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Cryosorption storage of gaseous hydrogen for vehicularapplication – a conceptual design

Indranil Ghosh*, Sudipta Naskar, Syamalendu Sekhar Bandyopadhyay

Cryogenic Engineering Centre, Indian Institute of Technology, Kharagpur 721 302, West Bengal, India

a r t i c l e i n f o

Article history:

Received 21 May 2009

Received in revised form

7 October 2009

Accepted 9 October 2009

Available online 7 November 2009

Keywords:

Fuel cell vehicle

Hydrogen storage

Adiabatic

Cryosorption

Transient analysis

* Corresponding author. Tel.: þ91 3222 28358E-mail address: indranil@hijli.iitkgp.erne

0360-3199/$ – see front matter ª 2009 Profesdoi:10.1016/j.ijhydene.2009.10.026

a b s t r a c t

A conceptual design for the cryosorption storage of gaseous hydrogen in activated carbon

for vehicular application has been presented. In this work, a novel concept for the storage/

discharge of hydrogen has been proposed. This system ensures faster filling and gradual

release of hydrogen on demand. These two features are important for making onboard

hydrogen storage effective for small cars. Numerical models for adsorption and desorption

half cycles are presented. Assuming that the pressurisation and depressurisation are

occurring adiabatically, transient analysis has been done to critically study the effective

hydrogen storage capacity of activated carbon. The amount of activated carbon required to

store hydrogen for travelling a specific distance has been computed.

ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1. Introduction hydrogen storage target set by the US Department of Energy

Transportation sector will be one of the beneficiaries of

‘‘hydrogen economy’’ if it is implemented successfully. The

thought of using hydrogen as vehicular fuel has been

conceived long back. The use of hydrogen as a fuel for internal

combustion engines was first demonstrated in 1930s by Erren

and Hastings-Campbell [1]. Its high energy density per unit

mass and relatively low ‘‘global warming’’ potential, make it

an attractive choice to evade the fuel crisis in future. Even

though large scale commercial production of hydrogen from

the fossil fuel is associated with the cogeneration of CO2, the

release of this ‘‘green house gas’’ to the environment can be

restricted with the adoption of an effective CO2 capture and

sequestration scheme.

However, one of the major problems of using hydrogen as

the vehicular fuel is its low energy density per unit volume.

Researchers, all over the world, are now trying to achieve the

8; fax: þ91 3222 255303.t.in (I. Ghosh).sor T. Nejat Veziroglu. Pu

(DOE). The US-DOE has put forward year wise target (for every

five years) starting from 2005 [2]. Storage targets regarding

volumetric and gravimetric hydrogen density, refuelling time,

costs, cycle life and loss of usable hydrogen have been made

increasingly challenging recently. For the year 2010, the

gravimetric storage density has been set at 6 weight percent,

while the volumetric capacity target is 45 kg/m3. In general,

the storage density of hydrogen is enhanced by using the

following techniques: a) compression, b) liquefaction, c)

reversible metal and chemical hydrides and d) physical

adsorption of hydrogen [3–5]. The first two methods are the

most commonly used means for current test vehicles [6].

Storage of hydrogen as compressed gas in tanks is the most

mature storage technology at present. While high pressure

gaseous hydrogen (GH2) storage has lower volumetric storage

density with the associated safety hazards, liquefied hydrogen

(LH2) is considered to be a good alternative in view of its

blished by Elsevier Ltd. All rights reserved.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 1 6 1 – 1 6 8162

gravimetric storage density. However, liquefaction of

hydrogen is energy intensive and the boil-off losses of LH2 is

a serious concern. The energy required to produce LH2 is more

than three times the energy required to compress gaseous

hydrogen to 70 MPa [7–9]. Reversible metal hydride storage

offers reasonably dense H2 storage and positive safety char-

acteristics. But it has limitations due to its heavy mass, cost

and additional energy requirement to release H2. Desorption

temperatures for some of the metal hydrides are relatively

high for vehicular application [10]. In this background,

adsorption storage of hydrogen in carbonaceous materials or

carbon nanotubes probably offers the best option for meeting

the requirements for onboard storage for fuel cell vehicles

(FCV) [11–13].

