energies

Article
An Analysis on the Compressed Hydrogen Storage System for
the Fast-Filling Process of Hydrogen Gas at the Pressure of
82 MPa
Ji-Qiang Li 1 , Ji-Chao Li 1 , Kyoungwoo Park 2 , Seon-Jun Jang 2 and Jeong-Tae Kwon 2, *

1 Department of Mechanical Engineering, Graduate School, Hoseo University, Asan 31499, Korea;
ljq7436@naver.com (J.-Q.L.); jichao@naver.com (J.-C.L.)
2 Division of Mechanical & Automotive Engineering, Hoseo University, Asan 31499, Korea;
kpark@hoseo.edu (K.P.); mweagle@hoseo.edu (S.-J.J.)
* Correspondence: jtkwon@hoseo.edu; Tel.: +82-41-540-5803; Fax: +82-41-540-5808

Abstract: During the fast-filling of a high-pressure hydrogen tank, the temperature of hydrogen
would rise significantly and may lead to failure of the tank. In addition, the temperature rise also
reduces hydrogen density in the tank, which causes mass decrement into the tank. Therefore, it
is of practical significance to study the temperature rise and the amount of charging of hydrogen
for hydrogen safety. In this paper, the change of hydrogen temperature in the tank according to
the pressure rise during the process of charging the high-pressure tank in the process of a 82-MPa
hydrogen filling system, the final temperature, the amount of filling of hydrogen gas, and the change
of pressure of hydrogen through the pressure reducing valve, and the performance of heat exchanger
for cooling high-temperature hydrogen were analyzed by theoretical and numerical methods. When



high-pressure filling began in the initial vacuum state, the condition was called the “First cycle”.


When the high-pressure charging process began in the remaining condition, the process was called
Citation: Li, J.-Q.; Li, J.-C.; Park, K.;
the “Second cycle”. As a result of the theoretical analysis, the final temperatures of hydrogen gas were
Jang, S.-J.; Kwon, J.-T. An Analysis on
calculated to be 436.09 K for the first cycle of the high-pressure tank, and 403.55 for the second cycle
the Compressed Hydrogen Storage
analysis. The internal temperature of the buffer tank increased by 345.69 K and 32.54 K in the first
System for the Fast-Filling Process of
cycle and second cycles after high-pressure filling. In addition, the final masses were calculated to be
Hydrogen Gas at the Pressure of 82
MPa. Energies 2021, 14, 2635.
11.58 kg and 12.26 kg for the first cycle and second cycle of the high-pressure tank, respectively. The
https://doi.org/10.3390/en14092635 works of the paper can provide suggestions for the temperature rise of 82 MPa compressed hydrogen
storage system and offer necessary theory and numerical methods for guiding safe operation and
Academic Editor: Paolo Defilippis construction of a hydrogen filling system.

Received: 6 April 2021 Keywords: hydrogen storage tank; compressed hydrogen; high-pressure filling; thermodynamics;
Accepted: 1 May 2021 heat transfer
Published: 4 May 2021

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with regard to jurisdictional claims in 1. Introduction
published maps and institutional affil- Faced with growing energy shortages, environmental pollution, ecological deteriora-
iations.
tion, the development of clean and efficient new energy is the only way to solve the above
problems. Hydrogen has become the most promising secondary energy of the 21st century
for its excellent advantages such as broad source, no polluting product, high combustion
efficiency, and reproducible ability. It has important strategic significance for solving the
Copyright: © 2021 by the authors. problems of energy shortage and environmental pollution puzzling all over the world [1–4].
Licensee MDPI, Basel, Switzerland. With the deepening of research, hydrogen energy has been used in aviation and space-
This article is an open access article flight, clean utilization of fossil energy, fuel cell vehicles, national defense and the military
distributed under the terms and industry, mass energy storage, and other fields [5]. However, a hydrogen energy system is
conditions of the Creative Commons
a large and complex engineering system, including production, storage, and utilization of
Attribution (CC BY) license (https://
hydrogen. In order to promote the practicality of the hydrogen energy economy, science
creativecommons.org/licenses/by/
researchers and energy policy experts from all over the world have carried out a lot of
4.0/).

Energies 2021, 14, 2635. https://doi.org/10.3390/en14092635 https://www.mdpi.com/journal/energies

