

c14 ¼ c15

C_ 17 þ C_ cw;1 þ Z_ COND ¼ C_ 18 þ C_ 19 þ C_ cw;2 C_ 27 þ C_ W;3SC þ Z_ 3SC ¼ C_ 28 C_ 19 þ C_ W;COMP þ Z_ COMP ¼ C_ 29

ccw;1 ¼ 0c17 ¼ c18 ¼ c19

C_ 30 þ Z_ PEME ¼ C_ 33 þ C_ 34 C_ 53 þ C_ W;COMP þ Z_ COMP ¼ C_ 54 C_ 37 þ C_ 39 þ Z_ HE1 ¼ C_ 38 þ C_ 40

c30 ¼ 0

C_ 43 þ C_ Q;HE2 þ Z_ HE2 ¼ C_ 44 C_ 38 þ Z_ MR ¼ C_ 39

e

costs associated with capital investment, operating and maintenance, and all entering exergy streams, as follows: X X C_ e;k þ C_ w;k ¼ C_ q;k þ C_ i;k þ Z_k e

(16)

i

C_ j ¼ cj E_j

(17)

here, subscript j shows the number of each state. Moreover, there are some parameters playing important roles in the exergoeconomic assessment of an energy converting system as follows [23]: cP;k ¼

C_ P;k _ P;k Ex

(18)

cF;k ¼

C_ F;k _ F;k Ex

(19)

fk ¼

Z_k

Z_ k þ C_ D;k þ C_ L;k

_ D;k C_ D;k ¼ cF;k Ex

Auxiliary equations

C_ 1 þ Z_ HPT ¼ C_ 2 þ C_ W;HPT C_ 6 þ Z_ LPT ¼ C_ 7 þ C_ W;LPT

(20)

(21)

here, cP;k , cF;k , fk and C_ D;k are the average cost per unit product exergy, the average cost per unit fuel exergy, exergoeconomic factor and the cost rate related to the exergy destruction. For the proposed cogeneration near zero-emission system, the average product unit cost was calculated via Eq. (22), considering the exergy rate associated with all products (power, hydrogen and methanol) [44].

c6 ¼ c7 c2 ¼ c3 e c2gw ¼ c3gw c11 ¼ 7:8  106 $=kJc12 ¼ 1225  m_ 12 kJ=kg c24 ¼ c25 ¼ c26 c16 ¼ c17 e e e e e c39 ¼ c40 e

P C_ fuel þ Z_k  C_ env nk

cp ¼

i¼1 np P E_Pi

(22)

i¼1

here, C_ fuel is the fuel cost that consumed in the combustion chamber of the S-Graz cycle plus the cost of geothermal hot Pnk _ Zk is the sum of capital investment cost for each water, i¼1 system component, C_ env is the environmental protection cost, Pnp _ EPi is the sum of which is discussed in the next section and i¼1 exergies produced by the system (power, hydrogen and methanol). It should be mentioned that, since the presented system prevents the environmental impact, the cost associated with the environmental protection should be subtracted from the current costs.

Exergoenvironmental analysis The main aim of the presented system investigation was to introduce a novel zero-emission cogeneration system in order to produce power, hydrogen and methanol, simultaneously. It seems that in order to analyze an energy system, not only mechanical power or heat energy should be considered, but also more attention should be paid on the system environmental impact. Nevertheless, various exergy and exergoeconomic assessments have been done for cogeneration systems in the literature, a large number of these scientific studies do not address environmental effects, while there is a narrow relation between the system performance and its environmental impact. In order to decrease the CO2 production as the main greenhouse gas along with the emitted NOx, it

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is necessary to decline the fuel consumption in an energy system [45]. The value of the extracted CO2 from the S-Graz cycle can be calculated from the combustion molar balance in the combustion chamber. The next pollutant that prevented from emitting to the atmosphere in this study was NOx. In oxy-fuel combustion, almost all of the nitrogen can be separated before the combustion process. Also, nitrogen oxides, which were prevented from emitting to the atmosphere, depend on the some combustion characteristics and can be calculated as follows [44]:
 0:15  1016 t0:5 exp 71100 TPz mNOx ¼
0:5 CC PCC 0:05 DP PCC

(23)

where, t (the residence time in the combustion zone) is assumed to be 0.002 s. TPZ, PCC and DP3 are combustion flame temperature, combustor inlet pressure and pressure drop across the combustion chamber. However, the amount of NOx is outlined in term of gram per kg of fuel. The environmental cost rates in terms of ($/s) are stated in the following equation [44]: C_ env ¼ cNOx m_ NOx þ cCO2 m_ CO2

(24)

here, cCO2 and cNOx are considered to be 0.024 $/kg and 6.853 $/kg, respectively.