Hydrogen driven vehicles are powered by the energy

generated by the H2 fuel cell, or it can be used directly in the

Internal Combustion (IC ) engine to drive the vehicle. Since

performance of the former option is better with respect to

emissions and efficiency as compared to those of the IC engine

vehicles [14–16], the present work has been focused on the

storage requirement of hydrogen for a vehicle driven by fuel

cells. A novel concept of storing/releasing this hydrogen in/

from activated carbon at cryogenic temperature has been

proposed in this article. A transient modelling of this cry-

osorption storage system has been developed to compute the

mass of activated carbon necessary for travelling a specified

distance.

2. Design criteria

Worldwide, the development of hydrogen driven vehicle is

aimed at making it economically competitive with the

conventional IC engine vehicles powered by gasoline [17–20].

A typical hydrogen fuel cell vehicle system is shown in Fig. 1.

Gaseous hydrogen will be stored by adsorption on activated

carbon in refilling station. When the vehicle is on road,

hydrogen will be discharged from the storage system by pro-

grammed depressurisation of the bed. The rate of the

hydrogen uptake by the fuel cell will vary depending on the

speed of the vehicle. In the fuel cell, H2 will produce electricity

by the electrochemical reaction with air/O2, and the fuel cell

power in turn will drive the vehicle.

Fig. 1 – Schematic of hydrogen driven

It is important to benchmark some of the key parameters

based on which the storage system for the hydrogen driven

car can be designed and simulated. Assuming that the FCV

has to cover same range of distance compared to the

conventional ICE vehicle, the following major design criteria

have been set. The FCV has been thought as a lightweight

carriage (with Curb weight of nearly 1200 kg) meant for 4

passengers. The maximum attainable speed is around

120 km/hr to cover a distance of 500 km between two subse-

quent refilling. There could be few choices while selecting fuel

cells. A comparison of different fuel cell systems shows that

the Proton Exchange Membrane (PEM) offers high power

density while its operating temperature [14] is relatively low.

Accordingly, PEM fuel cell has been considered for this

conceptual analysis.

3. Conceptual storage system

In order to achieve the DOE set target of hydrogen storability,

the adsorption storage system has been found most promising

among the existing means of storing the gas. Selection of

proper adsorbent is equally important task for this purpose.

An extensive literature review has been made for this purpose

to finally choose activated carbon as the most suitable

adsorbent compared to other carbonaceous materials. Storing

hydrogen in carbon nanotubes can be another option [21–23].

But, this has not been considered for this work, since it has

been reported in the literature [24,25] that there are lot of

discrepancies in the results of adsorption/desorption studies

by research groups.

As the refilling of hydrocarbon fuel is done in refuelling

station, similar practical situation is envisaged for cryogenic

adsorption storage of gaseous hydrogen in FCV. The refilling of

on-board adsorption storage of hydrogen and its discharge for

the FCV is shown schematically in Fig. 2.

The system considered for this study is as follows. Speci-

fied quantity of activated carbon is stored in a high pressure

(w4–5 MPa) vessel made of stainless steel. The thickness of

the container is appropriate for the operating pressure. Dead-

end filling mode is considered. While one end of the tank is

closed, inflow and delivery of hydrogen occurs through the

other end. The charging and discharging of gaseous fuel is

controlled by the two control valves. An arrangement is made

Fuel Cell Vehicle (FCV) system.

Fig. 2 – Schematic of the conceptual cylindrical storage

vessel for charging/discharging of H2.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 1 6 1 – 1 6 8 163

to cool the tank if necessary. Besides, the entire vessel is

adequately insulated to minimise heat in leak from the

ambient.

During charging step, compressed gaseous hydrogen, after

being cooled with liquid nitrogen in a heat exchanger, is filled

in to the vessel through valve V-1. During this operation, the

discharge valve V-2 remains closed and the charging valve is

kept open. Initially, when the differential pressure across the

proportionate valve is high, it is partially opened to control

large flow rate of gaseous hydrogen. On the other hand,

towards the end of filling process, when the pressures on both

sides are nearly equal, larger opening is necessary to maintain

the flow of hydrogen. Adsorption of hydrogen on activated

carbon is associated with heat of adsorption. The heat of

adsorption is not deliberately allowed to move out of the

system, although provision has been kept for the same. Due to

this, the temperature of activated carbon bed and the storage

vessel increases. Consequently, the quantity of hydrogen

uptake also diminishes. While reduction in hydrogen storage

capacity can be compensated by putting additional quantity of

carbon in the bed, this adiabatic filling of gaseous hydrogen

offers two advantages. One, pressurisation of the system is

rapid without the removal of heat. Hence, one does not need to

wait for long in a hydrogen filling station. Two, the heat of

adsorption retained on the adsorbing bed compensates for the

endothermic heat of desorption, which otherwise would result

in substantial decrease in the bed temperature during the

discharge step. However, the final temperature of the system

after complete desorption, with the present storage option, is

going to get back ideally at its initial filling temperature i.e.

