Journal Article

1. 1
An insight into spray pulsed reactor through mathematical
modelling of catalytic dehydrogenation of cyclohexane
Praveen Siluvai Antonya
, Rajiv Ananth Sohonyb
, Rajesh B. Biniwalea
*,
a
Environmental Materials Division, National Environmental Engineering Research Institute,
CSIR, Nagpur 40020, India
b
Environmental Systems Design and Modelling, National Environmental Engineering
Research Institute, CSIR, Nagpur 40020, India
*Corresponding author Tel: +91712-2249885 Extn. 410, Mobile: +919822745768,
Fax: +91712-2249900, Email: rb_biniwale@neeri.res.in
Abstract
A mathematical model has been developed to study the impact of nozzle-catalyst distance
and bulk gas temperature on the conversion and hydrogen evolution rate in a spray pulse
reactor. The effects of reactor configuration and operating parameters on conversion and
evolution rate were predicted with more than 90% accuracy. Reactor optimization and
sensitivity analysis were carried out and an optimal design ofnozzle-catalyst distance 5 cm
and bulk gas temperature of 50 °C were proposed. The optimized design was predicted to
increase the conversion from approximately 32 to 74%. The model could be in general used
fordesigning any endothermic heterogeneous catalytic reaction in a spray pulse reactor.
Keywords:Spray-pulsed reactor, mathematical modelling, heterogeneous catalytic system,
dehydrogenation

2. 2
1. Introduction
Greener fuel is considered as the only alternative to ease the deleterious effect of harmful
pollutants emitted by the use of fossil fuels. Among the various options for greener energy,
hydrogen wasrecognized as one of the potential candidate. In spiteof hydrogen is beingwell
established in industry scale, its storage and transport are limiting its use in many
applications. Among the wider storage & transport options, liquid organic hydride (LOH)
method wasidentifiedas a potential option based on its simplicity and few merits[1]. In LOH
method, hydrogen is transported by hydrogenating aromatic compounds (such as benzene,
toluene, naphthalene etc.) at the hydrogen production source to form cycloalkanes. The
cycloalkanes (such as cyclohexane, methylcyclohexane, decalin etc.) are then transported to
the gasoline station using conventional tankers.In the gasoline station, hydrogen is delivered
back after dehydrogenation and the aromatics are sent back for recycling. The aromatics just
act a carrier for transporting hydrogen from the source to the destination. In the above steps,
dehydrogenation of cycloalkanes is highly endothermic (204 kJ/mole) and considered as a
limiting factor. Thus, from acatalysis &engineering standpoint, efficient dehydrogenation
reactor is considered as a prime importance to make the technology economically feasible.
Different dehydrogenation systems were investigated by researchers in the past with batch,
fixed bed and membrane reactors [2–6]. Although, flow and membrane type reactors were
proposed for continuous production, they suffer from various limitations.The advantages and
limitations of various reactors were summarized by Biniwaleet.al[7]. Among the various
reactors deliberated by the author, spray pulse reactor was proposed as a potential
candidate for the dehydrogenation reaction,owing to its high heat transfer efficiency and
conversion. Knowing the potential of the spray pulse reactor, various research groups
worked on spray pulse reactor to understand the reactor for improving its efficiency. Various
researchworkswere conducted with various catalysts, metal loadings, pulse width and pulse