Results and discussions To model the proposed cogeneration system, a simulation code using Engineering Equation Solver (EES) software was developed. The validation was performed for the dual fluid ORC and the PEM electrolyzer, separately. Table 4 indicates a comparison between the results of the present model for the dual fluid ORC and those of reported by Shokati et al. [25] in terms of exergy destruction within the components. Moreover, Fig. 6 represents a comparison between the results of the present model for the PEM electrolyzer and those of reported by Ni et al. [30]. Referring to Table 4 and Fig. 6, there were good agreements between the obtained results in the present model and those reported in the literatures. Table 5 outlines the thermodynamic properties of each stream in the proposed system. This table includes temperature, pressure and mass flow rate of each state within the

Table 4 e Comparison between the Shokati et al.’s results and present work for the dual fluid ORC components exergy destruction rate [kW]. Components HPT LPT HPE LPE HPPH LPPH HPFP LPFP COND

Shokati et al. [25]

Present work

259.8 332.7 625.5 1190 252.7 846.1 13.5 11.6 108.1

259.8 332.7 625.5 1196 252.7 846.1 13.45 11.61 110.1

Fig. 6 e Comparison of the present simulation results with those of reported by Ni et al. [30] for the PEM electrolyzer.

whole system and these data are carried out by energy analysis of the system. In addition, Figs. 7 and 8 illustrate the details of exergy streams and exergy destruction within the dual fluid ORC and S-Graz cycle, respectively, by e-Sankey diagrams. Referring to Fig. 7, The most exergy destructive component employed in the dual fluid ORC was LPE followed by LPPH mainly due to temperature mismatching within these heat exchangers. Moreover, as it was expected the highest value of exergy destruction within the S-Graz cycle belongs to the combustion chamber. In fact, all the sources of irreversibility, i.e. combustion, mixing and temperature difference are presented in the combustion chamber and not much can be done in enhancing the combustion chamber performance. Fig. 9 represents portion of the each four main unit in the system capital investment cost. The obtained result is based on the assumptions which mentioned before, while half of the produced hydrogen is fed to the MSU and the rest was stored in hydrogen tanks. The figure shows that the most important part of the system is the S-Graz cycle, from the viewpoint of capital investment (not exergoeconomic). As it was expected, the obtained result was in contradiction with that of obtaining from exergy analysis (from the viewpoint of exergy destruction). Exergy analysis stated that the most effective section is the geothermal driven ORC, while the economic results revealed that the components employed in the S-Graz cycle have more effect on the system performance. It seems that, using advanced and high technology based equipment in this oxy-fuel cycle (like a high temperature gas turbine, which operates with a temperature of 1673 K) was the main reason of the shown result in this figure. To give detailed information about the S-Graz cycle capital investment cost, Fig. 10 is presented. Referring to this figure, the high temperature turbine (HTT) was the major turbomachinery component and is responsible for 70% of the capital investment cost of the cycle, which confirmed the previous reports about methane-fired version of this cycle [3]. Table 6 outlines the main results obtained from the exergoeconomic analysis, including, produced net power by the SGraz cycle, produced hydrogen, stored hydrogen, produced methanol, consumed CO2, total capital investment cost, cost of produced power by the ORC, cost of produced power by the

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Table 5 e Thermodynamic properties of each state in proposed system (50% of produced hydrogen is stored). System Dual fluid ORC

S-Graz cycle

PEM

MSU

State

Temperature (K)

Pressure (bar)

Stream composition

Mass flow rate (kg/h)

1gw 2gw 3gw 4gw 1 2 3 4 5 6 7 8 9 10 cw1 cw2 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

