A STUDY OF THE TITANIUM TETRACHLORIDE OXIDATION IN A ROTATING ARC PLASMA JET by Imad Mohammed Hassan Mahawili, B.Sc.(Eng.), A.C.G.I. August, 1974 A thesis submitted for the Degree of Doctor of Philosophy of the University of London Department of Chemical Engineering & Chemical Technology Imperial College, London, SW7
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A STUDY OF THE TITANIUM TETRACHLORIDE
OXIDATION IN A ROTATING ARC PLASMA JET
by
Imad Mohammed Hassan Mahawili, B.Sc.(Eng.), A.C.G.I.
August, 1974
A thesis submitted for the Degree of Doctor of Philosophy of the University of London
Department of Chemical Engineering & Chemical Technology Imperial College, London, SW7
ABSTRACT
The object of this work was to determine the kinetics
of the titanium tetrachloride oxidation reaction. A
fundamental requirement for kinetic studies in high
temperature flow systems is the homogeneous initiation
of the chemical reaction. This implies the need to supply
thermal energy uniformly across a section. The use of a
magnetically rotated plasma jet to achieve this condition
has been investigated. A new method for the qualitative
assessment of thermal mixedness using.a probe based on a
corona discharge has been developed. This has been used
in designing a new reactor based on the rotating arc
plasma jet.
The oxidation reaction of titanium tetrachloride
has been investigated in this reactor over a temperature
range of 970 - 1498°K, Evidence of a slow chlorine
reassociation process was discovered, and was best
described by:
[ dC121 • 9743 ± 2200) - 0.632 x 10-4 Exp(- dt RT
Taking this into account, the oxidation reaction was
found to proceed according to the following rate
expression:
d[ric14] 10.030 1060 dt _ - 0.360 x 10-4 Exp(-
RT
Dilute systems were used in this investigation and the
lack of dependence of these rate expressions on the
reactant concentrations may not be applicable for more
concentrated systems.
ACKNOWLEDGMENTS
The efforts and contributions of many people made
possible the completion of this work. Certainly, the
technical guidance and support of Professor F. J.
Weinberg is unequalled. His unfailing human concern
throughout the research period is most appreciated.
Discussions with Dr. A. R. Jones added further
insight to many parts of this work, and is gratefully
acknowledged.
The professionalism and speed in the fabrication
of equipment, as provided by Tony Jones, Colin Smith,
Ken Grose, of the glassblowing workshop; and Bert
Lucas, Russ Harris, of the main workshop, is greatly
appreciated. The efforts of Trevor Agus is duly
acknowledged.
My thanks are due to Tioxide International for
their financial support, and to Mr. E. R. Place for
valuable discussions.
To my wife, Jamie, I give my thanks and apprecia-
tion for typing this thesis, and for her continuous
- support and encouragement.
ii
TABLE OF CONTENTS
Page Number
ABSTRACT
ACKNOWLEDGMENTS ii
LIST OF FIGURES vi
LIST OF TABLES ix
LIST OF SYMBOLS
CHAPTER 1 Introduction 1
CHAPTER 2 The Magnetically Rotated Arc Plasma Jet 9
2.1 Description of the Rotating Arc Plasma Jet 9
2.2 Measurement of Arc Frequency of Rotation
2.3 The Interaction Between the Gas Flow and the Rotating Arc
CHAPTER 3 The Addition of Titanium Tetrachloride and Oxygen to the Rotating Arc Plasma Jet
3.1 Introduction 21
3.2 Preliminary Experiments 22
3.3 Condition for Achieving Low Mean Gas Temperatures in the Plasma Jet • 28
CHAPTER 4 Techniques for the Investigation of the Method of Mixedness 35
4.1 Introduction 35
4.2 Optical Methods 36
4.3 The Use of Thermocouples 38
