-1-
THERMODYNAMICS OF HYDROGEN STORAGE
Klell M., Zuschrott M., Kindermann H. , Rebernik M.
HyCentA Graz and Graz University of Technology, Austria
ABSTRACT
Keywords: compressed gaseous hydrogen, liquid hydrogen, thermodynamic model, self
pressurization, boil-off
As an energy carrier and with respect to fossil fuels, hydrogen has advantages with regard to
availability and environmental impact, though several technical and economical problems
require solution before industrial application, particularly with respect to production and
storage. Hydrogen can be stored as a highly compressed gas at up to 700 bar, cryogenically
liquefied at -253 °C or in bound form. Following an overview of the characterising features of
these three types of storage, the thermodynamics of gaseous and liquid hydrogen storage will
be analysed in more detail.
In the case of gaseous storage, the negative Joule-Thomson coefficient of hydrogen plays a
role, causing warming of tank facilities during filling and thus raising filling time.
Liquid hydrogen storage raises questions principally regarding pressure build-up, pressure
relief (boil-off) and filling. Numerical models of liquid tank systems will be presented,
covering cases of thermodynamic equilibrium and transient behaviour with superheated gas
phase and accompanied by simulations of pressure build-up. Here it can be seen that
temperature increases occurring in the superheated gas phase only reach a few degrees. The
simulation results are compared with measurements carried out on cryogenic containers at
HyCentA, though the potential for improvement in the quality of measurements is apparent.
The chilling of connecting pipes and containers, so critical to hydrogen wastage, is also
simulated and compared with measurements. In combination, the numerical models presented
are capable of supporting appropriate parameter optimisation with respect to pressure,
temperature and fill level in the presence of pressure build-up, boil-off and chilling.
By virtue of its relatively high energy storage density, currently not achievable either through
gaseous or bound storage, cryogenic storage offers advantages in terms of range for mobile
applications. However, installation complexity and boil-off gas losses need to be minimised if
filling stations are to be competitive in the longer term.
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1.
INTRODUCTION
As an energy carrier and with respect to fossil fuels, hydrogen has several advantages.
Hydrogen is the most abundant element in nature and thus theoretically in unlimited supply.
However, as a result of its high reactivity, hydrogen is practically only encountered in
compounds and has to be generated through the use of primary energy, though a large number
of partially renewable generation processes with particularly renewable energies exist.
Hydrogen can be burnt in internal combustion engines producing low levels of pollutants, and
in fuel cells free of pollutants. Combustion takes place according to equation (1), with the
reverse reaction corresponding with hydrogen generation during electrolysis. Thus the use of
hydrogen in a closed loop is possible.
2 H2 + O2 => 2 H2O , ∆H = − 572 kJ/mol
(1)
Calorific value Hu = 120 MJ/kg = 33.3kWh/kg
Before hydrogen can reach widespread industrial application, several economical and
technical problems require solution, particularly with regard to efficient generation and
storage. Several properties of hydrogen are summarised in Table 1.
Table 1: Properties of hydrogen [ 1 ]
Melting point Tsch
Boiling point Ts at 1.013 bar
Critical temperature
Critical pressure
Critical density
Density of liquid at 1.013 bar and 20 K
Density of gas at 1.013 bar and 20 K
Density of gas at 1.013 bar and 273 K
Density of gas at 300 bar and 273 K
Density of gas at 700 bar and 273 K
Density of gas at 700 bar and 2000 K
Calorific value Hu gravimetric
Calorific value volumetric at 1.013 bar and 300 K
Calorific value volumetric at 300 bar
Calorific value volumetric liquid
Specific heat capacity
Specific heat capacity
Latent heat of vaporisation at Ts
Thermal conductivity at 1.013 bar and 300 K
Gas constant
Molar mass
Diffusion coefficient
Dynamic viscosity at 1 bar and 300 K
Ignition limits in air
Ignition temperature
Minimum ignition energy
Laminar flame velocity
Flame temperature in air
-259.15 °C (13.9 K)
-252.76 °C (20.39K)
-239.96 °C (33.19 K)
13.15 bar
31.4 kg/m³
70.8 kg/m³
1.3408 kg/m³
0.09 kg/m3
22.1 kg/m3
41.6 kg/m3
8.01 kg/m3
33.3 kWh/kg = 120 MJ/kg
2.8 kWh/m³ = 10.1 MJ/m³
766 kWh/m³ = 2750 MJ/m³
2.36 kWh/l = 8.5 MJ/l
cp 14.32 kJ/kgK
cv 10.17 kJ/kgK
445.4 kJ7kg = 31.5 kJ/l
0.184 W/mK
4124 J/kgK
2.02 g/mol
0.61 cm²/s
8.91 x 10-6 Ns/m²
4.0 – 75.6 Vol-%
560 °C
0.017 mJ
2,7 m/s
ca. 2100 °C
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At normal temperature and pressure, hydrogen is a colourless, odourless gas with no toxic
effects. It is the lowest density element and therefore requires a large storage volume, whilst
also having a high diffusion coefficient. After Helium, element No. 1 has the lowest melting
and boiling points. Hydrogen is highly inflammable (EU rating F+ and R12) with broadly
spaced ignition limits in air (lower explosion limit 4% by volume, upper explosion limit
75.6% by volume) and low ignition energy (0.017 mJ for a stoichiometric air mixture). As
with all fuels, the use of hydrogen requires compliance with safety regulations, with EU
safety sheets specifying:
S9:
S16:
S33:
keep containers in a well-aired location
keep away from ignition sources – do not smoke (explosion areas)
take precautions against electrostatic charge
Because hydrogen is a very light and diffusive gas, increasing concentrations can normally be
prevented easily through adequate ventilation. In the case of compressed gas CGH2 storage,
compliance with pressure vessel regulations is required. Direct contact with cryogenic liquids
and gases can cause serious frostbite or freeze-burns. Furthermore, exposure to cryogenic
hydrogen can cause embrittlement of a variety of materials including most plastics and mild
steel, which can in turn lead to fracture and leakage.
2.
STORAGE OF HYDROGEN
The properties of hydrogen give rise to technical and economical challenges with regard to its
storage. There are three basic types of hydrogen storage:
•
•
•
2.1.
Storage of cryogenic liquid hydrogen at around -253 °C,
Storage of compressed gaseous hydrogen at up to 700 bar
Storage in bound form
Storage of liquid hydrogen
Relatively high storage densities can be achieved with liquid hydrogen (50 – 70 kg/m³).
