- Email: [email protected]
hydrogen-fueled gas turbine system for decentralized applications
Sustainable Energy Technologies and Assessments 36 (2019) 100560
Contents lists available at ScienceDirect
Sustainable Energy Technologies and Assessments journal homepage: www.elsevier.com/locate/seta
Thermodynamic modeling and parametric study of a small-scale natural gas/hydrogen-fueled gas turbine system for decentralized applications
T
Alexandros Arsalis Research Centre for Sustainable Energy (FOSS), University of Cyprus, Kallipoleos 75, Nicosia 1678, Cyprus
ARTICLE INFO
ABSTRACT
Keywords: Gas turbine Natural gas Hydrogen combustion Dual-fueled Thermodynamic modeling Parametric study
In this study a detailed thermodynamic model of a small-scale natural gas/hydrogen-fueled gas turbine system is presented. The thermodynamic model includes both a basic thermodynamic analysis and an exergy analysis. Exergy analysis aims on the identification of exergy destruction in the various system components. Specifically, it is investigated how hydrogen addition in the fuel supply can affect exergy loss. Off-design modeling is also implemented to realistically evaluate performance at part-load operation. A parametric study is conducted to examine the effect of hydrogen ratio on system performance. The hydrogen ratio is varied from 0 to 0.9, to examine the behavior of the developed model at different hydrogen contents. The results suggest that hydrogen addition to the natural gas fuel supply can change the operational behavior of the gas turbine cycle. Although net electrical efficiency is only marginally increased as hydrogen ratio is increased (0.347 vs. 0.356), the exergetic efficiency is more significantly affected, mainly due to the reduction of combustor losses as hydrogen content increases (0.338 vs. 0.360). Also, hydrogen addition has a positive effect in terms of carbon emissions, since even a tiny hydrogen injection at a hydrogen ratio of 0.1 (on a volumetric basis) results in a 6.1% reduction in CO2 emissions, as compared to methane-only fueling. Overall, the results suggest that even a small amount of hydrogen addition to the gas turbine cycle can have a significantly positive effect in terms of system efficiency and operational cost.
Introduction Decentralized, small-scale power systems are gaining momentum to create a more flexible energy system infrastructure. Several system configurations have already been proposed as alternatives to electricityonly, or in general, large-scale power stations [1,2]. Centralized systems occasionally create network congestion and transmission/distribution losses. On the other hand, on-site power generation results in the generation of local emissions, and it could be problematic if the system is located within larger cities/urban residential areas. Renewable energy sources eliminate emissions during power generation, but renewable power supply can never match demand without energy storage. Especially in the case of solar photovoltaic (PV) technology, where electricity is only produced during daytime, storage or combination with other power technologies is required. One viable possibility is the combination of natural gas-fired gas turbine cycles with PV technology. In these combined systems, apart from the generation of a portion of the electricity needed by the supplied electricity network from the PV system, excess electricity can be converted to hydrogen and mixed with the natural gas supply for combustion in the gas turbine cycle. It has been suggested that hydrogen generated from electrolysis
can be injected to natural gas streams, directly or after modification to synthetic methane. The latter is more complicated because it needs integration to a CO2 stream for the methanation process [3]. So far, the mixing of hydrogen to natural gas has received rather limited attention in terms of detailed mathematical modeling, and most configurations available in the literature, consider the re-generation of electrical energy via fuel cell technology. However, the possibility of injecting hydrogen to natural gas eliminates the need for an additional subsystem (i.e. a fuel cell unit), provided hydrogen content is significantly lower than natural gas content during combustion. The thermophysical characteristics of hydrogen differ significantly from natural gas, specifically hydrogen is lighter and more reactive than methane [4]. Although the use of different fuels can create instability to the operation of the gas turbine, since heat release variation could favor thermo-acoustic combustion instability [5], it has also been suggested that the operational window of a hydrogen-rich syngas-fired gas turbine is similar to the one for natural gas, primarily because the heating value of the two species is almost identical [6]. For hydrogenonly combustion, the heating value is significantly higher than methane, resulting in a reduction of the hot gas mass flow and the power output of the gas turbine, although water vapor content in the exhaust
E-mail address: [email protected]. https://doi.org/10.1016/j.seta.2019.100560 Received 23 February 2019; Received in revised form 22 October 2019; Accepted 24 October 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Nomenclature
el, net s
a, b, c, d , e Chemical reaction coefficients (−) Ef , in Energy rate of fuel (W) eai Excess air of species i (−) G Ratio of reduced mass flow rate to its design value (−) H Enthalpy per mole of fuel (J/kmol) h¯ Specific enthalpy (J/kmol) Lower heating value (J/kmol) LHV M Molecular weight (kg/kmol) mi Mass flow rate of species i (kg/s) N Power output at off-design (W) N Ratio of reduced power output to its design value (−) n Rotating speed (rpm) n Ratio of reduced rotating speed to its design value (−) ni Molar flow rate of species i (kmol/s) p Pressure (Pa) rH2, vol Hydrogen ratio (−) S Entropy per mole of fuel (J/K-kmol) Specific entropy (J/K-kmol) s¯ Temperature (oC, K) T V Volumetric flow rate (m3/s) v¯ Specific volume (m3/kmol) W Power output (W) x Mass fraction (−) Standard specific chemical exergy for stream i (J/kg) x CH , i x q, i Specific physical exergy for stream i (J/kg) y Mole fraction (−)
µ
Net electrical efficiency (−) Isentropic efficiency (−) Ratio of reduced efficiency to its design value (−) Mass flow rate ratio (−) Pressure ratio (−) Ratio of reduced pressure ratio to its design value (−) Total pressure recovery coefficient (−)
Subscripts/Superscripts
1, 2, ...,k a b c des f g gen gt i in ref s t
Streams Air Combustor Compressor Design (full-load operation) Fuel Gas (vapor state) Electric generator Gas turbine cycle Species Inlet Reference state Isentropic Turbine
Abbreviations EES PV
Greek symbols
Engineering Equation Solver Photovoltaic
Efficiency (−) gas increases (with an increase in specific heat capacity) [7]. This increase favors the generation of work at an identical turbine inlet temperature, while the increased moisture content results to an increase in turbine power output [6]. Also, small hydrogen contents in a natural gas-based combustion process in a gas turbine cycle can have a positive effect in terms of reducing unburned methane and CO emissions, in addition to CO2 emission reduction [8]. A recent study suggested that a natural gas-fueled gas turbine can be easily converted for hydrogen fueling, with a modification of its control software, and without any changes to the moving components [9]. The size and structure of the
combustion chamber of an existing natural gas-fueled gas turbine cycle will not need to be modified in the case of hydrogen injection, because hydrogen addition in the fuel allows reduction of natural gas at the same time, provided the combustion temperature is kept fixed. Since the energy density of hydrogen is higher than methane, the total fuel flow rate entering the combustion chamber will be lower in comparison to a methane-only system [10,11]. Currently, the open literature includes a very limited number of studies on methane/hydrogen fueled gas turbine systems. Ebaid et al. [12], studied an 100 MWe PV/hydrogen-fueled gas turbine hybrid
Fig. 1. Schematic representation of the natural gas/hydrogen-fueled gas turbine cycle.
2
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
system. Simplistic assumptions were considered for the gas turbine model to determine load consumption, in relation to the generation of electricity from the PV system. The authors assumed that the gas turbine would be fueled only with hydrogen and that the gas turbine would operate only at design conditions with a fixed thermal efficiency at 44%. Guandalini et al. [3], considered hydrogen injection to a centralized natural gas grid, in relation to large-scale wind turbine systems. Although part-load operation was considered through regression functions based on an industrial turbine, actual modeling of the gas turbine cycle was not implemented. The current study attempts to provide a detailed thermodynamic modeling of a natural gas/hydrogen-fueled gas turbine system, using both first and second law approaches. Also, the modeling includes both design and off-design considerations, so that system operation at partload conditions will not be compromised by simplistic fixed conditions. The developed system model sets a basis for future application-specific systems, including PV modules, electrolyzer stacks, hydrogen storage units, and heat integration and recovery to satisfy realistic load profiles. A parametric study is conducted to examine the effect of hydrogen ratio on key parameters, such as the power output, the fuel mass flow rate, the heat input rate, the flue gas composition, the thermodynamic and exergetic efficiencies, and the exergy destruction ratio. The parametric study also investigates the effect of hydrogen injection in terms of CO2 emission reduction, which is a significant factor in the design of sustainable energy systems.
System modeling of the gas turbine cycle The mathematical modeling, including the calculation of all thermophysical properties, and the associated parametric study are conducted with the commercially available software Engineering Equation Solver (EES) – Professional version. The values of the isentropic efficiencies for the compressor and turbine depend on the load of the gas turbine cycle power output. In this study a part-load model, based on the methodology developed in [15,16], has been formulated to determine part-load performance. Therefore, based on a selected load, the value of the isentropic efficiency is calculated through data interpolation. Thermodynamic model The total power output of the gas turbine is given by the sum of the partial power outputs resulting from the combustion of methane and hydrogen fuels: (1)
Wgt = Wgt ,CH4 + Wgt ,H2
The generated net electrical power output resulting from the expansion of the hot flue gas in the turbine can be given as a function of the enthalpies of the processes from air compression to turbine expansion. Through an energy balance of products and reactants for the combustion of methane fuel, terms can be rearranged to solve for power output:
System configuration
Wgt ,CH4 = nCH4 ·((H3,CH4
H4,CH4 )
aCH4 ·(h¯2
h¯1))·
(2)
gen
h¯1 and h¯2 are the specific enthalpies of air at the compressor inlet and the compressor outlet, respectively. The above equation is solved for nCH4 to determine the molar flow rate of the methane fuel. The molar flow rate of air for methane combustion is given by:
The system configuration is shown in Fig. 1. The combustor of the gas turbine cycle is fueled with natural gas and hydrogen, and the generated flue gas is expanded in the turbine to generate electricity via an electric generator. The following assumptions have been made for this study:
(3)
na,CH4 = aCH4 · nCH4
The volumetric flow rate of air for methane combustion entering the compressor is given by:
1. For calculation simplicity, natural gas is assumed to have the thermophysical properties of methane. 2. A catalytic combustion process is assumed for the gas turbine cycle to allow complete chemical reaction of the fuel reactants. 3. The combustion temperature is fixed and therefore it remains constant at part-load conditions, although at more realistic conditions, this value would normally drop slightly and steadily with decreasing load [6]. The reason of keeping the combustion temperature constant is to avoid mismatch of data calculation for the part-load model, since data from the part-load model are fed to the thermodynamic model, and therefore variation of combustion temperature would create inconsistency in the calculation of the isentropic efficiencies with the part-load model. 4. Ambient conditions are set at a pressure of 1 atm and a temperature of 15 °C. The pressure and temperature values at the inlet of the air compressor are set equal to the ambient conditions. The fuel temperature is assumed to remain constant and equal to ambient conditions. 5. The electric generator efficiency is fixed at 0.972 [13], for a gas turbine nominal power output of 12.9 MWe. The latter value is taken from available manufacturer’s data for an industrial gas turbine (Siemens SGT-400) [13]. A pressure ratio of 16.8 is assumed for the air compressor [13]. 6. A constant pressure drop of 5% is assumed for the combustor process [14]. 7. The model assumes that the gas turbine will respond to an electric load. Therefore, the electric load is treated as an input parameter.
