Established Methods Based on Compression and Cryogenics - Hydrogen Generation, Storage, and Utilization - page 81

and

γ − 1

γ − 1

=

V
V

P
P

γ

1 2

,

(5.15)

2 1

where γ = C p / C v is the specific heat ratio, and C p and C v are the specific
heats of hydrogen. For an ideal hydrogen gas, γ = 1.4. The work W Q done
in the adiabatic process is

γ − 1

γ P

P

γ

2

W

Q =

nRT − 1 .

(5.16)

1

γ − 1

1

Usually, the compression process is carried out under several stages, and
the total work required for an l l-stage process is

γ − 1

γ P

P

∑

l

γ

i + 1

W = nRT − 1 .

(5.17)

Q 1

γ − 1

i = 1

i

Multiple stage compression could significantly reduce the required energy.
For example, for a two-stage compression, if the initial and final pressures
are fixed at P 1 and P 2 , when the intermediate pressure P

i =

PP

1 2 , Equation

(5.17) gives the minimum work required,

γ − 1

2 γ P

P

2 γ

2

W

Q =

nRT − 1 .

(5.18)

1

γ − 1

1

If 1 mole of hydrogen is compressed from 1 atm at 20°C, Figure 5.4 shows
the comparison of the works W Q required for a one-stage and a two-stage
compression as a function of the final pressure P 2 . To compress the hydrogen
to 70 MPa, the two-stage process only requires ∼56% of energy of the one-
stage process. The higher the final pressure, the more the energy saved.
Similarly, a three-stage process, with intermediate pressure

γ − 1

3 γ P

P

3 γ

2 3 / 1 3 / 1 3 / 2 3 / 2

P = P P , P = P P and W = nRT − 1 ,

i 1 1 2 i 2 1 2 Q 1

γ − 1

1

can further reduce the required work (Fig. 5.4). Thus, with the increase of
number of compression stages, the required energy is reduced. But no sig-
nificant energy efficiency gain is expected when l > 3.
When the pressure becomes higher, the behavior of hydrogen gas deviates
from that of an ideal gas, and the compression process can be better