448 407.5 385 368 402.5 375 357 357.5 402.5 334.5 310.5 303 303.5 334.5 298 305.5 423 423 1673 846 402 402 305 305 305 305.5 305.5 305.5 306 838 610 610 402 873 566 298 353 353 353 353 353 385 338 503 573 313 313 313 313 333 355 337 313 378 325 e e 313 313 328

70 70 70 70 13 5 5 13 13 9 4.04 4.04 9 9 1 1 40 40 40 1 1 1 0.04 0.04 0.04 1 1 1 180 180 40 40 1 40 100 1 1 1 1 1 1 50 50 50 45 45 45 1.5 1.5 1.5 1.5 1 1 1.3 1.3 e e 45 1 50

H2O H2O H2O H2O Isopentane Isopentane Isopentane Isopentane Isopentane Isobutane Isobutane Isobutane Isobutane Isobutane H2O H2O CH4 O2 CO2, H2O CO2, H2O CO2, H2O CO2, H2O CO2, H2O H2O CO2 H2O H2O H2O H2O H2O H2O H2O CO2, H2O CO2, H2O CO2 H2O H2O H2 H2O, O2 H2O O2 H2, CO2 H2, CO2 H2, CO2 H2, CO2, H2O, CH3OH H2, CO2, H2O, CH3OH H2O, CH3OH H2O, CH3OH H2O, CH3OH H2O, CH3OH H2O, CH3OH CH3OH CH3OH H2O H2O H2, CO2 H2, CO2 H2, CO2 H2, CO2 H2, CO2

298800 298800 298800 298800 224136 224136 224136 224136 224136 263232 263232 263232 263232 263232 2796120 2796120 360 1440 2152, 6077 2152, 7204 2152, 7204 990, 3314 990, 3314 3314 990 3314 810 2504 2504 2504 1127.5 1376.5 1162, 3890 1162, 3890 990 250 250 24.76 28.7, 196.5 28.7 196.5 12.38, 90.08 61.9, 450.4 61.9, 450.4 49.52, 360.32, 36.87, 65.58 49.52, 360.32, 36.87, 65.58 36.87, 65.58 36.87, 65.58 36.87, 65.58 36.87, 65.58 36.87, 65.58 65.58 65.58 36.87 36.87 Trace Trace 49.52, 360.32 49.52, 360.32 49.52, 360.32

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Fig. 7 e Details of exergy destruction within dual fluid ORC.

S-Graz cycle, cost of produced hydrogen, cost of produced methanol, cost of environmental protection, average product unit cost and total system exergetic efficiency, while the stored hydrogen was half of the produced rate. As listed in this table, the cost of produced power by the S-Graz cycle was much higher than that of produced by the ORC. This is because, the capital investment cost associated with the SGraz cycle is highly more than that of invested for ORC. In addition, cost of produced hydrogen was obtained to be 6.081 $/kg which is the function of cost of the produced electricity by

the ORC. Also, referring to Table 6, the average product unit cost was 24.88 $/GJ, while the same economic value was considered for each unit of exergy in products (power, stored hydrogen and methanol). Besides, the exegy efficiency of 40.66% is completely comparable with similar published research studies [46]. Furthermore, calculated equal cost of 23.76 $/h for the environmental protection reveals that the presented system benefits the environment 23.76 $ in each our considering utilized CO2 in the methanol synthesis unit and separated N2 in the oxy-fuel cycle. It is a worth mentioning

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Fig. 8 e Details of exergy destruction within S-Graz cycle.

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Fig. 9 e Breakdown of the whole presented system capital investment cost.

Fig. 10 e Breakdown of the S-Graz cycle capital investment cost.

Table 6 e Obtained results associated with the exergoeconomic analysis (50% of produced hydrogen is stored). Main parameters

Values

Produced net power by the S-Graz cycle (kW) Produced hydrogen (kg/h) Stored hydrogen (kg/h) Produced methanol (kg/h) Consumed CO2 (kg/h) Total capital investment cost ($/h) Cost of produced power by the ORC (cent/kWh) Cost of produced power by the S-Graz cycle (cent/kWh) Cost of produced hydrogen ($/kg) Cost of produced methanol ($/kg) Cost of environmental protection ($/h) The average product unit cost ($/GJ) Total system exergetic efficiency (%)

2605.5 24.76 12.38 65.58 90.08 318.672 2.368 6.588 6.081 1.44 23.76 24.88 40.66

that, the reported results in this table are a function of stored hydrogen (ratio of stored hydrogen to produced hydrogen). Therefore, it seems that investigating effects on the system performance of this parameter can be of interest.