(4)
V1,CH4 = na,CH4 · v¯1 Similarly, for hydrogen:
Wgt ,H2 = nH2 ·((H3,H2
H4,H2)
aH2 ·(h¯2
h¯1))·
(5)
gen
na,H2 = aH2 ·n H2
(6)
V1,H2 = na,H2 · v¯1
(7)
The total volumetric flow rate of air entering the compressor is the sum of the partial volumetric flow rates: (8)
V1 = V1,CH4 + V1,H2
The sum of the two partial volumetric flow rates is the total flow rate of air needed to enter the combustor for the reactions with methane and hydrogen. The lower heating value of methane on a molar basis is given by: Table 1 Values of the constant parameters in the thermodynamic model at design. Parameter description
pamb Tamb Tf gen
Wgt
The above input values for the gas turbine cycle at design conditions are tabulated in Table 1.
c
b
3
Value Ambient pressure Ambient temperature Fuel temperature
1 atm 15 °C 15 °C
Gas turbine power output
12.9 MWe
Compressor pressure ratio Combustor efficiency
16.8 0.95
Electric generator efficiency
0.972
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
LHVCH4 = h¯ CH4, ref
2·h¯ H2O, g , ref
h¯ CO2, ref
Ef , in,CH4 = nCH4 · LHVCH4
cycle efficiency and fuel mass flow rate have been calculated, the partload isentropic efficiencies for the compressor and turbine are calculated. The calculated data are then saved as a lookup table in the main model of the gas turbine cycle, and are used through interpolation to calculate performance at any given operating load condition. To avoid unrealistic operating schemes, the exhaust temperature of the combustor is kept constant at all loads. On the other hand, the rotating speed of the compressor and the turbine can be allowed to vary; therefore they are reduced as the load decreases. Since it is assumed that the compressor and turbine are connected in a single shaft, the rotating speed of the compressor is always assumed to be equal to the rotating speed of the turbine. The compressor rotating speed at full-load conditions is fixed at 14,100 rpm, per manufacturer’s data [13]. The design data mentioned in the description below are those identified at design. The fuel mass flow rate is defined as the difference between turbine and compressor mass flow rates:
(9) (10)
Similarly, for hydrogen:
LHVH2 = h¯ H2, ref
h¯ H2O, g, ref
Ef , in,H2 = n H2 · LHVH2
(11) (12)
The total energy rate of fuel and the corresponding net electrical efficiency, on an LHV basis, are given by:
Ef , in = Ef , in,CH4 + Ef , in,H2 el, net
=
(13)
Wgt Ef , in
(14)
The auxiliary equations for the thermodynamic model of the gas turbine cycle are given in Appendix A. These include the equations needed for the calculation of the reaction coefficients for the combustion of both methane and hydrogen in the gas turbine cycle for both the stoichiometric and actual reactions. Additionally, the mass balance and energy balance equations are given for the gas turbine cycle.
m f = mt
(22)
mc
The gas turbine cycle efficiency ratio is [15]: gt
= 3.18· N
4.69·N 2 + 3.69·N 3
1.18·N 4
(23)
The power output ratio is defined as the ratio of off design to design net power output for the gas turbine cycle:
Exergy analysis An exergy analysis can provide an in-depth evaluation of the sources of irreversibility in an energy system. For the current system configuration, exergy analysis is used to reveal the trend of exergy destruction when varying hydrogen content in the total fuel. The methodology for exergy analysis has been described in detail in a previous publication [17]. The main equations are summarized in Table 2. The exergy destruction for each system component is calculated through exergy balances. The exergy balances for the compressor, turbine, and combustor are the following, respectively:
N =
N Ndes
(24)
Similarly, for gas turbine cycle efficiency: gt
gt
=
(25)
gt , des
m1·xq,1 + Wc = m2· xq,2 + Xdes, c
(15)
The previous equation is solved for gt to determine the off-design efficiency of the gas turbine cycle. Similarly, the off-design mass flow rate ratio is determined based on a curve function for the fuel consumption ratio [15]:
m3· xq,3 = m4 · xq,4 + Wt + Xdes, t
(16)
Gf = 0.288 + 0.624·N + 0.088·N 2
Xf + m2· xq,2 + mf ·x q, f = m3·xq,3 + Xdes, comb
(17)
Gf =
The associated exergy destruction ratios for the above components are defined as [18]:
yD, c
Xdes, c = Xf
yD, t = yD, comb
(19)
Xdes, comb = Xf
(20)
c, des
c
(27)
=
=
p2, des (28)
p1, des
p2
(29)
p1
The ratio of reduced pressure ratio to its design value, the ratio of reduced rotating speed to its design value, the ratio of reduced efficiency to its design value, and the ratio of reduced mass flow rate to its design value, are the following, respectively [15]:
The total rate of exergy destruction is the sum of component exergy destruction rates:
Xdes = Xdes, c + Xdes, t + Xdes, comb
mf mf , des
For the compressor, the pressure ratio is defined for design and offdesign conditions, respectively:
(18)
Xdes, t Xf
(26)
(21)
c
Part-load model
=
c
(30)
c , des
Table 2 Modeling equations used in the exergy analysis.
The gas turbine cycle must be able to respond to off-design conditions, i.e. at power output below the nominal power output of 12.9 MWe. In a previous study, [15] the compressor and turbine mass flow rates were provided to the model as input parameters and based on those values two output variables were determined, namely isentropic efficiency and pressure ratio. The study included typical curve functions to approximate gas turbine cycle efficiency and fuel mass flow rate at part-load conditions. However, since the modeling needs of the current study are different, it is assumed that after the part-load gas turbine
Variable description
Xf 2
XPH , i
XCH , i
Xi
4
Exergy rate of fuel (W) Exergetic efficiency (−) Physical exergy for stream i (W) Chemical exergy of stream i (W) Total exergy of stream i (W)
Model equation
Xf = mCH4 · hCH4 + mH2·h H2 2
=
Wgt Xf
XPH , i = mi ·x q,i XCH , i = mi· x CH ,i Xi = XPH , i + XCH ,i
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
nc =
c
nc nc, des
Parameter description
c
=
(32)
c , des
Gc =
Table 3 Values of the input parameters for the validation of the system model at design.
(31)
mc · mc, des ·
Tamb gen
T1 p1
Wgt c
(T1, des )
T4
(33)
p1, des
The performance formulas for the compressor are applied to determine the off-design to design ratio for the pressure ratio and the ratio of reduced efficiency to its design value, respectively [15]: 2
c
= c1· Gc + c2· Gc + c3
c
= (1
nc · 2 Gc
nc Gc
c2 = c3 =
(
DEN = p · 1
p
nc DEN
m nc
) + n ·(n c
c
m) 2
b
(36)
t
nt = nc
(39)
mt mc = µ· mt , des mc, des
(40)
t
=
p3
(42)
(43)
t
=
nt =
t , des
nt nt , des
=
1.4
0.4·
nt nt , des
= (1
t·(1
nt )2)·
nt · 2 Gt
nt Gt
(50)
Operation at design conditions At design conditions it is assumed that the gas turbine system will generate the nominal power output, i.e. 12.9 MWe. However, methane-
For the turbine, the ratio of reduced pressure ratio to its design value, the ratio of reduced rotating speed to its design value, the ratio of reduced efficiency to its design value, and the ratio of reduced mass flow rate to its design value, are the following, respectively [15,19]: t
where
System performance
(44)
p4
1 1
The system model is validated against measured manufacturer’s data extracted from a Siemens industrial gas turbine, namely SGT-400 [13]. The values of the input parameters for the validation are tabulated in Tables 3 and 4, respectively. The graph in Fig. 2 shows the simulation data against the experimental data for different part-loads against turbine exhaust mass flow rate. The graph shows a good agreement between the two data sets, and therefore it can be assumed that the system model has been modeled with adequate accuracy in comparison to an actual system.
p3, des p4, des
2 t 2 t , des
Model validation
and µ are set as constants [15].
=
(48)
p3, des
This section starts with a validation of the system model with available experimental data. Next the system model of the gas turbine cycle is analyzed at design conditions, and then at off-design conditions. Finally, the results of the parametric study are presented in detail, with emphasis on the performance of the system and its effect on key parameters.
The pressure ratio at design and off-design conditions is defined as follows, respectively: t , des
(T3, des )
Results and discussion
(41)
c
=µ=1
mt , des ·
T3 p3
The value of t is 0.3.
(37)
(38)
where
mt ·
(49)
nt , des = nc, des
= ·
16.8 555 °C
p·m·n c m2·nc3 DEN
The term b is a pressure loss coefficient for the combustor, set at a typical value of 0.95 [14]. The equations below relate the turbine parameters to the compressor parameters
t
12.9 MWe
Compressor pressure ratio Turbine exhaust temperature
(47)
T3, des mt = · · mt , des T3
2·m·nc2 DEN
The values for the remaining constants are m = 1.06, p = 0.36 and c4 = 0.3. Finally, a similar process to the compressor section is repeated for the turbine. Initially some parameters must be defined. For calculation simplicity, at off-design conditions the condition set at design operation for the pressure drop in the combustor is retained, i.e.:
p3 = p2 ·
Gas turbine power output
The performance formulas for the turbine are applied to determine the off-design to design ratio for the mass flow rate and the ratio of reduced efficiency to its design value, respectively [15]:
The constants c1, c2 and c3 are found with the following functions [16]:
c1 =
15 °C 0.972
t , des
Gt = (35)
Ambient temperature Electric generator efficiency
t
=
(34)
nc )2)·
c4·(1
t
Value
Table 4 Values of the output parameters for the validation of the system model at design. Parameter description
(45)
el, net
T3 m1 m3
(46) 5
Value Net electrical efficiency
Turbine inlet temperature Compressor mass flow rate Turbine mass flow rate
0.348
1173 °C 39.68 kg/s 40.42 kg/s
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Table 6 Values of the key output parameters at design conditions. Parameter description el, net
Value Net electrical efficiency
0.348
Partial power output (hydrogen)
0.43 MWe
Energy rate of methane fuel
35.9 MW
Energy rate of hydrogen fuel
1.2 MW
Total energy rate of fuel
37.1 MW
Fuel mass flow rate (methane) Fuel mass flow rate (hydrogen) Total fuel mass flow rate
0.717 kg/s 0.010 kg/s 0.727 kg/s
Partial power output (methane)
Wgt,CH4 Wgt,H2 Ef ,in,CH 4 Ef ,in,H2 Ef ,in mCH4 mH2
mf
12.47 MWe
Fig. 2. Validation of the system model against manufacturer data (Siemens industrial gas turbine SGT-400 [13]).
to-hydrogen ratio could vary, depending on the availability of hydrogen at a particular time-segment. Therefore, a specific parameter could be defined here, which can be easily varied, namely hydrogen ratio, i.e. the ratio of hydrogen fuel flow rate to total fuel flow rate on a volumetric (or mole) basis:
rH2, vol =
v H2 vf
(51)
For the reasons explained in the previous sections, a typical value for this parameter at 10% is chosen to initially determine the thermophysical properties of the system at design conditions. For the streams shown in Fig. 1, the values of temperature, pressure, mass flow rate, and mole fractions are tabulated in Table 5. The key output parameters of the system model are tabulated in Table 6.
