International Journal of Engineering and Technology Volume 4 No.

12, December, 2014

Modeling of Non-isothermal Continuous Stirred Tank Adsorption Tower

(CSTAT) for Sulphur trioxide Hydration using Vanadium Catalyst
Goodhead, T.O. and Abowei, M.F.N
Department of Chemical/Petrochemical Engineering
Rivers State University of Science & Technology
Port Harcourt, Nigeria

ABSTRACT

This paper presents development of design equations to evaluate the performance of Non-isothermal continuous stirred tank
adsorption tower (CSTAT) for sulphuric acid production from sulphur trioxide hydration using vanadium catalyst. The
performance parameters as a function of kinetics data considered in this work include reactor volume, height, space velocity,
space time and heat duty. Model performance equation were developed to determine the functional parameters of the reactor.
The developed performance models were simulated using Matlab R2007B within the operational limits of conversion degree
and other kinetic parameters. The results of simulation demonstrated reproducible behavior as adsorption tower functional
dimensions have prefect correlation to each other.

Keywords: Modelling Non-Isothermal CSTAT Sulphuric Acid

1. INTRODUCTION of sulphur dioxide to sulphur trioxide in fixed bed catalytic

reactors (Charles 1977) and (Fogler 1994)
Sulphuric acid is a very important commodity chemical and The stoichiometric Chemistry for the production of sulphuric
indeed, a nations sulphuric acid production is a good indicator acid is presented, thus;
of its industrial strength (Chenier, 1987). Hence the continue
search for the development of suitable design model to optimize
its production capacity (Austin 1984). Previous works of
S O2
SO2
Goodhead and Abowei (2014) focused, development of design
models for H2SO4 production based on semi batch, Isothermal
plug Flow (IPF) and Non isothermal plug flow (NIPF). The most SO2 1
2 O2
SO3
recent similar work of (Goodhead and Abowei 2014)
recommended further modification on the model equations. In 1
this present paper, we considered development of non-
isothermal Continuous Stirred Tank adsorption tower (CSTAT)
primarily to evaluate the performance of the tower as a function H 2O S O3
H 2 SO4
of kinetic parameters.
Through the years, several catalyst formulations have been
2. KINETICS EVALUATION employed, but one of the traditional catalytic agents has been
Vanadium pentoxide (V2O5) (Dueker and West 1975). Its
principal applications include; ore processing, fertilizer
manufacturing, oil refining, waste water processing, chemical
Great deal of work is reported on the kinetics aspect of H2SO4
synthesis etc. [Faith, 1965].
Industrial scale production and it is dependent on the oxidation

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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

The general schematic presentation for the production of sulphuric acid is given below.

Air

Figure 1: Contact process for making sulfuric acid and Oleum from sulfur.

In the industrial chemical process, heterogeneous fluid-fluid that the irreversible biomolecular nature of the reaction have Hr
reactions are made to take place for one of three reasons. First, = -25kcal/mol at 250C.
the product of reaction may be a desired material. Such reactions
are numerous and can be found in practically all areas of the Following the outcome of the work of Chenier [1987] as cited
chemical industry where organic and inorganic synthesis are above, the rate expression for the formation and production of
employed. Fluid-fluid reactions may also be made to take place sulphuric acid is summarized as in equation (3).
to facilitate the removal of an unwanted component from a fluid.
Thus the absorption of a solute gas by water may be accelerated -RA = K2 SO3 H 2O 3
by adding a suitable material to the water which will react with
the solute being absorbed. The third reason for using fluid-fluid
systems is to obtain a vastly improved product distribution for Hence from equation (2.33) the amount of SO3 and H2O that have
homogeneous multiple reactions than is possible by using the reacted at any time t can be presented as;
single phase alon

