Table 2.2: Cost of different electrolysers, according to type and rated power.
Source Year Type Rated Power CAPEX (e/kW)
Demo4Grid [42] 2017 AWE 2.5 MW 680
Haeolus [43] 2018 PEME 2.5 MW 1328
Demo4Grid [42] 2017 AWE 5.0 MW 550
Demo4Grid [42] 2017 AWE 10 MW 530
Refhyne [44] 2018 PEME 10 MW 1000
Demo4Grid [42] 2017 AWE 20 MW 515
FCH JU [40] 2020 AWE ——— 600
FCH JU [40] 2020 PEME ——— 900
(future prospects[41]) 2024 AWE ——— 480
(future prospects[41]) 2024 PEME ——— 700
Figure 2.3:H2density under certain temperature and pressure conditions [46].
where m is the total mass of gas molecules in kg and R is hydrogen’s specific gas constant, which has a value of 4124.18 Nm/mol K.
Density is defined as mass per unit volume (kg/m3), so Equation2.5is rewritten as:
p=ρRT (2.6)
However, these equations were only considered to be accurate until the 20th century when they were found to be just good approximations. As the name suggests, the Ideal Gas Law can only describe the behaviour of an ideal gas, a theoretical substance made of molecules that occupy negligible space and do not exert an attractive force on each other. But, in a real gas, its particles occupy space, reducing the available volume to hold more gas, and they attract each other, further increasing the pressure. The Ideal Gas Law can only closely describe the behaviour of a real gas at pressures up to 100 bar and at ambient temperatures. Above that, as the pressure increases, the results become less and less precise [47], as evidenced in Figure2.4.
Further ahead, it will be shown howH2storage is done at pressures up to 700 bar. If used to determine hydrogen’s density in those situations, these equations would result in significant errors, but it is possible to correct them. At high pressures, the Ideal Gas Law leads to an overestimation of the density ofH2and so, if this relation is used to computeρH2, the resulting density is higher than the actual value. In other words, this means that the gas actually fills more volume than anticipated by the Ideal Gas Law, or that, if the volume cannot be increased, the gas will suffer an increase in pressure. Thus, by ignoring the space occupied by the molecules, the subsequent deviation from the Ideal Gas Law is in the form of compression and the gas occupies more space than predicted. One way of compensating for it is by using a compressibility factor Z. This factor, which depends on temperature, pressure and the nature of the gas, is derived from data obtained
Figure 2.4: CompressedH2density assuming an ideal gas and a non-ideal gas [48].
through experimentation [48]. Then, the adjusted gas law is established as :
p=ZρRT (2.7)
Figure2.5describes the variation of the compressibility factor forH2with the temperature at high pressures. At ambient temperature, a value of 1.2 is reached at 300 bar. This means that if the Ideal Gas Law is used to calculate the mass ofH2inside a container, the result will be 20 % greater than the real value [49].
Figure 2.5: Compressibility factor Z ofH2gas for different values of p and T [49].
A procedure to calculate theH2compressibility factor is described in [50]. According to this method, the value of Z forH2can be computed using Equation2.8.
Z=
9
∑
i=1 5
∑
j=1
vi jpi−1 100
T j−1
(2.8) where
vi j=
1.000 3.054·10−4 −1.458·10−3 2.345·10−3 5.204·10−4
−4.278·10−4 2.475·10−2 −8.763·10−3 −3.201·10−2 1.359·10−2
−5.033·10−6 7.602·10−5 −6.130·10−4 1.589·10−3 2.781·10−4 3.259·10−7 −3.771·10−6 3.0545·10−5 3.0545·10−5 −7.691·10−5
−3.247·10−9 −1.041·10−8 5.529·10−7 −3.121·10−6 3.716·10−6
−8.725·10−11 2.5607·10−9 −2.393·10−8 8.810·10−8 −8.608·10−8 2.304·10−12 −4.8093·10−11 3.665·10−10 −1.167·10−9 1.047·10−9
−1.936·10−14 3.648·10−13 −2.550·10−12 7.534·10−12 −6.450·10−12 5.684·10−17 −1.018·10−15 6.781·10−15 −1.915·10−14 1.590·10−14
To conclude, by using this methodology, it is possible to get accurate values forH2density at high pressures, even when considering changeable temperature and pressure conditions.
2.4.2 Hydrogen compression thermodynamics
The required work for compressing gases depends on the thermodynamics behind the com-pression and on the nature of the substance. The calculation of the required energy for compress-ing the gas is usually simplified by assumcompress-ing an adiabatic or an isothermal process. The adiabatic process happens without the transference of any heat or mass between the thermodynamic system and the environment and at a constant entropy (isentropic), meaning that the temperature of the gas changes without any heat being exchanged between the fluid and its surroundings [51].