Fig. 3. Variation of compressor and turbine isentropic efficiencies for part-load operation of the gas turbine cycle.
stops to decrease linearly with decreasing load at loads below 60%. A similar trend is observed in the case of mass flow rate. As mentioned earlier (Section “Part-load model”), the exhaust temperature of the combustor in the computational simulations is kept constant at all loads to avoid unrealistic results. Also, both the compressor and the turbine are connected to the same shaft. However, these assumptions do not allow an optimum reduction of the air mass flow rate, as the load is reduced. More fuel is needed at part-load (especially at loads below 60%, as observed in Figs. 3 and 4) to achieve the desired power output from the gas turbine cycle. Therefore, for a higher fuel consumption (in relation to the generated power output), both net electrical and
Operation at off-design conditions The set of values for isentropic efficiency for the compressor and turbine are calculated with the part-load model and fed to the thermodynamic model; they are shown graphically in Fig. 3. The performance of the system in terms of net electrical efficiency is shown graphically in Fig. 4. Both figures suggest that as the load decreases, isentropic and net electrical efficiencies deteriorate rapidly, suggesting that system operation below 60% would be very inefficient and must be avoided. This trend is also evident in Fig. 5, where fuel consumption Table 5 Thermophysical property values at design conditions. Parameter description
Tk pk mk yCO2, k yH2 O, k
yN2, k yO2, k
Stream 1
2
3
4
Temperature at stream k (K) Pressure at stream k (Pa) Mass flow rate at stream k (kg/s) Mole fraction of CO2 at stream k
288 101,325 39.7085 0
708 1,702,260 39.7085 0
1445 1,617,147 40.4356 0.031
828 107,405 40.4356 0.031
Mole fraction of N2 at stream k
0.790
0.790
0.764
0.764
Mole fraction of H2O at stream k Mole fraction of O2 at stream k
0
0.210
0
0.210
6
0.067 0.138
0.067 0.138
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Fig. 7. Effect of part-load operation on total, methane, and hydrogen fuel consumption.
Fig. 4. Performance of the gas turbine cycle in terms of net electrical efficiency at part-load operation.
Fig. 8. Effect of part-load operation on the values of excess air for natural gas and hydrogen fuels.
Fig. 5. Fuel consumption and power output generation for the system at partload operation.
Fig. 6. Variation of inlet air and exhaust flue gas for the system at part-load operation.
Fig. 9. Effect of hydrogen ratio variation on the values of partial power output (methane vs. hydrogen).
isentropic efficiencies will deteriorate at off-design conditions. In Figs. 6 and 7, it is shown that low efficiency occurs at loads below 60%, because the system consumes more air (also more fuel, generating
more flue gas). Specifically, in Fig. 6, the mass flow rate curves for both the flue gas and air stop to decrease linearly below the load of 60%; while the exact same effect also occurs for the fuel flow rate curves, as 7
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Fig. 10. Effect of hydrogen ratio variation on total fuel mass flow rate. Fig. 12. Effect of hydrogen ratio variation on thermodynamic and exergetic efficiencies.
Fig. 11. Effect of hydrogen ratio variation on the molecular composition of the exhaust flue gas.
shown in Fig. 7. Therefore if the system must be operated at loads lower than 60%, it must be recuperated for heat recovery, e.g. with a district heating energy network [17,20]. In Fig. 8, it is shown that more air is needed at part-load due to the system becoming less efficient with decreasing load. This trend is similar for both fuels.
Fig. 13. Effect of hydrogen ratio variation on exergy destruction ratio for every system component.
and exergetic efficiencies is shown. The effect appears to be more significant for exergetic efficiency, because it is entropy dependent. The reason for this is more clearly identified in Fig. 13, where the exergy destruction ratios for every system component are shown. Specifically, it is observed that net electrical efficiency for the gas turbine cycle improves slightly as hydrogen ratio is increased (0.347 and 0.356 for a hydrogen ratio of 0 and 0.9, respectively). On the other hand, the improvement of exergetic efficiency is more evident, mainly due to the significant reduction of combustor losses as hydrogen ratio increases (0.338 and 0.360 for a hydrogen ratio of 0 and 0.9, respectively). Therefore, hydrogen combustion results in a higher power output as compared to methane-only combustion. As the hydrogen content in the fuel increases, combustor losses are significantly decreased. This is because the exergy destruction in the combustor depends on the total mass flow rate of fuel entering the combustor (as defined in equation (17)), since the total fuel mass flow rate decreases with increasing hydrogen content, as already shown in Fig. 10. In turn, the exergy destruction ratio for the combustor yD, comb in equation (20) is also reduced. The combustion process becomes more efficient, mainly owing to the higher energy density of hydrogen in comparison to methane. On the other hand, for the compressor and turbine, with increasing hydrogen content, losses increase because of the need to increase the air inflow for combustion (see Fig. 8), but in this case losses are marginal, and therefore hydrogen variation is rather insignificant. This is because although the excess air for hydrogen
Parametric study: Variation of hydrogen ratio An important aspect for this study is the variation of hydrogen ratio. Although hydrogen ratio would not typically exceed 0.1, in order to examine the response of the system model at different hydrogen contents, hydrogen ratio is varied from 0 to 0.9. The net electrical efficiency remains almost constant as the value of hydrogen ratio is altered, but other key parameters change significantly. In Fig. 9 it is shown how partial power output is affected with increasing hydrogen ratio in the total fuel. In Fig. 10 it is shown that as hydrogen content in the total fuel increases, the total mass flow rate of fuel decreases, along with the heat input rate. The mass flow rate of fuel is almost two times higher without any hydrogen in comparison to a hydrogen ratio of 0.9. Another important aspect of hydrogen ratio variation is the amount of flue gas at the exhaust of the gas turbine, since flue gas would normally be released in the environment. Therefore it would be desirable to reduce CO2 emissions at the lowest possible level [21]. In Fig. 11, it is shown that the CO2 mole fraction with a hydrogen ratio of 0.1 and 0.5 drops by 6.1% and 24.2%, respectively, as compared to methane-only fueling. Therefore even tiny hydrogen contents can result to a reduction in CO2 emissions, which is also beneficial in terms of operational cost and total lifecycle cost for the system [20]. In Fig. 12, the effect of varying hydrogen ratio on thermodynamic 8
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
combustion is significantly higher than methane combustion, the comparatively more efficient combustion of hydrogen decreases flue gas generation, and therefore the flow rate of incoming air remains practically unchanged. Finally, for a hydrogen ratio of 0.1, CO2 emissions are reduced by 6.1% as compared to no hydrogen content in the fuel, with a further reduction to 24.2% for a hydrogen ratio of 0.5.
respectively). However, the improvement of exergetic efficiency is more significant, mainly due to the high reduction of combustor losses, as hydrogen ratio increases (0.338 and 0.360 for a hydrogen ratio of 0 and 0.9, respectively). Therefore, for the same amount of total fuel flow rate, hydrogen combustion results in a higher power output, in comparison to methane-only combustion. Also, hydrogen addition affects positively the system performance in terms of CO2 emissions, since even a hydrogen ratio of 0.1 (on a volumetric basis) results in a 6.1% reduction in CO2 emissions, with a further reduction to 24.2% for a hydrogen ratio of 0.5, as compared to methane-only fueling. The developed model can be used as a basis for future more application-specific studies in the field of decentralized power generation, combining various technologies (e.g. a PV-electrolyzer-gas turbine system).