The reaction mechanism as presented in equation (2.28) showed RA K2 C A0 C A0 X A C Bo C A0 X A

chain reaction character is tics [Austin, 1984]. Gibney and
ferracid (1994) reported on the photo-catalysed oxidation of 4
SO32- by (dimethyl-glyoximato) (SO3)23- and its (Co(dimethyl-
glyoximato) (SO3)32. Where
The work adopted inverse reaction for the kinetic data CAo = Initial concentration of SO3 (moles/Vol)
generation, thus.
CBo = Initial concentration of H2O ( moles/Vol)

SO3 H 2O
H 2 SO4 2 XA = Fractional conversion of SO3 (%)

-RA = Rate of disappearance of SO3 (mole/ Vol/t)

is described as irreversible bimolecular chain reaction. Further
research into the works of Erikson, [1974] and Huie, et al In this work, the rate expression (-RA) as in equation (4) will be
[1985] established the reaction as second order reaction with rate used to develop the hypothetical semi-batch reactor, continuous
constant K2 = 0.3 mole/sec. performed abinitio calculation and stirred tank reactor and plug flow reactor design equations with
determined the energetic barrier and established conclusively inculcation of the absorption coefficient factor as recommended
in the works of Coulson and Richardson (1978). This is achieved
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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

by modifying equation (4) as illustrated below. The hypothetical

concentration profile of the absorption of sulphur trioxide by
steam (H2O) is represented in figure.2

Liquid film

CBi Liquid (steam)

Inter face
Concentration
Gas (SO3) CAi

ZL
Gas Film CBL

r
Distance normal to phase boundary

Figure 2: Absorption with chemical Reaction

Sulphur trioxide (A) is absorbed into the steam (B) by diffusion. Therefore the effective rate of reaction by absorption is defined by

RA
rDL
C Ai C AL rK L (C Ai C AL ) 5
ZL

Invoking the works of Krevelen and Hoftyzer, the factor r is related to C Ai, DL and KL to the concentration of steam B in the bulk liquid
CBL and to the second order reaction rate constant K2 for the absorption of SO3 in steam solution. Thus

K 2 DL C BL
1
2
r = KL . 6

Substituting equation (5) into (6) results in

1 1 1
- RA = (CA) CBL2 K 2 2 DL2 .. 7

Previous reports [ Octave levenspiel 1999] showed that the amount of SO 3 (CA) and steam (CBL) that have reacted in a bimolecular type
reaction

with conversion XA is CAO XA. Hence equation (7) can be rewritten as

K 2 2 D L2 C BO C AO X A 2 C A0 C A0 X A
1 1 1

- RA =

8
(m X A ) (1 X A ) .
1 1 3 1
= K 2 2 DL2 C A0 2 2

Where

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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

CB0
m=
C A0
m =- The initial molar ratio of reactants

-RA = Rate of disappearance of SO3

K2 = Absorption reaction rate constant

DL = Liquid phase diffusivity of SO 3.

KL = Overall liquid phase mass transfer coefficient

r = Ratio of effective film thickness for absorption with chemical reaction.

3. MATERIALS AND METHOD

3.1 Development of Performance Model

3.1.1 Reactor Volume

For non-isothermal operation of the continuous stirred tank reactor, the reactor volume model is obtained from the auto-thermal balance
principle (Conlson & Richardson, 1979), which is expressed mathematically as:

Rate of heat Rate of heat Rate of heat

Production = Removal by out + Removal by 9

By reaction Flow of product Heat transfer

But,

rate of heat production by reaction = ( -HR) RAVR 10

rate of heat removal by out flow of product = G PCP (T-To) 11
rate of heat removal by heat transfer = UAt (T-Tc) 12

Equation (10- 12), Which upon substitution into equation (9) gives

( -HR) RAVR = GPCP (T-T0) + U At (T-Tc) 13

From which,

GPCP T T0 UAt T Tc
VR = 14
H R RA
Recall that

C A20 m X A 1 X A
1 1 3 1
2 2
- RA = K 2 DL 2 15

Putting equation (15) into (14) yields

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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