However its very low boiling point at -253 °C means that the generation of liquid hydrogen is
very difficult and requires 20% to 30% of its energy content. The storage of liquid hydrogen
is technically challenging. Containers with high levels of insulation are used, consisting of an
inner tank and an outer container with an insulating vacuum between them, see Figure 1. The
austenitic stainless steel most commonly used for such tanks retains its excellent plasticity
even at very low temperature and does not embrittle. The evacuated space between the nested
containers is filled with multi layer insulation (MLI) having several layers of aluminium foil
alternating with glass fibre matting.
With today’s liquid hydrogen storage systems, the storage weight is around 20 kg/kg stored
H2. As a result of inevitable inward heat leakage without active cooling, hydrogen evaporates
in the container leading to increases in pressure and temperature. Liquid hydrogen containers
must therefore always be equipped with a suitable pressure relief system and safety valve.
Liquid storage therefore takes place in an open system in which released hydrogen has to be
dealt with by means of catalytic combustion, dilution or alternative consumption. Evaporation
losses on today’s tank installations are somewhere between 0.3% and 3% per day, through
larger tank installations have the advantage as a result of their lower surface area to volume
ratio.
The intended consumption of hydrogen requires additional arrangements like cryo-pumps,
deliberate energy injection for vaporisation or the raising of tank pressure. Apart from the
tank itself, the filling support infrastructure is also technically involved, with transfer pipes,
filling connectors etc also requiring vacuum insulation and chilling to -253 °C prior to liquid
filling.
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
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inner container
super-insulation
level sensor
filling pipe
gas outlet
liquid outlet
filling port
outer container
inner container support
liquid hydrogen (-253°C)
safety valve
gaseous hydrogen
(+20°C to +60°C to
engine);
main shut-off valve
electrical heating
hydrogen heater
selector valve for gas / liquid
Source: Linde gas
Figure 1: Liquid hydrogen tank
Source: Quantum Technologies
Figure 2: Compressed hydrogen tank
2.2.
Storage of gaseous hydrogen
For compressed hydrogen storage the gas is normally compressed to pressures between 200
bar and 350 bar, though more recently storage pressures of 700 bar and even higher have been
under trial. Gaseous hydrogen storage takes place in a closed system, with the result that
gaseous hydrogen can be stored without losses even for extended periods. At 700 bar, the
density of 40 kg/m³ is somewhat more than half that for liquid storage, whilst the energy
required for compression is around 15% of the fuel energy content. Such enormous pressures
require consideration of questions regarding material choice, component dimensioning and
safety, with such tank systems ending up just as heavy as liquid systems; storage weight is
around 20 to 30 kg/kg stored H2. An example of a compressed hydrogen tank is shown in
Figure 2.
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2.3.
Storage of bound hydrogen
Chemically binding offers another form of storage, subdivided into the following three types:
Chemical reaction: hydrogen is bound and released through chemical reactions. Chemical
compounds of hydrogen are known as hydrides, the most common being water, alcohol and
carbon-based (e.g. petrol, diesel) hydrides.
Absorption: In absorptive hydrogen storage, the hydrogen molecules nestle in the spaces
between the atoms in a material and are chemically bound. This type of chemical binding is
also described as a hydride. Metal hydrides, for example with light or alkali metals, are
common storage materials, see Figure 3.
Figure 3: Metal hydride storage
Adsorption: In the case of adsorption, hydrogen is physically or chemically bound to the
surface of a material, an example being deposition on carbon in the form of nanotubes.
The important evaluation criteria for bound hydrogen storage are temperature, pressure and
duration for charging and discharging the system as well as the potential number of charging
cycles. Despite theoretically high storage densities, most forms of bound storage are still at
the trial stage, with commercially available storage materials offering a storage weight of
around 30-50 kg/kg stored H2.
2.4.
Summary and comparison of storage modes
To give an overview, the achievable volumetric and gravimetric hydrogen densities of
different hydrogen storage modes have been summarised in Figure 4. It is obvious that, with
regard to volumetric storage density, bound storage has the greater potential. A greater
amount of hydrogen per unit volume can be stored in compounds than in pure form. Due to
the fact that this often requires high temperatures and pressures as well as long filling times,
gaseous and liquid storage tends to prevail at the moment. We shall analyse these forms of
storage in greater detail in the following.
Figure 5 shows the dependency of density on the pressure for liquid and gaseous compressed
hydrogen. The dotted line represents the operating ranges prevalent today. It is clear that
gaseous hydrogen only reaches the densities of liquid hydrogen at pressures of more than
1000 bar. The graph also shows the minimum work required for the liquefaction and
compression of hydrogen in percentages of the heat value. Isothermal compression work
assumes an ideal cooling process. For the isentropic compression work, the final compression
temperature was limited to 700 K. In order not to exceed this temperature limit, a cooling
process had to be taken into account, starting at a final compression pressure of approx. 30
bar. The liquefaction and compression work represented here does not take into account the
cycle efficiencies that lie at about 50% with compressors and 30% with liquefaction.
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
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160
density
BaReH9
<373 K, 2 bar
140
Volumetric H2 density [kg H2/m³]
5 g/cm³
2 g/cm³
Mg2FeH6
620 K, 1 bar
LaNi5H6
300 K, 2 bar
120
NaBH4
dec. 680K
MgH2
620 K, 5 bar
NaAlH4
dec. > 520K
Mg2NiH4
550 K, 4 bar
KBH4
dec. 580K
80
0.7 g/cm³
Al(BH4)3
dec.373K
m.p. 208K
Cnano H0.95
FeTiH1.7
300 K, 1.5 bar
100
1 g/cm³
LiAlH4
dec. 400K
C8H18
LiBlH4
dec. 553K
liq.
CH4liq.
b.p. 112K
C4H10liq.
b.p. 272K
LiH
dec. 650K
H2liq.
20.3K
20000
60
H2
physisorbed
on carbon
5000
2000
40
H2
chemisorbed
on carbon
1000
Pressurized H2Gas
(composite material)
p[bar]
800
20
500
200
130
0
0
5
10
15
20
25
Gravimetric H2 density [kg H2/kg]
Figure 4: Density of hydrogen storage modes [ 9 ]
12
90
80
work of condensation
10
70
density [ kg/m³]
isentropic work of compression
8
50
6
40
density as gas
30
20
4
work of isothermal compression
2
10
0
1
10
100
0
1000
pressure [bar]
Figure 5: Density of LH2 and GH2 dependent on pressure
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
work [%Hu]
density as liquid
60
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3.
