journal of engineering modeling of non-isothermal...

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

ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 709

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

Sulphuric acid is a very important commodity chemical and

indeed, a nation’s sulphuric acid production is a good indicator

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

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

recent similar work of (Goodhead and Abowei 2014)

recommended further modification on the model equations. In

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

of kinetic parameters.

2. KINETICS EVALUATION

Great deal of work is reported on the kinetics aspect of H2SO4

Industrial scale production and it is dependent on the oxidation

of sulphur dioxide to sulphur trioxide in fixed bed catalytic

reactors (Charles 1977) and (Fogler 1994)

The stoichiometric Chemistry for the production of sulphuric

acid is presented, thus;

22 SOOS

3221

2 SOOSO

1

Through the years, several catalyst formulations have been

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

synthesis etc. [Faith, 1965].

4232 SOHOSOH

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.

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

In the industrial chemical process, heterogeneous fluid-fluid

reactions are made to take place for one of three reasons. First,

the product of reaction may be a desired material. Such reactions

are numerous and can be found in practically all areas of the

chemical industry where organic and inorganic synthesis are

employed. Fluid-fluid reactions may also be made to take place

to facilitate the removal of an unwanted component from a fluid.

Thus the absorption of a solute gas by water may be accelerated

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

homogeneous multiple reactions than is possible by using the

single phase alon

The reaction mechanism as presented in equation (2.28) showed

chain reaction character is tics [Austin, 1984]. Gibney and

ferracid (1994) reported on the photo-catalysed oxidation of

SO32- by (dimethyl-glyoximato) (SO3)2

3- and its (Co(dimethyl-

glyoximato) (SO3)32.

The work adopted inverse reaction for the kinetic data

generation, thus.

4223 SOHOHSO 2

is described as irreversible bimolecular chain reaction. Further

research into the works of Erikson, [1974] and Huie, et al

[1985] established the reaction as second order reaction with rate

constant K2 = 0.3 mole/sec. performed abinitio calculation and

determined the energetic barrier and established conclusively

that the irreversible biomolecular nature of the reaction have Hr

= -25kcal/mol at 250C.

Following the outcome of the work of Chenier [1987] as cited

above, the rate expression for the formation and production of

sulphuric acid is summarized as in equation (3).

-RA = K2 OHSO 23 3

Hence from equation (2.33) the amount of SO3 and H2O that have

reacted at any time t can be presented as;

AABoAAAA XCCXCCKR 0002

4

Where

CAo = Initial concentration of SO3 (moles/Vol)

CBo = Initial concentration of H2O ( moles/Vol)

XA = Fractional conversion of SO3 (%)

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

In this work, the rate expression (-RA) as in equation (4) will be

used to develop the hypothetical semi-batch reactor, continuous

stirred tank reactor and plug flow reactor design equations with

inculcation of the absorption coefficient factor as recommended

in the works of Coulson and Richardson (1978). This is achieved

Air



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

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

)( ALiALALiA

L

LA CCrKCC

Z

rDR ………………………… 5

Invoking the works of Krevelen and Hoftyzer, the factor r is related to CAi, 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

r = L

BLL KCDK 2

1

2 ………………. 6

Substituting equation (5) into (6) results in

- RA = (CA) 21

21

21

2 LBL DKC ……………………………….. 7

Previous reports [ Octave levenspiel 1999] showed that the amount of SO3 (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

- RA = AAAAAOBOL XCCXCCDK 0022

12

12

1

= )1()( 21

23

21

21

02 AAAL XXmCDK …………………….

Where

Liquid film

Gas (SO3)

Liquid (steam) Concentration

CAi

Gas Film ZL

CBL

Inte

r fa

ce

r Distance normal to phase boundary

CBi

8



m =

0

0

A

B

C

C

m =- The initial molar ratio of reactants

-RA = Rate of disappearance of SO3

K2 = Absorption reaction rate constant

DL = Liquid phase diffusivity of SO3.

