Thermoeconomic analysis of large solid oxide fuel cell plants: Atmospheric vs. pressurized performance

Energy 55 (2013) 142e155

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Review

Thermoeconomic analysis of large solid oxide fuel cell plants: Atmospheric vs. pressurized performance M. Gandiglio*, A. Lanzini, P. Leone, M. Santarelli, R. Borchiellini Department of Energy, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 August 2012 Received in revised form 18 March 2013 Accepted 24 March 2013 Available online 6 May 2013

A detailed thermoeconomic analysis of two large solid oxide fuel cell-based power plants operating at atmospheric pressure and 20 bar, respectively, is assessed in this work. The analyzed systems employ SOFC-GT (gas turbine) modules as main power generators; a bottom HRSC (heat recovery steam cycle) to generate additional electricity from the SOFC-GT exhaust hot gases is also included. The thermodynamic and economic performance of the two plant configurations are studied in detail: the exergy analysis shows an enhanced exergetic performance for the pressurized cycle that features components with higher efficiency and consequently a lower rate of exergy destruction (w20% less than the atmospheric plant). The economic analysis considers the capital cost of each component within the system and is developed aiming at estimating the levelized cost of electricity. In order to match both exergetic and economic parts, a rigorous thermoeconomic analysis following the theory of Valero and Bejan [1,2] is implemented. A well-defined set of rules for the exergoeconomic balance around each plant component is specified and specific cost balance equations are thus derived. Results show how pressurized plant outperforms the atmospheric one, with a (on exergo-economic base) cost of electricity of 47.7 $/MWh instead of 64.2 $/MWh. Therefore, both exergetic and economic advantages result from the adoption of a pressurized SOFC-GT cycle in the framework of future advance power plants based on high-temperature fuel cells. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: SOFC Exergy analysis Thermoeconomic performance Pressurized SOFC SOFC power plant

1. Introduction SOFC science and technology made great advances over the past few decades. SOFC-based power cycles have the potential to significantly increase the fuel-to-electricity conversion rates of next generation power plants. In this work, a SOFC module with 220 MWe of installed capacity is analyzed: high power SOFC plants are not currently available but represent an interesting option for future power generation [3e5]. Some works have been published in literature dealing with large SOFC power plants with particular attention to the influence of selected variables (fuel utilization, excess air ratio, temperature) over the system efficiency and economy [6,7]. State of the art of SOFCs confirms that SOFCs are presently operated mostly at atmospheric

* Corresponding author. E-mail addresses: [email protected], (M. Gandiglio).

[email protected]

0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.03.059

pressure: pressurization yields better stack polarization and enables its integration with efficient heat recovery bottoming cycles based on gas turbine plus Rankine cycles, as demonstrated at prototype scales [8e10]. In this study, SOFC modules are operating at the relatively high pressure of 20 bar in order to reap the benefits of close integration with large commercial heavy-duty gas turbines. Several previous works available in the literature carried out a techno-economic analysis of SOFC power plants (e.g., [11e13]). In this work, for thermoeconomic analysis is intended a rigorous method that evaluates the exergoeconomic performance of investigated plants. Generally a techno-economic analysis is an energy analysis followed by an economic analysis: a thermoeconomic analysis is instead an integrated energy, exergy and economic analysis. The main advantages of thermo-economic vs. techno-economic are:
the exergy rate measures the maximum rate of energy that can be exploited to produce useful work. It thus represents a more sensible way (compared to energy analysis, where energy is

M. Gandiglio et al. / Energy 55 (2013) 142e155

throughout conserved) to evaluate a plant component performance through the calculation of the rate of exergy destroyed and exergoeconomic cost.
The integration of the exergy and economic analyses together enables to calculate indexes (e.g., exergetic factor, exergoeconomic factor) that well summarize the exergy and exergoeconomic performance of single components within the plant. Once determined, such indexes can be used to easily compare among them different plant configurations. The thermoeconomic analysis combines together the first and second law of thermodynamics with cost balances evaluated at the system component level. Such methodological approach helps to understand the cost formation process within the power plant while providing a tool to identify and eventually minimize the overall plant product cost (e.g., electricity). The methodology followed in this study is the one originally proposed by Valero and Tsatsaronis in their theory, [1,14] and in papers about power plants [15]: examples of previous works dealing with this method to analyze different power plant configurations include combined cycle power plants [16e19], a simple gas turbine cycle [20], a combined heat and power system [21], a control system for energy plants [22], a trigeneration generator based on a gas-diesel engine [23], desalination processes [24], a phosphoric acid fuel cell plant [25], a PV-hydrogen system [26] and also a fuel cell hybrid power system [27]. Thermoeconomic analysis have also been carried out from Esen et al. on heat pump systems coupled with ground or air [28,29], together with energy and exergy analysis of the same [30]. Several previous works carried out exergy analysis applied to fuel cell systems: in the work of Calise et al. [31,32] combined SOFCGT plants (1.5 MW) have been analyzed and models for each component were used. In this work, the same approach was

143

employed for a comparison between atmospheric and pressurized systems, not studied so far. The thermoeconomic evaluation tool developed here is thus quite general and could be applied to every conventional or innovative power cycle once thermodynamic data of fluid streams and capital cost of components are available. In this work, the focus is on atmospheric vs. pressurized operation concerning large SOFC power production. In particular the benefits of pressurization both in exergetic and exergoeconomic terms will be demonstrated. 2. Plant configurations The power island is configured as a SOFC hybrid system: a primary SOFC power generator coupled to a bottoming cycle to recover additional power from hot exhaust. The atmospheric plant has got a three pressure levels HRSC (heat recovery steam cycle) while the pressurized presents a gas turbine which recovers mechanical work from hot exhaust gases and a bottoming HRSC with only two pressure levels. The considered plant size is w270 MW of net electricity export for the atmospheric one and w280 MW for the pressurized one (Figs. 1 and 2). All the analyzed plants are fed by natural gas: one important feature of fueling with natural gas is that the operating temperature of the SOFC (800  C) corresponds well to the temperature needed for the fuel internal reforming at the anode. The corresponding endothermic reforming reactions help reducing the air-cooling of the fuel cell stack that would otherwise be required by energyintensive cathode air-cooling [33]. The SOFC is operated at 800  C, with an operating voltage calculated as following:

Vcell ¼ Vrev ðT; p; yÞ  ASR$j:

Fig. 1. Atmospheric SOFC plant.