Energies 2021, 14, 2635 2 of 18

systematic research. The development of hydrogen energy is gaining more and more
attention from the international community [6].
In the development of hydrogen energy, the density of hydrogen is low at normal
temperatures and pressures. How to realize safe and efficient storage and transportation of
hydrogen is one of the key problems for the large-scale application of hydrogen [7]. Ac-
cording to different storage methods, it can be divided into chemical hydrogen storage and
physical hydrogen storage [8]. Chemical hydrogen storage is realized by hydrogen com-
pound, which is generated through chemical reaction or chemical changes [9,10], including
metal hydride, coordination hydride, and organic liquid hydride. Physical hydrogen stor-
age is a traditional way to store hydrogen, including liquid and high-pressure hydrogen
storage; liquid hydrogen storage is to store the liquefied low-temperature hydrogen (about
20 K) in the tank, which often adopts a high-vacuum adiabatic low-pressure tank as strict
heat insulation is required in order to minimize the vaporization of liquid hydrogen storage.
High-pressure hydrogen storage is to directly store the high-pressure gaseous hydrogen in
a tank, which usually requires the pressure of tens of MPa in order to get a high volume
density for hydrogen storage [11].
By comparing the above hydrogen storage methods, chemical hydrogen storage is
far from meeting the requirements of a vehicle system because of material costs, control
of actual reaction temperatures, the pressure of absorbing and releasing hydrogen, and
the weight of materials. Liquid hydrogen storage has the disadvantages of high energy
consumption and complex equipment because it requires more than 30% consumption
of liquid hydrogen for hydrogen storage energy and the adiabatic layer further increases
the weight of the tank. Thus, it is not a good prospect for application, though it has high-
quality density. High-pressure storage is a common method of vehicle-mounted hydrogen
storage at present because of its fast speed of absorbing and releasing hydrogen, simple
equipment structure, and low energy consumption of compression in comparison to other
hydrogen storage methods [12]. There are methods for storing the amount of hydrogen
fuel in different forms, as shown in Table 1 [13–17].

Table 1. Types and comparisons of high-pressure hydrogen storage.

Classification Type Features Comments

High efficiency, low energy
High-pressure
Compressed hydrogen consumption, simple High material cost
storage
equipment structure
Liquefied
Liquid hydrogen High-quality hydrogen High energy consumption
low-temperature
storage storage density and complex equipment
hydrogen
High safety, high purity, and High cost of hydrogen
Chemical
Metal hydride high hydrogen storage storage and the chemical
hydrogen storage
density. reaction process is difficult
Ultra-low temperature,
Physical hydrogen Porous coordination High hydrogen storage
Complex equipment
storage network density
structure

The key technology for compressed hydrogen for widespread use is the tank. The
requirements for material used in the tank are safety, reliability, and cost-effectiveness [2].
According to the division in ANSI HGV 2 Tanks [18], high-pressure hydrogen storage
tanks are divided into four basic types: type I, all-metal tank; type II, hoop-wrapped
tank with the inner container; type III, materials (liner, composite shell); type IV, carbon
fiber-reinforced polymer. Type I and type II are heavier, which make it difficult to get
high hydrogen storage density, and are suitable for hydrogen-filling stations, but not for a
vehicle-mounted tank. Type III and type IV adopt light and high-intensity fibers, which
not only reduces the mass of the hydrogen tank, but also bears higher pressure; thus, it is
widely used as vehicle-mounted hydrogen storage tank. Table 2 shows the four different
types of hydrogen storage tanks (Type I to Type IV) [13,19–21].
Energies 2021, 14, 2635 3 of 18

Table 2. Comparison of hydrogen storage tanks.

Types Materials Advantages Comments

Heavy, internal corrosion, low For hydrogen
Type I All Metal
hydrogen storage density stations
Hoop-wrapped tank with Heavy, short life, serious hydrogen
Type II For industrial
inner container embrittlement problem
Materials (Liner, Lightweight, high burst pressure, no
Type III Vehicular use.
Composite shell) permeation
Lightweight, lower burst pressure.
Carbon fiber-reinforced Vehicular use.
Type IV Permeation through liner. High
polymer Longer life
material cost

During the cyclic experiment of hydrogen gas, the change of temperature is significant
as the temperature of hydrogen rises sharply during filling because of compression of
hydrogen, conversion of kinetic energy into internal energy, and negative Joule–Thomson
effect [22]. In the high-pressure filling process, the internal pressure of the tank increases,
and thermal stress may occur due to the temperature rise of hydrogen. Therefore, it is of
practical significance to study the temperature rise and the amount of charging of hydrogen
for hydrogen safety.
In the research on temperature rise during fast filling, many domestic and overseas
research institutions and scholars have conducted research from the perspectives of theo-
retical and simulation. Previous research studies have paved the way for advancements
in the filling of hydrogen gas. Theoretical study is based on a simplified model, which
combines mass and energy law, real gas equations and receives the expression of tempera-
ture and pressure after filling. At the thermodynamic model of the reference [22], it takes
the internal energy and kinetic energy of hydrogen in the tank into account, and neglects
the heat transferred by internal hydrogen to the environment as the filling time is short.
This assumes that the hydrogen’s initial temperature is the same as the temperature of
hydrogen within the tank before the filling process. The result is that temperature rise can
be calculated accurately by using relevant parameters in the process of theoretical analysis.
Hosseini et al. [23] studied the effect of the initial conditions on temperature rise
based on energy analysis, and found that higher initial pressure resulted in smaller final
temperature rise. Yang et al. [24] conducted model analysis on the fast-filling of hydrogen
by taking advantage of ideal and real gas in adiabatic and isothermal conditions. The result
shows that the filling time under adiabatic and isothermal conditions is the lower and upper
limit for a given final target pressure. The reference [25] established a thermodynamic
model based on the energy equation, which can analyze and obtain the filling’s mass and
final temperature after filling. Monde et al. [26] developed a theoretical model to study the
effects of the heat transfer coefficient on the final temperature. The results showed that
the use of an appropriate constant heat transfer coefficient calculated final temperature is
feasible. Yong Zhi et al. [27] developed a two-dimensional axisymmetric model, and the
effects of the boost mode and supercharged the hydrogen tank temperature rise rate during
the rapid inflation by the model. The expression of temperature change can be clearly
understood by theoretical study, which concludes that the temperature rise of hydrogen
mainly depends on filling parameters. Besides, the geometric parameters and types of
tanks may affect the temperature and mass after filling. The various theoretical analyses of
temperature rise are shown in Table 3.
Energies 2021, 14, 2635 4 of 18

Table 3. Theoretical studies of final temperature.