4.4 The Corona Probe . ***** •••• 43
4.4.1 Preliminary Experiments Using the Corona Probe . . 45
11
17
21
iii
Page Number
4.4.2 Current, Voltage, and Temperature Characteristics of the Corona Probe 47
CHAPTER 5 The Use of the Corona Probe in Assessing Thermal Mixedness 53
5.1 Introduction 53
5.2 Analysis of Thermal Mixedness Using the Corona Probe 53
5.3 The Injection Anode Reactor 61
CHAPTER 6 Reaction Parameter, Their Measurement and Quantitative Analysis 70
6.1 Introduction 70
6.2 Temperature Measurement 70
6.3 Particle Size and Gas Concentration Measurement 71
6.4 Gas Analysis 74
CHAPTER 7 The Mathematical Procedure for the Kinetics Investigation 76
7.1 Introduction 76
7.2 Assumptions 76
7.3 Concentration-Time Domain 77
7.4 The Rate Expression 78
7.5 The Arrhenius Rate Expression and the Method of Solution 80
CHAPTER 8 The Kinetics Investigation of the Oxidation Reactions Its Results, Analysis, and Discussion 84
8.1 Introduction 84
8.2 Reactor Wall Material 84
8.3 Experimental Procedure 84
8.4 Qualitative Experimental Observations 85
iv
Page Number
8.4.1 Temperature Measurement. . . 85
8.4.2 Concentration Measurements , 86
8.5 Experimental Results, Their Analysis and Discussion ***** 86
8.5.1 Experimental Results 86
8.5.2 Chlorine Reassociation Process 94
8,5.3 The Rate of the Oxidation Reaction 103
8,5.4 Error Estimation in the Reaction Rate 109
8.5.5 Observations on Particles, 109
CHAPTER 9 Conclusion •• ******** . . . . . 121
REFERENCES 124
APPENDIX 1 Computer Programmes 130
Figure Number
Fig. 1.1
Fig. 2.1
Fig. 2.2
Fig. 2.3
Fig. 2.4
Fig. 2.5
Fig. 2.6
Fig. 3.1
Fig. 3.2
Fig. 3.3.
Fig. 3.4
Fig. 3.5
Fig. 3.6
Fig. 3.7
Fig. 4.1
Fig. 4.2-1 Fig. 4.5 f
Fig. 4.6
Fig. 4.7
Fig. 4.8
Fig. 4.9
Fig. 4.10- Fig. 4.13 -I
Fig. 4.14
LIST OF FIGURES
Figure Title Page Number
Flow Diagram for the Manufacture of Titanium Dioxide Pigments . . . 2
On heating TiO2 oxygen is lost, leaving non-stoichiometric
TiO2,- x depends on the temperature and on the pressure
of oxygen.
Table 1.1 Physical Properties of Titanium Dioxide (1, 2, 37}
3
Appearance: Colourless liquid fumes strongly in air.
Specific Gravity: 0°C : 1.7604
10°C 1.74
136.41°C : 1.52
Boiling Point: 136.41°C
Melting Point: - 23 - 30°C
Heat of Fusion: 12.90 cal per gram.
Molecular heat of Vapourisation (by Clausius-Clapeyron equation): 8960 cal at 25°C, and 8620 cal at
boiling point.
Specific Heat: Temp. °K cal/mole °K
298 34.704 400 34.936 500 35.153 1000 36.237
Equilibrium Data: Temp. °K Equilibrium Species Present
400-2600 TiC1 (g)
2600-2800
TiC13(g)
2800-3200
TiC12(g)
3200-4000
TiCl(g)
Table 1.2 Physical Properties of Titanium Tetrachloride (1, 2,-37)
The process is economically attractive, as the chlorine
produced may be recycled for the chlorination of mineral
rultile.
There are several ways of carrying out this
reaction, and an extensive literature exists mainly in
the form of patents (3-22). What most of the literature
omits is information regarding the kinetics of the
oxidation reaction; this being of prime importance in
optimising the formation of titanium dioxide particles,
which for use as a pigment should have a mean size of
around 0.25 Am. The present study has the investigation
of these kinetics as one of its main objectives.
Numerous ways have been used in attempts at
producing a controlled environment for the investigation
of reaction kinetics. These involve the introduction of
a perturbance in the thermodynamic equilibrium and
measuring the variation of temperature and concentration
of one or more of the species with respect to time.