a temperature corresponding to the liquid nitrogen tempera-

ture. Thus, the activated carbon adsorbent with its high

porosity, in a sense, acts as a regenerator where the heat of

adsorption is stored during one half of the cycle and it provides

the heat of desorption during the other half of the cycle.

Charging of hydrogen continues till the pressure inside the

vessel reaches equilibrium with the supply pressure. On

completion of the filling process, the ‘charge valve’ is closed

and the storage tank is disconnected from the hydrogen

supply unit. The vehicle with the on-board filled container is

set for drive. In the discharge step, gas flow rate to the fuel cell

of the vehicle is adjusted from the desorbing bed.

A fast adiabatic filling process develops a temperature

gradient (in the range of 50–60 �C) within the porous activated

carbon adsorbent bed. Activated carbon being a bad conductor

of heat, situation is aggravated. Thus, the transient heat

transfer modelling of the system becomes essential. The

amount of adsorbent necessary to store hydrogen for

a specific distance, sizing of the storage vessel, etc. should be

determined from the study of dynamic charging and dis-

charging process. An attempt has been made in the following

section to develop the mathematical models for the same.

4. Mathematical modelling

Ideally, adsorption and desorption processes can be described

by the same mathematical model except that the initial and

boundary conditions for the two situations are different. In case

of vehicular application, the duration of charging and dis-

charging of hydrogen to/from porous adsorbent is widely

different. While the process of filling hydrogen into the storage

tank should be carried out as fast as possible, delivery of stored

hydrogen may continue for a much longer period depending on

the speed of the vehicle ranging from zero (halt) to the

maximum limit (highest speed). Adsorption and desorption of

gases, being surface phenomena, occurs quite fast. As a result,

it is appropriate for an engineering application to assume the

occurrence of instantaneous equilibrium for both the

processes. Thus, the same energy and mass balance equations

remain applicable during the pressurisation and depressur-

isation of gases. Additionally, the following major assumptions

have been made while developing the mathematical model.

a) The adsorber vessel is cylindrical in shape and made up of

stainless steel. The length of the adsorbent bed is few times

longer than the diameter of the bed. The L/D ratio of the bed is 4.

b) The bed is homogeneously packed with spherical adsorbent

particles of activated carbon.

c) The gas behaviour has been assumed to be ideal within the

temperature and pressure range of our interest. The gas does

not undergo any phase change.

d) The gas velocity inside the adsorption bed varies linearly

with length, while the initial velocity is governed by the

‘proportionate’ valve.

e) The adsorbent bed is insulated properly to prevent any kind

of heat-in-leak during adsorption as well as desorption.

f) According to assumption (a), it is reasonable to formulate

one dimensional analysis for temperature and density along

the axial direction.

The governing heat and mass transfer equations have been

formulated on the basis of above assumptions. The mass

balance equation can be written as [26]

3vr

vtþ 3

v

vx

�ur� Dax

vr

vx

�þ ð1� 3ÞrsMH2

vrðx; tÞvt

¼ 0 (1)

The first and third terms on the left hand side stand for the

accumulation of gas within the inter-particle space and the

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 1 6 1 – 1 6 8164

amount of gas adsorbed, respectively. The convective flux

including axial dispersion is incorporated within the model by

the term in the middle.

The energy balance equation can be formulated as:

�A1rCP

Aþ A1

A

�1� 3

3

�rsCps þ

A2

3ArwCpw � Rr

�vT

vt

���

1� 3

3

�DHrs

vqðx; tÞvt

�þ v

vx

�rCpuT

�¼ 0 ð2Þ

The first three terms in Eq. (2) symbolise the rate of heat

accumulation within the bulk gas phase, adsorbent, and the

container wall, respectively. The fourth and fifth term stand

for the generation of heat due to compression and adsorption,

respectively. The expression with spatial variation denotes

convective heat flux.