THERMODYNAMICS OF GASEOUS STORAGE
As can be seen in Figure 5, the storage of gaseous hydrogen requires compression to high
pressures of up to more than 700 bar in order to achieve storage densities similar to those of
liquid hydrogen storage.
On a thermodynamic level, what is interesting is the compression on the one hand and the
relaxation during the filling of a pressure tank on the other. We shall not go into the details of
compression technology and the efficiency factors that can be achieved with it. With flowing
gases, compression is generally linked with a temperature increase, while expansion leads to a
decrease in temperature. During the filling of the tank, pressure is decreased by a restriction.
The associated change in temperature is described by the Joule-Thomson coefficient.
Joule-Thomson coefficient
The Joule-Thomson coefficient µ describes the extent and direction of the temperature change
for an isenthalpic change in state (index H):
⎛ ∂T ⎞
µ JT = ⎜⎜ ⎟⎟
⎝ ∂p ⎠ H
(2)
A positive Joule-Thomson coefficient means that a decrease in temperature takes place along
an isenthalp with a pressure decrease. In the T-s diagram, this is reflected as a falling
isenthalp with a pressure decrease (cooling down during relaxation in a restriction).
A negative Joule-Thomson coefficient means that an increase in temperature takes place
along an isenthalp with a pressure decrease. In the T-s diagram, this is reflected as a rising
isenthalp with pressure decrease (heating up during relaxation in a restriction).
Ideal gases do not experience a change in temperature while enthalpy remains constant. This
means that the Joule-Thomson coefficient is zero.
The Joule-Thomson effect also occurs when a gas or gas mixture experiences a change in
temperature during an isenthalpic pressure change. With real gases, attractive or repulsive
forces operate between the particles. In most cases, for instance in the case of gases in air at
normal pressure, attracting forces prevail. If the median distance between particles increases,
energy works against the attracting forces that are at work between the particles. This energy
results from the kinetic energy of the gas, which is being reduced in the process. On average,
the particles slow down, resulting in the cooling down of the gas. An ideal gas does not show
any Joule-Thomson effect, as no interaction occurs between its particles.
Hydrogen warms up during the relaxation phase, which indicates a negative Joule-Thomson
coefficient. The effects of the negative Joule-Thomson coefficient become particularly
apparent during the filling of high-pressure hydrogen tanks in vehicles. The relaxation of
hydrogen from 350 bar to 50 bar produces a warming by about 16 K (see Figure 6), causing a
corresponding reduction in the volume transferred to the tank. The losses that occur during
the filling process are reduced by cooled fillings or slow fillings with heat dissipation into the
external environment, whereas in the second case a significant increase in the filling time has
to be accepted, which otherwise only requires several minutes.
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Density
Pressure
Enthalpie
[kg/m³]
[bar]
[kJ/kg]
∆T
Solid phase
Figure 6: T-s diagram (relaxation from 400 bar to 50 bar)
4.
THERMODYNAMICS OF LIQUID STORAGE
In a liquid hydrogen container, pressure will increase up to the maximum permissible
container pressure (pressure build-up time) due to the unavoidable heat input and the resulting
vaporisation. From this point onwards, hydrogen must be blown off (boil-off) and the
container becomes an open system. On a thermodynamic level, what is of interest is the
calculation of the pressure and temperature increases over the course of time against the heat
input, particularly the length of the pressure build-up time until boil-off is reached, and the
vaporisation rate and/or the rate of the effusing hydrogen.
Figure 7: Reservoir tank and conditioning container at the HyCentA Graz
st
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4.1.
General description of the cryo-container system
For a general illustration, we shall first of all look at a cryo-container with an inflowing mass
flow rate me and an outflowing mass flow rate ma as an open system. It is assumed that this
system is in a thermodynamic equilibrium, i.e. all state variables are equally distributed within
the system. In particular, we find the same pressure throughout the system and the same
temperature of the boiling liquid hydrogen and the saturated hydrogen vapour. This system
can be described by applying the first law of thermodynamics and the law of conservation of
mass. Despite the simplifying assumptions underlying the model, it can only describe the
principles of the relevant processes in the tank system, i.e. the pressure build-up resulting
from heat input, the evaporation resulting from heat input (boil-off), the effusion in order to
decrease pressure, and the refuelling process, cf. for instance [ 2 ], [ 3 ], [ 5 ], [ 11 ].
me
ma
Q
U , p, t
W
Figure 8: System of a cryo-container
The first law of thermodynamics for open systems applies:
dAt + dQa + ∑ dmi .(hi + e ai ) = dU + dE a
(3)
Neglecting kinetic and potential energy yields:
dAt + dQa + ∑ dmi .(hi ) = dU
(4)
In this general solution, the mechanical work A (e.g. shaft work) and the work of the
dV
are considered separately.
volumetric change − p ⋅
dt
dV
dU
= Q1, 2 + A1, 2 + me ⋅ he − m a ⋅ ha − p ⋅
dt
dt
(5)
For internal energy, it follows that:
U = m ⋅ u = ρ ⋅V ⋅ u
(6)
dU
du
dV
dρ
= ρ ⋅V ⋅
+ ρ ⋅u ⋅
+V ⋅u ⋅
dt
dt
dt
dt
(7)
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ρ ⋅V ⋅
du
dV
dρ
dV
+ ρ ⋅u ⋅
+V ⋅u ⋅
= Q1, 2 + A1, 2 + me ⋅ he − m a ⋅ ha − p ⋅
dt
dt
dt
dt
(8)
From the law of conservation of mass, it follows that:
dm
dρ
dV
= me − ma = V ⋅
+ρ⋅
dt
dt
dt
ρ ⋅V ⋅
du
dV
+ u ⋅ (me − m a ) = Q1, 2 + A1, 2 + me ⋅ he − ma ⋅ ha − p ⋅
dt
dt
(9)
(10)
Internal energy is represented as a function of density and pressure Æ u = u ( ρ , p)
du ⎛ ∂u ⎞ dρ ⎛ ∂u ⎞ dp
+⎜ ⎟
=⎜ ⎟
dt ⎜⎝ ∂ρ ⎟⎠ p dt ⎜⎝ ∂p ⎟⎠ ρ dt
⎛ ∂u ⎞ dρ
⎟⎟
+ ρ ⋅V
⎝ ∂ρ ⎠ p dt
ρ ⋅ V ⋅ ⎜⎜
(11)
⎛ ∂u ⎞ dp
⋅ ⎜⎜ ⎟⎟
=
⎝ ∂p ⎠ ρ dt
dV
= Q1, 2 + A1, 2 + me ⋅ he − ma ⋅ ha − p ⋅
− u ⋅ (me − ma )
dt
(12)
⎛ ∂u ⎞ dp
⎟⎟
=
⎝ ∂p ⎠ ρ dt
ρ ⋅ V ⋅ ⎜⎜
⎛ ∂u ⎞ dρ
dV
= Q1, 2 + A1, 2 + me ⋅ (he − u ) − ma ⋅ (ha − u ) − p ⋅
− ρ ⋅ V ⋅ ⎜⎜ ⎟⎟
dt
⎝ ∂ρ ⎠ p dt
(13)
With the law of conservation of mass:
⎛ dV ⎞
me − ma − ρ ⋅ ⎜
⎟
dρ
dt ⎠
⎝
=
dt
V
(14)
⎛ ∂u ⎞ dp
⎟⎟ .