Such techniques are discussed in great detail by several
authors (23, 24,25 ), and Table 1.3 summarises the more
common of these with typical values for some of their
parameters (26). Differences between these techniques
lie mainly in the means of introducing the perturbance„
and the way in which the reaction is distributed in
time. The perturbation must be initiated homogeneously
and in a time short compared with the reaction half-life.
For reasons which will become apparent later, the
method of interest in this work is that of flow reactors,
where thermal initiation is usually used. This can be
achieved by passing the reactants through a heated duct
5
Type of System
Reaction Pressure Speed Temperature Range msec. Range o,4%. ATM. _
Discharge Flow 10 300-800 0.1-1.0
Photolysis 10 300-800 0.1-1.0
Shock Tube 10 - 2 1000-10,000 0.1-10
Static Reaction 10 300-1300 0.1-1.0 Vessel
Premixed Flames 1 1000-2500 0.1-5
Stirred Reactors 1 300-2000 1.0-10
Flow Reactors 1 300-2000 0.1-10
Table 1.3 Sumary of Experimental Methods For Kinetics Studies
after Branch (26)
6
wall, or mixing them with a pre-heated inert gas. Thermal
addition and equilibrium must be effected uniformly in
a time much shorter than the reaction time. The
chemical reaction is distributed spacially and, at a
particular point, under constant flow conditions, the
composition approaches a stationary value. The axial
temperature and composition are monitored by means of
suitable probes.
In order to obtain unambiguous kinetic information,
the flow conditions, i.e. radial and axial profiles of
velocity, temperature and composition must be clearly
defined. The theoretical analysis of these parameters
is discussed, e.g. by Branch (26). However, plug flow,
that is with no radial gradients would be an ideal
model to choose for obtaining and interpreting kinetic
data. This can be approached realistically in the
region of developing turbulent flows (26).
A rapid and efficient way of introducing thermal
energy into a flowing gas is by means of a high
frequency magnetically rotated electrical discharge,
as discussed in Chapter 2. This type of plasma jet
is used for electrically augmenting combustion reactions
(27 - 29). A detailed account of its design and develop-
ment is given by Cox (35).
The present study investigates the possibility of
using such a plasma jet as a flow reactor for chemical
synthesis and kinetic studies. The criterion determining
its suitability is its ability to distribute the electri-
cal energy input uniformly to the cross-section of the
stream of flowing reactants.
7
The investigation begins by considering the flow
of oxygen and titanium tetrachloride in argon through
the plasma jet. A theoretical and experimental analysis,
given in Chapter 3, shows that a uniform thermal distri-
bution can only be achieved at the expense of having
undesirably high gas temperatures. This problem was
overcome by the use of a post-arc injection reactor.
The presence of uniform thermal distribution was
confirmed experimentally by the use of a probe, developed
for the purpose, which exploits the dependence of the
break-down potential of a corona discharge on local gas
density. The design specifications for this reactor,
including operating conditions, are given in Chapter 5.
The oxidation of titanium tetrachloride is
investigated kinetically using the post-arc injection
reactor. The progress of the reaction is followed by
monitoring the temperature and chlorine concentration
variation along the reactor centreline. The mathematical
procedure for the reduction of such data into useful
kinetic information is presented.in Chapter 7. The
experimental results are presented and analysed in
Chapter 8. It is discovered from these results that
the chlorine reassociation occurs at a much slower rate
than has been previously assumed. The analysis of this
process is considered essential in order to gain further
insight into the oxidation reaction. Rate expressions
for the chlorine reassociation process and the titanium
tetrachloride oxidation reaction are discussed and pre-
sented in Chapter 8.