Conclusions This study presents a detailed thermodynamic model, considering both first law and second law analyses, of a small-scale natural gas/ hydrogen-fueled gas turbine cycle, along with performance evaluation at both design and off-design conditions. Evaluation of performance at off-design conditions is very important, because in real-life conditions, the system will operate mostly at off-design, with several part loads. Therefore, it is necessary to develop a simulation model that determines performance at off-design conditions, as accurately as possible, to correspond to realistic operation. The system model is validated against measured manufacturer’s data from an industrial gas turbine and results show a good agreement between the model and the reference data. In general, the results suggest that hydrogen addition to the natural gas fuel supply could alter significantly the operation of the gas turbine cycle. It is observed that net electrical efficiency can slightly improve, as hydrogen ratio is increased (0.347 and 0.356 for a hydrogen ratio of 0 and 0.9,
Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Appendix A At the air compressor exit the specific enthalpy is determined as follows [14]:
h¯s,2 h¯2 = h¯1 +
h¯1 (52)
c
where h¯1 is the specific enthalpy at the inlet, and h¯s,2 is the isentropic specific enthalpy at the outlet (J/kg). The stoichiometric reactions of methane and hydrogen with air are the following, respectively:
CH 4 + as,CH4 (0.21O2 + 0.79N2) H2 + as,H2 (0.21O2 + 0.79N2)
bs,CH4 CO2 + cs,CH4 H2 O + ds,CH4 N2 bs,H2 H2 O + cs,H2 N2
The following expressions provide the conservation for carbon, hydrogen, oxygen and nitrogen atoms, respectively, for methane fuel:
1 = bs,CH4 4 = 2·cs,CH4 as,CH4 ·2·0.21 = 2·bs,CH4 + cs,CH4 as,CH4 ·2·0.79 = 2·ds,CH4
(53)
Similarly, for hydrogen:
2 = 2·bs,H2 as,H2 ·2·0.21 = bs,H2 as,H2 ·2·0.79 = 2·cs,H2
(54)
The actual reaction of methane and hydrogen with excess air are the following, respectively:
CH 4 + aCH4 (0.21O2 + 0.79N2) H2 + aH2 (0.21O2 + 0.79N2)
bCH4 CO2 + cCH4 H2 O + dCH4 N2 + eCH4 O2 bH2 H2 O + c H2 N2 + d H2 O2
The corresponding conservation expressions for methane and hydrogen, respectively, are given as follows:
aCH4 = (1 + eaCH4 )· as,CH4 1 = bCH4 4 = 2· cCH4 aCH4 ·2·0.21 = 2·bCH4 + cCH4 + 2· eCH4 aCH4 ·2·0.79 = 2·d CH4
(55)
9
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
aH2 = (1 + eaH2 )· as,H2 2 = 2· bH2 aH2 ·2·0.21 = bH2 + 2· d H2 aH2 ·2·0.79 = 2·c H2
(56)
The enthalpies of the reactants entering the combustor, per mole of fuel, for methane and hydrogen, respectively, are given by:
H2,CH4 = h¯ CH4,2 + 0.21·aCH4 ·h¯ O2,2 + 0.79·aCH4 ·h¯ N2,2
(57)
= h¯ H2,2 + 0.21·aH2 · h¯ O2,2 + 0.79· aH2 ·h¯ N2,2
(58)
H2,H2
The enthalpies of the products exiting the combustor, per mole of fuel, for methane and hydrogen, respectively, are given by:
H3,CH4 = bCH4 · h¯ CO2,3,CH4 + cCH4· h¯ H2O,3,CH4 + dCH4 ·h¯ N2,3,CH4 + eCH4 ·h¯ O2,3,CH4
(59)
H3,H2 = bH2 ·h¯ H2O,3,H2 + c H2·h¯ N2,3,H2 + d H2· h¯ O2,3,H2
(60)
Assuming no energy losses in the combustion process, an energy balance on the combustor, for methane and hydrogen, respectively, can be applied:
H3,CH4 = H2,CH4
(61)
H3,H2 = H2,H2
(62)
The mole fractions in the combustion products for methane and hydrogen, respectively, are given by: bCH 4
yCO2,3,CH4 =
bCH4 + c CH 4 + dCH 4 + eCH 4 c CH4
yH2O,3,CH4 =
bCH 4 + c CH4 + dCH4 + eCH 4 dCH4
yN2,3,CH4 =
bCH 4 + cCH 4 + dCH 4 + e CH4
yO2,3,CH4 =
bCH 4 + cCH 4 + dCH 4 + eCH 4
yH2O,3,H2 =
eCH 4
(63)
bH2 bH2 + c H2 + dH2 c H2
yN2,3,H2 =
bH2 + c H2 + dH2
yO2,3,H2 =
bH2 + c H2 + dH2
dH2
(64)
The entropy of the products exiting the combustor, per mole of fuel, for methane and hydrogen, respectively, are given by:
S3,CH4 = bCH4 ·¯sCO2,3,CH4 + cCH4·¯sH2O,3,CH4 + dCH4 ·¯s N2,3,CH4 + eCH4 ·¯sO2,3,CH4
(65)
S3,H2 = b H2 · s¯H2O,3,H2 + c H2·¯sN2,3,H2 + d H2· s¯O2,3,H2
(66)
The entropy of the products exiting the isentropic turbine, per mole of fuel, for methane and hydrogen, respectively, are given by:
Ss,4,CH4 = bCH4 · s¯CO2, s,4,CH4 + cCH4·¯sH2O, s,4,CH4 + dCH4 ·¯s N2, s,4,CH4 + eCH4 · s¯O2, s,4,CH4
(67)
Ss,4,H2 = bH2 ·¯sH2O, s,4,H2 + cH2· s¯N2, s,4,H2 + d H2· s¯O2, s,4,H2
(68)
Considering an entropy balance on the isentropic turbine:
Ss,4,CH4 = S3,CH4
(69)
Ss,4,H2 = S3,H2
(70)
The enthalpy of the products exiting the isentropic turbine, per mole of fuel, for methane and hydrogen, respectively, are given by:
Hs,4,CH4 = bCH4 · h¯ CO2, s,4,CH4 + cCH4· h¯ H2O, s,4,CH4 + dCH4 · h¯ N2, s,4,CH4 + eCH4 · h¯ O2, s,4,CH4 Hs,4,H2
= bH2 ·h¯ H2O, s,4,H2 + cH2· h¯ N2, s,4,H2 + d H2·h¯ O2, s,4,H2
(71) (72)
The total enthalpy of the products exiting the isentropic turbine, per mole of fuel, is given by: (73)
Hs,4 = Hs,4,CH4 + Hs,4,H2 The enthalpy of the products exiting the actual turbine, per mole of fuel, for methane and hydrogen, respectively, are given by:
H4,CH4 = H3,CH4
H4,H2 = H3,H2
(H3,CH4
(H3,H2
Hs,4,CH4 )·
Hs,4,H2 )·
(74)
t
(75)
t
where:
H4,CH4 = bCH4 ·h¯ CO2,4,CH4 + cCH4·h¯ H2O,4,CH4 + d CH4 ·h¯ N2,4,CH4 + eCH4 · h¯ O2,4,CH4
(76)
H4,H2 = bH2 ·h¯ H2 O,4,H2 + c H2·h¯ N2,4,H2 + dH2· h¯ O2,4,H2
(77)
10
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
The total molar flow rate of inlet air to the compressor is the sum of the partial molar flow rates needed for the combustion of methane and hydrogen: (78)
na = na,CH4 + na,H2
The resulting flue gas exiting the combustor can be related to the reactants with a molar flow rate balance, summing the flue gas flow rates from the combustion of the two fuels: (79)
n3 = nCH4,3 + nH2,3 The above equation can be analyzed as follows:
nCH4,3 = na,CH4 + nCH4 n H2,3 = na,H2 + n H2
(80)
The partial molar flow rates can be related to the corresponding mole fractions as follows:
ni,CH4,3 = nCH4,3· yi,3,CH4 ni,H2,3 = n H2,3· yi,3,H2
(81)
In the above equations i is the product species, i.e·H2O, CO2, O2, and N2. A molar flow rate balance results in the following general expression: (82)
ni,3 = ni,CH4,3 + ni,H2,3 The mole fractions are found with the following general expression:
yi,3 =
ni,3 n3
(83)
Assuming no change of composition in the flue gas during expansion in the turbine: (84)
yi,4 = yi,3 When mass fractions must be determined, the following relations deriving from the composition relations for gas mixtures are used:
M4 =
yi,4 ·Mi
(85)
i
x i,4 = yi,4 ·
Mi M4
(86)
References [11]
[1] Arsalis A, Alexandrou AN. Design and modeling of 1–10 MWe liquefied natural gasfueled combined cooling, heating and power plants for building applications. Energy Build 2015;86:257–67. https://doi.org/10.1016/j.enbuild.2014.10.025. [2] Arsalis A, Alexandrou AN, Georghiou GE. Thermoeconomic modeling of a smallscale gas turbine-photovoltaic-electrolyzer combined-cooling-heating-and-power system for distributed energy applications. J Cleaner Prod 2018;188:443–55. https://doi.org/10.1016/j.jclepro.2018.04.001. [3] Guandalini G, Campanari S, Romano MC. Power-to-gas plants and gas turbines for improved wind energy dispatchability: energy and economic assessment. Appl Energy 2015;147:117–30. https://doi.org/10.1016/j.apenergy.2015.02.055. [4] Ströhle J, Myhrvold T. An evaluation of detailed reaction mechanisms for hydrogen combustion under gas turbine conditions. Int J Hydrogen Energy 2007;32:125–35. https://doi.org/10.1016/j.ijhydene.2006.04.005. [5] Park J, Lee MC. Combustion instability characteristics of H2/CO/CH4 syngases and synthetic natural gases in a partially-premixed gas turbine combustor: part IFrequency and mode analysis. Int J Hydrogen Energy 2015;41:7484–93. https:// doi.org/10.1016/j.ijhydene.2016.02.047. [6] He F, Li Z, Liu P, Ma L, Pistikopoulos EN. Operation window and part-load performance study of a syngas fired gas turbine. Appl Energy 2012;89:133–41. https:// doi.org/10.1016/j.apenergy.2010.11.044. [7] Shih HY, Liu CR. A computational study on the combustion of hydrogen/methane blended fuels for a micro gas turbines. Int J Hydrogen Energy 2014;39:15103–15. https://doi.org/10.1016/j.ijhydene.2014.07.046. [8] Juste GL. Hydrogen injection as additional fuel in gas turbine combustor. Evaluation of effects. Int J Hydrogen Energy 2006;31:2112–21. https://doi.org/10.1016/j. ijhydene.2006.02.006. [9] Funke H, Keinz J, Boerner S, Hendrick P, Elsing R. Testing and analysis of the impact on engine cycle parameters and control system modifications using hydrogen or methane as fuel in an industrial gas turbine. Prog Propul Phys 2016;8:409–26. https://doi.org/10.1051/eucass/201608409. [10] Wright IG, Gibbons TB. Recent developments in gas turbine materials and
[12] [13] [14] [15] [16] [17]
[18] [19] [20] [21]
11
technology and their implications for syngas firing. Int J Hydrogen Energy 2007;32:3610–21. https://doi.org/10.1016/j.ijhydene.2006.08.049. Bianchini A, Pellegrini M, Saccani C. Solar steam reforming of natural gas integrated with a gas turbine power plant. Sol Energy 2013;96:46–55. https://doi. org/10.1016/j.solener.2013.06.030. Ebaid MSY, Hammad M, Alghamdi T. THERMO economic analysis OF PV and hydrogen gas turbine hybrid power plant of 100 MW power output. Int J Hydrogen Energy 2015;40:12120–43. https://doi.org/10.1016/j.ijhydene.2015.07.077. Siemens. Industrial gas turbine SGT-400 2017. http://www.energy.siemens.com/ hq/en/fossil-power-generation/gas-turbines/sgt-400.htm. [accessed December 1, 2017]. Klein S, Nellis G. Thermodynamics. New York, NY: Cambridge University Press; 2012. Zhang N, Cai R. Analytical solutions and typical characteristics of part-load performances of single shaft gas turbine and its cogeneration. Energy Convers Manage 2002;43:1323–37. https://doi.org/10.1016/S0196-8904(02)00018-3. Wang W, Cai R, Zhang N. General characteristics of single shaft microturbine set at variable speed operation and its optimization. Appl Therm Eng 2004;24:1851–63. https://doi.org/10.1016/j.applthermaleng.2003.12.012. Arsalis A, Alexandrou AN. Thermoeconomic modeling and exergy analysis of a decentralized liquefied natural gas-fueled combined-cooling e heating-and-power plant. J Nat Gas Sci Eng 2014;21:209–20. https://doi.org/10.1016/j.jngse.2014.08. 009. Bejan A, Tsatsaronis G, Moran MJ. Thermal design and optimization. Wiley; 1996. Saravanamuttoo H, Rogers G, Cohen H, Straznicky P, Nix A. Gas turbine theory. 7th ed. Pearson; 2017. Arsalis A, Alexandrou AN, Georghiou GE. Thermoeconomic modeling and parametric study of a photovoltaic-assisted 1 MWe combined cooling, heating, and power system. Energies 2016;9:663. https://doi.org/10.3390/en9080663. Pilavachi PA, Stephanidis SD, Pappas VA, Afgan NH. Multi-criteria evaluation of hydrogen and natural gas fuelled power plant technologies. Appl Therm Eng 2009;29:2228–34. https://doi.org/10.1016/j.applthermaleng.2008.11.014.