Cost flow diagram within the whole system is presented in Fig. 11 in detail. As the figure shows, costs associated with geothermal hot water temperature and pure methane as well as the oxygen are the system input costs, while costs related to the zero emission power produced by the S-Graz cycle, half of the produced hydrogen by the PEME along with the generated methanol are the output terms. As can be seen, produced power by the S-Graz cycle has the maximum cost flow in the system, followed by hydrogen producing from electrolyzer and utilized methane in the oxy-fuel combustion chamber. Fig. 12 illustrates the effect of the stored hydrogen ratio on the consumed CO2 and generated CH3OH in the MSU. When the stored hydrogen changed from 10 to 90% of produced hydrogen, rate of consumed CO2 and produced CH3OH decreased from 162.1 to 18.02 kg/h and 118 to 13.12 kg/h, respectively. This is because, 3 mol of hydrogen were needed to combine with each mole of captured CO2 and complete the methanol production process (see Eq. (7)). Then decreasing consumed CO2 and produced CH3OH with decreasing supplied hydrogen to MSU is reasonable. In fact, change in the ratio of stored hydrogen from 10 to 90% means that the stored hydrogen increases from 2.476 to 22.28 kg/h.

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Fig. 11 e Cost flow diagram of the proposed cogeneration system.

Fig. 12 e Consumed CO2 and produced CH3OH versus stored hydrogen.

Fig. 13 shows changes in the total exergetic efficiency and average unit cost of products with variation in the stored hydrogen ratio. Based on this figure, an increase in the stored hydrogen led to inflation in the system exergetic efficiency. It is valuable mentioning that, although utilizing more hydrogen in the MSU leads to more CH3OH, but the methanol production has its own exergy destruction (just like other thermodynamic processes). Then, storing the maximum amount of hydrogen

Fig. 13 e Exergetic efficiency and average product unit cost versus stored hydrogen.

was favorable from the viewpoint of the second law efficiency. However, as mentioned before, methanol production as a liquid fuel has widespread advantages, which compensate the exergy destruction in this unit. Also, referring to Fig. 13, the average unit cost of products reduced as the stored hydrogen ratio increased. As aforesaid, this is because of a reduction in the total exergy destruction. In fact, decreasing destroyed exergy increases the exergy rate in system products, which lead to a reduction in the average product unit cost. It can be

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these units. However, it should be pointed out that the recommendations made for enhancing exergoeconomic performance of separate units, in exergy based analysis, doesn’t necessarily mean a better performance for the whole system, because the performance of other units can be deteriorated by improving the performance of one unit.

Conclusion

Fig. 14 e Obtained exergy destruction cost and exergoeconomic factor for different parts of the proposed system.

stated in other words, that reducing exergy destruction decreases exergy destruction cost which results in lower values of the average unit product cost of the system. When the stored hydrogen ratio changed from 10 to 90% of the produced hydrogen, the second law efficiency and the average unit product cost of the system varied from 39.34 to 42.08% and 25.07 to 23.89 $/GJ, respectively. Exergy destruction cost rate and exergoeconomic factor associated with different parts of the presented cogeneration system are illustrated in Fig. 14, while the stored hydrogen was half of the produced hydrogen. Before conducting the figure explanation, it should be mentioned that the cost sources in a component may be divided into two parts. The first is associated with capital investment and operating and maintenance costs (non-exergyrelated expenses), while the second includes the cost of exergy destruction and exergy loss. A low value of the exergoeconomic factor obtained for a component proposes that cost savings in the entire system might be reached by improving the component efficiency (reducing the exergy destruction) even if the capital investment for this component will increase. On the other hand, a high value of this factor suggests a decrease in the investment costs of this component at the expense of its exergetic efficiency. Based on this figure, the highest value of the exergy destruction cost rate belongs to the S-Graz cycle (151.74 $/h) followed by the MSU (123.1$/h). Not only destroyed exergy but also cost of supplied fuel affects the exergy destruction cost rate in each unit. Moreover, as can be seen, the highest exergoeconomic factor refers to the ORC unit, which clarifies the importance of paying more attention to this section from the exergoeconomic viewpoint. The exergoeconomic factor of 70.37% indicated that the purchasing cost for the ORC is dominant (comparing with the exergy destruction cost) and replacing it with a cheaper one (lower purchasing cost) is suggested to improve the system economic performance. The lowest f value was calculated for the MSU suggesting employing more expensive unit with higher exergetic efficiency for enhancing the system exergoeconomic performance. Furthermore, the exergoeconomic values calculated for the S-Graz cycle and PEME show that there is a balance between purchasing and exergy destruction costs related to