The energy consumed by an adiabatic compression is calculated by applying the undermen-tioned expression [52]:
W = γ γ−1p0V0
"
p1 p0
γ−1
γ
−1
#
(2.9) where W is the specific compression work (J/kg),γ is the heat capacity ratio (1.41 forH2),p0and p1are the initial and final pressures (Pa) andV0is the initial specific volume (11.1m3/kgforH2).
Mostly due to its very low density, H2 requires a larger amount of energy than methane or helium to be compressed to the same pressure [51].
Contrarily, in an isothermal process, the temperature of the gas remains constant during the compression and the required energy can be obtained using the next equation [52]:
W =p0V0ln p1
p0
(2.10)
Figure 2.6: Adiabatic compression work for methane, helium and hydrogen [52].
Under real conditions, theoretical isothermal and isentropic compression can act as boundaries for realistic compression work. In the case of H2, the difference in energy consumption as a percentage of its HHV is exhibited in Figure2.7[51].
Figure 2.7: Energy required for compressing hydrogen compared to its HHV [52].
In general, the compressed gas must be cooled down after each stage of compression to make it a less adiabatic and more isothermal process and, therefore,H2is normally compressed in different stages. Multistage compressors are fitted with intercoolers and can operate between those two limiting curves. Besides, hydrogen easily transfers heat resulting from the compression to cooler walls, nearing the isothermal process. As seen in Figure2.7 for a final pressure of 800 bar, the compression energy requirements would amount to about 13 % of the energy content ofH2[52].
2.4.3 Hydrogen compressor power calculation
In [45], the power of an isentropic (reversible and adiabatic) single-stage process is given by:
Pss=
γ−1 γ
Z ηisen
TsucqMR¯
"
pdisc psuc
γ−1γ
−1
#
(2.11) where Z is the average compressibility factor,ηisenis the isentropic efficiency,Tsucis the suction temperature (K),qmis the molar flow rate (mole/s),pdiscis the discharge pressure (bar) andpsucis the suction pressure (bar). Meanwhile, the power of an isentropic multistage process [45] is given by:
Pms=N γ−1
γ Z
ηisen
TsucqMR¯
"
pdisc psuc
γγ−1N
−1
#
(2.12) where N is the number of stages and is calculated according to
N= log
Pdisc Psuc
log(x) (2.13)
where x is the compression ratio for single-stage. As reported in the literature [45], the value of x is usually between 2.1 and 4. Finally, a compressor’s rated power is given by [45]:
PCP= Pms ηmotor
(2.14) whereηmotoris the efficiency of the motor driving the compressor. The isentropic efficiency,ηisen, of an older compressor is between 60% and 65%, but in a more recent device, its value can reach up to 80% or even 85% [53]. In the meantime, the motor efficiency,ηmotor, can have a value up to 95% [45].
In [54], it is calculated the energy consumed by a real compressor. It is assumed an adiabatic compression model with a global efficiency of 50 %. This efficiency value already considers the efficiency of electrical power transformation and other supplementary systems, such as cooling.
The obtained results are provided in Table2.3.
Table 2.3:H2compressors estimated energy consumption [54].
Year psuc[bar] pdisc [bar] Stages Energy [KWh/kg]
2017
1 200 4 5.0
500 5 6.3
30 200 2 1.7
500 3 2.7
2025
15 200 2 2.4
500 3 3.5
60 200 1 1.1
500 2 2.0
2.4.4 Hydrogen compressor cost
The CAPEX ofH2compressor skids andH2filling stations is given in [55]. A compressor skid is a structure which consists of a compressor, drivers, vessels, piping and other equipment required for the compression [56]. Meanwhile, in a filling station, H2 is supplied to a tube trailer, a type of semi-trailer that consists of several clustered high-pressureH2 tanks [57]. For both structures, their CAPEX can be calculated according to Equation2.15.
CAPEXCP=A Q Qre f
!a
+B Q Qre f
!b
·
pdisc psuc
pre f
!c
· pdisc pre f
!d
(2.15) where Q is the flow rate in kg/h,Qre f is the reference flow rate equal to 50 kg/h, pre f is the reference pressure (50 bar for compression skids and 200 bar for filling stations) and A, B, a, b, c and d are numerical coefficients whose values are reported in Table2.4.
Table 2.4: Parameters for the proposed correlation [55].
Coefficient Filling station Compression skid
A 550 100
B 300 300
a 0.66
b 0.66
c 0.25
d 0.25