G p C p T T0 UAt T Tc
VR = 16
H R m X A 2 1 X A
1 1 3 1
2 2 2
K 2 D L C A0
Where,
GP = Mass flow rate of product, (Kg/sec)
CP = Specific heat of product, (KJ/Kg K)
U = Overall heat transfer coefficient of material, (KJ/Sec m3K).
At = Effective area of heat transfer, (m2)
XA = Conversion degree
T = Operational temperature of reaction, (K)
T0 = Initial temperature of reaction, (K)
Tc = Temperature of cooling fluid, (K)
HR = Heat of reaction, (KJ/mol)
CA0 = Initial concentration not SO3, (mol/m3)
K2 = Absorption reaction rate constant, (1/sec)
DL = Liquid phase diffusivity of SO 3, (m2/sec)
m = Initial molar ratio of reactants.

3.1.2 Reactor Height

Considering a reactor with cylindrical shape we have

VR = r 2 h 17

VR
h = 18
r 2
Putting equation (16) into equation (18) results in

G p C p T T0 UAt T Tc
h = 19
r 2 H R K C A20 m X A 1 X A
1 1 3 1
2 2
2 D L
2

3.1.3 Space Time

The space time Ts is mathematically defined (octave levenspiel, 1986 and coulson & Richardson, 1979) as

Volume of reactor VR
Ts = = 20
Volumetric flow rate V0

But

Mass flow rate of reaction Mixture G

V0 = = 21
Density of reaction mixture p
Putting equation (21) into (20) results in

p
Ts = VR 22
Gp

Substituting equation (16) into (22) gives

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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

p G pC p T T0 UAt T Tc
Ts = 23
H R GP K C A20 m X A 1 X A
1 1 3 1
2 2
2 D L
2

3.1.4 Space Velocity

This is the reciprocal of the space time, T s and expressed mathematically as

1 V
Vs = 0 24
Ts VR

Then, from equation (23) it is possible that,

H R G p K C A20 m X A
1 X A
1 1 3 1
2 2
2 D L
2

p G pC p T T0 UAt T Tc
Vs = 25

3.1.5 Heat Generation Per Reactor Volume

The steady state heat generation model for reactor is given (Rase, 1977) as

Q = (-Hr) FA0 XA 26

The heat generation per reactor volume is obtained by dividing both sides of equation (26) by the reactor volume, i.e

Rq = Q

H R FA0 XA 27
VR VR

Putting equation (16) into (27) results in

H R 2 FA0 X A K 22 D 22 C A20 m X A 1 X A
1 1 3 1
2
Rq = 28
G pCP T T0 UAt T Tc

Figure 4 demostrates hypothetical non-isothermal continuous stirred tank adsorption tower(CSTAT) for sulphur trioxide hydration process.

Fig. 3 Hypothetical model of a Jacketed CSTAT

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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

The computation of the functional parameters of the reactor as computational procedure is given in Fig 4 Performance
dimensions such as reactor volume, length, space time, space
shown in figure velocity, heat generation per unit volume, and heat exchanger
functional parameters capable of maintaining non-isothermal
conditions were cleverly inculcated into the computer algorithm.
3.2 Computational Method The equations of these performance measures were expressed as
a function of fractional conversions and characteristic
operational temperature.
The developed models as presented in section 3.1 were
programmed using MATLAB, and the flow chart describing the

START

READ
Gp, Cp, Tc, Vo, U, AT, T0, CAO,
HR, K2, DL, M, D1

INITIALIZE
XA = 0.95
T = 313

PRINT
T; XA; VR, h; Ts; Vs;
QG ; RQ

XA = XA + 0.01

No XA. > 0.99

Yes
T = T + 10

T > 363
Yes
STOP

Figure:4 Flow chart Describing the computational procedure of non-Isothermal CSTAT performance dimension

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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

3.2.1 Input parameter Evaluation

The reactor performance models were evaluated with variables obtained from stoichiometric calculations from the reaction mechanism
presented in section 1 equation 2. Such functional variables inculcated into the computer algorithm for the purpose of simulation of the
performance dimensions include molar flow rate, concentration etc.