=
⎝ ∂p ⎠ ρ dt
ρV ⋅ ⎜⎜
⎛ dV ⎞
me − ma − ρ ⋅ ⎜
⎟
⎛ ∂u ⎞
dV
dt ⎠
⎝
= Q1, 2 + A1, 2 + me ⋅ (he − u ) − ma ⋅ (ha − u ) − p ⋅
− ρ ⋅ V ⋅ ⎜⎜ ⎟⎟ ⋅
dt
V
⎝ ∂ρ ⎠ p
dp
=
dt
dV ⎤
⎡
⋅ ⎢Q12 + A12 + me ⋅ (he − u ) − ma ⋅ (ha − u ) − p ⋅
−
dt ⎥⎦
⎛ ∂u ⎞ ⎣
ρV ⎜⎜ ⎟⎟
⎝ ∂p ⎠ ρ
(15)
1
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−
⎡ ⎛ ∂u ⎞
⎛ ∂u ⎞
⎛ ∂u ⎞ ⎛ dV ⎞⎤
.⎢ ρ ⋅ ⎜⎜ ⎟⎟ ⋅ me + ρ ⋅ ⎜⎜ ⎟⎟ ⋅ ma + ρ ² ⋅ ⎜⎜ ⎟⎟ ⋅ ⎜
⎟⎥
∂ρ ⎠ p
∂ρ ⎠ p ⎝ dt ⎠⎥⎦
⎛ ∂u ⎞ ⎢⎣ ⎝ ∂ρ ⎠ p
⎝
⎝
ρV ⎜⎜ ⎟⎟
⎝ ∂p ⎠ ρ
1
With specific enthalpy:
h=u+
u = h−
dp
=
dt
p
(17)
ρ
p
(18)
ρ
⎧⎪
⎡
p
⎛ ∂u ⎞ ⎤ ⎫⎪
⋅ ⎨Q1, 2 + A1, 2 + m e ⋅ ⎢he − h + − ρ ⋅ ⎜⎜ ⎟⎟ ⎥ ⎬ −
ρ
⎛ ∂u ⎞
⎝ ∂ρ ⎠ p ⎥⎦ ⎪⎭
⎢⎣
ρV ⎜⎜ ⎟⎟ ⎪⎩
⎝ ∂p ⎠ ρ
1
1
−
⎛ ∂u ⎞
ρV ⎜⎜ ⎟⎟
⎝ ∂p ⎠ ρ
⎧⎪
⋅ ⎨− m a
⎪⎩
⎤ ⎫⎪
⎡
⎛ ∂u ⎞
⎛ ∂u ⎞ ⎤ dV ⎡
p
⋅ ⎢ ρ ² ⋅ ⎜⎜ ⎟⎟ − p ⎥ ⎬
⋅ ⎢ha − h + − ρ ⋅ ⎜⎜ ⎟⎟ ⎥ +
ρ
⎝ ∂ρ ⎠ p
⎝ ∂ρ ⎠ p ⎥⎦ dt ⎢⎣
⎥⎦ ⎭⎪
⎢⎣
(19)
⎛ ∂u ⎞
Transformation of the derivative ⎜⎜ ⎟⎟
⎝ ∂ρ ⎠ p
⎛ p⎞
⎛
p⎞
∂ρ
∂p
∂⎜⎜ ⎟⎟
∂⎜⎜ h − ⎟⎟
⋅ρ − p⋅
ρ ⎠ ∂h
ρ
⎛ ∂u ⎞
∂h ∂ρ
∂ρ
⎜⎜ ⎟⎟ = ⎝
−
=
− ⎝ ⎠=
ρ²
∂ρ
∂ρ
∂ρ
∂ρ
⎝ ∂ρ ⎠ p
(20)
p = const.
Æ
∂p
=0
∂ρ
(21)
⎛ ∂u ⎞
∂h p
Æ ⎜⎜ ⎟⎟ =
+
⎝ ∂ρ ⎠ p ∂ρ ρ ²
The general form for the pressure gradient
dp
=
dt
1
⎛ ∂u ⎞
ρV ⎜⎜ ⎟⎟
⎝ ∂p ⎠ ρ
1
−
⎛ ∂u ⎞
ρV ⎜⎜ ⎟⎟
⎝ ∂p ⎠ ρ
(22)
dp
for the equilibrium model is as follows:
dt
⎧⎪
⎡
⎛ ∂h ⎞ ⎤ ⎫⎪
⋅ ⎨Q1, 2 + A1, 2 + me ⋅ ⎢he − h − ρ ⋅ ⎜⎜ ⎟⎟ ⎥ ⎬ −
⎝ ∂ρ ⎠ p ⎦⎥ ⎪⎭
⎪⎩
⎣⎢
⎧⎪
⋅ ⎨m a
⎪⎩
⎡
⎛ ∂h ⎞
⎛ ∂h ⎞ ⎤
⋅ ⎢ha − h − ρ ⋅ ⎜⎜ ⎟⎟ ⎥ + ρ ² ⋅ ⎜⎜ ⎟⎟
⎝ ∂ρ ⎠ p
⎝ ∂ρ ⎠ p ⎥⎦
⎢⎣
⎛ dV
⋅⎜
⎝ dt
⎞⎫⎪
⎟⎬
⎠⎪⎭
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4.2.