A relatively novel carbon capturing system was introduced and analyzed in detail, using exergoeconomic and environmental principles. The presented system includes a geothermal driven ORC, PEME, S-Graz cycle and MSU. Oxy-fuel combustion technology is one of the carbon capturing methods, which was employed in the S-Graz cycle. The ORC unit provided the needed power by the PEME to produce renewable hydrogen. Then, part of the produced hydrogen was fed to the methanol reactor in the MSU to produce CH3OH and the rest was stored in the hydrogen tanks. In fact, methanol production was suggested to hydrogenate the captured CO2 from the S-Graz oxy-fuel cycle and producing widely used liquid fuel. Besides, considering different CCS technologies, like pre- and post-combustion instead of oxyfuel combustion chamber and compare the results with those reported in the present study highly recommended for future research work. The main itemized conclusions obtaining from the present study can be as follows:
Among the all, the S-Graz cycle has the highest value of purchasing equipment cost because of high technology equipment employed in this cycle.
The cost of produced power by the S-Graz cycle was much higher than that of produced by the ORC.
The highest exergoeconomic factor belongs to the ORC while the lowest was related to the MSU. Therefore, more attention should be paid for these units to improve the system economic performance.

Nomenclature A c CC

COMP COND CP CRF CV C_ DT e E_ Eact;i Eelectric F FD FP G H

heat transfer surface area (m2) cost per exergy unit [$/GJ] combustion chamber compressor condenser condenser pump capital recovery factor control valve cost flow rate [$/s] distillation tower specific physical exergy [kJ/kg] exergy flow rate (kW) activation energy in cathode or anode (kJ) electric energy input rate (kW) Faraday constant (C/mol) flash drum feed pump Gibbs free energy (J/mol) specific enthalpy [kJ/kg]

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HE HPE HPFP HPPH HPT HRSG HTT J J0 ref Ji L LMTD LPE LPFP LPPH LPT m_ MR N_ PEME Q_ R RPEM s S ST T U V V0 Vact Vact;a Vact;c _ W

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heat exchanger high pressure evaporator high pressure feed pump high pressure preheater high pressure turbine heat recovery steam generator high temperature turbine current density [A/m2] exchange current density (A/m2) pre-exponential factor (A/m2) loss logarithmic mean temperature difference low pressure evaporator low pressure feed pump low pressure preheater low pressure turbine mass flow rate [kg/s] methanol reactor molar mass flow rate (mol/s) proton exchange membrane electrolyzer heat transfer rate [kW] gas constant (kJ/kg K) proton exchange membrane resistance (U) specific entropy [kJ/kg K] entropy [kJ/K] storage tank temperature overall heat transfer coefficient [kW/m2 K] valve reversible potential (V) activation overpotential (V) anode activation overpotential (V) cathode activation overpotential (V) power [kW]

Zk Z_ k

capital investment cost ($) levelized investment cost of the system components [$/s]

Greek letters ε exergy efficiency sðxÞ local ionic PEM conductivity (s/m) proton conductivity in PEM (s/m) sPEM lðxÞ water content at location x in the membrane (U1) water content at the anode-membrane interface la (U1) lc water content at the cathode-membrane interface (U1) Subscripts ch chemical D destruction env environmental in inlet condition gw geothermal water K kth component ohm ohmic out outlet condition P pump ph physical 0 ambient condition

Appendix In fact, the exergetic desired output from each component, is the product and the utilized input exergy to generate the product is the fuel [23]. Fuel and product definitions for the system components are presented in Table A-1.