8
CHAPTER TWO
THE MAGNETICALLY ROTATED ARC PLASMA JET
2.1 Descri tion of the Rotatin Arc Plasma Jet
The direct addition of energy to a gas stream can
be achieved efficiently using a magnetically rotated
arc. Figure 2.1 is a schematic diagram of the rotating
arc plasma jet. The mechanical construction of this
device includes a water-cooled copper anode and a
tungston cathode housed in a copper frame. The
axial magnetic field is produced by passing direct
current through a coil made up of 4200 turns of 22
s.w.g. copper wire covered with a high temperature
resistance enamel. The coil is water-cooled to pre-
vent unnecessary overheating. Argon is introduced
in the arc zone as shown in Fig. 2.1. A small annulus
immediately surrounding the cathode allows the passage
of a sheath of argon which helps in cooling the cathode
and protects it from direct chemical attack when reac-
tants are present.
The electric power for the discharge is supplied
by two SRH222(s) Miller Welder d.c. generators. Each
of these is capable of supplying 150 amps. continuously.
They can be used singly or coupled in series or parallel
depending on the desired application. The discharge
is initiated using high frequency voltage pulses
supplied by a spark generator.
The current supplied to the magnetic field coil
is smoothed d.c. produced by rectifying the mains using
9
Cu —Anode
Water In
Sheath Argon
Fig. 2.1
Rotating Arc Plasma Jet
10
the circuit shown in Fig. 2.2. The voltage is con-
trolled by a Variac. This design arrangement allows
the field to be varied over a wide range. Figure 2.3
shows the connection of the various electrical supplies
to the plasma jet.
The interaction between the arc current, I, and
the magnetic field, B, leads to, the Lorentz force,
B "I, which manifests itself in the motion of the
arc around the cathode. This phenomenon is described
and discussed in detail by Cox (35) and others (32, 36).
The frequency of this rotation depends on the magnitudes
of both B and I (32).
The gas flowing through the cathode-anode annulus
encounters the rotating arc, details of which are dis-
cussed in a later section. It is necessary to assert
that this arrangement provides a unique method of
supplying large enthalpies in an extremely short time.
Furthermore, the motion of the arc is of primary import-
ance in distributing this enthalpy in the cross-section
of the flowing gas.
2.2 Measurement of Arc Fre uenc of Rotation
The arc frequency of rotation is a fundamental
parameter in the practical application of this plasma
jet. It can be measured using optical techniques (32)
or a search coil (35). It is more convenient in this
arrangement to use the latter.
The arc can be viewed as a cylinder, through
which a large current is flowing, and which is in
11
50V
2 N 3055
3000 ittE 200V
200 AF 350 V
1.8MSl
470 KG
39
Fig. 2.2 : Rectifier Circuit Diagram
To D.C. Field Coil ° <190 0
V
a ? •
•••••■••••"'.....•■■•+
Miller Welder Units
Plasma Jet Electrical Supply
■•■•■•••■...................... ..........................e1+ ,Cu—Anode W 4 E
—.—, Spark Generator
D.C.
Rectifier
41, A.C.
Mains Fig. 2.3
13
rotational motion. The current induces a magnetic
field around the cylinder, which can be picked up
using a search coil located near the region of the
arc and in the same plane, as shown in Fig. 2.4. The
current induced in the search coil will fluctuate with
the same frequency as that of the magnetic field. This,
in turn, varies with the frequency of the rotating arc.
Thus, if the search coil current is displayed on an
oscilloscope, its fluctuation is a direct measurement
of the arc rotation. The frequency can either be
measured by balancing the search coil signal against
a tunable output of a signal generator, or by direct
photography of the displayed signal.
The search coil used in this work is a Radio
Spares Reed Coil No. 2 having about 7000 turns. The
frequencies were measured directly by photographing
the display. Figure 2.5 represents graphs of field
current against frequency for several arc currents,
with an argon flow rate of about 140 cm3 s-1
The graphs indicate that for a fixed arc current,
the frequency of rotation is proportional to the field
current, i.e. to the magnetic field. A slight non-
linearity in the proportionality is also evident.
