Journal of Engineering Modeling of Non-isothermal...
Transcript of 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
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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
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ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 711
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
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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
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ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 713
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
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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
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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
T; XA; VR, h; Ts; Vs;
QG ; RQ
XA = XA + 0.01
XA. > 0.99
T = T + 10
T > 363
STOP
No
Yes
Yes
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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
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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
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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
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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
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ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 720
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
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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
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ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 722
function of the kinetic parameters with the aim of
establishing the optimum operational limit of
conversion and time frame.
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Sulphur Trioxide Hydration using Vanadium Catalyst”
International Journal of Innovative Science and Modern
Engineering (IJISME), Volume 2, Issue 9, Pp 9-16.
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International Journal of Modem Engineering Sciences
(Accepted – Paper No. 154)
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ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 723
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
International Journal of Engineering and Technology (IJET) – Volume 4 No. 12, December, 2014
ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 724
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
International Journal of Engineering and Technology (IJET) – Volume 4 No. 12, December, 2014
ISSN: 2049-3444 © 2014 – IJET Publications UK. All rights reserved. 725
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