(1)

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M. Gandiglio et al. / Energy 55 (2013) 142e155

Fig. 2. Pressurized SOFC plant.

The Nernst potential, Vrev is given by the reversible thermodynamic potential generated by the electrochemical oxidation of H2 and CO as a function of temperature, pressure and gas composition. The main SOFC parameters are summarized in Table 1 with all the plant main values; also those values are coherent with data reported in Refs. [34,35]. The previous equation represents a simple SOFC model that is able to incorporate the effects of fuel/oxidant composition by means of an accurate Nernst voltage calculation averaged between the SOFC inlet and outlet diffusion channels. The ASR (area specific resistance) is assumed here to be a constant that express the cell’s overall equivalent resistance, including “ohmic” þ “activation” þ “contact resistance” contributions. SOFC pressurization to 20 bar strongly improves plant performance enhancing Nernst voltage. Although the reformer is shown as a component separate from the SOFC, in reality the SOFC module is both the chemical and electrochemical reactor for the anode fuel. The so-called “hotbox” is physically what constitutes the SOFC reactor module. The designated fuel is compressed natural gas from the grid at 30 bar; therefore, no natural gas compression work on the anode Table 1 Baseline plant parameters for the SOFC hybrid plant. SOFC nominal temperature,  C Operating pressure (atm./pres.), bar Cell (stack) ASR, U cm2 Current density (atm./pres.), A cm2 Approx. power density (atm./pres.), mW cm2 Fuel inlet temperature,  C Air inlet temperature,  C Global fuel utilization (FU) factor Steam to carbon factor (S/C) Global air excess ratio (l)

800 w1/w20 0.28 0.64 w500 800 650 0.85 2 Variable

side of the SOFC is required. The natural gas must be deeply desulfurized before entering the SOFC: impregnated active carbons, zeolites, or a combination of both can efficiently remove sulfur compounds down to concentrations acceptable for the stack [36]. Partial anode exhaust recirculation is employed to provide an O/C mole ratio 2 at the anode inlet to prevent coking on the Ni based anode: the pre-heater duty is reduced by anode exhaust recirculation. On the cathode side, partial exhaust recirculation is also employed to pre-heat cathode feed stream at 650  C before entering the stack. To avoid significant reductions of Nernst voltage due to oxygen starvation, the cathode air flow is set to insure that the partial pressure of O2 in the cathode exhaust exceeds 10% vol. In the pressurized plant, the blower has been replaced with an axial cathode air compressor, used to pressurize the SOFC vessel; pressurization obviates the need for air pre-heaters because partial recirculation of the cathode exhaust at 800  C provides the additional heat needed to boost the cathode inlet flow to the required temperature. In both plants, the anode exhaust is combined with the cathode exhaust and burned to recover the chemical energy of the unspent H2 and CO. The resulting stream has a temperature between 1000 and 1050  C and, in the pressurized plant, is expanded in a turbine to both drive the air compressor and generate additional electricity. More detail on large SOFC power plant configuration can be found elsewhere [33,35,36]. AspenPlusÒ chemical process design software is used to calculate the performance of all plant components. 3. Methodology The first task required in a rigorous thermo-economic analysis, is the definition of the ‘productive structure’ of the analyzed plant.

M. Gandiglio et al. / Energy 55 (2013) 142e155

Each unit of the system has a particular ‘productive’ function that contributes to achieve the final productive objective. Following the approach of Tsatsaronis [2], the plant (system) structure sets the difference between which flow, or combination of flows, constitutes the product(s) of the single unit/component (P) and which is instead the resource(s) or fuel available (F). Tables 2 and 3 show the productive structure of the atmospheric and pressurized plants, respectively: the assumptions made here will constitute the basis for both exergy and exergoeconomic analyses presented in this work. No discharges or losses have been taken into account for different plant components. 3.1. Exergy analysis Assuming the absence of nuclear, magnetic, electrical and surface tension effects, total exergy of a system can be divided into four components: physical, chemical, kinetic and potential exergy, respectively [2].

b ¼ bPH þ bCH þ bK þ bP :

(2)

Kinetic and potential exergy can be ignored as only negligible variations of two quantities occur within the systems here analyzed compared to the variations of chemical and physical exergy. The specific physical (also called as thermo-mechanical exergy) exergy associated with a mass flow is:

bPH ¼ ðh  h0 Þ  T0 ðs  s0 Þ:

bCH ¼

X

Table 3 Productive structure of all the components of the pressurized analyzed plant. Subsystem

Resource/fuel

Product

Loss

Compressor Fuel mixer Fuel pre-heater Air mixer Reformer

Wc Gb;7 Gb;13  Gb;14 Gb;17

Gb;9  Gb;8 Gb;3  Gb;2 Gb;2  Gb;1 Gb;10  Gb;9 Gb;4  Gb;3

e e e e e

SOFC

Gb;4  Gb;5

  yk m*k  m*0;k :

T0 Tref

!

We þ Fref $ 1 

Gb;11  Gb;12 Gb;5  Gb;6 Gb;12  Gb;6 Gb;15 Gb;14  Gb;15

Air recirculator Fuel recirculator After e burner HRSC Turbine

T0 Tref 

!

e

Gb;17 Gb;7 Gb;13 Wh Wt

e e e Gb;16 e

The chemical exergy of a substance not present in the external environment was evaluated by considering an ideal reaction of the specified substance with other substances whose chemical exergy in the environment is known [2]. For instance, considering a pure hydrocarbon fuel CaHb at T0 and p0, its standard chemical exergy is calculated as following:

   b b gF þ a þ g O2  ag CO2  g H2 OðlÞ ðT0 ; p0 Þ 4 2    b b CH CH þ aeCH : þ e  a þ e CO2 2 H2 OðlÞ 4 O2

 bCH ¼ F

(5)

The exergy efficiency of the whole plant and every single component was evaluated following the assumption of Table 2; by definition, the efficiency is expressed by the summation of products exiting the k-component divided by the summation of fuels needed to generate them:

(4)

where yk is the molar fraction of the k-component in the gas mixture; m*k is the chemical potential of a gas specie in the restricted dead state, and m*0;k is the chemical potential of a gas specie in the dead state. It is worth to remind that in the dead state the gas specie is in thermo-mechanical (equilibrium of temperature and pressure) and chemical equilibrium (equilibrium of composition) with the external environment. The chemical composition of the environment has been assumed by the work of Dincer et al. [37].

