1

An insight into spray pulsed reactor through mathematical

modelling of catalytic dehydrogenation of cyclohexane

Praveen Siluvai Antonya, Rajiv Ananth Sohonyb, Rajesh B. Biniwalea*,

aEnvironmental Materials Division, National Environmental Engineering Research Institute,

CSIR, Nagpur 40020, India

bEnvironmental 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

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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

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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

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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.

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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

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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

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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

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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)

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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

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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

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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.

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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.

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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

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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.

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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.

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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)

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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

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

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

Fig. 1

Fig. 2

24

Fig. 1

Fig. 3

Fig. 4

25

Fig. 5

Fig. 6

0

0.5

1

1.5

2

2.5

0 20 40 60

Hyd

rog

en

evo

luti

on

ra

te

(mm

ol/m

in)

Time (min)

Experimental

Predicted

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60

Hyd

rog

en

evo

luti

on

ra

te (

mm

ol/

min

)

Time (min)

Experimental

Predicted

26

Fig. 7

Fig. 8

0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60

Hyd

rog

en

evo

luti

on

ra

te

(mm

ol/

min

)

Time (min)

Experimental

Predicted

270

272

274

276

278

280

0 2 4 6 8 10

Cata

lys

t s

urf

ac

e t

em

pe

ratu

re (

°C)

Time (s)

Experiement

Predicted

27

Fig. 9

Fig. 10

300

303

306

309

312

0 2 4 6 8 10

Cata

lys

t s

urf

ac

e t

em

pe

ratu

re (

˚C)

Time (s)

Experiment

Predicted

340

344

348

352

356

360

0 2 4 6 8 10

Cata

lys

t s

urf

ac

e t

em

pe

ratu

re (

˚C

)

Time (s)

Experiment

Predicted

28

Fig. 11

Fig. 12

40

45

50

55

60

250 290 330 370

Rea

cta

nt

va

po

rize

d (

% )

Catalyst surface temperature (˚C)

0

10

20

30

40

50

60

70

1 3 5 7 9 11 13 15 17

Rea

cta

nt

va

po

rize

d (

%)

Nozzle-catalyst distance (cm)

Vaporized (%)

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

Cyc

loh

ex

an

e c

on

ve

rsio

n (

%)

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

Rea

cta

nt

va

po

rize

d (

%)

Rea

cta

nt

co

nve

rsio

n (

%)

Bulk gas temperature (˚C)

Conversion (%)

Vaporized (%)

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