Furthermore, as the arc current increases a slightly
smaller value of the field current is required for
the same frequency of rotation. Work on this has been
carried out (32), with the following empirical expres-
sion often quoted:
f a IO.33 DO.6
14
Fig. 2.4
/ Cathode Ray Oscilloscope
Arc Rotation Measuring Equipment
15
X : 1 = 66 : 1 =82
Amps • : 1=100 s : 1=120
Fig.2 .5: Rotattng Arc Characteristic
1.2 c. E
1.0 4-
(-) 0.8 -a
U-
0.6
04 .41 400
I 500 600 700 800 900
t 1000 1100 1200
I I
1.8
lb
Arc Frequency: c.)/ Hz
Where f denotes the arc frequency, I is the arc current,
and B is the magnetic flux, which is proportional to
the field current. The family of curves in Fig. 2.5
show agreement with the empirical relationship in as
much as they exhibit a stronger dependence of the arc
frequency on the induced magnetic field than on the
arc current.
2.3 The Interaction Between the Gas Flow and the Rotating Arc
The gas flowing around the cathode encounters the
rotating arc when passing through the discharge gap
then leaves the anode in the form of a plasma jet.
This interaction results in an imprint of a high tem-
perature spiral in the emerging gas. It is made up of
regions that have encountered the arc directly, and
hence are at a high temperature, and regions that have
not encountered the arc, and these are cooler. Ideally,
these regions would be uniformly alternating with a
frequency equal to that of the arc, and a separation
distance, or pitch, between them related to the magni-
tudes of the linear gas velocity and arc frequency.
However, in practice this interaction can manifest itself
in the production of hot and cold gas turbules of varying
sizes and distribution. In either case, the emerging
gas is not uniformly heated. In order to investigate
methods of achieving uniform heating the following
model for the interaction process is considered:
Let Ux be the linear gas velocity, cm s-1, passing
through a zone in which an electric arc is rotating
17
with a frequency co , Hz. The arc is represented,
for simplicity, by a rotating solid cylinder. The gas
elements progress linearly by a distance, T, where:
U x T
w centimetres per arc revolution.
If the arc diameter is represented by (3, cm, then the
ratio:
is a measure of the spiral pitch. Thus, it can be
seen immediately that the value of r relates to the
thermal uniformity mentioned earlier. For example, when
the value of r is unity, the gas elements progress
linearly by one arc diameter per arc revolution. This
further implies that each of the gas elements at a cross-
section encounters the arc once as they pass through the
arc zone. Therefore, ideally, uniform heating of the
gas can be achieved if the ratio r is unity, i.e.
making:
Ux = bco
On the other hand, non-uniform heating is present if r
exceeds unity. The gas elements may encounter the arc
more than once if r is less than unity. However, as
will be seen later, this case is not achieved experi-
mentally.
Figure 2.6 represents a theoretical family of
constant frequency curves relating the spiral pitch to
the gas flow rate, which is presented instead of velocity
for practical convenience. The cross-sectional area of
18
12
11
10
9
8
7
-_ SPIRAL PITCH VS GAS FLOWRATE
100 200 300 400 500 600 700 800 900 1000
Gas Flowrate / cm3 Fig. 2.6
6- -c V
5
4 ""'
3
2
Hz = o.mcavt
A = 0.7140+1%2
(.0 ,-3000
<„,4000 5000
the anode jet is 0.7 cm2. A value of 1.4 mm for the
arc diameter based on work by Cox (33), was taken for
the theoretical calculation.
In practice, using the rotating arc plasma jet,
it has been shown (35) that for a particular gas flow
rate and arc current, the frequency can be increased
only up to a limited value since arc instability sets
in. In an attempt to explain this, Cox suggested that
this arose when the arc begins to catch up with its
own wake. Furthermore, the onset of this instability
is an indication of uniform gas heating. Using the
present work definitions, this uniform heating
criterion corresponds to the condition when the spiral
pitch is unity.
20
CHAPTER THREE
THE ADDITION OF TITANIUM TETRACHLORIDE AND
OXYGEN TO THE ROTATING ARC PLASMA JET
3.1 Introduction
The reaction between titanium tetrachloride and
oxygen takes place in accordance with the following
equations:
TiC14 + 02--o-Ti02 + 2C12 (1)
(rutile)
TiC14 + 02--*TiO2 2C12 (anatase)
TiO2 (anatase)--4-Ti02 (rutile)
Depending on the amount of oxygen used, it is possi-
ble to produce other oxides of titanium from this
reaction (4). Antipov (3) has investigated the oxi-
dation reaction, and reports that it proceeds in the
kinetic region if the temperature range is 600 - 1100°C.