Fref $ 1 

þ Gb;11  Gb;10

(3)

Reference environment conditions of restricted dead state (15  C, 1 atm) were assumed for inlet streams into the system. Specific molar enthalpies and entropies for every stream were sourced directly for the AspenPlusÒ simulation spreadsheet. The molar chemical exergy per mole of gas was instead calculated as following:

145

P

ðG$bÞproduct P : ðG$bÞfuel

εk ¼

(6)

Exergy, like mass and energy, is an extensive property so it can be transferred into or out of a control volume. The exergy balance for a control volume can be expressed, in its general form, as following:



dAt dt

 ¼

! X X T0 Fj  ðWt Þ þ Gi bi  Ge be  T0 $Si : 1 Tj e

X j

i

(7) Table 2 Productive structure of all the components of the atmospheric analyzed plant. Subsystem

Resource/fuel

Product

Loss

Blower Air pre-heater Fuel mixer Fuel pre-heater Air mixer Reformer

Wc Gb;15  Gb;16 Gb;7 Gb;14  Gb;15 Gb;18

Gb;9  Gb;8 Gb;10  Gb;9 Gb;3  Gb;2 Gb;2  Gb;1 Gb;11  Gb;10 Gb;4  Gb;3

e e e e e e

SOFC

Gb;4  Gb;5

Fref $ 1 

T0 Tref

!

We þ Fref $ 1 

T0 Tref 

!

e

þ Gb;12  Gb;11 Air recirculator Fuel recirculator After e burner HRSC

Gb;12  Gb;13 Gb;5  Gb;6 Gb;13  Gb;6 Gb;16

Gb;18 Gb;7 Gb;14 Wh

e e e Gb;17

Assuming steady operation, the previous equation becomes:

0 ¼

X

1

j

! X X T0 _ tþ Fj  W G i bi  Ge be  T0 $Si : Tj e

(8)

i

In compact notation the equation can be written as:

0 ¼ Jq  Wt þ

X X Gb;i  Gb;e  Jd : i

(9)

e

From which the rate of exergy destruction Jd can be calculated. The exergy destruction ratio is also a useful index that compares the rate of exergy destruction in a specified system k-component, to the exergy rate of the fuel entering the overall system; it is therefore defined as following:

yD;k ¼

JD;k Gb F;tot

:

(10)

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M. Gandiglio et al. / Energy 55 (2013) 142e155

The exergetic factor is another useful index that relates the rate of fuel spent in the k-component with the total fuel processed in the plant. The definition is the following:

fk ¼

Gb F;k : Gb F;tot

(11)

3.2. Economic analysis The economic viability of each plant was estimated using the EPRI TAG [38] revenue requirement methodology in conjunction with the capital cost database developed by Kreutz et al. [39]. Economic parameters used to estimate the cost of generating electricity are given in Table 4. All capital costs are escalated at mid-2007 US dollars using the Chemical Engineering Plant Cost Index [40]. For this study, the design and capital cost of SOFC modules were calculated following NETL references [35,41,42]; additional costs for SOFC piping and vessel insulation were taken from Siemens Westinghouse [43]. The cost of high temperature heat exchangers was estimated using data in Chemical Engineering Handbooks [44,45] and those reported in Refs. [46,47]. Spare SOFC capacity is assumed to be installed along with the normal capacity to compensate for stack degradation [35]. The TPC (total plant cost) for the two plants was calculated; considering a given value of interest during construction, the TPI (total plant investment) was also evaluated. The TPC or “overnight construction cost” includes engineering and overhead, general facilities, balance of plant, and both process and project contingencies. More in detail, in the analyzed power plants, the TPC has been determined by summing together capital costs of the main plant components: SOFC stack and related spare capacity, NG desulfurizer, anode and cathode recirculators, cathode air compressor, air and fuel recuperator, after-burner, HRSC (steam generator and steam turbines), BoP components (considered as 15% of other costs) and gas turbine group for the pressurized plant. The TPC is determined as the sum of two cost components: the Bare Erected Cost and the Engineering, Procurement and Construction Cost [47]. The BEC (bare erected cost) comprises the cost of process equipment, on-site facilities and infrastructure that support the plant (e.g., shops, offices, labs, road), and the direct and indirect labor required for its construction and/or installation. The EPCC (engineering, procurement and construction cost) comprises the BEC plus the cost of services provided by the

Table 4 Economic assumptions. Natural gas price, $/GJ, HHV Capacity factor Interest during construction, fraction of TPC O&M, fraction of TPC per year SOFC module lifetime Plant lifetime, yr Interest rate Income tax rate Capital depreciation Capital charge rate CCR Operating and maintenance fixed cost Carbon price, CO2 tax Repayment term of debt Contracting strategy

6.35 85% 11.4% 4% 5 20 10% 38% effective (34% federal, 6% state) 20 years, 150% declining balance 14.38% 35 $/KWe/year 0 $/ton CO2 15 years Owner assumes project risks for performance, schedule and costs

EPC (engineering, procurement and construction cost) contractor. EPC services include: detailed design, contractor permitting (i.e., those permits that individual contractors must obtain to perform their scopes of work, as opposed to project permitting, which is not included here), and project/construction management costs. The TPC (total plant cost) comprises the EPCC plus project and process contingencies. BEC, EPCC and TPC are overnight costs expressed in base-year dollars. The TPI is thus given by the sum of TPC and the allowance for funds during construction, taken as 11.4% of TPC (in accordance with NETL reports). Following again the DOE/NETL methodology, the LCOE (levelized cost of electricity) was calculated and used to compare together the two plant configurations. (Note the LCOE compares the prices of the two plants but also take into considerations the amount of power that they generate). To determine the LCOE, four cost terms have to be calculated. 1. Installed capital