Contents lists available at ScienceDirect
Sustainable Energy Technologies and Assessments journal homepage: www.elsevier.com/locate/seta
Thermodynamic modeling and parametric study of a small-scale natural gas/hydrogen-fueled gas turbine system for decentralized applications
T
Alexandros Arsalis Research Centre for Sustainable Energy (FOSS), University of Cyprus, Kallipoleos 75, Nicosia 1678, Cyprus
ARTICLE INFO
ABSTRACT
Keywords: Gas turbine Natural gas Hydrogen combustion Dual-fueled Thermodynamic modeling Parametric study
In this study a detailed thermodynamic model of a small-scale natural gas/hydrogen-fueled gas turbine system is presented. The thermodynamic model includes both a basic thermodynamic analysis and an exergy analysis. Exergy analysis aims on the identification of exergy destruction in the various system components. Specifically, it is investigated how hydrogen addition in the fuel supply can affect exergy loss. Off-design modeling is also implemented to realistically evaluate performance at part-load operation. A parametric study is conducted to examine the effect of hydrogen ratio on system performance. The hydrogen ratio is varied from 0 to 0.9, to examine the behavior of the developed model at different hydrogen contents. The results suggest that hydrogen addition to the natural gas fuel supply can change the operational behavior of the gas turbine cycle. Although net electrical efficiency is only marginally increased as hydrogen ratio is increased (0.347 vs. 0.356), the exergetic efficiency is more significantly affected, mainly due to the reduction of combustor losses as hydrogen content increases (0.338 vs. 0.360). Also, hydrogen addition has a positive effect in terms of carbon emissions, since even a tiny hydrogen injection at a hydrogen ratio of 0.1 (on a volumetric basis) results in a 6.1% reduction in CO2 emissions, as compared to methane-only fueling. Overall, the results suggest that even a small amount of hydrogen addition to the gas turbine cycle can have a significantly positive effect in terms of system efficiency and operational cost.
Introduction Decentralized, small-scale power systems are gaining momentum to create a more flexible energy system infrastructure. Several system configurations have already been proposed as alternatives to electricityonly, or in general, large-scale power stations [1,2]. Centralized systems occasionally create network congestion and transmission/distribution losses. On the other hand, on-site power generation results in the generation of local emissions, and it could be problematic if the system is located within larger cities/urban residential areas. Renewable energy sources eliminate emissions during power generation, but renewable power supply can never match demand without energy storage. Especially in the case of solar photovoltaic (PV) technology, where electricity is only produced during daytime, storage or combination with other power technologies is required. One viable possibility is the combination of natural gas-fired gas turbine cycles with PV technology. In these combined systems, apart from the generation of a portion of the electricity needed by the supplied electricity network from the PV system, excess electricity can be converted to hydrogen and mixed with the natural gas supply for combustion in the gas turbine cycle. It has been suggested that hydrogen generated from electrolysis
can be injected to natural gas streams, directly or after modification to synthetic methane. The latter is more complicated because it needs integration to a CO2 stream for the methanation process [3]. So far, the mixing of hydrogen to natural gas has received rather limited attention in terms of detailed mathematical modeling, and most configurations available in the literature, consider the re-generation of electrical energy via fuel cell technology. However, the possibility of injecting hydrogen to natural gas eliminates the need for an additional subsystem (i.e. a fuel cell unit), provided hydrogen content is significantly lower than natural gas content during combustion. The thermophysical characteristics of hydrogen differ significantly from natural gas, specifically hydrogen is lighter and more reactive than methane [4]. Although the use of different fuels can create instability to the operation of the gas turbine, since heat release variation could favor thermo-acoustic combustion instability [5], it has also been suggested that the operational window of a hydrogen-rich syngas-fired gas turbine is similar to the one for natural gas, primarily because the heating value of the two species is almost identical [6]. For hydrogenonly combustion, the heating value is significantly higher than methane, resulting in a reduction of the hot gas mass flow and the power output of the gas turbine, although water vapor content in the exhaust
E-mail address: [email protected]. https://doi.org/10.1016/j.seta.2019.100560 Received 23 February 2019; Received in revised form 22 October 2019; Accepted 24 October 2019 2213-1388/ © 2019 Elsevier Ltd. All rights reserved.
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Nomenclature
el, net s
a, b, c, d , e Chemical reaction coefficients (−) Ef , in Energy rate of fuel (W) eai Excess air of species i (−) G Ratio of reduced mass flow rate to its design value (−) H Enthalpy per mole of fuel (J/kmol) h¯ Specific enthalpy (J/kmol) Lower heating value (J/kmol) LHV M Molecular weight (kg/kmol) mi Mass flow rate of species i (kg/s) N Power output at off-design (W) N Ratio of reduced power output to its design value (−) n Rotating speed (rpm) n Ratio of reduced rotating speed to its design value (−) ni Molar flow rate of species i (kmol/s) p Pressure (Pa) rH2, vol Hydrogen ratio (−) S Entropy per mole of fuel (J/K-kmol) Specific entropy (J/K-kmol) s¯ Temperature (oC, K) T V Volumetric flow rate (m3/s) v¯ Specific volume (m3/kmol) W Power output (W) x Mass fraction (−) Standard specific chemical exergy for stream i (J/kg) x CH , i x q, i Specific physical exergy for stream i (J/kg) y Mole fraction (−)
µ
Net electrical efficiency (−) Isentropic efficiency (−) Ratio of reduced efficiency to its design value (−) Mass flow rate ratio (−) Pressure ratio (−) Ratio of reduced pressure ratio to its design value (−) Total pressure recovery coefficient (−)
Subscripts/Superscripts
1, 2, ...,k a b c des f g gen gt i in ref s t
Streams Air Combustor Compressor Design (full-load operation) Fuel Gas (vapor state) Electric generator Gas turbine cycle Species Inlet Reference state Isentropic Turbine
Abbreviations EES PV
Greek symbols
Engineering Equation Solver Photovoltaic
Efficiency (−) gas increases (with an increase in specific heat capacity) [7]. This increase favors the generation of work at an identical turbine inlet temperature, while the increased moisture content results to an increase in turbine power output [6]. Also, small hydrogen contents in a natural gas-based combustion process in a gas turbine cycle can have a positive effect in terms of reducing unburned methane and CO emissions, in addition to CO2 emission reduction [8]. A recent study suggested that a natural gas-fueled gas turbine can be easily converted for hydrogen fueling, with a modification of its control software, and without any changes to the moving components [9]. The size and structure of the
combustion chamber of an existing natural gas-fueled gas turbine cycle will not need to be modified in the case of hydrogen injection, because hydrogen addition in the fuel allows reduction of natural gas at the same time, provided the combustion temperature is kept fixed. Since the energy density of hydrogen is higher than methane, the total fuel flow rate entering the combustion chamber will be lower in comparison to a methane-only system [10,11]. Currently, the open literature includes a very limited number of studies on methane/hydrogen fueled gas turbine systems. Ebaid et al. [12], studied an 100 MWe PV/hydrogen-fueled gas turbine hybrid
Fig. 1. Schematic representation of the natural gas/hydrogen-fueled gas turbine cycle.
2
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
system. Simplistic assumptions were considered for the gas turbine model to determine load consumption, in relation to the generation of electricity from the PV system. The authors assumed that the gas turbine would be fueled only with hydrogen and that the gas turbine would operate only at design conditions with a fixed thermal efficiency at 44%. Guandalini et al. [3], considered hydrogen injection to a centralized natural gas grid, in relation to large-scale wind turbine systems. Although part-load operation was considered through regression functions based on an industrial turbine, actual modeling of the gas turbine cycle was not implemented. The current study attempts to provide a detailed thermodynamic modeling of a natural gas/hydrogen-fueled gas turbine system, using both first and second law approaches. Also, the modeling includes both design and off-design considerations, so that system operation at partload conditions will not be compromised by simplistic fixed conditions. The developed system model sets a basis for future application-specific systems, including PV modules, electrolyzer stacks, hydrogen storage units, and heat integration and recovery to satisfy realistic load profiles. A parametric study is conducted to examine the effect of hydrogen ratio on key parameters, such as the power output, the fuel mass flow rate, the heat input rate, the flue gas composition, the thermodynamic and exergetic efficiencies, and the exergy destruction ratio. The parametric study also investigates the effect of hydrogen injection in terms of CO2 emission reduction, which is a significant factor in the design of sustainable energy systems.
System modeling of the gas turbine cycle The mathematical modeling, including the calculation of all thermophysical properties, and the associated parametric study are conducted with the commercially available software Engineering Equation Solver (EES) – Professional version. The values of the isentropic efficiencies for the compressor and turbine depend on the load of the gas turbine cycle power output. In this study a part-load model, based on the methodology developed in [15,16], has been formulated to determine part-load performance. Therefore, based on a selected load, the value of the isentropic efficiency is calculated through data interpolation. Thermodynamic model The total power output of the gas turbine is given by the sum of the partial power outputs resulting from the combustion of methane and hydrogen fuels: (1)
Wgt = Wgt ,CH4 + Wgt ,H2
The generated net electrical power output resulting from the expansion of the hot flue gas in the turbine can be given as a function of the enthalpies of the processes from air compression to turbine expansion. Through an energy balance of products and reactants for the combustion of methane fuel, terms can be rearranged to solve for power output:
System configuration
Wgt ,CH4 = nCH4 ·((H3,CH4
H4,CH4 )
aCH4 ·(h¯2
h¯1))·
(2)
gen
h¯1 and h¯2 are the specific enthalpies of air at the compressor inlet and the compressor outlet, respectively. The above equation is solved for nCH4 to determine the molar flow rate of the methane fuel. The molar flow rate of air for methane combustion is given by:
The system configuration is shown in Fig. 1. The combustor of the gas turbine cycle is fueled with natural gas and hydrogen, and the generated flue gas is expanded in the turbine to generate electricity via an electric generator. The following assumptions have been made for this study:
(3)
na,CH4 = aCH4 · nCH4
The volumetric flow rate of air for methane combustion entering the compressor is given by:
1. For calculation simplicity, natural gas is assumed to have the thermophysical properties of methane. 2. A catalytic combustion process is assumed for the gas turbine cycle to allow complete chemical reaction of the fuel reactants. 3. The combustion temperature is fixed and therefore it remains constant at part-load conditions, although at more realistic conditions, this value would normally drop slightly and steadily with decreasing load [6]. The reason of keeping the combustion temperature constant is to avoid mismatch of data calculation for the part-load model, since data from the part-load model are fed to the thermodynamic model, and therefore variation of combustion temperature would create inconsistency in the calculation of the isentropic efficiencies with the part-load model. 4. Ambient conditions are set at a pressure of 1 atm and a temperature of 15 °C. The pressure and temperature values at the inlet of the air compressor are set equal to the ambient conditions. The fuel temperature is assumed to remain constant and equal to ambient conditions. 5. The electric generator efficiency is fixed at 0.972 [13], for a gas turbine nominal power output of 12.9 MWe. The latter value is taken from available manufacturer’s data for an industrial gas turbine (Siemens SGT-400) [13]. A pressure ratio of 16.8 is assumed for the air compressor [13]. 6. A constant pressure drop of 5% is assumed for the combustor process [14]. 7. The model assumes that the gas turbine will respond to an electric load. Therefore, the electric load is treated as an input parameter.