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 = GPCP (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,

VR =

AR

ctPP

RH

TTUATTCG

0 14

Recall that

- RA = AAAL XXmCDK 121

23

02

12

1

2 15

Putting equation (15) into (14) yields



VR =

AAALR

ctpp

XXmCDKH

TTUATTCG

121

23

02

12

1

2

0 16

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 SO3, (m2/sec)

m = Initial molar ratio of reactants.

3.1.2 Reactor Height

Considering a reactor with cylindrical shape we have

VR = hr 2 17

h = 2r

VR

18

Putting equation (16) into equation (18) results in

h =

AAALR

ctpp

XXmCDKHr

TTUATTCG

121

23

02

12

1

2

2

0

19

3.1.3 Space Time

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

Ts = rateflowVolumetric

reactorofVolume =

0V

VR 20

But

V0 = mixturereactionofDensity

MixturereactionofrateflowMass =

p

G

21

Putting equation (21) into (20) results in

Ts = R

p

pV

G

22

Substituting equation (16) into (22) gives



Ts =

AAALPR

ctppp

XXmCDKGH

TTUATTCG

121

23

02

12

1

2

0 23

3.1.4 Space Velocity

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

Vs =

Rs V

V

T

01 24

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

Vs =

ctppp

AAALpR

TTUATTCG

XXmCDKGH

0

21

23

02

12

1

2 1

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 =

R

AAR

R V

XFH

V

Q 0 27

Putting equation (16) into (27) results in

Rq =

ctPp

AAAAAR

TTUATTCG

XXmCDKXFH

0

21

23

02

1

22

1

20

21

28

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



The computation of the functional parameters of the reactor as

shown in figure

3.2 Computational Method

The developed models as presented in section 3.1 were

programmed using MATLAB, and the flow chart describing the

computational procedure is given in Fig 4 Performance

dimensions such as reactor volume, length, space time, space

velocity, heat generation per unit volume, and heat exchanger

functional parameters capable of maintaining non-isothermal

conditions were cleverly inculcated into the computer algorithm.

The equations of these performance measures were expressed as

a function of fractional conversions and characteristic

operational temperature.

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

START

INITIALIZE XA = 0.95 T = 313

READ Gp, Cp, Tc, Vo, U, AT, T0, CAO,

∆HR, K2, DL, M, D1

PRINT

T; XA; VR, h; Ts; Vs;

QG ; RQ

XA = XA + 0.01

XA. > 0.99

T = T + 10

T > 363

STOP

No

Yes

Yes



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 µa 5 x 10-3 Kg/m.sec

Viscosity of H2O at 600C µw 5 x 10-4 Kg/m.sec

Thermal conductivity of H2O at 200C Kw 0.6 w/mK

Thermal conductivity of H2SO4 at 270C Ka 0.25 W/mK

Thermal conductivity of Hastelloy KH 11.0 W/mK

4. RESULTS AND DISCUSSION

Industrial reactors for the production of sulphuric acid over a

range of reaction time t = 60 to 1800 Sec, degree of conversion

XA = 0.95 to 0.99 and operating temperature T = 313 to 363K

have been investigated and designed. The reactors have a

capacity of 1.389x103 Kg/hr of sulphuric acid. These reactors

were designed with hastelloy because it has excellent corrosion

and sulphuric acid resistance properties.

The reactors performance models developed in chapter three

were simulated with the aid of MATLAB R2007b. The results

provided information for the functional reactors’ parameters viz:

The reactor volume and the rate of heat generation per unit

volume of the continuous reactors and the semi-batch reactor.

The reactor length, space time, and space velocity for the



continuous reactors, while the height of reactor were obtained for

the continuous stirred tank reactors and the semi-batch reactor.

Similarly, information for the pressure drop in the plug flow

reactor, whose diameter Di was varied from 0.02 to 0.1 m was

also obtained. Suitable heat exchangers were also designed for

the isothermal reactors and the semi-batch reactor to remove the

heat of reaction occasioned during the process. It is the purpose

of this section to present and discuss the results of the reactor

types and the heat exchangers and to compare their performance.