 CInst$Capital

 $ TPI$CCR$106 ¼ : MWh 8766$CF$NEPO

(12)

where TPI is the total plant investment found before, CCR is the capital charge rate and 8766 are the total annual hours of work that are escalated by the capacity factor CF for power plants (Table 4). The NEPO is the net electrical power output and can be determined as the difference between the total gross power output (SOFC and HRSC) and the plant electricity consumption (air compressor and inverter losses). 2. Operating & Maintenance

CO&M ½$=MWh ¼

TPI$O&M$106 : 8766$CF$NEPO

(13)

where O&M is the Operating and Maintenance Fraction of TPC per year (Table 4). 3. Operating & Maintenance SOFC Modules

CO&M SOFC ½$=MWh ¼

SOFC Power AC$O&MATMPRES $103 : 8766$CF$NEPO (14)

where O&MATM is the operating and maintenance fixed cost for the atmospheric SOFC and it has been calculated assuming a lifetime of 5 years, a sparing capacity equal to 7.4% of the initial one and a fixed O&M cost of 35 $/kW/year for the atmospheric plant and 32 $/kW/year for the pressurized one. 4. Natural Gas The cost of natural gas has been assumed to be 6.35 $/GJ [48,49] based on HHV. The latter can be converted in $/MWh according with the following equation:

CNG ¼

6:35$HHV$3:6 : NEPO

(15)

Summing all the four costs, it can finally be found the levelized cost of electricity as follows:

LCOE½$=MWh ¼ CInst$Capital þ CO&M þ CO&M SOFC þ CNG :

(16)

M. Gandiglio et al. / Energy 55 (2013) 142e155

For the thermoeconomic analysis, it is also necessary to convert the price of components from M$ to $/s; for such conversion the CRF (capital recovery factor) was used according to the following definition [2]:

CRF ¼

A i$ð1 þ iÞn ¼ : P ð1 þ iÞn  1

(17)

where i is the interest rate and n the plant lifetime expressed in years. The CRF is used to determine the equal amounts A of a series of n money transaction, the present value of which is P. The value of the amounts A corresponds to the component capital cost while the present value P that has to be determined corresponds to the capital investment ZCI, that can finally be expressed for each subsystem as:

ZCI ¼

C i$ð1 þ iÞn $ : 3600$h ð1 þ iÞn  1

(18)

where C is the component capital cost and h are the annual operating hours (evaluated taking into account the capacity factor). To determine the actual cost generated in the process, eventually the capital investment cost term is summed together with operating and maintenance costs (expressed as a percentage of it):

propositions. In case of multiple outlet flows, for each unit a number of additional equations must be written equal to the number of output flows that are not loss flows minus one. For determining these additional equations, two additional propositions are required: 4. If an output flow of a unit is a part of the fuel of this unit, then it is understood that its unit exergetic cost is the same as that of the input flow from which it is originated. 5. If a unit has a product composed of several flows, then the same unit exergetic cost will be assigned to all of them. In addition to the exergy cost balance for each unit (n equations), the incident matrix has then (mn) auxiliary equations that can be written by using prepositions 2, 3, 4 and 5. The thermoeconomic cost balance for any single unit of the plant can be expressed as:

PF þ Z ¼ PP :

(19)

3.3. Thermoeconomic analysis Putting together the exergy and economic results into a common framework is the goal of thermoeconomic analysis. When economics is also taken into account, the perspective is widened by the introduction of two additional factors: market prices e which are not necessarily linked to the exergy of the processed resources, and cost for depreciation and maintenance of the installation needed for the productive process. To solve the fundamental problem, it is advisable to formulate it in a compact form. The plant has been defined before as a set of subsystems or units linked to each other and to the environment by another set of matter, heat and work flows [1]. The relation between flows and subsystems is set up through the incident matrix A [n x m], where n is the number of subsystems and m the number of stream flows within the system or plant: the matrix elements, aij, take the value þ1 if stream j enters the subsystem i, 1 if the stream leaves the subsystem, 0 otherwise (i.e. there is no physical relationship between them). The more detailed definition of the incidence matrix, the better are the chances to identify the causes of inefficiency within the studied plant. Valero et al. [1] have formulated a rational procedure for determining costs, based on five main propositions: 1. There are as many equations of exergetic cost balance as the number of units in the installation; 2. From the knowledge of the types of fuel entering the plant, an equation for each flow entering the system has to be formulated. 3. In the absence of external assessment, the cost value of a stream leaving the plant control volume is set to zero. If a unit (or component) has only one output flow (that is not a loss), the problem can be solving by applying the previous

(20)

And the final system of equations to be solved takes the following form:

A  P ¼ Z:

(21)

where matrix dimensions are:

½m  m  ½m  1 ¼ ½m  1: Z ¼ ZCI þ ZOM ¼ ZCI þ 4%$ZCI :

147

(22)

For instance, when analyzing the SOFC stack unit, there are four streams that leave this subsystem: the exhaust cathode air, the exhaust anode fuel, electrical power and a flux heat (transferred to the reformer); hence, three auxiliary equations are needed. By using propositions 5, each product (exergy increase of the cathodic flow, electrical power and heat flux for the reforming) has got the same unit thermoeconomic cost. Since the anodic flow decrease its exergy through the SOFC, proposition 4 is instead applied to evaluate to set its unit thermoeconomic cost the same as the fresh (inlet) anodic flow. To evaluate the two SOFC plants, the cost of exergy destruction and the exergoeconomic factor were calculated for every component. The cost of exergy destruction is the cost of the fuel entering the unit multiplied over the rate of exergy destroyed:

CD ¼ cF $Jd :

(23)

The exergoeconomic factor is defined instead as the total capital cost over to the sum of total capital cost and the cost of exergy destruction within a certain component:

fex ¼

Z : CD þ Z

(24)

Finally, the TCOE (“thermoeconomic” cost of electricity) is also introduced, which related the total thermoeconomic cost of the plant CD þ Z with the power generated by the same:

TCOE ¼

CD þ Z : Net Electrical Power

(25)

4. Results 4.1. Energy analysis The energy performance of the SOFC plant operating either at atmospheric pressure or 20 bar are briefly summarized in Table 5.