Table 4.1 Design functional variables

Quantity Symbol Value Unit

Effective Heat Transfer Area At 1.15 m2
Specific Heat of product (Conc H2SO4) Cp 1.38 KJ/KgK
Specific Heat of cooling fluid Cpc 4.2 KJ/KgK
Initial concentration of SO2 CA0 16,759 mol/m3
Fractional change in volume A -0.5
Product mass flow rate Gp 0.3858 Kg/sec
Operational temperature of reaction T 313 to 363 K
Initial temperature of reactants T0 303 K
Initial temperature of cooling fluid T0 298 K
Heat of reaction HR -88 Kj/mol
Overall Neat Transfer coefficient U 6.945 Kj/Secm2
Product Density (H2SO4) p 1.64x103 Kg/m3
Absorption reaction rate constant K2 0.3 1/sec
Conversion degree XA 0.95 - 0.99 %
Reactant molar flow rate FA0 3.937 mol/sec
Cooling fluid density c 1000 Kg/m3
Diameter of tubular reactor Di 0.02 to 0.1 m
Molar ratio of reactants m 1.0 to 1.5
Radius of CSTR and SBR r 0.1 to1.0 m
Liquid phase diffusivity of SO3 DL 17 m2/Sec
Volumetric flow rate of reactants V0 2.352 x10-4 m3/Sec
Specific heat capacity of H2O Cpw 4.2 KJ/KgK
Viscosity of H2SO4 at 90oC a 5 x 10-3 Kg/m.sec
Viscosity of H2O at 600C w 5 x 10-4 Kg/m.sec
Thermal conductivity of H2O at 200C Kw 0.6 w/mK
0
Thermal conductivity of H2SO4 at 27 C Ka 0.25 W/mK
Thermal conductivity of Hastelloy KH 11.0 W/mK

4. RESULTS AND DISCUSSION were designed with hastelloy because it has excellent corrosion
and sulphuric acid resistance properties.
Industrial reactors for the production of sulphuric acid over a The reactors performance models developed in chapter three
range of reaction time t = 60 to 1800 Sec, degree of conversion were simulated with the aid of MATLAB R2007b. The results
XA = 0.95 to 0.99 and operating temperature T = 313 to 363K provided information for the functional reactors parameters viz:
have been investigated and designed. The reactors have a The reactor volume and the rate of heat generation per unit
capacity of 1.389x103 Kg/hr of sulphuric acid. These reactors volume of the continuous reactors and the semi-batch reactor.
The reactor length, space time, and space velocity for the
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 International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