3. 3
frequency[4,8–17]. These works majorly targeted on developingan efficient catalyst for the
dehydrogenation reaction in a spray pulse reactor by changing the process conditions. Very
few efforts were put to understand the reactor design to improve its efficiency.Understanding
in terms of a deterministic mathematical model is one of the ways to predict the reactor
behaviour at various reactor conditions. To the best of our knowledge a mathematical model
of the spray pulse reactor has not been developed.
Hence, this study, aims to develop mathematical model for the spray pulse reactor with
dehydrogenation of cyclohexane as a model reaction to understand the impact of reactor
parameters on its performance.
2. Experimental
2.1 Catalyst
Pt/Al2O3 was used as catalyst for the dehydrogenation of cyclohexane. The Platinum was
loaded on alumiteusing wet impregnation method. The catalyst was then dried in oven for 2
hours at 90 °C. The catalyst was then activated by purging H2 gas in a closed reactor for 8 h.
For further details on synthesis procedure, please refer to the author’s previous papers[8].
2.2 Experimental set up
The experimental setup used is shown in Fig.1. A catalyst sheet is placed over a heater
plate at the bottom of the reactor. The temperature of the heater plate was controlled using a
PID controller. The reactant was sprayed from the top of the reactor on the catalyst surface
using a spray nozzle. The amount of reactant sprayed and the time interval of spray were
controlled using a pulse controller. The products were removed from the reactorby purging
nitrogen gas. The hydrogen separated from other products passing through the condenser
was quantified using GC-TCD (SHIMADZU make).
The spray pulsed reactor is different than the conventional gas-phase reactor. In

4. 4
conventional gas-phase reactors feed of the reactant is gas-phase (with or without dilution).
The concentration of reactant may be uniform however the reactant-catalysts contact for
gas-solid heterogeneous system is poor, particularly when packed bed is not used. In case
of spray-pulsed reactor, liquid reactant is injected on the heated catalyst surface (particularly
places as a flat mesh/cloth in this case) and gets evaporated on the surface thereby forming
a dense vapour phase on the catalysts surface. This improves the reactant-catalysts contact.
Since intermittent dry-wet conditions can be formed by manipulating spray-pulse injection
frequency the surface of the catalysts can be kept at a high temperature before next spray-
pulse is arrived on the surface. This typical operating characteristics makes spray pulse
reactor as more efficient reactor [11,16].
2.3 Infra-red image capturing& processing
The catalyst surface temperature was recorded with an IR camera (make-Nippon Avionics,
model-Neo thermo). The calibration of the software isprovided in the author’s previous work
on thermal studies[14]. Integral average method option was used to calculate the average
surface temperature as shown in Fig. 2.Software IRT Cronista trial version was used for IR
image analysis.
2.4 Bulk gas temperature and pressure measurement
The bulk gas temperature inside the reactor was measured for validating the energy balance
equations of the spray pulse reactor model. The temperature was measured using Pt-100
thermocouple fixed at the top of the reactor with its sensing end hanging inside the reactor
approximately at half of the height. The pressure was measured using a pressure
transducer.
3. Reactor background theory
The individual processes in the reactor are detailed in this section and also the basis of
model development is explained.

5. 5
3.1 Droplet dynamics
Understanding the droplet dynamics is vital in determining the appropriate heat transfer
equations to be incorporated in the model. The life cycle of droplets inside the reactor is
described in this section. At the start-up, reactant droplets are sprayed on the catalyst
surface with a spray nozzle. The average diameter of the droplets generated from the nozzle
depends on the nozzle characteristics and the weber number[18]. During transit, the droplets
are vaporized due of high heat flux in the reactor. The percentageof droplet vaporized is
controlled by the velocity of the droplet,nozzle-catalyst distance and the dropletphysical
properties[19,20]. The size of the droplets reaching the catalyst surface is reduced due to
evaporation loss during transit. A thin vapour layer is formed around the droplets after
impingement of droplets on the heated catalyst surface as shown in Fig. 3. Due to the thin
vapour layer formation,heat transfer from catalyst surface to droplet is controlled by
conduction[21–23]. The vapourfilmaround the droplets is increased due to the continuous
addition of heat from the catalyst surface. An Increase in the vapour film is followed by the
increase in the loss of vapour at the bottom of the droplet sphere which is also known as
poiseuille flow loss[11,24]. The cycle of increase in vapour film thickness andthe poiseuille
flow lossprogress untilthe whole droplet is consumed on the catalyst surface.Based on the
gross life cycle of the droplets,droplet generation models, transit vaporization loss model and
poiseuille vapour loss modelwere incorporated in the model.
3.2Kinetics
The reaction of cyclohexane on the catalyst surface is given by Eq. (1).
(1)
The gross mechanism of dehydrogenation of cyclohexane on Pt/Alumitesurface is as
follows: Initially, the cyclohexane present in the vapour film around the droplet is adsorbed
on the catalyst surface. The C-H bond in cyclohexane is cleaved to form benzene and