Author Equations Parameter

 
Pv αP
Liu et al. [22] λµT1 (T1 +αP1 )−α(λP1 T1 −P1 T1 ) Rg T = 1 + T
T2 = αT P −T P
T1 +αP1 + 1 P1 1 1
2 α = 1.9155 × 10−6 K/Pa
. .
m1 ex1 + mi texi = m2 ex2 + Ifilling mi = dmdt
i
M.H et al. [23] m2 ex2
ψf,1−2 = . ψf, 1−2 : The energy efficiency
m1 ex1 +(mi t)exi

dU = δQ − δW + he dn
. e
N. = Ni + Kt
Yang et al. [24]
(Ni + Kt)du/dt + uK = Q + he K Q = dQ/dt
R
P1 T1 V+λT0 (RT1 +αTPR1 ) mdt α = 1.9155 × 10−6 K/Pa
Wang et al. [25] T2 = P1 V+(RT1 +αTP1 ) mdt λ = cp /cv
R . R
m1 (aT1 −b)+he mdt+ qdt u = αT −R b
Li et al. [28] T2 = R . .
a(m1 + mdt) m2 = m1 + mdt
∗ .
dT
dt= (1 + α) Tt∗ −
+t
T t∗ = m0 /m, τ = t/t∗
Xiao et al. [29]
T∗ = (γT∞ + αTf )/(1 + α) T∗ : Characteristic temperature
 1+α
T∗ − T

T ∗ − T0
= 1+1 τ
t∗
t
= { (T−1T )
Zhou et al. [30] = { (T−1T )k 0
0 t
[(1 − P0 T(1 + βP/T)/P0 T(1 + βP0 /T0 ))γT∞ −
[(1 − P0 T(1 + βP/T)/P0 T(1 + βP0 /T0 ))γT∞ −
T + P0 T(1 + βP/T)/P(1 + βP0 /T0 )]}
T + P0 T(1 + βP/T)/P(1 + βP0 /T0 )]}

P1 Z2 cv1
n   o
Song et al. [31] 1 1 T1 P 1 Z2 PV = ZmRT
T2 = T1 c p i Ti cv2 − P2 Z1 + P 2 Z1

In order to study the relationship between temperature and parameters, some exper-
iments have studied temperature rise in the compression tank. Hirotain et al. [32] have
been carried out fast-filling tests of 34-L and 74-L type-III tanks with a working pressure
of 35 MPa, 65-L type-IV tanks, and 41-L type-III tanks, and 31-L type-IV tanks with a
working pressure of 70 MPa. The results showed that pressure mode (constant speed, first
fast and then slow, first slow and then fast, stepped pressure increase) has no obvious
effect on the temperature rise of type III tanks, but had a significant effect on type IV
tanks. Modnde et al. [33–35] studied the change of convective heat transfer coefficient
through the fast-filling test, and conducted a three-stage fast-filling test, indicating that
three-stage filling was one of the effective ways to address excessive temperature rise.
Dicken et al. [36,37] conducted fast-filling experiments on 35 MPa, 74 L type III gas tanks
with different initial pressures and different pressure rise rates. Since 63 thermocouples
were installed in the test tank, detailed distribution of the temperature in the tank was
obtained. Zheng Jinyang et al. [38] developed a 70 MPa fast-filling temperature rise test
device, conducted the first 70 MPa fast charging experiment in China, and analyzed the
influence of the gas tank structure on the temperature rise. Since the actual fast-filling
process will be affected by the specific hydrogenation system settings of the hydrogen
refueling station and the manufacturing process attributes of the hydrogen storage bottle
itself, the existing fast-filling temperature of the analysis results is weak, so the technical
standardization of detailed and universal quantitative analysis is being further promoted.
To sum up, since the actual fast-filling process will be affected by the specific hydro-
genation system settings of the hydrogen refueling station and the manufacturing process
attributes of the hydrogen storage bottle itself, the existing fast-filling temperature of the
analysis results is weak, so the technical standardization of detailed and universal quanti-
tative analysis is being further promoted. At present, there are relatively few studies on
70–100 MPa high-pressure filling experiments. The setting of fast-filling conditions such as
the filling control scheme of the fast-filling experiment of the hydrogen tank lacks sufficient
Energies 2021, 14, 2635 5 of 18

experiments, numerical and theoretical analysis as demonstration; for the temperature