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M. Gandiglio et al. / Energy 55 (2013) 142e155

Table 5 Plant performance results for the atmospheric and pressurized power plant. Atmospheric plant

Pressurized plant

kmol s1 MJ kmol1 MWt

0.437 932.7 407.6

0.437 932.7 407.6

V V V V MWe

85% 73% 0.50 2.08 3.17 0.746 0.985 0.866 0.926 223.7

85% 73% 0.55 1.56 2.24 0.793 1.020 0.927 0.973 238.0

Additional power from GT and ST  TIT after-burner exhaust C Air turbine power MW Air compressor consumption MW GT mechanical efficiency GT alternator efficiency GT net power, AC MWe HRSC steam expander MW

e e 4.1 98% 99.7% e 53.6

1019 123.5 82.9 98% 99.7% 39.6 25.4

Plant power output and efficiency Power output (AC) MWe Inverter efficiency AC electrical efficiency

263.1 96.0% 64.6%

292.9 96.0% 71.9%

Fuel input NG feed NG HHV NG fuel input (HHV) SOFC power island Global fuel utilization, FU Local fuel utilization, FU* Air recirculation fraction Global air utilization, l Local air utilization, l* Operating voltage Inlet Nernst voltage Outlet Nernst voltage Average Nernst voltage SOFC power (DC)

The HHV plant efficiency is w64% for atmospheric plant, and almost 6 percentage points higher in the pressurized configuration. Hence, pressurization provides a notable boost to plant efficiency. In the following, the thermoeconomic approach will be used to clarify these results and better understand in which components exergy losses take place. In the pressurized plant, it is also observed an increase in total power output because of the net GT work available. 4.2. Exergy analysis By using (specific) enthalpy and entropy values and mass flow rates, the chemical and physical exergy and the total exergy for each stream of the cycle were determined. To provide an example, the exergy values for the pressurized plant are given in Table 6. Starting from the inlet flows (stream S1, natural gas, and S8, air), the total (rate of) exergy increases through the heat-exchanger preheating the SOFC anode reactant and recirculation mixers; in the SOFC, the chemical energy of the fuel is finally converted into electrical power (and waste heat to a lesser extent). For this reason, the anode off-gas (stream S5) see strongly reduced its chemical exergy; otherwise, the (rate of) physical exergy results increased in the cathode side of the SOFC (from stream S10 to S11) due to the temperature rise that occurs as air not only bring oxygen to electrolyte, but is also the primary mean to remove excess heat generated in the exothermic SOFC reactions. The exhaust stream leaving the SOFC after-burner section decreases its exergy while pre-heating the fuel; the total (rate of) exergy finally also decreases in the turbine and the HRSC because part of its physical exergy is converted into mechanical power (through both a GT and STs integrated in an HRSC). Figs. 3 and 4 show the Sankey diagrams for both atmospheric and pressurized plants. Notably, in the pressurized configuration the high rate of exergy destroyed in the air pre-heater is completely

Table 6 Mass/energy streams for the pressurized plant: physical, chemical and total exergy. Mass/energy stream ID

Physical exergy [kJ/kg]

Chemical exergy [kJ/kg]

Total specific exergy [kJ/kg]

Total exergy [kW]

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 ¼ S_des W_c (blower) W_el (SOFC) W_t (Turbine) W_h (HRSC) F_ref
(1To/T)

7.05Eþ03 3.32Eþ04 2.97Eþ04 2.49Eþ04 2.87Eþ04 2.87Eþ04 2.87Eþ04 1.61E-02 1.34Eþ04 1.67Eþ04 2.02Eþ04 2.02Eþ04 3.11Eþ04 2.85Eþ04 7.66Eþ03 2.10Eþ03 2.02Eþ04 7.05Eþ03 n.a. n.a. n.a. n.a. n.a.

8.77Eþ05 8.77Eþ05 2.36Eþ05 2.00Eþ05 5.29Eþ04 5.29Eþ04 5.29Eþ04 1.71Eþ02 1.71Eþ02 1.97Eþ02 2.94Eþ02 2.94Eþ02 3.22Eþ02 3.22Eþ02 3.22Eþ02 3.22Eþ02 2.94Eþ02 8.77Eþ05 n.a. n.a. n.a. n.a. n.a.

8.84Eþ05 9.10Eþ05 2.66Eþ05 2.25Eþ05 8.16Eþ04 8.16Eþ04 8.16Eþ04 1.71Eþ02 1.35Eþ04 1.69Eþ04 2.05Eþ04 2.05Eþ04 3.14Eþ04 2.88Eþ04 7.98Eþ03 2.43Eþ03 2.05Eþ04 8.84Eþ05 n.a. n.a. n.a. n.a. n.a.

3.86Eþ05 3.98Eþ05 5.19Eþ05 5.60Eþ05 2.36Eþ05 1.12Eþ05 1.24Eþ05 9.89Eþ02 7.81Eþ04 2.00Eþ05 2.26Eþ05 1.02Eþ05 1.96Eþ05 1.80Eþ05 4.97Eþ04 1.51Eþ04 1.24Eþ05 3.86Eþ05 8.73Eþ04 2.38Eþ05 1.17Eþ05 2.41Eþ04 4.46Eþ04

avoided. The no need for air pre-heating through in heat-exchanger in the PSOFC plant, is the combination of two distinct plant layout design solutions that are:
air compression at over 20 bar already produces a relatively hot gas (found at almost 500  C);
recirculation of a fraction of the cathode exhaust to boost the temperature of the air exiting the compressor at level suitable for the SOFC. In the atmospheric plant, the worst component of the cycle is the air heat-exchanger followed by the after-burner (where combustion of the anode off fuel is carried out) that present an exergy efficiency of around 60% as shown in Tables 7 and 8: the main advantage of pressurizing the plant consists in the removal of these components and consequently of all disadvantages related to it. Analyzing all the exergy parameters (Tables 7 and 8), a w20% reduction in the rate of exergy destroyed is achieved in the pressurized plant. Exergy efficiencies of single components are quite similar in the two configurations, with only relatively small increase in total exergetic efficiency of SOFC and reformer in the pressurized system. Looking at the exergetic factor, it can be concluded that the SOFC and the after-burner are units that processing a high rate of the inlet plant resource (i.e., the inlet NG feed). In general, the pressurized plant outperforms the atmospheric one and brings a reduction of exergy destruction. 4.3. Economic analysis Following the EPRI-TAG methodology and taking base costs and scaling factors from DOE/NETL reports, capital costs of two power plants analyzed in this study were evaluated. In Table 9, costs for PSOFC plant are provided. The component with higher cost is the SOFC, which is responsible for nearly half of the total plant capital cost. The pressurized stack and surrounding power module have a higher bulk cost compared to the atmospheric one. (Note that spare capacity, activated at regular intervals is required