Table A-1 e Exergetic fuel and product definition for system components. Main unit Dual Fluid ORC

Component HPT LPT HPE LPE HPFP LPFP COND HPPH LPPH Total

S- Graz cycle

CC HTT HPT LPT HRSG FP CP COND 3SC CO2 COMP Total

Fuel E_1  E_2 E_6  E_7 E_gw;1  E_gw;2

Product _ HPT W _ LPT W

E_2  E_3 _ HPFP W

E_1  E_5 E_6  E_10 E_4  E_3

_ LPFP W _ E7  E_8

E_9  E_8 E_cw;2  E_cw;1

E_gw;2  E_gw;3 E_gw;3  E_gw;4 E_gw;1  E_gw;4

E_5  E_4 E_10  E_9

E_11 þ E_12 þ E_26 þ E_28 E_13 þ E_25  E_14 E_24  E_25  E_26 E_16  E_14 

E_17 E_15

_ net;ORC W E_13 _ HTT W _ HPT W _ LPT W

_ FP W _ CP W

E_24  E_23 E_23  E_22 E_20  E_18

E_17  E_18  E_19 _ 3SC W

E_cw;2  E_cw;1 E_28  E_27

_ CO2;COMP W E_11 þ E_12

E_29  E_19 _ net;SG E_29 þ E_21 þ W

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Table A-1 e (continued ) Main unit PEME MSU

Component Total

COMP HE1 HE2 MR Total

Considered cost equations are outlined in Table A-2. The cost equations listed in this table have been obtained by curve fitting to real cost data as a function of the decision parameters for each component [23]. However, the cost

Fuel

Product

_ PEME E_30 þ W _ COMP W

E_33 þ E_34 E_54  E_53

E_39  E_40 E_ _

E_38  E_37 E_44  E_43

E_38 E_36

E_39 E_47 þ E_49

Q HE2

estimated for each component should be levelized to the original year from the reference year using the marshal and swift cost index.

Table A-2 e The capital investment cost functions for the system main components [23,47,48]. Main unit Dual Fluid ORC

Component HPT

_ ZHPT ¼ 4750W HPT

LPT

_ 0:75 ZLPT ¼ 4750W LPT

HPE

0:85 ZHPE ¼ 309:14AHPE

LPE

ZLPE ¼ 309:14A0:85 LPE

HPFP

_ 0:65 ZHPFP ¼ 200W HPFP

LPFP

_ 0:65 ZLPFP ¼ 200W LPFP ZCOND ¼ 1773m_ 7

COND HPPH S- Graz cycle

0:75

ZHPPH ¼ 309:14A0:85 HPPH

LPPH

ZLPPH ¼ 309:14A0:85 LPPH

CC

ZCC ¼ 46:08ðm_ 12 þ m_ 26 þ m_ 28 Þð1 þ expð0:018T13  26:4ÞÞ

HTT HPT LPT HRSG

ZHTT



479:34m_ 13 P13 ¼ ln 1 þ expð0:036T13  54:4ÞÞ 0:92  hHTT P14

_ ZHPT ¼ 6000W HPT 0:7

ZLPT ¼

_ 0:7 6000W LPT


ZHRSG ¼ 4745

0:8 hs þ 11820m_ 23 þ 658m_ 14 logðT14  T15 Þ

FP

_ 0:65 ZFP ¼ 200W FP

CP

_ ZCP ¼ 200W CP ZCOND ¼ 1773m_ 17

 71:1m_ 27 P28 P28 Z3SC ¼ ln 0:9  h3SC P27 P27

 71:1m_ 19 P29 P29 ZCO2 ;Comp ¼ ln 0:9  hCO2 ;Comp P19 P19

COND 3SC CO2 COMP PEME MSU

Capital investment cost functions

_ PEME ZPEME ¼ 1000W COMP

0:65

ZComp ¼



 71:1m_ 53 P54 P54 ln 0:9  hComp P53 P53

HE1

0:85 ZHE1 ¼ 309:14AHE1

HE2

0:85 ZHE2 ¼ 309:14AHE2 _ ZMR ¼ 6852m46

MR

1 0:995 

P13 P12

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