rise mechanism of the fast-filling process, energy consumption optimization and complex
and changeable filling conditions. The effects of temperature rise and other aspects are
still in the accumulation stage and have not been fully understood; in addition, because
the hydrogen storage tank and its hydrogen filling system are a complex system, and
because the standardization process of the system is still in the research stage, only some
qualitative analysis can be given, but a quantitative analysis with wide applicability cannot
be provided at this time.
In this paper, we have two main extensions based on previous work reviews. First,
we described an experiment involving hydrogen gas in a large storage tank and obtained
the data of the pressure sensor during the fast-filling process. A theoretical model for
the final temperature and mass of hydrogen gas during filling processes was developed,
and analysis of the hydrogen temperature change, the amount of filling of hydrogen,
the pressure reducing valve, and the required capacity of the heat exchanger for cooling
the high-pressure tank through theoretical and numerical methods. Second, the real gas
equation of state and thermodynamic properties were calculated by the National Institute
of Standards and Technology (NIST) database: REFPROP 9.5. Final hydrogen mass and
final temperature from the theoretical adiabatic condition are estimated based on the mass
and energy balance method. Theoretical formulae fit the experimental/simulated data
very well. The results of the study will be very useful for future research and development
on hydrogen energy and high-pressure hydrogen stations.

2. Hydrogen Filling Modeling

The compression cycle in hydrogen filling returns to the process shown in Figure 1.
In this study, the hydrogen supplied at the pressure is compressed to 82 MPa through a
compression process, and then the hydrogen is stored in a high-pressure storage tank. This
is a system that lowers the pressure and stores it in the buffer tank so the compression cycle
can be repeated. Heat is generated during the compression process, storage process and
the process of passing the pressure reducing valve. Then, the heated hydrogen is cooled to
an appropriate temperature through a heat exchanger. As shown in Figure 1, the first stage
and second stage are compressors, and (1), (3), and (5) are heat exchangers, and (2), (4) are
pressure reducing valves.

Figure 1. Hydrogen compression system.

Energies 2021, 14, 2635 6 of 18

Conducting in an initial vacuum state (as the pressure is very small, we assume that
as a vacuum state) is called the “first cycle” and explaining the “second cycle” when there
is residual pressure inside the tank. Figure 2 is high-pressure tank for hydrogen storage.
The pressure uses a pressure transmitter (P601 series) on the tank; the error of the sensor is
±0.25% [39].

Figure 2. High-pressure tank for hydrogen storage

2.1. High-Pressure Tank

Theoretical model of the high-pressure filling process for the compression hydrogen
storage tank, as shown in Figure 3. The initial conditions of the system are as follows:
the pressure and temperature of the hydrogen compressed to high-pressure through the
compressor is 82 MPa, 313.15 K, and the flow rate is 29.05 kg/h. The size of the high-
pressure container that enters the hydrogen filling system is the same, with a length of
4.4197 m, an inner diameter of 0.3143 m, an outer diameter of 0.3985 m, the thickness of
0.0842 m, the volume of 0.343 m3 , and thermal conductivity of 16.3 W/m·K. The initial
state of the hydrogen storage tanks is a vacuum state in the first cycle, and there are
residual pressures of 11.3 MPa and 11 MPa, respectively, in the second cycle. As for the air
temperature, a value of 302.05 K was used to obtain conservative data. For the properties of
hydrogen according to the temperature and pressure data obtained through the REFPROP
9.5 [40] program were used.

Figure 3. Simplified high-pressure tank modeling.

The convection between hydrogen and tank wall is divided into two cases: during the
fast charging, the convection of the tank wall is dominated by forced convection; during
the slow discharge, it is dominated by natural convection. The heat transfer coefficient of
forced convection is calculated according to the Reynolds number (Re) and Prandtl number
Energies 2021, 14, 2635 7 of 18

(Pr). There is no way to know the flow region of hydrogen in the tank during calculation
because the thermodynamic model is adopted in the paper; thus, some Reynolds numbers
cannot be calculated, which means the heat transfer coefficient cannot be obtained. In this
case, by combining the document research results, the following assumption is made in
the paper concerning the flow of gas in the tank: after hydrogen flows through the inlet
valve and enters the tank, it flows to the tank bottom along the wall in a radiation shape,
converges in the middle of tank head, and mixes with the hydrogen flowing in near the
inlet valve after it flows back along the tank axis. We use the formula to calculate the
actual heat transfer coefficient between hydrogen gas and the wall. According to the actual
requirements of this study, the correlation of Nusselt number between the hydrogen and
the tank wall can be written as follows [41]:
Dh
NuDin = = 0.14Redin 0.67 (1)
k
The application range of the Reynolds number and Rayleigh number are respectively
given by:

6.6 × 104 < Redin < 1.8 × 105 and 6.3 × 1010 < RaDint < 1.3 × 1011 (2)

NuDin is the Nusselt number based on the inner diameter of tank, which represents the
convective heat exchange between hydrogen and the wall.
For the horizontal tank, the convective heat transfer coefficient of the external wall
can be calculated by using Equations (3)–(5).
n o2
Nuout = 0.752 + 0.387[Ra·f(Pr)]1/6 (3)

h i−16/9
f(Pr) = 1 + (0.559/Pr)9/16 (4)

hout = Nuout λ/L (5)

After calculating the natural convection heat transfer of the external wall by using an
empirical formula, it is found that its value shows little change. The main reason is that
the temperature change of the external wall is small and there is not much difference in
wind speed in the environment. It has been calculated as the constant value in many kinds
of literature about the temperature
rise of fast-filling. The method is also adopted in this
paper by setting it as 40 W/ m2 ·K .
Initial data in the tank is shown in Table 4. Ti and Pi are the temperature and pressure
of the filling hydrogen gas; m1 , T1 , P1 are the initial mass, temperature, and pressure
within the tank; T2 , m2 , P2 are the final temperature, mass, and pressure within hydrogen
storage tank after filling.
Energies 2021, 14, 2635 8 of 18

Table 4. Initial data of cycle system of the hydrogen storage tanks.