Pressure build-up of a cryo-container in thermodynamic equilibrium
As a concrete example, we shall calculate the pressure build-up resulting from heat input for a
system in thermodynamic equilibrium on the basis of the LH2 reservoir tank at the HyCentA
and compare it with measurements. Despite the optimised heat insulation, the small amount of
remaining heat input triggers off a warming process and thus increases pressure and
temperature, which causes the liquid hydrogen in the container to evaporate. For this reason,
it is necessary to let off hydrogen after the pressure build-up time once the maximum
operating pressure of the tank has been reached (boil-off).
In order to simulate the pressure increase and pressure build-up time in the LH2 storage
system, we shall first of all assume a closed system in thermodynamic equilibrium with a
constant heat input Q& a , see Figure 9. As mentioned previously, we assume that the pressure
and temperature of the boiling liquid hydrogen and the gaseous saturated hydrogen vapour
remain the same throughout the system.
p,T , m´´
Qa
p , T , m´
Figure 9: Cryo-storage system in a thermodynamic equilibrium system
With a given container volume of 17,600 l and a given total hydrogen mass m, the specific
volume v and the density ρ are determined in the total system. All possible states move
along an isochore in the T-s diagram. When a pressure is specified, the state in the system is
clearly determined.
The constant container volume V consists of the variable shares for the liquid and gaseous
hydrogen V ′ and V ′ , in which the following applies:
V=
m
ρ
= m v = V ′ + V ′′ = m′ v′ + m′′ v′′
(24)
The distribution of the mass in boiling liquid and saturated steam is described by the vapour
fraction x:
x=
m′′
m′′
=
m
m′ + m′′
m′′ = x . m
m′ = (1 − x ). m
(25)
Thermo physical property tables give the specific volumes for liquid and saturated steam for
each pressure so that the vapour fraction and the mass distribution can be determined:
x=
v − v′
v′′ − v′
(26)
With the vapour fractions of two states defined by a pressure increase ∆ p, the evaporated
hydrogen mass ∆ m′′ is also determined.
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 13 -
∆ m′′ = ∆ x . m
(27)
The pressure development over time for the HyCentA reservoir tank was measured for two
different hydrogen fill levels (37.7 mass % and 71.8 mass %), see Figure 10. This enables
calculation of all state variables using the relationships above.
9.8
37.7 mass% - Measurement
71.8 mass% - Measurement
9.7
Pressure [bar]
9.6
9.5
9.4
9.3
9.2
9.1
9
0
2
4
6
8
10
12
14
16
Time [h]
Figure 10: Pressure build-up for fill level=37.7 mass % and 71.8 mass %
For the pressure build-up from 9.1 to 9.7 bar, the following times were measured:
Pressure buildup rate [bar/h]
Fill level 37.7 mass %
Pressure
build-up
time [h]
14.7
Fill level 71.8 mass %
16.8
0.0357
Measurement
35
rho=40
rho=50
rho=30
33
p=15
p=10
rho=20
rho=60
0.0408
p=5
rho=15
2
4
31
3
rho=10
1
rho=6
29
rho=4
rho=2
T [K]
27
25
p=2
p=1
23
p=0.5
21
rho=1
x=0.1
19
x=0.2
x=0.3
x=0.4
x=0.6
x=0.7
x=0.8
x=0.9
x=0.5
rho=0.5
p=0.2
17
15
5
10
15
20
25
30
35
s [J/gK]
Figure 11: T-s diagram for the pressure-build up caused by heat input in an equilibrium
system
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 14 -
The changes in state as illustrated by the T-s diagram describe these processes particularly
well. In Figure 11, the process of pressure build-up at constant volume for the two fill levels
under investigation is represented full-scale. The pressure increase at fill level 37.7 mass%
proceeds along the isochore v =0.0376 m³/kg subcritically to the right of the critical specific
volume of v krit= 0.0319 m³/kg, running from point 1 at p1 = 9.1 bar in the 2-phase region to
point 2 at p2 = 9.7 bar. The vapour fraction x increases from 0.301 to 0.335, the gaseous
component increases from 140.89 kg by 15.65.8 kg to 156.548 kg. Without pressure
limitation and boil-off, the saturated vapour line would be reached at approx. 13 bar and the
entire hydrogen mass would become gaseous. The pressure increase with a fill level of 71.8
mass% proceeds along the isochore v =0.0254 m³/kg supercritically to the left of the critical
specific volume of point 3 at p1 = 9.1 bar in the 2-phase region up to point 4 at p2 = 9.7 bar.
The lines of the constant vapour fraction flatten out, the vapour fraction increases from 0.1001
to 0.1039 and the gaseous component increases slightly by about 2.602 kg, from 69.345 kg to
71.947 kg. Without pressure limitation and boil-off, the isochore would cut into the liquid
region at the saturated liquid line at approx. 13 bar. The vapour fraction goes down to zero,
and condensation would cause the entire hydrogen mass to become liquid.
The calculated progression of the vapour fractions for the two cases is represented in Figure
12 and Figure 13. Both vapour fractions increase over time, which means that liquid hydrogen
evaporates. As mentioned previously, the evaporation process proceeds more slowly in the
case of the supercritical isochores.
Figure 12 and Figure 13 also show the calculated progression of the fill levels. Both diagrams
show that the agreement between calculated and measured fill level progression is not entirely
satisfactory. It should be added at this point that the measurement of the fill level is based on
a pressure difference measurement in the tank under the assumption of a constant density,
which, like most fill level measurement techniques, is somewhat unreliable, and that the
model assumptions of the thermodynamic equilibrium are only able to represent
approximations of the system.
The reason for the pressure build-up is the heat input. The specific heat quantity can be read
from the T-s diagram as the area below the constant-volume change in state. During the
pressure build-up, the system can be described by means of the first law of closed systems:
dQa = dU = d (m u ) = m du
(28)
With the formulae from the previous section and appropriate boundary and initial conditions,
equation (23) yields the interrelation between pressure increase and heat input Q:
dp Q
1
= .
dt V
⎛ ∂u ⎞
ρ .⎜⎜ ⎟⎟
⎝ ∂p ⎠ ρ
(29)
In our case, we can determine heat inputs of 99 W and 102 W for the fill levels of 37.7 mass
% and 71.8 mass % from the measured pressure-build up curves.