The initial conditions for the charge model are

rðx; t ¼ 0Þ ¼ r0 and Tðx; t ¼ 0Þ ¼ T0 (3)

The boundary conditions for the partial differential equa-

tions, at x¼ 0 can be written as

urð0; tÞ � Daxvr

vxð0; tÞ ¼ ur0 and Tð0; tÞ ¼ T0 (4)

Similarly, the boundary conditions at x¼ L are written as

vr

vxðL; tÞ ¼ 0 and

vTvxðL; tÞ ¼ 0 (5)

While Eqs. (1) and (2) for the mass and energy balance still

remain valid for the discharge model, the initial conditions are

different. Since the adsorbent bed is pressurised up to the

charging limit, desorption starts from that pressure level. This

has been set as an initial condition for the mass balance

equation in the desorption model. However, the temperature

reached at the end of the adiabatic charging process is not

known a priori. However, the ultimate temperature, due to

adiabatic heat of adsorption, is more than the initial value at

which adsorption begins. The final average bed temperature is

determined using the adsorption model and the same is

considered as the starting temperature for desorption. It

constitutes the other initial condition necessary for the energy

balance equation in the discharge model.

Values of different characteristic dimensions and property

data used in the modelling primarily depend on the type of

adsorbents and material of construction. Later in the article,

use of C034 has been suggested as the adsorbent stored in

stainless steel container. The activated carbon particles have

been assumed spherical with an average particle diameter of

5� 10�3 m. The density of activated carbon is taken as 340 kg/

m3, while the void fraction of the packed bed has been

assumed to be 50%.

4.1. Solution technique

The partial differential equations have been solved numeri-

cally. At the outset, discretisation of the partial differential

equation has been carried out using finite difference method.

The discretisation equation, involving the values of depen-

dent variable for a set of grid points, is constructed adopting

central difference scheme and Euler implicit method. Fully

implicit method, which offers unconditional stability main-

taining the requirement of simplicity and physically satis-

factory behaviour, has been employed for this purpose. The

discretisation equation in the generalised form can be written

for the grid points, j¼ 1, 2, 3. N,

AW;j�1rj�1 þAP;jrj þAE;jþ1rjþ1 ¼ Qj (6)

In Eq. (6), the running index j¼ 1 and N correspond to the

boundary conditions. This equation has been derived from the

mass balance Eq. (1) to obtain density profile. Similar expres-

sion results from the energy balance Eq. (2) for temperature.

It is evident that the coefficients of Eq. (6) generate a tri-

diagonal matrix, which can be solved using standard tech-

niques like Thomas algorithm [27]. A computer code has been

written in Cþþ to simulate the adsorption and desorption

models. The solution is advanced in time over the length of

the bed in axial direction.

In order to enhance the accuracy of numerical calculations,

grid independence test has been performed both for time and

length. The pressure profile developed in the storage vessel is

recorded independently for each incremental value of time

and length. Better is the performance with large number of

sections along the length and smaller duration of time. The

number of divisions for length (w95) beyond which changes in

pressure profile are negligible has been used to calculate the

final results. Similarly, smaller time interval (w30 sec) has

been preferred for the time domain to record the pressure and

temperature variations.

4.2. Validation of the model

The model has been validated using the experimental and

computed results available in the literature for similar work

but for charging at ambient temperature [28]. While the model

proposed by Lamari et al. [28] assumes thermal linkage

between the storage vessel and the surroundings, for the

present work we need to include an additional heat-in-leak

term so that the present model can be compared with the

results of Lamari et al. [28]. When the outer surface of the

container is exposed to ambient condition, heat transfer to/

from the surroundings modifies the energy balance Eq. (2)

with an extra factor, which is proportional to hamb (T-Tamb).