First Cycle
High-Pressure Tank Buffer Tank
Pi (MPa) 82 Pi (MPa) 23
Ti (K) 313.15 Ti (K) 313.15
P1 (MPa) 0 P1 (MPa) 0
T1 (K) 0 T1 (K) 0
m1 (kg) 0 m1 (kg) 0
P2 (MPa) 820 P2 (MPa) 20
T2 (K) Final temperature T2 (K) Final temperature
m2 (kg) Final mass m2 (kg) Final mass
Second Cycle
High-Pressure Tank Buffer Tank
Pi (MPa) 82 Pi (MPa) 23
Ti (K) 313.15 Ti (K) 313.15
P1 (MPa) 11.3 P1 (MPa) 11
T1 (K) 300.15 T1 (K) 304.55
m1 (kg) 2.82 m1 (kg) 2.74
P2 (MPa) 82 P2 (MPa) 20
T2 (K) Final temperature T2 (K) Final temperature
m2 (kg) Final mass m2 (kg) Final mass

2.2. Heat Exchanger

In the hydrogen compression system, it is a heat exchanger installed to lower the
temperature of high-temperature hydrogen before passing through the compressor and
entering the high-pressure container. The system’s heat exchanger uses a reverse flow-type
double-tube heat exchanger. The double-tube heat exchanger is composed of a single
tube and a jacket, and the high-temperature fluid flows through the inner tube. The
low-temperature fluid flows outward, and the heat is transferred through the tube wall
under normal conditions. The specification of the heat exchanger is shown in Table 5. The
double-pipe heat exchanger is shown in Figure 4.

Table 5. Heat exchanger specification.

.
L(m) IDa (m) ODp (m) IDp (m) mh (kg/s) Twi (K) Two (K) Tho (K)
4 0.0355 0.0143 0.0079 0.0081 280.15 285.15 303.15

Figure 4. Temperature distributions for a counter-flow heat exchanger.

2.3. Pressure Reducing Valve

The pressure reducing valve is a valve used to reduce the fluid pressure, and plays a
role in lowering the outlet pressure to a desired pressure by adjusting the high-pressure at
Energies 2021, 14, 2635 9 of 18

the inlet with the adjusting screw and disk in the valve. The pressure reducing valve is
shown in Figure 5.

Figure 5. Pressure reducing valve.

Hydrogen has a very low inversion temperature, resulting in a phenomenon where

the Joule–Thomson effect is reversed and the temperature rises. The Joule–Thomson effect
appears according to the value of the Joule–Thomson coefficient, and the slope of the
isoenthalpy line is the Joule–Thomson coefficient in that state, whose physical significance
is the change rate of gas temperature with pressure after the experiment. The expression is
shown in Equation (6).
∂T V
µJT = ( )h = (αT − 1) (6)
∂P Cp
If µJT is positive, gas temperature reduces with reduction of pressure; on the contrary,
gas temperature rises with reduction of pressure. For ideal gas, µJT = 0; for real gas, it may
not be. During the fast-filling of hydrogen, µJT of hydrogen is negative, which is the rise of
gas temperature after throttling, as shown in Figure 6. During the filling of the hydrogen
storage tank, the change of pressure in a large range makes the compressed hydrogen have
a significant real gas effect with a certain temperature rise, so the hydrogen has throttling
effect at different pipes and valve, which leads to a temperature rise of hydrogen gas.

Figure 6. Joule–Thomson effect.

3. Theoretical Results
3.1. Thermodynamic Analysis of the Filling Process
3.1.1. Model Assumptions
The temperature in the tank rises by filling the tank with hydrogen gas at high pressure.
The model is analyzed through the following assumptions.
- The temperature and pressure in the initial hydrogen storage tank are constant.
- During the high-pressure filling process, the outer wall of the tank of hydrogen natural
convective heat transfer coefficient constant. Tamb = 302.05 K. And neglect kinetic
energy and gravitational force variations.
- The temperature of hydrogen entering the tank is constant.
- The hydrogen gas is evenly distributed in temperature and pressure, and the tempera-
ture of the tank wall is also evenly distributed in the hydrogen storage tank
- The volume of the hydrogen storage tank is constant. As a result, it is possible to
ignore the change in potential energy supplied with hydrogen to the hydrogen storage
Energies 2021, 14, 2635 10 of 18

tank and the change in kinetic energy of the high-pressure container through the
compressor.
- The process of high-pressure filling hydrogen into the tank through the compressor is
an adiabatic process, and heat exchange with the outside is not performed.