The functional parameters of the reactors are tabulated in figures

17, 18, 19, 20, 21, 22, 23, and 24. And appendix 1-2. The results

showed that the reactor volume is dependent on operating

temperature T and degree of conversion XA. The volume of the

reactor would tend to infinity at 100% conversion. The variation

of the reactor volume, as a result of sulphur trioxide addition to

water, with reaction time, operating temperature and degree of

conversion is illustrated in figures 5, 6, 7, 8, 9, 10, 11, and 12.

From the results it was observed that volume of the reactors

increases with increasing degree of conversion and decreases

with increasing operating temperature. This characteristic

behavior was observed to be in agreement with the usual reactor

prototypes dependable features of performance parameters vis-

a–vis the kinetic data (Abowei 1989).

Figures 11 and 12 illustrated the variation of heat generation per

unit volume of the reactors as a function of reaction time t,

operating temperature T and degree of conversion within the

limits t, T and XA as specified. A plot of heat generation RQ

versus operating temperature T was curvilinear and found to be

increasing with increasing operating temperature T within the

range of XA = 0.95 to 0.99. Similar plots were made RQ versus

XA within the range of T = 313 to 363K. The graphs were also

curvilinear with negative gradient. At fairly above 99%

conversion of sulphur trioxide, there was a sharp drop tending to

the abscissa of the graph. This behavior explains the infinity of

the rate of heat generation per unit reactor volume at 100%

degree of conversion of sulphur trioxide. Finally the rate of heat

generation per unit reactor volume decreases with increasing

reaction time and degree of conversion within the range of

temperature as specified.

Figures 5 to 10 illustrated the variation of space time with

operating temperature and degree of conversion XA as specified

within the range of T = 313 to 363K and XA = 0.95 to 0.99. The

plots were curvilinear as well within the range of T and XA

investigated. However, for the addition of sulphur trioxide to

water, the highest conversion was observed for the highest space

time with the lowest operating temperature.

The space time TS, was observed to be increasing with

increasing degree of conversion and decreases with increasing

operating temperature within the range specified.

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

310 320 330 340 350 360 3700

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-3

TEMPERATURE (K)

RE

AC

TO

R V

OLU

ME

(

m3)

xA=95

xA=96

xA=97

xA=98

xA=99



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

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

0.94 0.95 0.96 0.97 0.98 0.99 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8x 10

-4

CONVERSION DEGREE

RE

AC

TO

R V

OLU

ME

(m

3)

313

323

333

343

353

363

310 320 330 340 350 360 3700

1

2

3

4

5

6

TEMPERATURE (K)

SP

AC

E T

IME

(se

c)

xA=95

xA=96

xA=97

xA=98

xA=99



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

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

0.94 0.95 0.96 0.97 0.98 0.99 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

CONVERSION DEGREE

SP

AC

E T

IME

(se

c)

313

323

333

343

353

363

310 320 330 340 350 360 3700

5

10

15

20

25

30

35

TEMPERATURE (K)

SP

AC

E V

ELO

CIT

Y(s

ec-1

)

xA=95

xA=96

xA=97

xA=98

xA=99



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

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

0.94 0.95 0.96 0.97 0.98 0.99 10

5

10

15

20

25

30

35

CONVERSION DEGREE

SPAC

E VE

LOCI

TY (s

ec-1

)

313

323

333

343

353

363

310 320 330 340 350 360 3700

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

7

TEMPERATURE (K)

HE

AT

GE

NE

RA

TE

D P

ER

UN

IT V

OLU

ME

(kJ/s

ec.m

3)

xA=95

xA=96

xA=97

xA=98

xA=99



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

a reasonable assumption as long as the operation of the

reactors is within the sonic limit. An observation

deduced from this work is that the operating

temperature tends to influence the reactor performance.

Generally the operation is favoured by low temperature.

This confirms the reason why heat exchangers should

be incorporated in the design. The consideration of the

optimum limit of degree of conversion XA from 0.95 to

0.99 is reasonable because at 100% conversion of

sulphur trioxide, the functional parameters of the

reactors will all tends to infinity. In this case the

dimensions of the reactors have no limit.