The geometrical and physicochemical parameters of Lamari

et al. [28] for charging have been incorporated in our model. The

results are presented in Fig. 3. When the computed tempera-

ture profiles of this work at the entrance of the bed (Fig. 3a) and

the middle of the bed (Fig. 3b) for charging considering external

heat transfer are compared with the computed profiles at T1

and T2 locations of Fig. 6(a) (for <Q>¼ 0.91� 10�3 Nm3/s) and

also the corresponding experimental data of Fig. 10 of Lamari

et al. [28], it is observed that the nature of the temperature

profiles simulated with the present model matches closely with

that of the simulated profiles as well as experimental results of

Lamari et al. [28]. It may be noted that the maximum temper-

ature rise predicted by the present model for the entrance and

middle of the bed is only 3% higher than the maximum

temperatures predicted from simulation and reported from

experimental results by Lamari et al. [28].

Fig. 3 – Validation of the developed model for charging at ambient temperature and physicochemical and geometrical

parameters of Lamari et al. [28]. (a) Location (x): Entrance (open end) of the bed, (b) Location (x): Middle of the bed.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 1 6 1 – 1 6 8 165

5. Results and discussions

The conceptual design of the cryosorption hydrogen storage

for vehicular application begins with the selection of appro-

priate activated carbon and the operating conditions like

charging pressure and temperature. Subsequently, an

approximate estimation of the dimensions of the storage

vessel is made for the storage of a specified amount of

hydrogen within activated carbon. Adiabatic filling of

hydrogen within the adsorbent bed and its release from the

vessel has been simulated using the transient analysis. When

the heat of adsorption is not removed, rapid charging process

develops sharp temperature gradient within the bed reducing

the effective storage capacity of hydrogen. An iterative

procedure must be adopted to arrive at the final dimensions of

the storage and the amount of activated carbon needed to

store the specified quantity of hydrogen.

Selection of the specific grade of adsorbent (activated

carbon) and the operating temperature and pressure for the

adsorption storage have been done by careful examination of

Fig. 4 – Average bed pressure vs charging time with

different flow rates Length of bed [ 1.4 m, Diameter of

bed [ 0.33 m.

the physical characteristics of the various grades of activated

carbon and their equilibrium adsorption capacity for gaseous

hydrogen at various temperatures and pressures from the

published literature [29–33]. The equilibrium adsorption

capacities of all grades of activated carbon are higher for

hydrogen at cryogenic temperatures. However, in view of the

fact that in the cryogenic temperature range, a temperature

level of 77 K can be conveniently maintained by liquid

nitrogen (LN2) at atmospheric pressure, LN2 being an easily

available refrigerant in almost all countries in the world, the

initial temperature for adsorption half cycles has been chosen

as 77 K. Comparing the characteristics of various grades of

activated carbon reported in the literature [29–33], the grade of

activated carbon selected for this work is C034, for which the

equilibrium adsorption capacity data and the isotherms have

been reported by the researchers of Hydrogen Research Institute

[34]. While the authors have tried to fit the data using Ono-

Kondo model as well as Langmuir equation, the later has been

found to be more advantageous for use in the simulation

program [34]. While the isotherm is simple to incorporate in

Fig. 5 – Bed temperature vs charging time at different

locations Length of bed [ 1.4 m, Diameter of bed [ 0.33 m

Initial bed temperature [ 115 K, Pressurised H2

temperature [ 77 K.

Fig. 6 – Bed temperature vs distance at different charging

time Length of bed [ 1.4 m, Diameter of bed [ 0.33 m

Initial bed temperature [ 77 K, Pressurised H2

temperature [ 77 K.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 1 6 1 – 1 6 8166

the algorithm, it has been found to provide sufficient accuracy

over the range of pressures of our interest. The ultimate

charging pressure has been decided by careful observation of

the isotherm data reported in Ref [34]. It has been noted that

the adsorption capacity of this particular activated carbon

changes marginally beyond 4 MPa in the vicinity of 77 K. This

has led to set the final charging pressure at 4 MPa, while the

limit for desorption has been chosen to be atmospheric

pressure. The heat of adsorption/desorption for this adsor-

bent-adsorbate pair has been taken as 5.5 kJ/mol.

The amount of hydrogen necessary to travel a distance of

500 km is approximately 3.1 kg [35]. An approximate sizing of

the storage vessel is possible from the equilibrium adsorption

capacity of C034 at 4 MPa and 77 K [34,35]. With an equilibrium

adsorption capacity of 20.8 mol of H2/kg of carbon at that

temperature and pressure, one needs 74.5 kg of carbon to

store 3.1 kg of hydrogen. With the bulk density of 340 kg/m3 of

activated carbon, the volume of the storage system becomes

w220� 10�3 m3. A single storage of this volume is large

compared to conventional gasoline vehicle storage system.