6. 6
hydrogen. Due to the high temperature of the catalyst surface, the hydrogen is immediately
desorbed[11]. Due to the reaction of vapour,the cyclohexane vapour film thickness around
the liquid droplet is decreased. The liquid droplet in the centrethen further vaporizesdue to
the increase in the heat transfer coefficient owing to the decrease in the vapour film
thickness. The above cyclic process of vaporization and reaction persists until whole droplet
is depleted on the catalyst surface.
3.3 Integratedreactor model
Thedroplet dynamics model and the kinetics modelhave to be inter-linkedto the reactor
model to get an integrated model for the spray pulse reactor to get a clear understanding of
the performance of the reactor. For instance, in general large larger nozzle-catalystdistance
results in a large evaporation loss. In such cases, overall conversion is reduced irrespective
of highly selective catalyst. Therefore, this study aims at developing an integrated
mathematical model for optimal designing of the spray pulse reactor. A schematic diagram of
the model development for the spray pulse reactor is shown in Fig. 4.
4. Mathematical modelling
4.1 Kinetics of dehydrogenation of cyclohexane
The rate of the reaction using Pt/Al2O3 in a membrane reactor[25] is shown in Eq. (2).
(( ) )
( )
(2)
Where k, KB and Kp are the reaction rate constant, adsorption equilibrium constant for
benzene and the reaction equilibrium constant respectively. The terms pB, pC and pH are the

7. 7
partial pressures of benzene, cyclohexane and hydrogen in the membrane reactor.In the
spray pulse reactor, as the catalyst is surrounded by reactant vapour, the partial pressure of
H2 and C6H6in Eq. (2) are negligible. The modified rate expression is shown in Eq. (3) for
spray pulse reactor conditions afterincluding the negligible partial pressure condition. The
rate expression derived is zero order with respect to the reactant concentration which agrees
with the zero order rate expression reported by Shukla and group[8] for the spray pulse
reactor.
(3)
The constant k and KB were calculated based on the rate expression Eq. (2).
4.3 Reactor modelling
The key assumptions in the model development are
1. The bulk gas temperature inside the reactor is uniform throughout the reactor.
2. The spray is uniformly distributed on the catalyst surface.
3. The average droplet size generated by the nozzle is approximately same.
The above stated assumption may be justified as follows. At the start up, the reactor was
purged with nitrogen for almost 3 h after the heater was on. Continuous heating of reactor for
3 h is expected to eliminate the local temperature distribution inside the reactor. The uniform
distribution of spray wasassumed due to experimental constraints. In addition, estimating the
spatial distribution of droplets emerging from the nozzle requires sophisticated experimental
set up to study which was not the objective of this work. However, the assumptions were in
fact justified by the reasonably good predictionsimulated by our model.
The bulk gas mass balance is given byEq. (4). In the right hand side part of Eq. (4), first term
is the mass flow rate of nitrogen and the rate of vaporization of unreacted cyclohexane
droplet on the catalyst surface is noted in the second term. The rate of evolution of hydrogen