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 15 -
0.35
40.0
39.5
0.3
39.0
Fill Level [mass-%]
38.0
0.2
37.5
0.15
37.0
36.5
Vapour fraction [-]
0.25
38.5
0.1
36.0
Fill Level - Measurement
0.05
Fill Level - Calculation 99W
35.5
Vapour fraction - measured
Vapour fraction - calculated 99W
35.0
0
2
4
0
6
8
10
12
14
16
Time [h]
Figure 12: Progression of fill level and vapour fraction at 37.7 mass %
75.0
0.35
Fill Level - Measurement
Fill Level - Calculation 102W
74.5
Vapour fraction - meassured
0.30
Vapour fraction - calculated 102W
74.0
Fill Level [mass-%]
73.0
0.20
72.5
0.15
72.0
71.5
Vapour fraction [-]
0.25
73.5
0.10
71.0
0.05
70.5
70.0
0.00
0
2
4
6
8
10
12
14
16
18
Time [h]
Figure 13: Progression of fill level and vapour fraction at 71.8 mass %
For a more detailed insight into the energy distribution within the system, in the following we
shall look at the internal energies for the gaseous and liquid components separately. These
subsystems both constitute open systems with mass transfer. The following applies:
dQa = dU = dU ′ + dU ′′ = d (m′ u ′) + d (m′′ u′′) = m′ du′ + u ′ dm′ + m′′ du′′ + u′′ dm′′
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
(30)
- 16 -
Applying the law of conservation of mass:
d m′′ = − d m′
(31)
We obtain the following result:
dQa = m′ d u ′ + m′′ d u′′ + dm′′( u′′ − u ′)
10000
(32)
Fill Level 5 mass%:
u1:
88.71kJ/kg
u2:
107.29kJ/kg
mges: 252.486kg
8000
Fill Level 95 mass%:
u1:
-80.358kJ/kg
u2:
-72.477kJ/kg
mges: 843.57kg
Energy [kJ]
6000
4000
dU´
2000
dU´´
0
0
10
20
30
40
50
60
70
80
90
100
-2000
dU´
dU´´
dU´+dU´´
-4000
Fill Level [mass%]
Figure 14: Distribution of internal energy with respect to fill level
10000
Fill Level 37,7 mass%:
mgesA: 467.56kg
mgA: 326.67kg
mgE:
mlA:
140.89kg
mlE:
8000
Fill Level 71,8%:
mgesA: 692.715kg
mgA: 69.345kg
mlA:
623.37kg
311.012kg
156.548kg
mgE:
mlE:
71.947kg
620.768kg
Energy [kJ]
6000
4000
m´du´
dm´´(u´´-u´)
2000
0
0
10
m´´du´´
20
30
40
50
60
70
80
90
100
-2000
m´´du´´
m´du´
dm´´(u´´-u´)
Qa
-4000
Fill Level [mass%]
Figure 15: Distribution of interior energy with respect to fill level – detail
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 17 -
The entire exterior heat input thus serves to increase the internal energy of the total system.
This energy increase can be divided into the two quotients dU ′ and dU ′′ of the gas phase and
the liquid phase, based on equation (30). As the distribution of the quotients only changes
minimally over time, it can be treated as a constant for any particular container fill level and
be represented with respect to the latter. In Figure 14, the components of internal energy for
liquid and saturated vapour are plotted with respect to fill level. Together they make up the
total heat input that increases with the fill level. From a fill level of approx. 70 mass %, the
internal energy of the gas phase decreases. A more detailed picture results when we look at
the changes of internal energies for the gaseous and liquid mass separately and take into
account the common component for evaporation according to equation (32), see Figure 15.
We notice that the share m′′ d u′′ is negative, attributable to the fact that the internal energy
decreases along the saturated vapour curve while temperature increases. The energy share for
evaporation decreases with respect to fill level, until it becomes negative with high fill levels
above 80 mass %, due to the condensation that occurs. The energy share of the liquid phase
increases accordingly. Due to the higher evaporation share, pressure build-up will occur more
quickly with lower fill levels than with higher fill levels, despite the overall heat input being
lower.
4.3.
Pressure build-up of a thermodynamic non-equilibrium cryo-container
In order to increase predictive strength compared with the equilibrium system and better to
evaluate the differences between measurements and calculations for mass and fill level
progression during pressure build-up, we shall introduce a thermodynamic non-equilibrium
model. It is assumed that, although the same pressure prevails throughout the container and
the entire liquid phase remains at the corresponding equilibrium temperature, the gas phase
may reach a higher temperature. Of the possible temperature distributions in the container
based on Figure 16, we shall look at the average case, i.e. the even superheating of the gas
phase with a temperature Tg above the equilibrium temperature T ′ of the liquid phase.
As this is also a closed system, the specific volume v and the density ρ of the total system are
determined if we have a given container volume and a given total hydrogen mass, as in the
equilibrium system. All possible states again move on an isochore in the T-s diagram; see the
representation of the two fill levels treated in equilibrium in Figure 18 (not full scale).
Container pressure: 9.7 bar
Figure 16: Temperature distributions in the container
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 18 -
Ug , p , Tg, mg
Qa
Ul , p , T´, m´
Figure 17: Thermodynamic non-equilibrium cryo-storage system
The constant container volume V again consists of the variable components for the liquid and
gaseous hydrogen V ′ and Vg . Unlike in the equilibrium system, the gaseous quotient may be
in a superheated state. Instead of equation (24), the following applies:
V=
m
ρ
= m v = V ′ + Vg = m′ v′ + mg v g
(33)
p+deltap
2´
471.8
2g
v37
v71.8
237
2´´
371.8
1´
p
1´´
137
T[K]
delta qzu71.8
delta qzu37
s[kJ/kgK]
Figure 18: T-s diagram for pressure build-up due to heat input in an inhomogeneous system
The breakdown of mass into boiling liquid and superheated gas can no longer be definitely
described by the vapour fraction. The mass fraction is an additional variable that can be
described by the evaporated mass dmg.. If we look at equation (33) and Figure 18, we can see
that, in the equilibrium case, the superheated gas mass can only decrease against the saturated
vapour mass, as the specific volume of the superheated gas will definitely increase compared
with the saturated vapour. This means that less liquid mass will evaporate, the liquid volume
will expand more and the gas volume will be compressed. To determine the additional degree
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 19 -
of freedom of the breakdown of mass, a further measurement is required; either of the
progression of the fill levels or the temperature in the gas region. Unfortunately, such
measurements are difficult to carry out and often rather unreliable.