Besides, the thickness of the vessel also increases with

diameter. Therefore, two cylindrical tanks of equal volume

have been chosen to start simulation. Keeping the length to

diameter ratio at 4, the dimension of each container becomes

1.3 m in length and 0.327 m in diameter. In order to calculate

the thickness of the container, ASME Boiler and Pressure Vessel

Code, Section VIII, Division 1 has been used [36]. If the storage

tank is made of stainless steel AISI 304L, the minimum

thickness required has been found to be 5.3� 10�3 m. Simu-

lation of filling and discharge has been initiated with the

configurations described under section 3. Since the beds are

exactly identical, results of analysis for a single cylinder are

applicable for the other one.

It has been observed earlier in Fig. 3 that the temperature

distribution within the adsorbent bed during dead-end filling

under adiabatic condition can be substantially different from

the situation when external heat transfer is included. The

magnitude and the nature of the temperature gradient present

in the bed largely depend on the rate of heat exchange with the

surrounding. The existence of a large temperature gradient

along the axial direction of the bed, in presence of external

heat transfer, is essentially due to the poor thermal conduc-

tivity of the granular activated carbon. Situation aggravates

under adiabatic condition. In this situation, the temperature of

the bed near entry region reaches slightly larger maxima and

gradually decreases with time (Fig. 3a), while it remains almost

steady beyond the middle of the bed (Fig. 3b). Hydrogen at

relatively lower temperature enters the system to cause a local

fall in temperature. On the other hand, heat of adsorption does

not escape from the interior of the bed causing rise in

temperature near the middle of the bed and onwards. Similar

observations have been reported by Lamari et al. [28] for rapid

charging when the bed of activated carbon gets too little time

for dissipation of heat and behaves similar to charging at

adiabatic conditions (Ref. Fig. 11 in [28]). Additionally, it may be

noted from Fig. 3 that the temperature distribution within first

300 sec (roughly) are marginally different irrespective of the

filling process being adiabatic or non-adiabatic.

In view of the fact that a passenger on transit may not like

to spend much time in hydrogen refilling station, the charging

time should be as minimum as possible. It has been set arbi-

trarily as 300 sec (5 min). In order to attain the maximum

pressure within the stipulated time, hydrogen flow rate must

be adjusted suitably. Average bed pressure variation with time

corresponding to different flow rates of hydrogen is shown in

Fig. 4. Comparatively smaller flow rate, for the obvious reason,

will take longer time to fill the bed. Filling process with higher

flow rate helps to achieve the ultimate pressure quickly. The

adverse effect of the latter is associated with a larger and more

rapid rise in temperature with an eventual reduction in the

adsorption capacity.

Assuming the bed to be initially at 77 K, the final temper-

ature of the bed on completion of the charging process has

a sharp temperature gradient along the length of the bed. On

an average, the overall rise in temperature is about 60 K. As

a result, there is substantial decrease in the effective storage

ability of the absorbent. Now, with this reduced adsorption

capacity, one needs to modify the overall dimension of the

vessel for accommodating 3.1 kg of hydrogen. The diameter

and length of the cylindrical tank have been altered from its

original value to 0.330 m and 1.4 m respectively. In addition to

that, an extra cylinder is required to cope up with the rise in

temperature. Thus one has to carry three cylinders altogether

for storing 3.1 kg of hydrogen on board.

From our simulation, it has been observed that the average

bed temperature at the end of the discharge remains well

above 77 K. If desorption begins at 140 K, the bed ultimately

reaches an average temperature of 115 K before it is

completely discharged. This may be due to the fact that

stainless steel wall of the storage vessel retains substantial

part of the heat of adsorption during rapid charging and

behaves as thermal reservoir. This heat content of the vessel

wall compensates for a good part for the endothermicity of

desorption. Since desorption occurs for a comparatively longer

duration, adsorbent gets sufficient time to equilibrate with the

heat content of the wall. Consequently, the average bed does

not come back to its original temperature of 77 K. Therefore,

Table 1 – Duration of discharge for different vehicularspeed (using a single cylinder).