8. 8
and benzene is shown in the third and fourth term respectively andthe mass flow rate of bulk
gas at the outlet is shown in the final term.
(4)
The droplet diameter from the nozzle was estimated from the sprinkler spray models[18].The
rate of evaporation of droplet during transit was calculated based on the droplet evaporation
models [20]. The rate of vaporization of droplets on the catalyst surface has been estimated
based on the film model [24]. Similarly, for nitrogen the component mass balance is shown
in Eq. (5).
(5)
The component balance of cyclohexane in the bulk gas is shown in Eq. (6).The source term
for the mass balance of cyclohexane (NC_vap) is zero, except during the time of arrival of the
pulse feed. As pulse time is extremely smaller relative to the outlet term in the mass balance,
inclusion of the source term directly will result in convergence problems. Hence, after
calculating the transit vaporization loss, the source term was directly added to the density of
cyclohexane term taking into account of the volume of the reactor.
(6)
The mass balance for the benzene is shown in Eq. (7). The source term for benzene can be
represented by the rate of formation of benzene on the catalyst surface.
(7)

9. 9
Similarly, the mass of hydrogen in the bulk gas is given inEq. (8). The multiplication factor 3
is included to account for 3 moles of hydrogen produced for every one mole
dehydrogenation of cyclohexane.
(8)
The cyclohexane droplet on catalyst surface is depleted due to reaction and Poiseuille flow
as discussed in the reactor theory. The governing equation for liquid cyclohexane on the
catalyst surface is given in Eq. (9).
( ) (9)
Where Nl is the amount of cyclohexane present on the catalystsurface andNl_in is the rate of
liquid cyclohexane input to the catalyst surface.Similar to cyclohexane vapour mass balance,
the input rate term is relatively very high compared to the outlet rate as it is a few millisecond
sprays. Hence, after estimating the transit evaporation loss, the unevaporated quantity was
directly added to the mass of the liquid cyclohexane term. The mass balance equations were
converted into moles for convenience.
The mass and energy balance has to be integrated to obtain a complete model for the spray
pulse reactor. The energy balance for the solid catalyst present on the heater plateis shown
is an Eq. (10). Themeasured values of the bulk gas temperature are listed in table 1.
( ( ))
(10)
The first term on the right hand side of Eq. (10) denotes the rate of heat input to the catalyst,
the second term denotes the rate of heat output from the catalyst due to evaporation and

10. 10
third term denotes the rate of heat output from the catalyst surface due to reaction. The flow
at the outlet is driven by the pressure difference between the reactor and the condenser at
the outlet. Quasi steady state conditions allowed the outlet flow to be determined by Hagen
Poiseuille equation as shown in Eq. (12).
(11)
In Eq.(12), the pressure inside the reactor (PR) was calculated using the ideal gas law. The
partial pressure of each of the component gases required for calculating the total pressure
were estimated from gas phase component mass balance at each time step. The following
initial conditions were used to solve the differential equations (Eq. 4-12).
Before the start-up of the reactor, the nitrogen was purged for 3 h continuously. Hence the
reactor contained was filled with only nitrogen. Therefore, at t=0s
; ; ; ; ;
The formulated equations were solved in Matlab 2010 (b). The equations were discretized by
finite difference scheme and solved using forward Euler’s method. The ordinary differential
equations were solved using time step size 0.01 (s).
5. Results and discussion
5.1 Model validation
The model was validated for catalyst temperature and hydrogen evolution rate. Pulse
frequency of 0.1 Hz and a pulse width of 1ms were maintained during the experiments and