Furthermore, if the oxidation temperature is 1000 - 1100°C
then pigment-grade titanium dioxide can be obtained with
95 - 97% particles smaller than 1 Am. Literature and
patents ( 1, 3 - 22 ) reveal that the above temperature
is widely used for the formation of pigment titanium
dioxide by the chloride route. The objective of this
work is to investigate the possibility of using the
rotating arc plasma jet for the oxidation of titanium
tetrachloride.
21
3.2. Preliminary
Figure 3.1 represents the apparatus flow sheet for
the oxidation of titanium tetrachloride in the plasma
jet. All gases are dried using silica-gel filled tubes,
and their flows accurately monitored using variable area
flow meters. An argon stream, dried by passing through
two consecutive packed beds of silica-gel, for extra
drying,'bubbles through liquid titanium tetrachloride
maintained at a constant temperature. The titanium
tetrachloride-laden argon stream leaves the bubbler
and immediately mixes with the other streams in an
electric heater, in order to prevent possible conden-
sation of the tetrachloride. The argon and reactants
stream then flows in the compartment around the cathode,
see Fig. 2.1, and encounters the rotating arc. The
product stream is quenched using cold air injection
through side arms in a quartz tube. The products are
then filtered for titanium dioxide particles and chlorine
scrubbed with sodium hydroxide solution.
The above system is designed for flexibility in
the input feeds of the reactants and diluent argon.
Thus, by varying the bubbler liquid temperature and the
argon flow rate the amount of titanium tetrachloride
picked up can be varied.
Preliminary experiments to test the behaviour of
the system showed that the argon plasma can only be
stabilised in the presence of the reactants if the
electric power is appreciably increased, and the concen-
tration of titanium tetrachloride and oxygen in the main
22
Dried Compressed Air --X Effluent
0
0,
0
Quartz Reactor Duct
Heat\er
Sheath Ar
D.C. Power Supply
TiCI4 Bubbler
Silica Gel Columns
Ti02/ Filter Column
Ar 02 Ar Fig. 3.1 :TiCI4 Oxidation System Howsheet
argon stream remained very low. The addition of polyatomic
molecules, such as these, in the region of the arc leads
to the dissipation of arc energy due to dissociation.
This causes extinction of the arc unless the power supplied
is sufficient to accommodate these processes.
The molar flows of the reactants which gave a
5 stable plasma were in the region of 9 x 10
- moles s
-1 for
oxygen and 4 x 10-5 moles s-1 for the titanium tetra-
chloride, making up no more than 1% of the total feed
stream.
These flows lead to considerable damage to the
inner surface of the anode, after a few minutes of the
experimental run. The cathode erosion was also appreciable,
as indicated by the changes in the size of its tip.
From these preliminary runs, samples of particles
were taken from the deposit on the anode wall, and various
positions inside the quench tube. Figures 3.2, 3.3, and
3.4 are electron micrographs of some -of these samples.
A chemical analysis revealed the presence of 12% copper
in samples taken from the anode wall. They also indicated
that there was no significant change in the type, quality,
and particle size, of the order 0.02 AM, between the
samples taken from different parts of the quench tube.
Some of the characteristics of these samples may be
generated by the sampling technique, and the resultant
micrographs may be more of what is happening at the
wall and the effect of sample preparation techniques
on the material.
24
3.2: Particles samples from anode inner wall.
Ma,7.= 20,000X
23
Fig. 3.3 : Particles sample from quartz quenching
duct.
Mag.= 20,000X
26
Fig.34: Particles sample from quartz quenching
duct.
Mag.= 100,000X
27
In these runs, the electric power transferred to
the gas is calculated by an enthalpy balance around the
anode to be about 60% of the total input.