As evident from the T-s diagram in Figure 18, the applied specific heat quantity corresponds
to the area below the isobar and thus equals the applied heat quantity in the equilibrium
system for all fill levels. In order to establish a correlation between the state variables and the
applied external heat flow, we shall once again apply the first law of thermodynamics
according to equation (28) to the thermodynamic non-equilibrium cryo-storage system
according to Figure 17. As in equation (30), the change of internal energy is again divided
into changes of the internal energy of the liquid phase and those of the gas phase; the latter
consisting of superheated hydrogen steam instead of saturated steam in this case:
dQa = dU = dU ′ + dU g = d (m′ u′) + d (mg u g ) = m′ du ′ + u ′dm′ + mg du g + u g dmg
(34)
Applying the law of conservation of mass:
d mg = − d m′
(35)
we obtain the following result:
dQa = mg d u g + m′ d u′ + dmg ( u g − u ′)
(36)
Again, this equation can only be solved numerically, due to the dependency of the
thermophysical properties on pressure and temperature. The step-by-step calculation of the
internal energy of the superheated gas phase u g and thus also the gas temperature is carried
out based on the specification of the evaporated mass ∆ mg and the applied heat quantity
∆ Qa , which is identical with the equilibrium scenario. The discretisation of equation (36)
results in the following for the n-th step:
∆ Qa n = mn′ ( un′ +1 − u′n ) + mg n ( u g n+1 − u g n ) + ∆ mg n ( u g n+1 − u g n )
(37)
Assuming that the system at first exists in equilibrium and the gas phase is saturated, we can
calculate the progression of the internal energy and thus the temperature of the superheated
gas. For the two fill levels under investigation, Figure 19 and Figure 20 show these
progressions for a variation of the evaporated mass ∆ mg. It appears that the gas phase with
both fill levels is only superheated by a few degrees, with the temperature of the gas phase
increasing with the decreasing ∆ mg. The emerging increases in temperature as compared to
the equilibrium model move within a range of a few degrees.
The simulation results and the comparisons with the measurements show that the relatively
simple thermodynamic modelling of the system with a superheated gas phase yield an
additional margin for the simulation and projection of the pressure build-up phase; the goal
being to achieve a match with improved measurement results.
In reality, however, the relations in the liquid storage system are considerably more complex.
On the one hand, the system again strives for a thermodynamic equilibrium; on the other, a
temperature distribution in a three-dimensional flow field will manifest itself. Several
publications deal with the temperature distribution in cryo-containers, see for instance [ 2 ],
[ 10 ]. It is generally assumed that the heat input in the internal tank causes the outermost
layers of the liquid phase to warm up. The change in density thus causes the liquid to rise up.
For this reason, a warmer layer on the surface of the liquid – the boundary layer to the gas
phase – emerges. A temperature gradient within the liquid phase is thus created, which in
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 20 -
principle constitutes a stable state. This layering furthermore causes a heat transfer in the gas
phase and the evaporation of part of the liquid phase. The pressure increase in the gas phase is
significantly influenced by the surface temperature in the liquid phase. The thermal layering
in the liquid and gaseous phases is calculated with numerical simulation models of varying
complexity, the main focus being on boundary layer phenomena. The recording of the
developing temperature gradients and flow states by means of measurements is generally
difficult. As an example, Figure 21 represents the temperature distribution in a cryo-container.
33.50
F3 T_SATT_G[0]
4 [kg/deltap]
3 [kg/deltap]
2 [kg/deltap]
1 [kg/deltap]
0 [kg/deltap]
-1 [kg/deltap]
-2 [kg/deltap]
-3 [kg/deltap]
-4 [kg/deltap]
-5 [kg/deltap]
33.00
Temperature [K]
32.50
32.00
31.50
31.00
30.50
30.00
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
Pressure [bar]
Figure 19: Temperature progressions at a fill level of 37 mass % (deltap = 0.1)
31.60
F3 T_SATT_G[0]
0 [kg/deltap]
31.50
-0.1 [kg/deltap]
-0.2 [kg/deltap]
31.40
-0.3 [kg/deltap]
-0.4 [kg/deltap]
-0.5 [kg/deltap]
Temperature [K]
31.30
-0.6 [kg/deltap]
-0.7 [kg/deltap]
31.20
-0.8 [kg/deltap]
-0.9 [kg/deltap]
31.10
31.00
30.90
30.80
30.70
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
Pressure [bar]
Figure 20: Temperature progressions at a fill level of 72 mass % (deltap = 0.1)
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 21 -
Figure 21: Temperature distribution in a cryo-container [ 10 ]
4.4.
Cooling and filling of a container
In addition to the pressure build-up behaviour of a hydrogen container, the filling of a
container is also of interest. Generally, containers are filled using a pressure gradient, and the
pressure in the container is kept constant by blowing off hydrogen during the filling process.
The goal is also the chilling of warm components such as connection lines in order to keep the
hydrogen losses as low as possible. The filling process from the LH2 reservoir tank to the
conditioning container is carried out through a vacuum-isolated pipe, which forms an open
system together with the conditioning container. Liquid hydrogen is removed with a vacuumisolated bellows valve.
System 1:
Reservoir tank
System 3:
conditioning container
System 2: pipework
Figure 22 shows the complete system, which is divided into three subsystems.
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 22 -
For the cryo-containers subsystem 1 and 3, which in this case constitute open systems, the
relations of the general homogeneous model according to section 4.1 apply. It is assumed that
both containers contain liquid hydrogen, i.e. they are at low temperature. As the heat input in
the reservoir tank can be disregarded for the time the filling takes, the change of the internal
energy dU1 depends only on the escaping mass dm and its specific enthalpy h1. The mass flow
m& coming from the reservoir tank then flows through system 2, i.e. the pipelines, see Figure
23.
If the temperature of system 2 (pipelines) is higher than the boiling temperature according to
pressure – which is usually the case – the pipeline system must first be chilled before liquid
hydrogen can be transported. The liquid hydrogen coming from the reservoir tank evaporates
in the pipelines and chills them through enthalpy of evaporation.
System 1:
Reservoir tank
System 3:
conditioning container
System 2: pipework
Figure 22: Filling system
m& f , m& g
m&
Figure 23: System 2: pipelines
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 23 -
m& f , m& g , h 2 , T LH 2
m& , h1 , T LH 2
ms , cs , T
Figure 24: Chilling of the pipeline
The liquid mass inflow m& leaves the system at the beginning of the filling process as gaseous
mass flow m& g . If the thermal mass of the pipelines reaches a temperature below the respective
boiling temperature according to pressure, a liquid mass flow m& f manifests itself. A segment
of the pipeline shows the chilling process in greater detail; see Figure 24 [ 12 ].