M. Gandiglio et al. / Energy 55 (2013) 142e155 Fig. 3. Sankey Diagram for the atmospheric plant. Blue flows corresponds to fuel, green to air, violet to exhaust gases, orange to heat, red to power and grey to exergy destruction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

149

150 M. Gandiglio et al. / Energy 55 (2013) 142e155 Fig. 4. Sankey diagram for the pressurized plant. Blue flows corresponds to fuel, green to air, violet to exhaust gases, orange to heat, red to power and grey to exergy destruction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

M. Gandiglio et al. / Energy 55 (2013) 142e155 Table 7 Exergy performance of the atmospheric plant. Component

Exergy efficiency ε [%]

Rate of exergy destroyed jD [MW]

Exergy destruction yd [%]

Exergetic factor f

Fuel HX Fuel mixer Fuel recirculator Reformer SOFC Blower Air HX Air mixer Air recirculator After-burner HRSC Total

71.8% 97.9% 100.0% 85.9% 96.1% 81.5% 60.4% 97.9% 100.0% 89.3% 65.6%

4.5 2.4 0.0 11.0 13.9 0.8 32.0 1.9 0.0 21.0 15.7 103.2

1.16% 0.63% 0.00% 2.88% 3.62% 0.21% 8.36% 0.50% 0.00% 5.47% 4.11%

0.04 0.30 0.30 0.20 0.93 0.01 0.21 0.24 0.24 0.51 0.20

to maintain a constant power output of the plant throughout its lifetime as stack performance gradually degrades over the time). Expensive pieces equipment of PSOFC plant are also the turbine exhaust-expander and air compressor; whereas in the atmospheric plant, air heat-exchanger is characterized by a high cost due to large exchange area required to pre-heat air up to w500  C. Table 10 shows the total investment cost and total plant cost for both power generation SOFC plants. Both are higher for the pressurized system. However, building and running plant expenses must be always weighed on total electricity produced. For this reason, levelized cost of electricity was the metric used to have a fair economic assessment of two SOFC systems under investigation. In fact, despite its higher capital and investment costs, the pressurized plant produces more electricity generation and eventually has a LCOE comparable to that of the atmospheric plant (Table 10). Economic analysis, like energy and exergy ones, bares out advantages of pressurized SOFC operation over atmospheric one. 4.4. Thermoeconomic analysis Thermoeconomic analysis was then applied to the SOFC plants considered in this study. For brevity, in Table 11 only thermoeconomic costs of streams in the pressurized plant are given. The cost of inlet fuel is the natural gas price in Table 4 converted from energetic (HHV) to exergetic terms; while the cost of inlet air is set to zero because the fluid is available in the environment. Also, the cost of the exhaust leaving the HRSC is

Table 8 Exergy performance of the pressurized plant. Component

Exergy efficiency ε [%]

Rate of exergy destroyed jD [MW]

Exergy destruction yd [%]

Exergetic factor f

Fuel HX Fuel mixer Fuel recirculator Reformer SOFC Compressor Air mixer Air recirculator After-burner Turbine HRSC Total

70.7% 98.1% 100.0% 91.2% 95.3% 88.3% 98.4% 100.0% 91.4% 90.4% 48.4%

4.7 2.4 0.0 3.9 15.2 10.2 2.0 0.0 18.5 12.5 10.5 80.0

1.23% 0.62% 0.00% 1.02% 3.94% 2.63% 0.53% 0.00% 4.80% 3.24% 2.72%

0.04 0.32 0.32 0.12 0.84 0.23 0.32 0.32 0.55 0.34 0.13

151

set to zero because no further heat recovery is carried out. Looking at Table 11, the specific thermoeconomic cost always increases its value through every component since each component comes with its capital investment and O&M cost. Furthermore, the increase of unit thermoeconomic cost through a single unit not only depends from the total cost associated with that component, but also from the position of the latter within the system. The deepest is the position of the unit into the system, the higher will be the cost. On the other hand, absolute thermoeconomic costs vary also according to the rate of exergy destruction associated with them. Tables 12 and 13 point out the main thermoeconomic parameters required to fully analyze the SOFC plants in this study. The first two columns give the cost of fuels/products for each subsystem (or component), where fuels and products are defined as in the productive structure of Table 1. Third and fourth columns are two sources of cost for each component: third column is the cost due to exergy destruction, while fourth column is the cost due to capital investment and O&M. The cost for exergy destruction depends on the rate of exergy destroyed in the single unit and on the fuel cost in the same component. Finally, column fifth gives the sum of two previous sources and thus represent the total thermoeconomic cost linked to each subsystem. Two relevant thermoeconomic parameters are also given in Tables 12 and 13: the relative cost difference, which indicates the increment in cost that a flow takes going through a certain unit, and the exergoeconomic factor. The latter express which of the two cost sources defined in column 3 and 4, respectively, is the most relevant. If exergoeconomic factor tends to zero, then cost for exergy destruction is the dominant issue and an alternative component or system layout might be required to avoid that loss. Otherwise, if exergoeconomic factor tends to one, then cost of the component is the relevant issue to be taken into account to improve plant economic performance. Equipments characterized by a low exergoeconomic factor in the studied systems are burner, HRSC, turbine compressor and expander (in the pressurized plant) and the air heat-exchanger (in the atmospheric plant). These components are therefore those whose exergetic performance should be enhanced or that should be avoided at all in the plant layout, if possible. Otherwise, there are components, especially the SOFC, with a very high investment cost which are critical to determine the economic profitability of the power plant. By taking into account the overall thermoeconomic cost of the plant and relating it to total power generated, a “thermoeconomic” COE can be determined and used to further compare together the performance of the analyzed SOFC systems. In other words, the TCOE combines both exergy and economic results. Table 14 summarizes the main exergy, economic and thermo-economic parameters calculated so far and shows also a better thermoeconomic performance of the pressurized system, with a TCOE 16.5 $/MWh lower than atmospheric case. 5. Discussion Results suggest that a large pressurized SOFC is in principle able to perform better than an atmospheric one. A 20% less of exergy destruction yields from SOFC operation at 20 bar; also, a LCOE comparable to that of the atmospheric case is produced. Looking at exergy and economic results combined together in a rigorous thermoeconomic assessment, the thermoeconomic cost of electricity was introduced and used to show the better overall performance of the pressurized plant, with a TCOE in the PSOFC plant 25% lower than in the atmospheric one. Looking at the Bejan-Tsatsaronis definition. “Thermoeconomy is the branch of engineering that combines exergy analysis and