(4)
V1,CH4 = na,CH4 · v¯1 Similarly, for hydrogen:
Wgt ,H2 = nH2 ·((H3,H2
H4,H2)
aH2 ·(h¯2
h¯1))·
(5)
gen
na,H2 = aH2 ·n H2
(6)
V1,H2 = na,H2 · v¯1
(7)
The total volumetric flow rate of air entering the compressor is the sum of the partial volumetric flow rates: (8)
V1 = V1,CH4 + V1,H2
The sum of the two partial volumetric flow rates is the total flow rate of air needed to enter the combustor for the reactions with methane and hydrogen. The lower heating value of methane on a molar basis is given by: Table 1 Values of the constant parameters in the thermodynamic model at design. Parameter description
pamb Tamb Tf gen
Wgt
The above input values for the gas turbine cycle at design conditions are tabulated in Table 1.
c
b
3
Value Ambient pressure Ambient temperature Fuel temperature
1 atm 15 °C 15 °C
Gas turbine power output
12.9 MWe
Compressor pressure ratio Combustor efficiency
16.8 0.95
Electric generator efficiency
0.972
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
LHVCH4 = h¯ CH4, ref
2·h¯ H2O, g , ref
h¯ CO2, ref
Ef , in,CH4 = nCH4 · LHVCH4
cycle efficiency and fuel mass flow rate have been calculated, the partload isentropic efficiencies for the compressor and turbine are calculated. The calculated data are then saved as a lookup table in the main model of the gas turbine cycle, and are used through interpolation to calculate performance at any given operating load condition. To avoid unrealistic operating schemes, the exhaust temperature of the combustor is kept constant at all loads. On the other hand, the rotating speed of the compressor and the turbine can be allowed to vary; therefore they are reduced as the load decreases. Since it is assumed that the compressor and turbine are connected in a single shaft, the rotating speed of the compressor is always assumed to be equal to the rotating speed of the turbine. The compressor rotating speed at full-load conditions is fixed at 14,100 rpm, per manufacturer’s data [13]. The design data mentioned in the description below are those identified at design. The fuel mass flow rate is defined as the difference between turbine and compressor mass flow rates:
(9) (10)
Similarly, for hydrogen:
LHVH2 = h¯ H2, ref
h¯ H2O, g, ref
Ef , in,H2 = n H2 · LHVH2
(11) (12)
The total energy rate of fuel and the corresponding net electrical efficiency, on an LHV basis, are given by:
Ef , in = Ef , in,CH4 + Ef , in,H2 el, net
=
(13)
Wgt Ef , in
(14)
The auxiliary equations for the thermodynamic model of the gas turbine cycle are given in Appendix A. These include the equations needed for the calculation of the reaction coefficients for the combustion of both methane and hydrogen in the gas turbine cycle for both the stoichiometric and actual reactions. Additionally, the mass balance and energy balance equations are given for the gas turbine cycle.
m f = mt
(22)
mc
The gas turbine cycle efficiency ratio is [15]: gt
= 3.18· N
4.69·N 2 + 3.69·N 3
1.18·N 4
(23)
The power output ratio is defined as the ratio of off design to design net power output for the gas turbine cycle:
Exergy analysis An exergy analysis can provide an in-depth evaluation of the sources of irreversibility in an energy system. For the current system configuration, exergy analysis is used to reveal the trend of exergy destruction when varying hydrogen content in the total fuel. The methodology for exergy analysis has been described in detail in a previous publication [17]. The main equations are summarized in Table 2. The exergy destruction for each system component is calculated through exergy balances. The exergy balances for the compressor, turbine, and combustor are the following, respectively:
N =
N Ndes
(24)
Similarly, for gas turbine cycle efficiency: gt
gt
=
(25)
gt , des
m1·xq,1 + Wc = m2· xq,2 + Xdes, c
(15)
The previous equation is solved for gt to determine the off-design efficiency of the gas turbine cycle. Similarly, the off-design mass flow rate ratio is determined based on a curve function for the fuel consumption ratio [15]:
m3· xq,3 = m4 · xq,4 + Wt + Xdes, t
(16)
Gf = 0.288 + 0.624·N + 0.088·N 2
Xf + m2· xq,2 + mf ·x q, f = m3·xq,3 + Xdes, comb
(17)
Gf =
The associated exergy destruction ratios for the above components are defined as [18]:
yD, c
Xdes, c = Xf
yD, t = yD, comb
(19)
Xdes, comb = Xf
(20)
c, des
c
(27)
=
=
p2, des (28)
p1, des
p2
(29)
p1
The ratio of reduced pressure ratio to its design value, the ratio of reduced rotating speed to its design value, the ratio of reduced efficiency to its design value, and the ratio of reduced mass flow rate to its design value, are the following, respectively [15]:
The total rate of exergy destruction is the sum of component exergy destruction rates:
Xdes = Xdes, c + Xdes, t + Xdes, comb
mf mf , des
For the compressor, the pressure ratio is defined for design and offdesign conditions, respectively:
(18)
Xdes, t Xf
(26)
(21)
c
Part-load model
=
c
(30)
c , des
Table 2 Modeling equations used in the exergy analysis.
The gas turbine cycle must be able to respond to off-design conditions, i.e. at power output below the nominal power output of 12.9 MWe. In a previous study, [15] the compressor and turbine mass flow rates were provided to the model as input parameters and based on those values two output variables were determined, namely isentropic efficiency and pressure ratio. The study included typical curve functions to approximate gas turbine cycle efficiency and fuel mass flow rate at part-load conditions. However, since the modeling needs of the current study are different, it is assumed that after the part-load gas turbine
Variable description
Xf 2
XPH , i
XCH , i
Xi
4
Exergy rate of fuel (W) Exergetic efficiency (−) Physical exergy for stream i (W) Chemical exergy of stream i (W) Total exergy of stream i (W)
Model equation
Xf = mCH4 · hCH4 + mH2·h H2 2
=
Wgt Xf
XPH , i = mi ·x q,i XCH , i = mi· x CH ,i Xi = XPH , i + XCH ,i
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
nc =
c
nc nc, des
Parameter description
c
=
(32)
c , des
Gc =
Table 3 Values of the input parameters for the validation of the system model at design.
(31)
mc · mc, des ·
Tamb gen
T1 p1
Wgt c
(T1, des )
T4
(33)
p1, des
The performance formulas for the compressor are applied to determine the off-design to design ratio for the pressure ratio and the ratio of reduced efficiency to its design value, respectively [15]: 2
c
= c1· Gc + c2· Gc + c3
c
= (1
nc · 2 Gc
nc Gc
c2 = c3 =
(
DEN = p · 1
p
nc DEN
m nc
) + n ·(n c
c
m) 2
b
(36)
t
nt = nc
(39)
mt mc = µ· mt , des mc, des
(40)
t
=
p3
(42)
(43)
t
=
nt =
t , des
nt nt , des
=
1.4
0.4·
nt nt , des
= (1
t·(1
nt )2)·
nt · 2 Gt
nt Gt
(50)
Operation at design conditions At design conditions it is assumed that the gas turbine system will generate the nominal power output, i.e. 12.9 MWe. However, methane-
For the turbine, the ratio of reduced pressure ratio to its design value, the ratio of reduced rotating speed to its design value, the ratio of reduced efficiency to its design value, and the ratio of reduced mass flow rate to its design value, are the following, respectively [15,19]: t
where
System performance
(44)
p4
1 1
The system model is validated against measured manufacturer’s data extracted from a Siemens industrial gas turbine, namely SGT-400 [13]. The values of the input parameters for the validation are tabulated in Tables 3 and 4, respectively. The graph in Fig. 2 shows the simulation data against the experimental data for different part-loads against turbine exhaust mass flow rate. The graph shows a good agreement between the two data sets, and therefore it can be assumed that the system model has been modeled with adequate accuracy in comparison to an actual system.
p3, des p4, des
2 t 2 t , des
Model validation
and µ are set as constants [15].
=
(48)
p3, des
This section starts with a validation of the system model with available experimental data. Next the system model of the gas turbine cycle is analyzed at design conditions, and then at off-design conditions. Finally, the results of the parametric study are presented in detail, with emphasis on the performance of the system and its effect on key parameters.
The pressure ratio at design and off-design conditions is defined as follows, respectively: t , des
(T3, des )
Results and discussion
(41)
c
=µ=1
mt , des ·
T3 p3
The value of t is 0.3.
(37)
(38)
where
mt ·
(49)
nt , des = nc, des
= ·
16.8 555 °C
p·m·n c m2·nc3 DEN
The term b is a pressure loss coefficient for the combustor, set at a typical value of 0.95 [14]. The equations below relate the turbine parameters to the compressor parameters
t
12.9 MWe
Compressor pressure ratio Turbine exhaust temperature
(47)
T3, des mt = · · mt , des T3
2·m·nc2 DEN
The values for the remaining constants are m = 1.06, p = 0.36 and c4 = 0.3. Finally, a similar process to the compressor section is repeated for the turbine. Initially some parameters must be defined. For calculation simplicity, at off-design conditions the condition set at design operation for the pressure drop in the combustor is retained, i.e.:
p3 = p2 ·
Gas turbine power output
The performance formulas for the turbine are applied to determine the off-design to design ratio for the mass flow rate and the ratio of reduced efficiency to its design value, respectively [15]:
The constants c1, c2 and c3 are found with the following functions [16]:
c1 =
15 °C 0.972
t , des
Gt = (35)
Ambient temperature Electric generator efficiency
t
=
(34)
nc )2)·
c4·(1
t
Value
Table 4 Values of the output parameters for the validation of the system model at design. Parameter description
(45)
el, net
T3 m1 m3
(46) 5
Value Net electrical efficiency
Turbine inlet temperature Compressor mass flow rate Turbine mass flow rate
0.348
1173 °C 39.68 kg/s 40.42 kg/s
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Table 6 Values of the key output parameters at design conditions. Parameter description el, net
Value Net electrical efficiency
0.348
Partial power output (hydrogen)
0.43 MWe
Energy rate of methane fuel
35.9 MW
Energy rate of hydrogen fuel
1.2 MW
Total energy rate of fuel
37.1 MW
Fuel mass flow rate (methane) Fuel mass flow rate (hydrogen) Total fuel mass flow rate
0.717 kg/s 0.010 kg/s 0.727 kg/s
Partial power output (methane)
Wgt,CH4 Wgt,H2 Ef ,in,CH 4 Ef ,in,H2 Ef ,in mCH4 mH2
mf
12.47 MWe
Fig. 2. Validation of the system model against manufacturer data (Siemens industrial gas turbine SGT-400 [13]).
to-hydrogen ratio could vary, depending on the availability of hydrogen at a particular time-segment. Therefore, a specific parameter could be defined here, which can be easily varied, namely hydrogen ratio, i.e. the ratio of hydrogen fuel flow rate to total fuel flow rate on a volumetric (or mole) basis:
rH2, vol =
v H2 vf
(51)
For the reasons explained in the previous sections, a typical value for this parameter at 10% is chosen to initially determine the thermophysical properties of the system at design conditions. For the streams shown in Fig. 1, the values of temperature, pressure, mass flow rate, and mole fractions are tabulated in Table 5. The key output parameters of the system model are tabulated in Table 6.