11. 11
simulations. The experimental and predicted hydrogen evolution rates are shown in Fig. 5,
Fig. 6 and Fig. 7 at 300 °C, 330 °C and 375 °C respectively. An unsteady state behaviour is
encountered in the experimental data, due to the accumulation of product gases inside the
spray pulse reactor. In other words, the hydrogen evolution rate from the catalyst surface
was higher compared to the outlet gas flow rate from the reactor. The steady state was
attained after 25th
min, 23rd
min and 18th
min for 300°C, 330°C and 375°C catalyst
temperatures respectively. The quicker steady rate was obtained in 375°C due to the instant
mixing of the product gases compared to lower temperatures. The slightest deviation from
the experimental values at the start up is attributed to the instantaneous mixing assumption
made in the model.
The experimental rate was predicted with high accuracy. R2
values 0.976, 0.950 and 0.966
were obtained for 300 °C, 330 °C and 375 °C respectively. Relatively low R2
values were
observed at high catalyst temperatures due to larger volumetric expansion of gases and
rapid mixing. The deviation was observed in the model due to bulk mixing assumption. Few
small peaks were noted in the experimental values at 330 °C and 370 °C. The differences
are attributed to the instantaneous movement of local hydrogen to the exit.
In addition to the hydrogen evolution, the model was also validated for catalyst temperature
variation. The catalyst temperature was measured with a high resolution IR camera as
explained in the materials and method. The surface temperature of the catalyst was
recorded with respect to time for each pulse. The simulated and experimental values were
compared and shown in Fig. 8, Fig. 9 and Fig. 10 for 300 °C, 330 °C and 375 °C catalyst set
temperatures. At steady state, 278.5 °C, 310 °C and 349 °C were observed on the catalyst
surface for set temperature 300 °C, 330 °C and 375 °C respectively. The difference in
temperature could be attributed to the constant heat loss from the catalyst surface by
convection.

12. 12
Largest temperature drop observed may be attributed to the instantaneous absorption of
available heat of vaporization and heat of reaction. A temperature drop of 3.5 °C, 5 °C and
7.5 °C were observed for catalyst set temperatures 300 °C, 330 °C and 375 °C. A relatively
higher temperature drop trend was observed with the increase in the catalyst set
temperatures. This can be attributed to the large availability of instant heat at 375 °C
compared to 330 °C and 300 °C respectively. A steady state revival time of 6.9, 5.8 and 4.6
seconds were observed for 300 °C, 330 °C and 375 °C respectively. The revival time for the
catalyst were inversely related to the time taken to achieve the set value.This behaviour can
be explained as follows.Assuming the heating rate is same, higher temperature catalyst is
expected to reach the set temperature faster due to the less availability of reactant on the
catalyst surface.
The model predicted the surface phenomenon reasonably well which was substantiated by
the large R2
values. R2
values of 0.763, 0.957, and 0.923 were obtained for 300 °C, 330 °C
and 375 °C respectively. Although the model predicted reasonably well, two slight deviations
were observed. The first deviation was noted in the instantaneous temperature drop and the
second was at the steady state revival time. Analysing the catalyst temperature variation
trends at 300 °C, 330 °C and 375 °C, indicates that the temperature drop was always under
predicted by the model. This can be ascribed to the uniform spray and uniform temperature
distribution assumption in the model as compared to experimental value. The second
deviation was observed in the steady state revival time of different catalyst temperatures. A
quicker steady-state time was observed in the case of 330 °C and 375 °C, whereas in 300
°C the model falls behind the experimental data. The assumption of film boiling heat transfer
regime may be attributed to the observed deviation. However, in actual case, depending
upon the reactants, pressure, and temperature of the system the conditions for film boiling
regime may change. The film boiling ranges were selected and calculated relative to water.

13. 13
5.2 Performance analysis of the reactor
The model developed was then applied for optimizing the reactor and sensitivity analysis.
The percentage of reactant vaporized at 17 cm nozzle-catalyst distance is shown in Fig. 11.
It clearly depicts that almost 58% of the reactant is vaporized before reaching the catalyst
surface at 370 °C. Large vaporization is observed due to the high temperature of the bulk
gas surrounding the travel path of the droplets. It clearly indicates that the vaporization
losses in a spray pulse reactor have to be minimized to achieve high conversion. The
economy of the LOH process is also increased as it facilitates the separation of hydrogen
from the least amount of product gas.The above objectives can be attained simply by
optimizing the nozzle-catalyst distance and bulk gas temperature.A standard condition of 0.1
Hz and 1 ms was used throughout the simulation based on the experimental conditions
employed.
5.2.1. Nozzle-catalyst distance
The nozzle-catalyst distance is addressed as just distance during the discussion for
convenience. The distance is identified as an important parameter due to its large influence
on conversion and evaporation loss. The percentage of reactant vaporized during transit at
different distances is shown in Fig. 12. It should be noted that the relationship between
evaporation loss and distance is almost linear in the graph. This is feasible because travel
time is increased by the increase in distance which in turn increases the heat input to the
droplets. The above scenario may well suit to the current experimental set up as the linear
relationship can’t be generalized. Nevertheless, the evaporation loss is dependent on the
droplet size, reactor temperature, surface tension and density of the droplet, and evaporation
regime which are not discussed in detail in this study.
It is shown in Fig. 12 that almost 58% of the reactants are vaporized at 17 cm nozzle
distance. Simulation studies revealed that only 5% of the reactants are vaporized at a
nozzle-catalystdistance of 1 cm compared to 58% at a distance of 17 cm. Hence it is evident