Work free days of 65 is allowed to produce the specified

quantity i.e. 1.389 x 103Kg/hr of sulphuric acid. Sulphur

trioxide, SO3 can be produced by catalytic oxidation of

sulphur dioxide using vanadium pentoxide as catalyst.

From the results of the computation for the non-

isothermal CSTAT it was found that; if the degree of

conversion, XA was 0.95, the operational temperature,

T was 313K, the reactor volume, VR were 2.5957E-

05m3 and 7.8263E-06m3 when the reactant molar ratio,

m=1.0 and 1.5 respectively but increase of XA, and T

resulted in increase of the reactor volume up to

1.1432E-04 to 1.2781E-03m3 when m=1.0, T=363K

and XA= 0.95 to 0.99 and 3.4469E-05 to 1.7897E-04m3

when m=1.5.

Critical examination of the results of the reactor types

gives the following analysis:

a. At the same operating temperature, change in

degree of conversion, XA from 0.95 to.0.99

curvilinearly increases the reactor volume and

space time of the non-isothermal CSTAT, while

the rate of heat generation per reactor volume and

space velocity decreases by the same proportion.

b. At the same degree of conversion, change in

operating temperature from 313 to 363K linearly

increases the reactor volume and space time of the

non-isothermal CSTAT, while the rate of heat

generation per reactor volume and space velocity

decreases curvilinear by the same proportion.

5. CONCLUSION AND

RECOMMENDATION

Model equation for the design of non-isothermal

CSTAT have been proposed for the production of

sulphuric acid via sulphur trioxide hydration process

using vanadium catalyst. Computer programs were

developed and utilized to simulate the performance

parameters over a temperature interval of T=313 to

363K, and conversion degree, XA=0.95 to 0.99. The

result of the performance evaluation parameters shows

the usual dependable characteristics of the kinetic data.

Further work need to be done to evaluate the

performance of the various adsorption towers as a

0.94 0.95 0.96 0.97 0.98 0.99 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

7

CONVERSION DEGREE

HE

AT

GE

NE

RA

TE

D P

ER

UN

IT V

OLU

ME

(kJ/s

ec.m

3)

313

323

333

343

353

363



function of the kinetic parameters with the aim of

establishing the optimum operational limit of

conversion and time frame.

REFERENCES

Abowei, M. F.N. (1989). Computer-aided design of

heat exchanger for P.F. reactor in the addition of

ethylene oxide. Part 1: Design equation development.

Modeling, simulation and control, B. AMSE press, vol.

25, no. 4, pp. 15-24.

Ancheya – Juarez, J. C., A. Strategy for Kinetic

Parameter Estimation in the Fluid Catalytic Cracking

Process, Ind. Eng. Chem. Res., 36 (12): pp 5170- 5174,

1997.

Austin, G. T. (1984), Shreve’s Chemical process

industrial. Fifth edition, publisher McGraw-Hill,

pp370-345.

Charles G. Hill, jr (1977), An Introduction to chemical

engineering Kinetics & Reactor design, 1st edition, John

Wiley & Sons USA, pp5-16, pp509-523.

Chenier, P. J. (1987), Survey of industrial chemistry,

John Wiley & Sons, New York, pp45-47.

Coulson, J. M., Richardson, J. F. (1978), Chemical

Engineering, vol.2, 3rd Edition, Pergamon press Inc.,

New York, pp.529-530, 547-550.

Coulson J. M., Richardson J. F. “Chemical

Engineering” Vol. 3, 2nd Edition, Pergramon Press Inc.

New York (1979). Pp. 3 -10, 36 -42.

Duecker and West (1975), Manufacture of Sulphuric

acid, Reinhold, New York.

Erikson, T. E. (1974), Chem Soc, Faraday Trans. I, 70,

203.

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

pp. 747 -755, John Wiley 8 Sons New York.

Fogler, H. S. (1994) Elements of Chemical Reaction

Engineering. 2nd edition Prentice-Hall Inc., India.

Gibney, S. C., and Ferracid, G. (1994) Photocatalysed

Oxidation, Journal of Horganic Chemistry, Vol. 37, pp.

6120-6124.