3.1.2. Model Equation

The conservation of mass and energy equations of hydrogen from our previous
research [3]. The equations are given by:
Conservation of mass equation:

dm . .
= mi − me (7)
dt
Conservation of energy equation

dE . . . .
= Q − W + mi hi − me he (8)
dt
Real gas equation of the state

ρRT
P= (9)
1 − Bρ

During the high-pressure filling process, the temperature and pressure of compressed
hydrogen in the tank will change greatly, so the real gas model with sufficient accuracy
must be adopted to accurately describe the change of thermodynamic state of hydrogen.
The real gas equation of state was found to be the most suitable. Where, B = 0.007691 m3 for
hydrogen. Compared with the REFPROP 9.5 data, the results obtained from Equation (9)
have a relative error of no more than 4% in the range of 300 K< T < 410 K for hydrogen [42].
Solutions of the mass balance of Equation (7) and the energy conservation of Equation
(8) are as follows:
m2 (hi − u2 ) = m1 (hi − u1 ) (10)
u = cv T , h = cp T (11)
From Equations (10) and (11), the following equations are obtained:

Q = m2 cv2 T2 − m1 cv1 T1 − (m2 − m1 )cp0 Ti (12)

Using the real gas equation of state, the following equation is obtained:
P1 cp0 Ti R
h i
P1 cv1 T1 R
P2 T0 cp0 + PR2 B RQ
V + RT1 +BP1 − RT1 +BP1
T2 = P1 Ti cp0 R
(13)
RQ P1 T1 cv1 R
P2 cv2 − V − RT +BP + RT +BP
1 1 1 1

3.2. High-Pressure Tank for First Cycle Analysis

The first cycle is a vacuum and Q = 0, the Equation (13) can be obtained:
cp0
T2 = Ti (14)
cv2

Specific heat coefficients cp and cv were calculated by using the REFPROP 9.5, a pro-
gram produced and supplied by the National Institute of Standards and Technology (NIST).
The transfer of the tank wall and inner wall consists of three parts, convection between the
flow of high-temperature hydrogen in the tank and the tank wall, heat conduction in the
wall surface, and convection between the external wall and the surroundings, as shown
in Figure 7. Heat transfer between the hydrogen in the high-pressure container and the
external air occurs on the surface of the high-pressure container and occurs in the form of
conduction and convection. Radiant heat transfer was neglected because of the difference
Energies 2021, 14, 2635 11 of 18

between the surface of the high-pressure tank and the outside temperature was expected
to be relatively small [43].
. . . ∆T ∆T
Q = Q1 + Q2 = + (15)
R1 R2
T∞1 − Tw1 . T + T∞2 .
= Qave , 2 = Qave (16)
R1 R2
. .
where Q1 is the heat transfer rate of the hydrogen storage tank, Q2 is the heat transfer
rate on both sides of the hydrogen storage tank. The heat transfer rate from the center of
the container to the outside is equal to the sum of the heat transfer rate at the cylindrical
part and the heat transfer rate at the side of the container, as shown in Equation (16).
Immediately after high-pressure filling is completed, the temperature of the inner wall and
the outer wall of the tank is determined by the temperature difference between hydrogen
in the tank and external air, and the heat transfer phenomenon from the tank to the outside.

Figure 7. Temperature differences of the wall reference on the side of the hydrogen storage tank.

The result values for the buffer tank and high-pressure tank were shown in Table 6,
and were calculated using the same method as obtained for the high-pressure tank of the
first cycle of analysis.

Table 6. Results of the first cycle of the compressed hydrogen storage tanks.

Condition High-Pressure Tank Buffer Tank

P2 (MPa) 82 20
T2 (K) 436.09 440.15
m2 (kg) 11.58 3.49
Q(kJ) 23125.09 7071.45
R1 (K/W) 0.00706 0.00716
R2 (K/W) 0.625
.
Q1 (kW) 18.99 17.71
.
Q2 (kW) 0.214 0.2006
.
Qave (kW) 9.61 9.76
Tw1 (K) 417.75 420.64
Tw2 (K) 343.55 344.18

3.3. High-Pressure Tank Second Cycle Analysis

As in the first cycle, the inflow temperature and pressure supplied through the com-
pressor and heat exchanger are the same as 82 MPa and 313.15 K, but there is a residual
pressure of 11.3 MPa after the first cycle in the high-pressure tank. When hydrogen gas is
Energies 2021, 14, 2635 12 of 18

supplied and filled in a high-pressure tank with residual pressure, the temperature of the
hydrogen tank can be expressed as shown in Equation (17):
P1 cp0 Ti R
h i
P1 cv1 T1 R
P2 T0 cp0 + PR2 B RQ
V + RT1 +BP1 − RT1 +BP1
T2 = P1 Ti cp0 R
(17)
P1 T1 cv1 R
P2 cv2 − RQ V − RT +BP + RT +BP
1 1 1 1

During the high-pressure filling process, Q = 0. The following equation is obtained:

P1 cp0 Ti R
h i
P1 cv1 T1 R
P2 T0 cp0 + PR2 B RT −
1 +BP1 RT1 +BP1
T2 = P1 Ti cp0 R
(18)
P1 T1 cv1 R
P2 cv2 − RT +BP + RT +BP
1 1 1 1

The Equation (18) can be simplified as:

P2 Ti cp0 RT1 + P1 T1 cv1 BP2

T2 = (19)
P2 cv2 RT1 + P2 cv2 BP1 − P1 cv1 RT1 + P1 Ti cp0 R

The calculation of final temperature was based on the experimental pressure data from
the reference [32]. The final temperature during this time with different equations is shown
in Figure 8. It can be seen from the curve in Figure 8 that the curve of the fitting formula of
Song et al. [31] is a little higher than the other. The reason for this situation may be ignored
heat transfer. In the initial stage of high-pressure filling, the final temperatures have little
difference. As the pressure increases, the difference in temperature rise becomes larger.