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M. Gandiglio et al. / Energy 55 (2013) 142e155

Table 9 Cost of components for the pressurized plant. Plant component SOFC power core Pressurized SOFC Pres. SOFC spare capacity Burners After-burner Fuel processing NG desulfurizer Turbo-machinery Anode recirculator Cathode recirculator GT air compressor GT air/exhaust expander þ BoP Heat-exchangers Medium-T SS HX (fuel recuperator) Heat recovery steam cycle Boiler/steam generator, ductwork, & stack Steam turbine (ST), condenser, steam piping, auxiliaries

Scaling parameter

Base Cost scaling Base cost. Required Component Component OC Component OC cost capacity. So factor Co (2007 M$) capacity OC cost (M$) cost with BOP (M$) with BOP ($/kWe)

SOFC power output, MWe SOFC power output, MWe

1

1

0.657

228.5

150.2

150.2

531

1

1

0.049

228.5

11.2

11.2

40

Heat duty, MWt

1

0.46

0.424

73.03

3.1

3.6

13

NG volumetric flow, kmol/s

1

0.84

1.257

0.44

0.6

0.8

3

1.0

0.497

2.89

0.3

0.4

1

1.00

5.132

6.05

1.4

1.7

6

82.91 123.52

10.4 10.1

12.3 12.0

42 41

2340.5

2.7

3.2

11

Anode exhaust flow, 4.27 kmol/s Cathode exhaust flow, 21.71 kmol/s Power output, MW 232.0 Power output, MW 464.0

0.8 0.8

Exchange area, m2

100

0.36

Boiler duty, MWth

355

1.00

52

84.7

12.4

14.7

50

ST gross power, MW

232

0.67

30

25.4

13.5

16

54

226.1

768

Power plant BoP and auxiliaries BOP (feedwtr. CW. elec. controls. Percentage of TPC sitework. buildings) Total Plant Cost (TCP), 2007 M$

0.877

15.5%

economic evaluations to provide the system designer or operator with information not available through conventional energy analysis and economic evaluations but crucial to the design and operation of a cost-effective system” [2], it’s clearly understood the meaning of the values of Table 14: with a only economic analysis the values of LCOE are similar for both plants. That can be justified by the higher plant cost of the PSOFC system over the atmospheric one, which is mitigated by its higher electricity power generation. From these values none of the plants seems to have higher performance if compared to the other one. With a thermoeconomic analysis, on the other hand, parameters related to the exergy performance of the plants are melted together with total plant costs and consequently the exergetic benefits of the pressurized plant surface and that is the reason why the TCOE is higher for the PSOFC plant if compared to the atmospheric one.

Table 10 Economic performance of the atmospheric and pressurized plant.

Total plant cost, TPC [$/kWe] Allowance for funds during construction, AFDC [$/kWe] Total plant investment, TPI [$/kWe] Levelized cost of electricity, LCOE [$/MWh] Installed capital O&M O&M SOFC modules Natural gas

23.8 29.2

Atmospheric plant

Pressurized plant

753 86

768 88

838 59.42 16.18 4.04 3.55 35.65

855 55.62 16.50 4.12 3.35 31.64

Table 11 Thermoeconomic costs for the pressurized plant. Mass/energy stream

Thermoeconomic cost P [$/s]

Unit thermoeconomic cost c* [$/kJ]

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18¼S Des W_c (blower) W_el (SOFC) W_t (turbine) W_h (HRSC) F _ref

6.79 7.22 9.60 10.73 4.52 2.14 2.37 0.00 2.17 5.62 6.29 2.85 5.01 4.59 1.27 0.00 3.45 6.79 2.11 6.06 3.37 1.41 1.14

1.76E05 1.82E05 1.85E05 1.92E05 1.92E05 1.92E05 1.92E05 0.00Eþ00 2.78E05 2.81E05 2.78E05 2.78E05 2.56E05 2.56E05 2.56E05 0.00 2.79E05 1.76E05 2.55E05 2.55E05 2.73E05 5.57E05 2.55E05

M. Gandiglio et al. / Energy 55 (2013) 142e155

153

Table 12 Thermoeconomic performance of the atmospheric plant. Sub-system

Fuel cost cf [$/kJ]

Product cost cp [$/kJ]

Cost for exergy destruction CD [$/h]

Cost of components Z [$/h]

Total cost CD þ Z [$/h]

Relative cost difference r [%]

Exergoeconomic factor fex

Desulfurisator HX fuel Mixer fuel Reformer SOFC Fuel recirculator Blower HX air Mixer air Air recirculator After-burner HRSC Total Cost [$/h] TCOE [$/MWhe]

1.79E05 3.54E05 4.39E05 2.46E05 2.03E05 2.03E05 2.46E05 3.54E05 4.39E05 4.38E05 3.15E05 3.54E05

1.79E05 5.03E05 4.48E05 2.86E05 2.46E05 2.04E05 4.64E05 5.91E05 4.48E05 4.39E05 3.54E05 5.89E05

0.00 568.81 382.37 975.42 1017.19 0.00 69.90 4082.30 304.23 0.00 2379.61 2006.24

12.37 43.02 0.00 0.00 4213.89 3.43 203.74 95.36 0.00 31.86 59.63 901.13

12.37 611.84 382.37 975.42 5231.07 3.43 273.64 4177.66 304.23 31.86 2439.24 2907.37 17350.51 64.19