continuous reactors, while the height of reactor were obtained for operating temperature T and degree of conversion within the
the continuous stirred tank reactors and the semi-batch reactor. limits t, T and XA as specified. A plot of heat generation RQ
Similarly, information for the pressure drop in the plug flow versus operating temperature T was curvilinear and found to be
reactor, whose diameter Di was varied from 0.02 to 0.1 m was increasing with increasing operating temperature T within the
also obtained. Suitable heat exchangers were also designed for range of XA = 0.95 to 0.99. Similar plots were made RQ versus
the isothermal reactors and the semi-batch reactor to remove the XA within the range of T = 313 to 363K. The graphs were also
heat of reaction occasioned during the process. It is the purpose curvilinear with negative gradient. At fairly above 99%
of this section to present and discuss the results of the reactor conversion of sulphur trioxide, there was a sharp drop tending to
types and the heat exchangers and to compare their performance. the abscissa of the graph. This behavior explains the infinity of
the rate of heat generation per unit reactor volume at 100%
The functional parameters of the reactors are tabulated in figures degree of conversion of sulphur trioxide. Finally the rate of heat
17, 18, 19, 20, 21, 22, 23, and 24. And appendix 1-2. The results generation per unit reactor volume decreases with increasing
showed that the reactor volume is dependent on operating reaction time and degree of conversion within the range of
temperature T and degree of conversion X A. The volume of the temperature as specified.
reactor would tend to infinity at 100% conversion. The variation
of the reactor volume, as a result of sulphur trioxide addition to Figures 5 to 10 illustrated the variation of space time with
water, with reaction time, operating temperature and degree of operating temperature and degree of conversion X A as specified
conversion is illustrated in figures 5, 6, 7, 8, 9, 10, 11, and 12. within the range of T = 313 to 363K and XA = 0.95 to 0.99. The
From the results it was observed that volume of the reactors plots were curvilinear as well within the range of T and XA
increases with increasing degree of conversion and decreases investigated. However, for the addition of sulphur trioxide to
with increasing operating temperature. This characteristic water, the highest conversion was observed for the highest space
behavior was observed to be in agreement with the usual reactor time with the lowest operating temperature.
prototypes dependable features of performance parameters vis-
avis the kinetic data (Abowei 1989). The space time TS, was observed to be increasing with
increasing degree of conversion and decreases with increasing
Figures 11 and 12 illustrated the variation of heat generation per operating temperature within the range specified.
unit volume of the reactors as a function of reaction time t,
-3
x 10
1.4

1.2
REACTOR VOLUME (m3)

1
xA=95
xA=96
0.8 xA=97
xA=98
xA=99
0.6

0.4

0.2

0
310 320 330 340 350 360 370
TEMPERATURE (K)

Figure 5: Plots of Reactor Volume against Temperature for Non-Isothermal CSTAT

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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

-4
x 10
1.8
313
323
1.6
333
343
1.4
REACTOR VOLUME (m3) 353
363
1.2

0.8

0.6

0.4

0.2

0
0.94 0.95 0.96 0.97 0.98 0.99 1
CONVERSION DEGREE

Figure 6: plot of Reactor Volume against Conversion Degree for Non-Isothermal CSTAT

xA=95
4
SPACE TIME (sec)

xA=96
xA=97
xA=98
3 xA=99

0
310 320 330 340 350 360 370
TEMPERATURE (K)

Figure 7: Plots of Space Time against Temperature for Non-Isothermal CSTAT

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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

0.8
313
323
0.7
333
343
0.6 353
363
SPACE TIME (sec)

0.5

0.4

0.3

0.2

0.1

0
0.94 0.95 0.96 0.97 0.98 0.99 1
CONVERSION DEGREE

Figure 8: Plot of Space Time against Conversion Degree for non-isothermal CSTAT

35

30
xA=95
xA=96
25
SPACE VELOCITY(sec-1)

xA=97
xA=98
xA=99
20

15

10

0
310 320 330 340 350 360 370
TEMPERATURE (K)

Figure 9: Plots of Space Velocity against Temperature for Non-Isothermal CSTAT

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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

35
313
323
30 333
343
353
25 363
SPACE VELOCITY (sec-1)

20

15

10

0
0.94 0.95 0.96 0.97 0.98 0.99 1
CONVERSION DEGREE

Figure 10: plot of Space Velocity against Conversion Degree for non-Isothermal CSTAT

7
x 10
4.5
HEAT GENERATED PER UNIT VOLUME(kJ/sec.m3)

4
xA=95
xA=96
3.5
xA=97
xA=98
3
xA=99

2.5

1.5

0.5

0
310 320 330 340 350 360 370
TEMPERATURE (K)

Figure 11: Plots of Heat Generated per unit Volume against Temperature for Non-Isothermal CSTAT

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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

7
x 10
4.5

HEAT GENERATED PER UNIT VOLUME (kJ/sec.m3)

313
4 323
333
3.5 343
353
3 363

2.5

1.5

0.5

0
0.94 0.95 0.96 0.97 0.98 0.99 1
CONVERSION DEGREE

Figure 12 plot of Heat Generated per Unit Volume against Conversion Degree for non-Isothermal CSTAT