Figure 8. Final temperature during the time with different equations.

In addition to the value of T2 , the other values were calculated by the same method as
in first cycle. The resulting values for the buffer tank and high-pressure tank are shown in
Table 7, and were calculated using the same method as the high-pressure tank.
The rise of hydrogen gas pressure over time is shown in Figure 9. It can be seen that
the pressure basically increases linearly. Figure 10 shows the corresponding temperature
valuations by using an accurate equation for the temperature rise calculation of the storage
tank. The upward trends of (a) and (b) are basically the same. The error is obtained from
the linear regression of the experimental pressure measurement. In the initial stage of
fast-filling, the temperature rises grow rapidly, and as the ratio of the termination pressure
to the initial pressure decreases, the temperature rises gradually increases slowly and
remains stable towards the end of the filling process.
Energies 2021, 14, 2635 13 of 18

Table 7. Results of the second cycle of the compressed hydrogen storage tanks.

Condition High-Pressure Tank Buffer Tank

P2 (MPa) 82 20
T2 (K) 403.55 345.69
m1 (kg) 2.82 2.74
m2 (kg) 12.26 4.35
Q(kJ) 18599.90 2794.74
R1 (K/W) 0.00706 0.00716
R2 (K/W) 0.625
.
Q1 (kW) 14.38 6.10
.
Q (kW) 0.162 0.061
. 2
Qave (kW) 7.27 3.082
Tw1 (K) 389.66 339.53
Tw2 (K) 333.48 315.38

Figure 9. The experimental results of the pressure measurement over time. (a) The pressure value of the high-pressure tank
for the second cycle; (b) pressure value of the buffer tank for the second cycle.

Figure 10. The theoretical results of the temperature for the second cycle. (a) Temperature values of the high-pressure tank,
and (b) temperature values of the buffer tank.
Energies 2021, 14, 2635 14 of 18

4. Hydrogen Compressor Heat Exchanger Analysis

The heat exchanger section is (1), (2) and (5), as shown in Figure 1. The heat capacity
required in the firstcycle and the second cycle is the same through the heat exchanger (1).
On the other hand, in heat exchangers (3) and (5), the hydrogen that h passed through the
pressure-reducing valve flows into the heat exchanger and heat exchange with the cooling
water occurs. The required capacity to reach the target temperature was calculated using
the Log Mean Temperature Difference (LMTD) method. The working principle of the heat
exchanger is shown in Figure 11.
. .
mh cph ∆Th = mw cpw ∆Tw (20)
.
Q = Utotal Atotol ∆T (21)

Figure 11. The heat exchanger. (a) Counter-flow heat exchanger; (b) working principle diagram of the heat exchanger.

In order to obtain the necessary refrigeration capacity of the heat exchanger, the total
heat transfer coefficient Utotal is required, which can be obtained through the heat transfer
coefficient values of hydrogen and cooling water. The heat transfer rate through the heat
exchanger has the same value in the hydrogen and cooling water. The Re number in the
cooling water, which is an annular tube, was calculated using the hydraulic diameter, to
determine laminar and turbulent flow.
 1
hD DRePr 3
Sieder − Tate equation : Nu = k = 1.86 L (22)
Modified Dittus − Boelter equation : Nu = hD
k = 0.023Re0.8 Prn

The Nu number is obtained by Equation (21), and the n-value has a value of 0.3 when
the fluid is cooled and 0.4 when the fluid is heated.
(Thi − Twi ) − (Th0 − Tw0 )
LMTD = (23)
ln[(Thi − Twi )/(Tho − Tw0 )]

In a double-tube heat exchanger, the temperature difference is obtained by using the

log mean temperature difference (LMTD) using the temperature difference of two fluids at
both ends. Using the same method, the required refrigeration capacity of heat exchangers
(3) and (5) was calculated by different conditions in the first cycle and the second cycle, as
shown in Table 8.
Energies 2021, 14, 2635 15 of 18

Table 8. Heat exchanger performance required in the first cycle and second cycle.