Energy balance of the chilling process:
- ms ⋅ cs ⋅
dT
= −m& LH 2 ⋅ rH 2 + α ⋅ A ⋅ (T U −T )
dt
(38)
The term α ⋅ A ⋅ (TU − T ) corresponds to the transferred heat flow from radiation and
convection and is much smaller than the term of the evaporation enthalpy m& LH 2 ⋅ rH 2 and can
thus be disregarded. The following differential equation results:
- T (t ) = −
m& LH 2 ⋅ rH 2
ms ⋅ cs
⋅t + C
(39)
Boundary condition: t = 0 , T = TU
This results in the following temperature progression:
- T (t ) = TU −
m& LH 2 ⋅ rH 2
ms ⋅ cs
⋅t
(40)
Energy balance for the pipelines:
- dm12 ⋅ h1 − dm23 ⋅ h2 = dU 2
(41)
The system of the conditioning container is represented in Figure 25. The inflowing mass
consists either of gaseous or liquid hydrogen, depending on the temperature of the pipes.
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 24 -
m& f , m& g
Figure 25: System 3: conditioning container
Energy balance for the conditioning container:
- dm23 ⋅ h2 = dU 3
(42)
The chilling process usually requires several minutes and the evaporating hydrogen must
generally be regarded as a loss. It is disposed of into the environment via a flue at the
HyCentA. In the case of liquid fillings, losses in the dimension from 20 % up to more than 60
% of the filling mass must be expected [ 13 ].
In the following, we shall present some comparisons between simulations and measurements
of two fillings at the HyCentA.
For a filling out of the reservoir tank Figure 26 shows the comparison between simulation and
measurement of pressure and fill level progression for a filling attempt with cold connection
pipes and a fill level of 30 % in the conditioning container with a pressure of 3.7 bar. Figure
27 represents the calculated progression of the vapour fraction and the liquid and gaseous
hydrogen mass in the conditioning container. It is obvious that, at the beginning of the filling
process, the pressure in the conditioning container rises quickly due to the pressure
equalisation between the reservoir tank and the conditioning container and the rapid inflow of
warmer, gaseous hydrogen. The gas mass and the vapour fraction increase until the inflow of
liquid hydrogen starts. From this point onwards, the liquid mass in the container increases and
the vapour fraction goes down, as does the gaseous mass due to the opening of a release
pressure valve on the conditioning container. This valve has the task of maintaining the
required pressure difference to the reservoir tank. The pressure continues to go down until the
end of the filling process. After the end of the filling process, the cold valve is shut off and
hydrogen is continued be blown off until the target pressure of 3.3 bar has been reached.
5.
SUMMARY AND OUTLOOK
The models presented here and the comparison of the calculated results with the
measurements show that, by means of relatively simple thermodynamic simulations,
satisfactory results for the calculation of pressure build-up and filling processes can be
achieved, including the chilling of components. The influence of heat input, different fill
levels and filling scenarios was reflected sufficiently. For the future, calculations of variants
and experiments are planned in order to determine parameters such as pressure differences,
superheating of the gas phase or supercooling of the liquid phase by means of pressure
increase for an optimal filling with minimal losses. An improvement of the quality of the
measuring results is desirable.
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
- 25 -
From the point of view of storage density, the liquid storage of hydrogen currently offers the
best results. The extremely low storage temperature, however, places high demands on the
materials used and on the insulating capacities of storage systems. A highly sophisticated
production and processing system is also necessary in order to avoid losses caused by
diffusion, evaporation and impurity. Further efforts are necessary to minimise these losses and
to reduce complexity in order to establish this form of storage as a competitive alternative to
gaseous and bound storage.
5
25
End of filling
Pressure [bar rel]
Pressure - Simulation [bar rel]
Mass [kg]
Mass - Simulation [kg]
4.8
4.6
24
23
4.4
22
4.2
21
4
20
3.8
19
3.6
18
3.4
17
Mass [kg]
Pressure [bar rel]
Start of filling
Start of LH2 delivery
3.2
16
3
0
20
40
60
80
100
120
140
15
160
Time [s]
Figure 26: Comparison simulation – measurement of pressure and mass LH2
Start of filling
25
0.25
m_liquid [kg]
m_gas [kg]
End of filling
Start of LH2 delivery
0.20
15
0.15
10
0.10
5
0.05
Mass [kg]
20
0
0
20
40
60
80
100
120
140
0.00
160
Time [s]
Figure 27: Simulation of vapour fraction and mass GH2 and LH2
“1st International Symposium on Hydrogen Internal Combustion Engines” September 28 – 29, 2006
Vapour fraction [-]
Vapour fraction [-]
- 26 -
6.
BIBLIOGRAPHY
[1]
http://www.hydrogen.org , http://www.hyweb.de
[2]
Gursu, S.; Sherif, S. A.; Veziroglu, T. N.; Sheffield, J. W.: Analysis and
Optimization of Thermal Stratification and Self-Pressurization Effects in Liquid
hydrogen Storage Systems – Part 1: Model Development. Journal of Energy
Resources Technology, Vol 115, p.221-227. September 1993
[3]
Kindermann, H.: Thermodynamik der Wasserstoffspeicherung. [Thermodynamics
of hydrogen storage], diploma thesis, HyCentA Graz, Montanuniversität Leoben,
2006
[4]
Klell, M., Pischinger, R., Sams, Th., Thermodynamik der
Verbrennungskraftmaschine. [Thermodynamics of the internal combustion
engine], Springer Verlag
[5]
Lin, C. S.; Van Dresar, N. T.; Hasan, M.: A Pressure Control Analysis of
Cryogenic Storage Systems, Journal of Propulsion and Power 2004, Vol.20 No.3,
p. 480-485
[6]
Peschka, Walter: Flüssiger hydrogen als Energieträger – Technologie and
Anwendungen [Liquid hydrogen as an energy carrier – technology and
applications]
[7]
Peschka, Walter: Wasserstoffantrieb für Kraftfahrzeuge [Hydrogen power for
motor vehicles], ÖVK. 1997
[8]
Rebernik, M.: Beschreibung des thermischen Verhaltens eines kryogenen
Speichersystems für den Einsatz in Kraftfahrzeugen, [Description of the thermal
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