14. 14
that, evaporation loss is largely curtailed by reducing the distance. Although evaporation loss
is very low at 1 cm, catalyst coverage is reduced at such short distance.In addition, at lower
distances, the droplet formation ability of nozzle will also be lessened. This decrease in the
droplet formation ability will be accompanied by the formation of liquid pool on the catalyst
surface and reduction in the overall conversion. Hence, there an optimum distance has to be
maintained to enhance coverage area and proper droplet formation. This optimum distance
is defined by the property of the nozzle. Based on the sheet break distance of the nozzle, the
nozzle-catalyst distance is calculated[18] from Eq. (13).
(12)
Where rbu is the sheet break up distance, Do is the orifice diameter, We is the weber number
of the jet and C is the proportionality constant depending upon the orifice used.In the present
study, an optimal distance of 5 cm was used based on the nozzle spray property and
feasibility.Maximum conversion is not ensured by maintaining a minimum sheet breaking
distance as it is just a criteria for droplet formation. Although the droplets are formed, they
focus on a very small area on the catalyst surface. Hence, the catalyst coverage area of the
nozzle has to be increased by increasing the spray angle of the nozzle. A comparative
conversion bar chart is shown in Fig. 13 at initial height (H1) with initial spray angle (Ѳ),
optimal height (H2) with initial spray angle and optimal height with optimal spray angle (ф). It
is clearly evident that the conversion is more than doubled by optimizing the height and
increase the nozzle spray angle. The results clearly demonstrate that high conversion can
be achieved by optimization of nozzle-catalyst distance.
5.2.2. Bulk gas temperature
The overall conversion of the spray pulse reactor is majorly reduced by the evaporation loss.
Although this problem has been looked upon by reducing the distance, it has its own
limitations on minimum sheet breaking distance as discussed in the previous section.

15. 15
Nevertheless, the vaporization can also be controlled by decreasing the bulk gas
temperature. The effect of bulk gas temperature on evaporation loss is shown in Fig. 14 at
375 °C and nozzle-catalyst distance 5 cm. An optimized nozzle-catalyst distance of 5 cm
was used throughout the bulk gas temperature simulations. A linear relationship is observed
between the bulk gas temperature and the evaporation loss. This is corroborated by the
proportional relationship between heat transfer and temperature difference. The slightest
deviation from the linear behaviour may be attributed to the nonlinear dependence of heat
transfer coefficient on droplet variables and dynamic conditions.
A graph of evaporation loss versus bulk gas temperature is shown in Fig. 14, where
evaporation loss is 20% at 210 °C, whereas as at 50 °C, the loss is just 5 %. The decrease
in the evaporation was observed due to the decrease in the driving force for evaporation.
The influence of bulk gas temperature on the overall conversion is clearly indicated by the
above results. It should be noted that there is a 3 time decrease in evaporation loss from 210
°C to 50 °C. Therefore, high conversion can only be achieved not only by optimizing nozzle-
catalyst distance but also bulk gas temperature.
6. Conclusions
A mathematical model has been developed for the spray pulse reactor. The simulation
results were validated with the hydrogenevolution rate and catalyst temperature dynamics.
The underlying phenomena of the reaction were sufficiently explained by the model. The
optimized operating conditions have been revealed by the model. 5 cm nozzle-catalyst
distance, 50 °C bulk gas temperature and 375 °C catalyst temperature were found to be
optimum. This work may be taken as a based study for the future modelling research, so that
a more rigorous model could be developed for the spray pulse reactor useful for endothermic
catalytic reaction.Although we have used cyclohexane as candidate LOH, theresults of this
study are useful for other LOHs.