Fig. 3. Variation of compressor and turbine isentropic efficiencies for part-load operation of the gas turbine cycle.
stops to decrease linearly with decreasing load at loads below 60%. A similar trend is observed in the case of mass flow rate. As mentioned earlier (Section “Part-load model”), the exhaust temperature of the combustor in the computational simulations is kept constant at all loads to avoid unrealistic results. Also, both the compressor and the turbine are connected to the same shaft. However, these assumptions do not allow an optimum reduction of the air mass flow rate, as the load is reduced. More fuel is needed at part-load (especially at loads below 60%, as observed in Figs. 3 and 4) to achieve the desired power output from the gas turbine cycle. Therefore, for a higher fuel consumption (in relation to the generated power output), both net electrical and
Operation at off-design conditions The set of values for isentropic efficiency for the compressor and turbine are calculated with the part-load model and fed to the thermodynamic model; they are shown graphically in Fig. 3. The performance of the system in terms of net electrical efficiency is shown graphically in Fig. 4. Both figures suggest that as the load decreases, isentropic and net electrical efficiencies deteriorate rapidly, suggesting that system operation below 60% would be very inefficient and must be avoided. This trend is also evident in Fig. 5, where fuel consumption Table 5 Thermophysical property values at design conditions. Parameter description
Tk pk mk yCO2, k yH2 O, k
yN2, k yO2, k
Stream 1
2
3
4
Temperature at stream k (K) Pressure at stream k (Pa) Mass flow rate at stream k (kg/s) Mole fraction of CO2 at stream k
288 101,325 39.7085 0
708 1,702,260 39.7085 0
1445 1,617,147 40.4356 0.031
828 107,405 40.4356 0.031
Mole fraction of N2 at stream k
0.790
0.790
0.764
0.764
Mole fraction of H2O at stream k Mole fraction of O2 at stream k
0
0.210
0
0.210
6
0.067 0.138
0.067 0.138
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Fig. 7. Effect of part-load operation on total, methane, and hydrogen fuel consumption.
Fig. 4. Performance of the gas turbine cycle in terms of net electrical efficiency at part-load operation.
Fig. 8. Effect of part-load operation on the values of excess air for natural gas and hydrogen fuels.
Fig. 5. Fuel consumption and power output generation for the system at partload operation.
Fig. 6. Variation of inlet air and exhaust flue gas for the system at part-load operation.
Fig. 9. Effect of hydrogen ratio variation on the values of partial power output (methane vs. hydrogen).
isentropic efficiencies will deteriorate at off-design conditions. In Figs. 6 and 7, it is shown that low efficiency occurs at loads below 60%, because the system consumes more air (also more fuel, generating
more flue gas). Specifically, in Fig. 6, the mass flow rate curves for both the flue gas and air stop to decrease linearly below the load of 60%; while the exact same effect also occurs for the fuel flow rate curves, as 7
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
Fig. 10. Effect of hydrogen ratio variation on total fuel mass flow rate. Fig. 12. Effect of hydrogen ratio variation on thermodynamic and exergetic efficiencies.
Fig. 11. Effect of hydrogen ratio variation on the molecular composition of the exhaust flue gas.
shown in Fig. 7. Therefore if the system must be operated at loads lower than 60%, it must be recuperated for heat recovery, e.g. with a district heating energy network [17,20]. In Fig. 8, it is shown that more air is needed at part-load due to the system becoming less efficient with decreasing load. This trend is similar for both fuels.
Fig. 13. Effect of hydrogen ratio variation on exergy destruction ratio for every system component.
and exergetic efficiencies is shown. The effect appears to be more significant for exergetic efficiency, because it is entropy dependent. The reason for this is more clearly identified in Fig. 13, where the exergy destruction ratios for every system component are shown. Specifically, it is observed that net electrical efficiency for the gas turbine cycle improves slightly as hydrogen ratio is increased (0.347 and 0.356 for a hydrogen ratio of 0 and 0.9, respectively). On the other hand, the improvement of exergetic efficiency is more evident, mainly due to the significant reduction of combustor losses as hydrogen ratio increases (0.338 and 0.360 for a hydrogen ratio of 0 and 0.9, respectively). Therefore, hydrogen combustion results in a higher power output as compared to methane-only combustion. As the hydrogen content in the fuel increases, combustor losses are significantly decreased. This is because the exergy destruction in the combustor depends on the total mass flow rate of fuel entering the combustor (as defined in equation (17)), since the total fuel mass flow rate decreases with increasing hydrogen content, as already shown in Fig. 10. In turn, the exergy destruction ratio for the combustor yD, comb in equation (20) is also reduced. The combustion process becomes more efficient, mainly owing to the higher energy density of hydrogen in comparison to methane. On the other hand, for the compressor and turbine, with increasing hydrogen content, losses increase because of the need to increase the air inflow for combustion (see Fig. 8), but in this case losses are marginal, and therefore hydrogen variation is rather insignificant. This is because although the excess air for hydrogen
Parametric study: Variation of hydrogen ratio An important aspect for this study is the variation of hydrogen ratio. Although hydrogen ratio would not typically exceed 0.1, in order to examine the response of the system model at different hydrogen contents, hydrogen ratio is varied from 0 to 0.9. The net electrical efficiency remains almost constant as the value of hydrogen ratio is altered, but other key parameters change significantly. In Fig. 9 it is shown how partial power output is affected with increasing hydrogen ratio in the total fuel. In Fig. 10 it is shown that as hydrogen content in the total fuel increases, the total mass flow rate of fuel decreases, along with the heat input rate. The mass flow rate of fuel is almost two times higher without any hydrogen in comparison to a hydrogen ratio of 0.9. Another important aspect of hydrogen ratio variation is the amount of flue gas at the exhaust of the gas turbine, since flue gas would normally be released in the environment. Therefore it would be desirable to reduce CO2 emissions at the lowest possible level [21]. In Fig. 11, it is shown that the CO2 mole fraction with a hydrogen ratio of 0.1 and 0.5 drops by 6.1% and 24.2%, respectively, as compared to methane-only fueling. Therefore even tiny hydrogen contents can result to a reduction in CO2 emissions, which is also beneficial in terms of operational cost and total lifecycle cost for the system [20]. In Fig. 12, the effect of varying hydrogen ratio on thermodynamic 8
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
combustion is significantly higher than methane combustion, the comparatively more efficient combustion of hydrogen decreases flue gas generation, and therefore the flow rate of incoming air remains practically unchanged. Finally, for a hydrogen ratio of 0.1, CO2 emissions are reduced by 6.1% as compared to no hydrogen content in the fuel, with a further reduction to 24.2% for a hydrogen ratio of 0.5.
respectively). However, the improvement of exergetic efficiency is more significant, mainly due to the high reduction of combustor losses, as hydrogen ratio increases (0.338 and 0.360 for a hydrogen ratio of 0 and 0.9, respectively). Therefore, for the same amount of total fuel flow rate, hydrogen combustion results in a higher power output, in comparison to methane-only combustion. Also, hydrogen addition affects positively the system performance in terms of CO2 emissions, since even a hydrogen ratio of 0.1 (on a volumetric basis) results in a 6.1% reduction in CO2 emissions, with a further reduction to 24.2% for a hydrogen ratio of 0.5, as compared to methane-only fueling. The developed model can be used as a basis for future more application-specific studies in the field of decentralized power generation, combining various technologies (e.g. a PV-electrolyzer-gas turbine system).