Flow Rate(kg/s)

Vehicle speed(km/hr)

DischargeTime (sec)

DistanceTravelled (km)

0.207� 103 120 4980 166

0.138� 103 80 7440 165

0.103� 103 60 9960 166

0.069� 103 40 15000 167

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 1 6 1 – 1 6 8 167

simulation for the next filling process must assume an initial

bed temperature of 115 K while, gaseous hydrogen enters the

bed at 77 K. The time variation of the bed temperature distri-

bution is shown in Fig. 5. While the temperature profile (Fig. 5)

near entrance shows a peak followed by gradual decrease with

time, steady rise in temperature results beyond the middle of

the bed. Initial increase in temperature near the entry region is

due to heat of adsorption. Flow of gaseous hydrogen at 77 K

removes the heat of adsorption and finally cools the bed when

the adsorbents become saturated. By the time hydrogen

adsorption front moves axially beyond the middle of the

storage and reaches the other end of the bed (closed end), it

looses lot of refrigeration. Consequently, there is steady rise in

bed temperature during the end of the process. Fig. 6 shows the

spatial variation in temperature profile with time during the

charging process. Adsorbent bed at fairly uniform temperature

of 115 K is quickly charged with compressed hydrogen (at 77 K)

without allowing the heat of adsorption to escape out of the

bed. With the progress in charging process, temperature

distribution within the bed becomes extremely inhomoge-

neous as shown in Fig. 6. These results justify the necessity of

transient analysis for the complete process.

5.1. Simulation results of FCV and storage operation

Three adsorption storage vessels on-board are charged with

hydrogen and the vehicle is set to roll on the road. Depending

Fig. 7 – Time variation of the average bed pressure for

different hydrogen flow rate Length of bed [ 1.4 m,

Diameter of bed [ 0.33 m Initial bed temperature [ 115 K,

Pressurised H2 temperature [ 77 K.

on the speed of the vehicle, flow of hydrogen is governed by

the discharge valve. While the car can travel a distance of

500 km using 3.1 kg of stored hydrogen, its consumption

profile varies with the vehicular speed as shown in the first

two columns of Table 1. Simulations are carried out with these

specified flow rates of hydrogen. It has been observed from the

simulation results that the period for which hydrogen stored

in a single cylinder is consumed varies with the speed of the

vehicle. For the obvious reason, car travelling at a lower speed

uses hydrogen for a longer time, while the total distance

travelled by the car with different speed remains same. Fig. 7

shows the time variation of the average bed pressure for the

different flow rates of hydrogen. Simulated results show that

individual tank can support a journey of nearly 166 km using

the fuel stored in it.

6. Conclusion

In this work, adsorption storage of H2 at cryogenic tempera-

ture for fuel cell vehicle application has been studied theo-

retically. Numerical models with appropriate boundary

conditions have been developed for the unsteady state

adsorption and desorption cycles needed for the refilling of

the storage and delivery of H2 from the storage to the fuel cell

stack, respectively. Both adsorption and desorption has been

considered adiabatic. Simulation results using these models

are in good agreement with the results of Lamari et al. [28].

The conceptual design presented in this work includes three

0.33 m� 1.4 m 4 stainless steel storages with a total hydrogen

storage capacity of 3.1 kg. Four average vehicle speeds of 40,

60, 80 and 120 km/hr have been considered for the simulation

of the storage performance. With this stored mass of

hydrogen in the cryosorption storage, the vehicle is expected

to run for 500 km before next refilling.

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Nomenclature

A1: Internal area of the container (m2)A2: Area of the annular section (m2)A¼A1þA2: Total area (m2)Cp: Heat capacity of hydrogen (J/kg K)Cps: Heat capacity of activated carbon (J/kg K)Cpw: Heat capacity of wall (J/kg K)Dax: Axial dispersion coefficient (m2/s)hamb: Heat transfer coefficient between wall and ambient air

(W/m2 s)DH: Heat of adsorption/desorption (J/mol)L: Length of the storage (m)MH2 : Molecular weight of hydrogen (kg/kmol)R: Universal gas constant (J/kg K)T: Temperature (K)Tamb: Temperature of ambient air (K)t: time (s)u: Interstitial velocityq: Amount of gas adsorbed (kmol/kg)3: Void fractionr: Gas density (kg/m3)rs: Adsorbent density (kg/m3)rw: Density of the wall material (kg/m3)