16. 16
Acknowledgements
The funds provided by MNRE, New Delhi for the present project is acknowledged.
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Nomenclature
1. Model parameters
QN_in 100 Nitrogen input rate (ml/min)
MwN 28 Molecular weight of N2 (g/gmol)
MwB 78 Molecular weight of Benzene (g/gmol)
MwC 84.15 Molecular weight of cyclohexane (g/gmol)
MwH 2 Molecular weight of hydrogen (g/gmol)
VR 1.5 Volume of the reactor (l)
Dcat 2 Diameter of the catalyst surface(mm)
R 8.314 Universal gas constant (J/mol/K)
λc 32 Latent heat of vaporization of cyclohexane (kJ/mol)
∆HR° 206
Standard heat of reaction for dehydrogenation of
cyclohexane (kJ/mol)
ρN_in 1.165 Density of nitrogen at the inlet (kg/m3
)
CPcat 1100 Average specific heat of the catalyst (J/mol/K)
Cpc_l 156 Specific heat of liquid cyclohexane (J/mol/K)
Cpc_v 105.3 Specific heat of gaseous cyclohexane (J/mol/K)
CpN 1.04 Specific heat of nitrogen (J/mol/K)
CpB 82.44 Specific heat of benzene gas (J/mol/K)
CpH 14.5 Specific heat of hydrogen (kJ/kg/K)
Pa 101325 Atmospheric pressure (Pa)

20. 20
Lpi 300
Length of the outlet pipe from the reactor outlet to the
exit(mm)
dpi 3.175 Diameter of the pipe (mm)
µbulk 0.0005 Approximate bulk gas viscosity (Pa s)
Dnoz 0.2 Diameter of the nozzle (mm)
Vf 0.0453 Total volume of the feed per pulse (cm3
)
tp 0.001 Time interval between pulse arrival (s)
Ea 40 Activation energy of the reaction (kJ/mol)
Nc 2.68 Cyclohexane feed rate (mmol/min)
Kcat 3 Average thermal conductivity of the catalyst(W/m/K)
Kc_v 0.0350 Thermal conductivity of cyclohexane vapour(W/m/K)
Kl 0.121 Thermal conductivity of liquid cyclohexane (W/m/K)
mcat 1 Mass of the catalyst (g)
dnoz_cat 170 Distance between the nozzle and the catalyst (mm)

21. 21
2. Model Variables
ρbulk Average bulk density of the gases inside the reactor(kg/m3
)
QN_in Volumetric flow rate of nitrogen at the inlet (m3
/s)
Qout Volumetric flow rate of the reactor gases at the outlet (m3
/s)
Rc Rate of reaction of cyclohexane on the catalyst surface (mol/s)
ρN Average density of nitrogen inside the reactor(kg/m3
)
ρc Average density of cyclohexane inside the reactor (kg/m3
)
tp Time at which the reactant is sprayed on the catalyst surface (s)
ρB Average density of benzene inside the reactor (kg/m3
)
ρH Average density of hydrogen inside the reactor (kg/m3
)
Nvap Amount of reactant that is vaporized before reaching the catalyst (mol)
Mwbulk Average molecular weight of the bulk gas inside the reactor(g/gmol)
Nc_vap Rate of vaporization of cyclohexane from the catalyst surface (mol/s)
ρN Average density of nitrogen inside the reactor (kg/m3
)
∆Tfilm Temperature difference between the catalyst surface and the boiling point
of the cyclohexane (°C)
Rd Radius of the droplet present on the catalyst surface (m)
Nl Amount of liquid cyclohexane droplets present on the catalyst surface (mol)
Th Steady state temperature of the catalyst surface for a fixed set temperature
(°C)
Tcat Temperature of the catalyst surface (°C)
XC Thickness of the catalyst (m)
List of tables
Table 1 Reactor bulk gas temperatures for various catalyst set temperatures