0.1% 42.2% 2.1% 16.4% 20.8% 0.0% 88.7% 67.0% 2.1% 0.2% 12.3% 66.3%

1.0000 0.0703 0.0000 0.0000 0.8055 1.0000 0.7446 0.0228 0.0000 1.0000 0.0244 0.3099

Table 13 Thermoeconomic performance of the pressurized plant. Sub-system

Fuel cost cf [$/kJ]

Product cost cp [$/kJ]

Cost for exergy destruction CD [$/h]

Cost of components Z [$/h]

Total cost CD þ Z [$/h]

Relative cost difference r [%]

Exergoeconomic factor fex

Desulfurisator HX fuel Mixer fuel Reformer SOFC Fuel recirculator Compressor Mixer air Air recirculator Burner Turbine HRSC Total [$/h] TCOE [$/MWhe]

1.76E05 2.62E05 1.92E05 2.55E05 1.92E05 1.92E05 2.55E05 2.90E05 2.89E05 2.38E05 2.62E05 2.62E05

1.76E05 3.83E05 1.96E05 2.80E05 2.55E05 1.92E05 2.96E05 2.95E05 2.90E05 2.62E05 2.94E05 5.98E05

0.00 446.74 165.19 360.58 1050.49 0.00 933.68 211.75 0.00 1589.78 1178.38 991.77

12.37 52.96 0.00 0.00 5946.92 6.52 210.89 0.00 27.74 59.24 188.38 482.49

12.37 499.71 165.19 360.58 6997.41 6.52 1136.09 211.75 27.74 1649.03 1374.65 1495.17 13936.21 47.71

0.05% 46.36% 1.97% 9.67% 32.78% 0.08% 16.05% 1.67% 0.22% 9.82% 12.44% 128.59%

1.0000 0.1060 0.0000 0.0000 0.8499 1.0000 0.1782 0.0000 1.0000 0.0359 0.1428 0.3367

Nomenclature Table 14 Values of exergy destruction, levelized cost of electricity and thermoeconomic cost of electricity for atmospheric and pressurized plant.

Total exergy destroyed [MW] LCOE [$/MWh] TCOE [$/MWh]

Atmospheric plant

Pressurized plant

103.2 59.42 64.19

80.0 57.82 47.71

6. Conclusions The advantages shown by thermoeconomic analysis come from both exergy and economic analysis but are effective money profits and consequently are, as said before, crucial to the design and operation of a cost-effective system. Therefore, SOFC pressurization is beneficial to plant performance and should sought by plant manufacturers and SOFC technology developers in view of future ultra-efficient plants that converts NG into electricity. Currently, SOFC manufactures are already operating single cells and planar stacks at pressures in the range 3e10 bar. Benefits of pressurization, especially in the hybrid plant configuration, seems to fully justify research and development in this direction.

A b bCH bCH F bK bP bPH CD cF cP f fex G Gb h h0 i j m n p0 s s0 T0 Vcell

incidence matrix exergy for a unit (mole basis) chemical exergy fuel chemical exergy kinetic exergy potential exergy physical exergy cost for exergy destruction unit cost of fuel unit cost of product exergetic factor exergoeconomic factor molar flow total exergy enthalpy of a unit (mole basis) enthalpy in a restricted dead state (mole basis) interest rate current density number of streams number of subsystems pressure of the restricted dead state entropy of a unit (mole basis) entropy in a restricted dead state (mole basis) temperature of the restricted dead state operating voltage

154

Vrev yD yk Z ZCI ZOM

M. Gandiglio et al. / Energy 55 (2013) 142e155

Nernst voltage exergy destruction ratio molar fraction of the k-th component external assessment capital investment rate in the external assessment operating and maintenance rate in the external assessment

Greek letters εk exergy efficiency of k-th component m*k chemical potential of a gas specie in a restricted dead state m*0;k chemical potential of a gas specie in a dead state P thermoeconomic cost PF thermoeconomic cost of fuel flows PP thermoeconomic cost of product flows Si exergetic term for irreversibilities Fj heat stream Jd exergy destruction Jq exergetic term related to the heat streams Abbreviations ASR area specific resistance BEC bare equipment cost CCR capital charge rate CF capacity factor CRF capital recovery factor EPC engineering, procurement & construction FU global fuel utilization GHG green house gas GT gas turbine HHV high heating value HRSC heat recovery steam cycle LCOE levelized cost of electricity NEPO net electrical power output O/C oxygen-to-carbon (molar) ratio O&M operating and maintenance fraction of TPC per year O&MATM operating and maintenance fixed cost for the atmospheric SOFC O&MPRES operating and maintenance fixed cost for the pressurized SOFC PSOFC pressurized SOFC SOFC solid oxide fuel cell ST steam turbine TCOE thermoeconomic cost of electricity TPC total plant cost TPI total plant investment References [1] Valero A, Lozano MA, Muñoz M. A general theory of exergy saving: part I. On the exergetic cost, part II. On the thermoeconomic cost, part III. Saving and thermoeconomics. Computer-Aided Engineering of Energy Systems 1986;3: 1e22. Second Law Analysis and Modeling. [2] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. John Wiley and Sons; 1996. [3] Solid State Energy Conversion Alliance (SECA) DOE program, info available at the website: http://www.netl.doe.gov/technologies/coalpower/fuelcells/seca/. [4] Thijssen J. The impact of scale-up and production volume on SOFC manufacturing cost, DOE/NETL report. http://www.netl.doe.gov/technologies/ coalpower/fuelcells/publications/JT%20Manufacturing%20Study%20Report% 20070522.pdf, 2007. [5] Thijssen J. Scale-up of planar SOFC technology for MW-level combined cycle system, DOE/NETL. http://www.netl.doe.gov/technologies/coalpower/fuelcells/ publications/SOFC_GTHybrid_Scaleup_FinalReport.pdf, 2003. [6] Calì M, Santarelli M, Leone P. Design of experiments for fitting regression models on the tubular SOFC CHP100 kWe: screening test, response surface analysis and optimization. International Journal of Hydrogen Energy 2006;32(2007):343e58.

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