Conclusions This study presents a detailed thermodynamic model, considering both first law and second law analyses, of a small-scale natural gas/ hydrogen-fueled gas turbine cycle, along with performance evaluation at both design and off-design conditions. Evaluation of performance at off-design conditions is very important, because in real-life conditions, the system will operate mostly at off-design, with several part loads. Therefore, it is necessary to develop a simulation model that determines performance at off-design conditions, as accurately as possible, to correspond to realistic operation. The system model is validated against measured manufacturer’s data from an industrial gas turbine and results show a good agreement between the model and the reference data. In general, the results suggest that hydrogen addition to the natural gas fuel supply could alter significantly the operation of the gas turbine cycle. It is observed that net electrical efficiency can slightly improve, as hydrogen ratio is increased (0.347 and 0.356 for a hydrogen ratio of 0 and 0.9,
Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Appendix A At the air compressor exit the specific enthalpy is determined as follows [14]:
h¯s,2 h¯2 = h¯1 +
h¯1 (52)
c
where h¯1 is the specific enthalpy at the inlet, and h¯s,2 is the isentropic specific enthalpy at the outlet (J/kg). The stoichiometric reactions of methane and hydrogen with air are the following, respectively:
CH 4 + as,CH4 (0.21O2 + 0.79N2) H2 + as,H2 (0.21O2 + 0.79N2)
bs,CH4 CO2 + cs,CH4 H2 O + ds,CH4 N2 bs,H2 H2 O + cs,H2 N2
The following expressions provide the conservation for carbon, hydrogen, oxygen and nitrogen atoms, respectively, for methane fuel:
1 = bs,CH4 4 = 2·cs,CH4 as,CH4 ·2·0.21 = 2·bs,CH4 + cs,CH4 as,CH4 ·2·0.79 = 2·ds,CH4
(53)
Similarly, for hydrogen:
2 = 2·bs,H2 as,H2 ·2·0.21 = bs,H2 as,H2 ·2·0.79 = 2·cs,H2
(54)
The actual reaction of methane and hydrogen with excess air are the following, respectively:
CH 4 + aCH4 (0.21O2 + 0.79N2) H2 + aH2 (0.21O2 + 0.79N2)
bCH4 CO2 + cCH4 H2 O + dCH4 N2 + eCH4 O2 bH2 H2 O + c H2 N2 + d H2 O2
The corresponding conservation expressions for methane and hydrogen, respectively, are given as follows:
aCH4 = (1 + eaCH4 )· as,CH4 1 = bCH4 4 = 2· cCH4 aCH4 ·2·0.21 = 2·bCH4 + cCH4 + 2· eCH4 aCH4 ·2·0.79 = 2·d CH4
(55)
9
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
aH2 = (1 + eaH2 )· as,H2 2 = 2· bH2 aH2 ·2·0.21 = bH2 + 2· d H2 aH2 ·2·0.79 = 2·c H2
(56)
The enthalpies of the reactants entering the combustor, per mole of fuel, for methane and hydrogen, respectively, are given by:
H2,CH4 = h¯ CH4,2 + 0.21·aCH4 ·h¯ O2,2 + 0.79·aCH4 ·h¯ N2,2
(57)
= h¯ H2,2 + 0.21·aH2 · h¯ O2,2 + 0.79· aH2 ·h¯ N2,2
(58)
H2,H2
The enthalpies of the products exiting the combustor, per mole of fuel, for methane and hydrogen, respectively, are given by:
H3,CH4 = bCH4 · h¯ CO2,3,CH4 + cCH4· h¯ H2O,3,CH4 + dCH4 ·h¯ N2,3,CH4 + eCH4 ·h¯ O2,3,CH4
(59)
H3,H2 = bH2 ·h¯ H2O,3,H2 + c H2·h¯ N2,3,H2 + d H2· h¯ O2,3,H2
(60)
Assuming no energy losses in the combustion process, an energy balance on the combustor, for methane and hydrogen, respectively, can be applied:
H3,CH4 = H2,CH4
(61)
H3,H2 = H2,H2
(62)
The mole fractions in the combustion products for methane and hydrogen, respectively, are given by: bCH 4
yCO2,3,CH4 =
bCH4 + c CH 4 + dCH 4 + eCH 4 c CH4
yH2O,3,CH4 =
bCH 4 + c CH4 + dCH4 + eCH 4 dCH4
yN2,3,CH4 =
bCH 4 + cCH 4 + dCH 4 + e CH4
yO2,3,CH4 =
bCH 4 + cCH 4 + dCH 4 + eCH 4
yH2O,3,H2 =
eCH 4
(63)
bH2 bH2 + c H2 + dH2 c H2
yN2,3,H2 =
bH2 + c H2 + dH2
yO2,3,H2 =
bH2 + c H2 + dH2
dH2
(64)
The entropy of the products exiting the combustor, per mole of fuel, for methane and hydrogen, respectively, are given by:
S3,CH4 = bCH4 ·¯sCO2,3,CH4 + cCH4·¯sH2O,3,CH4 + dCH4 ·¯s N2,3,CH4 + eCH4 ·¯sO2,3,CH4
(65)
S3,H2 = b H2 · s¯H2O,3,H2 + c H2·¯sN2,3,H2 + d H2· s¯O2,3,H2
(66)
The entropy of the products exiting the isentropic turbine, per mole of fuel, for methane and hydrogen, respectively, are given by:
Ss,4,CH4 = bCH4 · s¯CO2, s,4,CH4 + cCH4·¯sH2O, s,4,CH4 + dCH4 ·¯s N2, s,4,CH4 + eCH4 · s¯O2, s,4,CH4
(67)
Ss,4,H2 = bH2 ·¯sH2O, s,4,H2 + cH2· s¯N2, s,4,H2 + d H2· s¯O2, s,4,H2
(68)
Considering an entropy balance on the isentropic turbine:
Ss,4,CH4 = S3,CH4
(69)
Ss,4,H2 = S3,H2
(70)
The enthalpy of the products exiting the isentropic turbine, per mole of fuel, for methane and hydrogen, respectively, are given by:
Hs,4,CH4 = bCH4 · h¯ CO2, s,4,CH4 + cCH4· h¯ H2O, s,4,CH4 + dCH4 · h¯ N2, s,4,CH4 + eCH4 · h¯ O2, s,4,CH4 Hs,4,H2
= bH2 ·h¯ H2O, s,4,H2 + cH2· h¯ N2, s,4,H2 + d H2·h¯ O2, s,4,H2
(71) (72)
The total enthalpy of the products exiting the isentropic turbine, per mole of fuel, is given by: (73)
Hs,4 = Hs,4,CH4 + Hs,4,H2 The enthalpy of the products exiting the actual turbine, per mole of fuel, for methane and hydrogen, respectively, are given by:
H4,CH4 = H3,CH4
H4,H2 = H3,H2
(H3,CH4
(H3,H2
Hs,4,CH4 )·
Hs,4,H2 )·
(74)
t
(75)
t
where:
H4,CH4 = bCH4 ·h¯ CO2,4,CH4 + cCH4·h¯ H2O,4,CH4 + d CH4 ·h¯ N2,4,CH4 + eCH4 · h¯ O2,4,CH4
(76)
H4,H2 = bH2 ·h¯ H2 O,4,H2 + c H2·h¯ N2,4,H2 + dH2· h¯ O2,4,H2
(77)
10
Sustainable Energy Technologies and Assessments 36 (2019) 100560
A. Arsalis
The total molar flow rate of inlet air to the compressor is the sum of the partial molar flow rates needed for the combustion of methane and hydrogen: (78)
na = na,CH4 + na,H2
The resulting flue gas exiting the combustor can be related to the reactants with a molar flow rate balance, summing the flue gas flow rates from the combustion of the two fuels: (79)
n3 = nCH4,3 + nH2,3 The above equation can be analyzed as follows:
nCH4,3 = na,CH4 + nCH4 n H2,3 = na,H2 + n H2
(80)
The partial molar flow rates can be related to the corresponding mole fractions as follows:
ni,CH4,3 = nCH4,3· yi,3,CH4 ni,H2,3 = n H2,3· yi,3,H2
(81)
In the above equations i is the product species, i.e·H2O, CO2, O2, and N2. A molar flow rate balance results in the following general expression: (82)
ni,3 = ni,CH4,3 + ni,H2,3 The mole fractions are found with the following general expression:
yi,3 =
ni,3 n3
(83)
Assuming no change of composition in the flue gas during expansion in the turbine: (84)
yi,4 = yi,3 When mass fractions must be determined, the following relations deriving from the composition relations for gas mixtures are used:
M4 =
yi,4 ·Mi
(85)
i
x i,4 = yi,4 ·
Mi M4
(86)
References [11]
[1] Arsalis A, Alexandrou AN. Design and modeling of 1–10 MWe liquefied natural gasfueled combined cooling, heating and power plants for building applications. Energy Build 2015;86:257–67. https://doi.org/10.1016/j.enbuild.2014.10.025. [2] Arsalis A, Alexandrou AN, Georghiou GE. Thermoeconomic modeling of a smallscale gas turbine-photovoltaic-electrolyzer combined-cooling-heating-and-power system for distributed energy applications. J Cleaner Prod 2018;188:443–55. https://doi.org/10.1016/j.jclepro.2018.04.001. [3] Guandalini G, Campanari S, Romano MC. Power-to-gas plants and gas turbines for improved wind energy dispatchability: energy and economic assessment. Appl Energy 2015;147:117–30. https://doi.org/10.1016/j.apenergy.2015.02.055. [4] Ströhle J, Myhrvold T. An evaluation of detailed reaction mechanisms for hydrogen combustion under gas turbine conditions. Int J Hydrogen Energy 2007;32:125–35. https://doi.org/10.1016/j.ijhydene.2006.04.005. [5] Park J, Lee MC. Combustion instability characteristics of H2/CO/CH4 syngases and synthetic natural gases in a partially-premixed gas turbine combustor: part IFrequency and mode analysis. Int J Hydrogen Energy 2015;41:7484–93. https:// doi.org/10.1016/j.ijhydene.2016.02.047. [6] He F, Li Z, Liu P, Ma L, Pistikopoulos EN. Operation window and part-load performance study of a syngas fired gas turbine. Appl Energy 2012;89:133–41. https:// doi.org/10.1016/j.apenergy.2010.11.044. [7] Shih HY, Liu CR. A computational study on the combustion of hydrogen/methane blended fuels for a micro gas turbines. Int J Hydrogen Energy 2014;39:15103–15. https://doi.org/10.1016/j.ijhydene.2014.07.046. [8] Juste GL. Hydrogen injection as additional fuel in gas turbine combustor. Evaluation of effects. Int J Hydrogen Energy 2006;31:2112–21. https://doi.org/10.1016/j. ijhydene.2006.02.006. [9] Funke H, Keinz J, Boerner S, Hendrick P, Elsing R. Testing and analysis of the impact on engine cycle parameters and control system modifications using hydrogen or methane as fuel in an industrial gas turbine. Prog Propul Phys 2016;8:409–26. https://doi.org/10.1051/eucass/201608409. [10] Wright IG, Gibbons TB. Recent developments in gas turbine materials and
[12] [13] [14] [15] [16] [17]
[18] [19] [20] [21]
11
technology and their implications for syngas firing. Int J Hydrogen Energy 2007;32:3610–21. https://doi.org/10.1016/j.ijhydene.2006.08.049. Bianchini A, Pellegrini M, Saccani C. Solar steam reforming of natural gas integrated with a gas turbine power plant. Sol Energy 2013;96:46–55. https://doi. org/10.1016/j.solener.2013.06.030. Ebaid MSY, Hammad M, Alghamdi T. THERMO economic analysis OF PV and hydrogen gas turbine hybrid power plant of 100 MW power output. Int J Hydrogen Energy 2015;40:12120–43. https://doi.org/10.1016/j.ijhydene.2015.07.077. Siemens. Industrial gas turbine SGT-400 2017. http://www.energy.siemens.com/ hq/en/fossil-power-generation/gas-turbines/sgt-400.htm. [accessed December 1, 2017]. Klein S, Nellis G. Thermodynamics. New York, NY: Cambridge University Press; 2012. Zhang N, Cai R. Analytical solutions and typical characteristics of part-load performances of single shaft gas turbine and its cogeneration. Energy Convers Manage 2002;43:1323–37. https://doi.org/10.1016/S0196-8904(02)00018-3. Wang W, Cai R, Zhang N. General characteristics of single shaft microturbine set at variable speed operation and its optimization. Appl Therm Eng 2004;24:1851–63. https://doi.org/10.1016/j.applthermaleng.2003.12.012. Arsalis A, Alexandrou AN. Thermoeconomic modeling and exergy analysis of a decentralized liquefied natural gas-fueled combined-cooling e heating-and-power plant. J Nat Gas Sci Eng 2014;21:209–20. https://doi.org/10.1016/j.jngse.2014.08. 009. Bejan A, Tsatsaronis G, Moran MJ. Thermal design and optimization. Wiley; 1996. Saravanamuttoo H, Rogers G, Cohen H, Straznicky P, Nix A. Gas turbine theory. 7th ed. Pearson; 2017. Arsalis A, Alexandrou AN, Georghiou GE. Thermoeconomic modeling and parametric study of a photovoltaic-assisted 1 MWe combined cooling, heating, and power system. Energies 2016;9:663. https://doi.org/10.3390/en9080663. Pilavachi PA, Stephanidis SD, Pappas VA, Afgan NH. Multi-criteria evaluation of hydrogen and natural gas fuelled power plant technologies. Appl Therm Eng 2009;29:2228–34. https://doi.org/10.1016/j.applthermaleng.2008.11.014.