The consideration of non-isothermity of the reactors is Critical examination of the results of the reactor types
a reasonable assumption as long as the operation of the gives the following analysis:
reactors is within the sonic limit. An observation
deduced from this work is that the operating a. At the same operating temperature, change in
temperature tends to influence the reactor performance. degree of conversion, XA from 0.95 to.0.99
Generally the operation is favoured by low temperature. curvilinearly increases the reactor volume and
This confirms the reason why heat exchangers should space time of the non-isothermal CSTAT, while
be incorporated in the design. The consideration of the the rate of heat generation per reactor volume and
optimum limit of degree of conversion X A from 0.95 to space velocity decreases by the same proportion.
0.99 is reasonable because at 100% conversion of b. At the same degree of conversion, change in
sulphur trioxide, the functional parameters of the operating temperature from 313 to 363K linearly
reactors will all tends to infinity. In this case the increases the reactor volume and space time of the
dimensions of the reactors have no limit. non-isothermal CSTAT, while the rate of heat
generation per reactor volume and space velocity
Work free days of 65 is allowed to produce the specified decreases curvilinear by the same proportion.
quantity i.e. 1.389 x 103Kg/hr of sulphuric acid. Sulphur
trioxide, SO3 can be produced by catalytic oxidation of 5. CONCLUSION AND
sulphur dioxide using vanadium pentoxide as catalyst. RECOMMENDATION
From the results of the computation for the non- Model equation for the design of non-isothermal
isothermal CSTAT it was found that; if the degree of CSTAT have been proposed for the production of
conversion, XA was 0.95, the operational temperature, sulphuric acid via sulphur trioxide hydration process
T was 313K, the reactor volume, VR were 2.5957E- using vanadium catalyst. Computer programs were
05m3 and 7.8263E-06m3 when the reactant molar ratio, developed and utilized to simulate the performance
m=1.0 and 1.5 respectively but increase of X A, and T parameters over a temperature interval of T=313 to
resulted in increase of the reactor volume up to 363K, and conversion degree, XA=0.95 to 0.99. The
1.1432E-04 to 1.2781E-03m3 when m=1.0, T=363K result of the performance evaluation parameters shows
and XA= 0.95 to 0.99 and 3.4469E-05 to 1.7897E-04m3 the usual dependable characteristics of the kinetic data.
when m=1.5. Further work need to be done to evaluate the
performance of the various adsorption towers as a
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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

function of the kinetic parameters with the aim of

establishing the optimum operational limit of Erikson, T. E. (1974), Chem Soc, Faraday Trans. I, 70,
conversion and time frame. 203.

Faith, K. C. (1965), Industrial Chemistry, Third edition

pp. 747 -755, John Wiley 8 Sons New York.
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Fogler, H. S. (1994) Elements of Chemical Reaction
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Modeling, simulation and control, B. AMSE press, vol. Oxidation, Journal of Horganic Chemistry, Vol. 37, pp.
25, no. 4, pp. 15-24.
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Ancheya Juarez, J. C., A. Strategy for Kinetic
Goodhead T.O and Abowei M.F.N (2014) Design of
Parameter Estimation in the Fluid Catalytic Cracking
Isothermal Plug Flow Reactor Adsorption Tower for
Process, Ind. Eng. Chem. Res., 36 (12): pp 5170- 5174,
Sulphur Trioxide Hydration using Vanadium Catalyst
1997.
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Trioxide Hydration using Vanadium Catalyst
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Sulphur Trioxide Hydration Using Vanadium
CatalystInternational Journal of Technology
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IJTEEE, Volume 2: Issue 9.
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Abowei M.F.N and Goodhead T. O (2014) Modelling
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acid, Reinhold, New York.