Goodhead T.O and Abowei M.F.N (2014) “Design of

Isothermal Plug Flow Reactor Adsorption Tower for

Sulphur Trioxide Hydration using Vanadium Catalyst”

International Journal of Innovative Science and Modern

Engineering (IJISME), Volume 2, Issue 9, Pp 9-16.

Goodhead T.O and Abowei M.F.N (2014) “Modelling

of Semi Batch Reactor Adsorption Tower for Sulphor

Trioxide Hydration using Vanadium Catalyst”

International Journal of Scientific and Engineering

Research, Volume 5, Issue 8.

Goodhead T.O and Abowei M.F.N (2014) “Modelling

of Non-Isothermal Plug Flow Reactor Adsorption for

Sulphur Trioxide Hydration Using Vanadium

Catalyst”International Journal of Technology

Enhancement and Emerging Engineering Research,

IJTEEE, Volume 2: Issue 9.

Abowei M.F.N and Goodhead T. O (2014) “Modelling

of Non-Isothermal CSTR Adsorption Tower for Sulpur

trioxide Hydration using Vanadium Catalyst”

International Journal of Modem Engineering Sciences

(Accepted – Paper No. 154)



APPENDIX 1: NON- ISOTHRMAL CSTAT

T

(K)

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

313

323

333

343

353

363

313

323

333

343

353

363

313

323

333

343

353

363

313

323

333

343

353

363

0.95

0.95

0.95

0.95

0.95

0.95

0.96

0.96

0.96

0.96

0.96

0.96

0.97

0.97

0.97

0.97

0.97

0.97

0.98

0.98

0.98

0.98

0.98

0.98

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2.5957e-005

4.3629e-005

6.1302e-005

7.8975e-005

9.6647e-005

1.1432e-004

3.6276e-005

6.0974e-005

8.5672e-005

1.1037e-004

1.3507e-004

1.5977e-004

5.5850e-005

9.3875e-005

1.3190e-004

1.6993e-004

2.0795e-004

2.4598e-004

1.0260e-004

1.7246e-004

2.4232e-004

3.1217e-004

3.8203e-004

4.5189e-004

1.3220e-002

2.2220e-002

3.1221e-002

4.0221e-002

4.9222e-002

5.8223e-002

1.8475e-002

3.1054e-002

4.3632e-002

5.6211e-002

6.8790e-002

8.1369e-002

2.8444e-002

4.7810e-002

6.7177e-002

8.6543e-002

1.0591e-001

1.2528e-001

5.2255e-002

8.7833e-002

1.2341e-001

1.5899e-001

1.9457e-001

2.3015e-001

1.1036e-001

1.8550e-001

2.6064e-001

3.3578e-001

4.1092e-001

4.8605e-001

1.5423e-001

2.5924e-001

3.6425e-001

4.6926e-001

5.7427e-001

6.7928e-001

2.3746e-001

3.9913e-001

5.6080e-001

7.2248e-001

8.8415e-001

1.0458e+000

4.3624e-001

7.3325e-001

1.0303e+000

1.3273e+000

1.6243e+000

1.9213e+000

9.0612e+000

5.3909e+000

3.8367e+000

2.9782e+000

2.4336e+000

2.0574e+000

6.4837e+000

3.8574e+000

2.7453e+000

2.1310e+000

1.7413e+000

1.4721e+000

4.2113e+000

2.5054e+000

1.7832e+000

1.3841e+000

1.1310e+000

9.5619e-001

2.2923e+000

1.3638e+000

9.7063e-001

7.5342e-001

6.1566e-001

5.2048e-001

1.2680e+007

7.5438e+006

5.3690e+006

4.1676e+006

3.4055e+006

2.8791e+006

9.1686e+006

5.4548e+006

3.8822e+006

3.0135e+006

2.4624e+006

2.0818e+006

6.0172e+006

3.5799e+006

2.5478e+006

1.9777e+006

1.6161e+006

1.3662e+006

3.3091e+006

1.9687e+006

1.4012e+006

1.0876e+006

8.8874e+005

7.5135e+005