(1)H/X (3)H/X (5)H/X

1st cycle 2nd cycle 1st cycle 2nd cycle
Thi (K) 323.15
446.59 413.15 443.15 347.65
.
Qh (KJ/s) 1.215 15.816 11.872 15.320 4.068
.
mw (kg/s) 0.0578 0.753 0.565 0.729 0.194
.
hw W/m2 K


204.27 2666.86 2120.51 2600.36 901.40
.
hh W/m2 K



1615.25 1435.40 1369.53 1420.15 1372.16
Utotal W/m2 K 181.333 933.146 832.112 918.515 544.022
∆T(K) 24.75 77.67 67.388 76.64 44.89
.
Q(RT) 0.186 3.004 2.324 2.918 1.012

5. Conclusions
In current hydrogen filling systems, hydrogen is compressed and stored at high
pressure in a tank through a compressor. In this process, the internal pressure of the
tank increases, and thermal stress may occur due to the temperature rise of the hydrogen.
In order to secure the reliability of the high-pressure tank, it is important to study and
predict the temperature rise of hydrogen gas. In this paper, the change in the hydrogen’s
temperature in the tank according to the pressure rise during the process of filling the
high-pressure tank in an 82 MPa hydrogen filling system. As such, the final temperature,
the amount of filling of hydrogen gas, the pressure-reducing valve, and the change and the
performance of the heat exchanger for cooling high-temperature hydrogen were analyzed
by theoretical and numerical methods.
As a result of the study, the following conclusions were drawn. First, as a result of the
theoretical approach, the internal temperature of the high-pressure tank was calculated to
increase by 436.09 K and 376.55 K on average in the first cycle and the second cycle. Second,
the hydrogen filling amount in the high-pressure tank and the buffer tank increased by
11.58 kg and 3.49 kg, respectively, in the first cycle, and increased by 9.44 kg and 1.61 kg,
respectively, in the second cycle. The amount of increased temperature decreased as the
cycle continued.
In this paper, the thermal insulation condition was assumed during the charging
process, and the heat transfer condition to the surroundings after charging was completed
and was analyzed considering only conduction and convection. Considering the abnormal
heat transfer process, not the adiabatic condition, and the radiant heat transfer, the time at
which thermal equilibrium takes place will be different. In the future, we will consider the
above to more accurately determine the temperature and thermal equilibrium. The works
of this paper will be useful for system design and operation in industrial sites that require
a hydrogen compression system.

Author Contributions: Conceptualization, J.-T.K. and K.P.; methodology, J.-T.K.; software, J.-Q.L.;
validation, S.-J.J. and J.-T.K.; formal analysis, J.-C.L.; investigation, J.-Q.L.; resources, K.P.; data
curation, S.-J.J.; writing—original draft preparation, J.-Q.L.; writing—review and editing, J.-Q.L.;
visualization, J.-C.L.; supervision, J.-T.K.; project administration, S.-J.J. and K.P.; funding acquisition,
S.-J.J. and K.P. All authors have read and agreed to the published version of the manuscript.
Funding: This study was a research project conducted by the Ministry of Trade, Industry and Energy
and supported by the Korea Energy Technology Evaluation Institute (KETEP) as an energy technology
development project. (No. 20200502001, No. 202000580002).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Energies 2021, 14, 2635 16 of 18

Nomenclature

Ain Internal surface area of tank, (m2 )

Aout External surface area of tank, (m2 )
Atotal Total surface area, (m2 )
h1 Internal heat exchange coefficient between hydrogen and tank wall, (W/m2 ·K)
h2 External heat exchange coefficient between tank wall and ambient fluid, (W/m2 ·K)
.
hi Specific enthalpy of incoming gas, (J/kg)
.
he Specific enthalpy of outflow gas, (J/kg)
cp Specific heat capacity of the hydrogen gas at constant pressure, (J/kg·K)
cv Specific heat capacity of the hydrogen gas at constant volume, (J/kg·K)
din Injector diameter, (m)
Din Internal diameter of the tank, (m)
Dout External diameter of the tank, (m)
L Length, (m)
M Hydrogen mass within the tank, (kg)
m1 m2 Initial and settled mass in the tank, (kg)
.
mi Mass flow rate into the tank, (kg/s)
.
me Mass outflow rate for discharge process, (kg/s)
Nuin Nusselt number of the gas, dimensionless. Nu = Dh k = 0.14Redin
0.67
.
4m
Redin Reynolds number of the flow based on tank internal diameter, Redin = πµd
in
RaDin Rayleigh number of the gas.
P Hydrogen pressure in the tank, (MPa)
Pi Settled pressure of hydrogen gas in the tank, (MPa)
P1 P2 Initial and settled pressure within the tank, (MPa)
P2 Final hydrogen pressure, (MPa)
.
t∗ Characteristic time, t∗ = m0 /m f or f illing
T Hydrogen temperature in the tank (K)
T1 The initial temperature of gas, (K)
Ti Temperature of filling hydrogen gas, (K)
T2 Final temperature of hydrogen gas in the tank, (K)
Tamb The ambient temperature, Tamb =302.05 K
T∗ Characteristic temperature, K
U Specific internal energy, (J/kg).
K Thermal conductivity (W/m· K.)
P Hydrogen density, (kg/m3 )
B Abel-Nobel constant, B=0.007691 m3 for hydrogen gas
R1 The total thermal resistance in the tank, (K/W)
R2 The total thermal resistance of the side, (K/W)
Rg Gas constant, J/mol K
Q Heat transferring to ambient, (kJ)
.
Q Heat transfer rate (W)
Utotal Total heat transfer coefficient
α Constant of compression, α = 1.9155 × 10−6 k/Pa
λ Ratio of specific heat under the constant of volume to that under pressure.
Z Compressibility factor
ψf,1−2 The energy e f f iciency
T Dimensionless time, τ = t/t∗
Subscripts
h hydrogen;
w water;

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