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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

APPENDIX 1: NON- ISOTHRMAL CSTAT

T XA m VR (m3) h (m) Ts (sec) Vs (sec-1) Rq (kJ/sec.m3)

(K)

313 0.95 1 2.5957e-005 1.3220e-002 1.1036e-001 9.0612e+000 1.2680e+007

323 0.95 1 4.3629e-005 2.2220e-002 1.8550e-001 5.3909e+000 7.5438e+006

333 0.95 1 6.1302e-005 3.1221e-002 2.6064e-001 3.8367e+000 5.3690e+006

343 0.95 1 7.8975e-005 4.0221e-002 3.3578e-001 2.9782e+000 4.1676e+006

353 0.95 1 9.6647e-005 4.9222e-002 4.1092e-001 2.4336e+000 3.4055e+006

363 0.95 1 1.1432e-004 5.8223e-002 4.8605e-001 2.0574e+000 2.8791e+006

313 0.96 1 3.6276e-005 1.8475e-002 1.5423e-001 6.4837e+000 9.1686e+006

323 0.96 1 6.0974e-005 3.1054e-002 2.5924e-001 3.8574e+000 5.4548e+006

333 0.96 1 8.5672e-005 4.3632e-002 3.6425e-001 2.7453e+000 3.8822e+006

343 0.96 1 1.1037e-004 5.6211e-002 4.6926e-001 2.1310e+000 3.0135e+006

353 0.96 1 1.3507e-004 6.8790e-002 5.7427e-001 1.7413e+000 2.4624e+006

363 0.96 1 1.5977e-004 8.1369e-002 6.7928e-001 1.4721e+000 2.0818e+006

313 0.97 1 5.5850e-005 2.8444e-002 2.3746e-001 4.2113e+000 6.0172e+006

323 0.97 1 9.3875e-005 4.7810e-002 3.9913e-001 2.5054e+000 3.5799e+006

333 0.97 1 1.3190e-004 6.7177e-002 5.6080e-001 1.7832e+000 2.5478e+006

343 0.97 1 1.6993e-004 8.6543e-002 7.2248e-001 1.3841e+000 1.9777e+006

353 0.97 1 2.0795e-004 1.0591e-001 8.8415e-001 1.1310e+000 1.6161e+006

363 0.97 1 2.4598e-004 1.2528e-001 1.0458e+000 9.5619e-001 1.3662e+006

313 0.98 1 1.0260e-004 5.2255e-002 4.3624e-001 2.2923e+000 3.3091e+006

323 0.98 1 1.7246e-004 8.7833e-002 7.3325e-001 1.3638e+000 1.9687e+006

333 0.98 1 2.4232e-004 1.2341e-001 1.0303e+000 9.7063e-001 1.4012e+006

343 0.98 1 3.1217e-004 1.5899e-001 1.3273e+000 7.5342e-001 1.0876e+006

353 0.98 1 3.8203e-004 1.9457e-001 1.6243e+000 6.1566e-001 8.8874e+005

363 0.98 1 4.5189e-004 2.3015e-001 1.9213e+000 5.2048e-001 7.5135e+005

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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

313 0.99 1 2.9021e-004 1.4780e-001 1.2339e+000 8.1046e-001 1.1819e+006

323 0.99 1 4.8779e-004 2.4843e-001 2.0739e+000 4.8217e-001 7.0315e+005

333 0.99 1 6.8538e-004 3.4906e-001 2.9140e+000 3.4317e-001 5.0044e+005

343 0.99 1 8.8296e-004 4.4969e-001 3.7541e+000 2.6638e-001 3.8845e+005

353 0.99 1 1.0805e-003 5.5032e-001 4.5942e+000 2.1767e-001 3.1742e+005

363 0.99 1 1.2781e-003 6.5095e-001 5.4343e+000 1.8402e-001 2.6835e+005

APPENDIX 2: NON -ISOTHERMAL CSTAT

T(K) XA m VR (m3) h (m) Ts (sec) Vs (sec-1) Rq (kJ/sec.m3)