22. 22
List of figures
Fig. 1 Experimental Set up
Fig. 2 Infra-red image of the catalyst surface
Fig. 3. Vapour film formation and reaction of cyclohexane droplets on the catalyst
surface
Fig. 4. Model development methodology
Fig. 5. Predicted and experimental hydrogen evolution rate for 0.1 Hz and catalyst set
temperature of 300 °C
Fig. 6. Predicted and experimental hydrogen evolution rate for 0.1 Hz and catalyst set
temperature of 330 °C
Fig. 7. Predicted and experimental hydrogen evolution rate for 0.1 Hz and catalyst set
temperature of 375 °C
Fig. 8. Predicted and experimental catalyst temperature for 0.1 Hz and catalyst set
temperature of 300 °C
Fig. 9. Predicted and experimental catalyst surface temperature for 0.1 Hz and catalyst
set temperature of 330 °C
Fig. 10. Predicted and experimental catalyst surface temperature for 0.1 Hz and catalyst
set temperature of 375 °C
Fig. 11. Effect of catalyst set temperature on reactant vaporization loss at nozzle-catalyst
distance 17 cm, 0.1 Hz pulse width
Fig. 12. Effect of nozzle-catalyst distance on reactant vaporization loss at 0.1 Hz and 375
°C catalyst temperature
Fig. 13. Effect of nozzle-catalyst distance and spray coverage on cyclohexane conversion
Fig. 14. Effect of bulk gas temperature on conversion and vaporization loss

23. 23
Fig. 1
Fig. 2

24. 24
Fig. 1
Fig. 3
Fig. 4

25. 25
Fig. 5
Fig. 6
0
0.5
1
1.5
2
2.5
0 20 40 60
Hydrogenevolutionrate
(mmol/min)
Time (min)
Experimental
Predicted
0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60
Hydrogenevolutionrate(mmol/min)
Time (min)
Experimental
Predicted

26. 26
Fig. 7
Fig. 8
0
0.5
1
1.5
2
2.5
3
0 10 20 30 40 50 60
Hydrogenevolutionrate(mmol/min)
Time (min)
Experimental
Predicted
270
272
274
276
278
280
0 2 4 6 8 10
Catalystsurfacetemperature(°C)
Time (s)
Experiement
Predicted

27. 27
Fig. 9
Fig. 10
300
303
306
309
312
0 2 4 6 8 10
Catalystsurfacetemperature(˚C)
Time (s)
Experiment
Predicted
340
344
348
352
356
360
0 2 4 6 8 10
Catalystsurfacetemperature(˚C)
Time (s)
Experiment
Predicted

28. 28
Fig. 11
Fig. 12
40
45
50
55
60
250 290 330 370
Reactantvaporized(%)
Catalyst surface temperature (˚C)
0
10
20
30
40
50
60
70
1 3 5 7 9 11 13 15 17
Reactantvaporized(%)
Nozzle-catalyst distance (cm)
Vaporized (%)

29. 29
Fig. 13
Fig. 14
32.06
17.12
61.51
0
10
20
30
40
50
60
70
H1/Ѳ H2/Ѳ H2/ф
Cyclohexaneconversion(%)
Nozzle-catalyst distance/Angle of spray
0
5
10
15
20
25
60
62
64
66
68
70
72
74
76
0 50 100 150 200 250
Reactantvaporized(%)
Reactantconversion(%)
Bulk gas temperature (˚C)
Conversion (%)
Vaporized (%)

30. 30
Table 1.
Catalyst set
temperature(°C)
Average catalyst
Surface temperature
(°C)
Reactor bulk
temperature (°C)
375 356 210
330 310 183
300 278 167