313

323

333

343

353

363

0.99

0.99

0.99

0.99

0.99

0.99

1

1

1

1

1

1

2.9021e-004

4.8779e-004

6.8538e-004

8.8296e-004

1.0805e-003

1.2781e-003

1.4780e-001

2.4843e-001

3.4906e-001

4.4969e-001

5.5032e-001

6.5095e-001

1.2339e+000

2.0739e+000

2.9140e+000

3.7541e+000

4.5942e+000

5.4343e+000

8.1046e-001

4.8217e-001

3.4317e-001

2.6638e-001

2.1767e-001

1.8402e-001

1.1819e+006

7.0315e+005

5.0044e+005

3.8845e+005

3.1742e+005

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

323

333

343

353

363

313

323

333

343

353

363

313

323

333

343

353

0.95

0.95

0.95

0.95

0.95

0.95

0.96

0.96

0.96

0.96

0.96

0.96

0.97

0.97

0.97

0.97

0.97

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

7.8263e-006

1.3155e-005

1.8483e-005

2.3812e-005

2.9140e-005

3.4469e-005

9.8730e-006

1.6595e-005

2.3317e-005

3.0039e-005

3.6761e-005

4.3483e-005

1.3288e-005

2.2334e-005

3.1381e-005

4.0428e-005

4.9475e-005

3.9859e-003

6.6997e-003

9.4134e-003

1.2127e-002

1.4841e-002

1.7555e-002

5.0283e-003

8.4518e-003

1.1875e-002

1.5299e-002

1.8722e-002

2.2146e-002

6.7673e-003

1.1375e-002

1.5982e-002

2.0590e-002

2.5197e-002

3.3275e-002

5.5930e-002

7.8585e-002

1.0124e-001

1.2390e-001

1.4655e-001

4.1977e-002

7.0557e-002

9.9137e-002

1.2772e-001

1.5630e-001

1.8488e-001

5.6495e-002

9.4959e-002

1.3342e-001

1.7189e-001

2.1035e-001

3.0053e+001

1.7879e+001

1.2725e+001

9.8775e+000

8.0713e+000

6.8236e+000

2.3823e+001

1.4173e+001

1.0087e+001

7.8298e+000

6.3981e+000

5.4090e+000

1.7701e+001

1.0531e+001

7.4949e+000

5.8177e+000

4.7539e+000

4.2055e+007

2.5020e+007

1.7807e+007

1.3822e+007

1.1295e+007

9.5487e+006

3.3688e+007

2.0042e+007

1.4264e+007

1.1072e+007

9.0476e+006

7.6489e+006

2.5291e+007

1.5047e+007

1.0709e+007

8.3126e+006

6.7926e+006



363

313

323

333

343

353

363

313

323

333

343

353

363

0.97

0.98

0.98

0.98

0.98

0.98

0.98

0.99

0.99

0.99

0.99

0.99

0.99

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

5.8522e-005

2.0122e-005

3.3822e-005

4.7522e-005

6.1223e-005

7.4923e-005

8.8623e-005

4.0637e-005

6.8304e-005

9.5972e-005

1.2364e-004

1.5131e-004

1.7897e-004

2.9805e-002

1.0248e-002

1.7226e-002

2.4203e-002

3.1180e-002

3.8158e-002

4.5135e-002

2.0696e-002

3.4787e-002

4.8878e-002

6.2969e-002

7.7060e-002

9.1151e-002

2.4882e-001

8.5553e-002

1.4380e-001

2.0205e-001

2.6030e-001

3.1855e-001

3.7680e-001

1.7278e-001

2.9041e-001

4.0804e-001

5.2568e-001

6.4331e-001

7.6095e-001

4.0190e+000

1.1689e+001

6.9540e+000

4.9492e+000

3.8417e+000

3.1392e+000

2.6539e+000

5.7878e+000

3.4434e+000

2.4507e+000

1.9023e+000

1.5545e+000

1.3142e+000

5.7425e+006

1.6873e+007

1.0039e+007

7.1446e+006

5.5458e+006

4.5317e+006

3.8311e+006

8.4404e+006

5.0215e+006

3.5739e+006

2.7741e+006

2.2669e+006

1.9164e+006

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