313 0.95 1.5 7.8263e-006 3.9859e-003 3.3275e-002 3.0053e+001 4.2055e+007

323 0.95 1.5 1.3155e-005 6.6997e-003 5.5930e-002 1.7879e+001 2.5020e+007

333 0.95 1.5 1.8483e-005 9.4134e-003 7.8585e-002 1.2725e+001 1.7807e+007

343 0.95 1.5 2.3812e-005 1.2127e-002 1.0124e-001 9.8775e+000 1.3822e+007

353 0.95 1.5 2.9140e-005 1.4841e-002 1.2390e-001 8.0713e+000 1.1295e+007

363 0.95 1.5 3.4469e-005 1.7555e-002 1.4655e-001 6.8236e+000 9.5487e+006

313 0.96 1.5 9.8730e-006 5.0283e-003 4.1977e-002 2.3823e+001 3.3688e+007

323 0.96 1.5 1.6595e-005 8.4518e-003 7.0557e-002 1.4173e+001 2.0042e+007

333 0.96 1.5 2.3317e-005 1.1875e-002 9.9137e-002 1.0087e+001 1.4264e+007

343 0.96 1.5 3.0039e-005 1.5299e-002 1.2772e-001 7.8298e+000 1.1072e+007

353 0.96 1.5 3.6761e-005 1.8722e-002 1.5630e-001 6.3981e+000 9.0476e+006

363 0.96 1.5 4.3483e-005 2.2146e-002 1.8488e-001 5.4090e+000 7.6489e+006

313 0.97 1.5 1.3288e-005 6.7673e-003 5.6495e-002 1.7701e+001 2.5291e+007

323 0.97 1.5 2.2334e-005 1.1375e-002 9.4959e-002 1.0531e+001 1.5047e+007

333 0.97 1.5 3.1381e-005 1.5982e-002 1.3342e-001 7.4949e+000 1.0709e+007

343 0.97 1.5 4.0428e-005 2.0590e-002 1.7189e-001 5.8177e+000 8.3126e+006

353 0.97 1.5 4.9475e-005 2.5197e-002 2.1035e-001 4.7539e+000 6.7926e+006

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International Journal of Engineering and Technology (IJET) Volume 4 No. 12, December, 2014

363 0.97 1.5 5.8522e-005 2.9805e-002 2.4882e-001 4.0190e+000 5.7425e+006

313 0.98 1.5 2.0122e-005 1.0248e-002 8.5553e-002 1.1689e+001 1.6873e+007

323 0.98 1.5 3.3822e-005 1.7226e-002 1.4380e-001 6.9540e+000 1.0039e+007

333 0.98 1.5 4.7522e-005 2.4203e-002 2.0205e-001 4.9492e+000 7.1446e+006

343 0.98 1.5 6.1223e-005 3.1180e-002 2.6030e-001 3.8417e+000 5.5458e+006

353 0.98 1.5 7.4923e-005 3.8158e-002 3.1855e-001 3.1392e+000 4.5317e+006

363 0.98 1.5 8.8623e-005 4.5135e-002 3.7680e-001 2.6539e+000 3.8311e+006

313 0.99 1.5 4.0637e-005 2.0696e-002 1.7278e-001 5.7878e+000 8.4404e+006

323 0.99 1.5 6.8304e-005 3.4787e-002 2.9041e-001 3.4434e+000 5.0215e+006

333 0.99 1.5 9.5972e-005 4.8878e-002 4.0804e-001 2.4507e+000 3.5739e+006

343 0.99 1.5 1.2364e-004 6.2969e-002 5.2568e-001 1.9023e+000 2.7741e+006

353 0.99 1.5 1.5131e-004 7.7060e-002 6.4331e-001 1.5545e+000 2.2669e+006

363 0.99 1.5 1.7897e-004 9.1151e-002 7.6095e-001 1.3142e+000 1.9164e+006

ISSN: 2049-3444 2014 IJET Publications UK. All rights reserved. 725