Thus, it can be concluded from these results that
the rotating arc plasma jet can be used to supply
energy for the oxidation reaction under consideration.
The reactant throughputs depend on the input power and
the stability of the rotating arc.
3.3 Conditions for Achievin• Low Mean Gas Tem eratures In the Plasma Jet
The aim of this section is to investigate and
establish the limits for the production of a mean
reaction temperature around 1100°C in the apparatus.
Detailed experiments were carried out in order to achieve
this objective. The following is a brief account of the
procedure employed:
Initially, the temperature of liquid titanium
tetrachloride in the bubbler was set at a constant
value of 50°C. The sheath argon flow rate was set at
about 40 cm3 s-1. It was expected that large through-
puts of gas would be used in these runs, thus the mag-
netic field coil current was chosen near its maximum
range of 1.6 - 1.8 amps. The flow of cooling water
supplied to the anode and cathode were monitored using
rotameters. The change in the water temperature was
measured using mercury-glass thermometers. When the
water flows were stable, the main plasma argon flow
rate was selected and the arc was initiated. The current
was then reduced to the minimum output delivered by the
28
power generators, which were connected in series. An
argon carrier stream bubbling through liquid TiC14 was
precalibrated for TiC14 content using a cold trap.
Oxygen and argon carrier stream flows were selected
such that the ratio 02:TiC14 = 2:1. When the system
reached a steady state, all relevant parameters, e.g.
arc current, arc voltage, cooling water temperatures,
etc. were recorded. This procedure was repeated for
several plasma argon flows with a series of different
reactant concentration.
Using the experimental results, the mean reaction
temperature was calculated using a theoretical model
for an enthalpy balance around the arc region, as shown
in Fig. 3.5 below:
Heat losses to anode & cathode
Ar 02 T1 TiCIk Arc zone
Ar T2
02 TiO2 Cl2
I Electrical energy input: IV J
Fig. 3.5 Enthalpy balance model around the arc zone
x x Sx
29
c CpAr (T1 - To) =
(b-a) Cp62 + c Cpkr] (T2 - To) +
IV b Cp0 J [a CPTiC1 2
Ca Cp4a0
2 + 2a Cph
2 +
The following assumptions were made:
i. Perfect mixing in the radial plane.
Complete and instantaneous reaction.
iii. Effects of dissociation of the various polyatomic species on the general enthalpy balance are neglected; this can only be justified in dilute reactant concen-trations.
iv. Negligible downstream or upstream radiation losses from the arc.
v. The heat capacities for species at the reaction temperature were taken at the mean value between 3000 - 6000°K 07) . However, significant error must be expected in any such calculation much above 6000°K.
The stoichiometry of the reaction was taken to be
represented by equation (1) of section 3.1. This was
solved simultaneously with the enthalpy equation to give:
Fig. 8.2o: Particles sample from the wall of position 3. Ma .= 100,000X
119
pigment grade particles, because of the rare encounter
between molecules. Nevertheless, it seemed of interest
to examine the particles in terms of the above criteria.
Furthermore, in order to produce pigmentary particles
from dilute systems one has to allow them to agglomerate
as for example on the wall.
120
CHAPTER NINE
CONCLUSIONS
The study of titanium tetrachloride oxidation in
a plasma jet revealed a number of interesting and
unexpected features, which necessitated changes both
in the experimental programme and in the analysis for
the reaction kinetics.
Initially, the thermal distribution in a gas
stream that has encountered the rotating arc was
investigated theoretically. This resulted in a
criterion which stated that uniform thermal distribution
in the cross-section is established when the gas progresses
linearly by one arc diameter per are revolution. In
attempting to achieve relatively low mean gas tempera-
tures suitable for the oxidation reaction of titanium
tetrachloride, this criterion led to the conclusion that
within the capability of the present plasma jet design
the attainment of uniform thermal distribution is
invariably associated with temperatures far exceeding
those required. Accordingly, a new reactor design was
sought for.
A new instrument was developed as a result of the
need for a more direct method for the investigation of
thermal mixedness. The instrument is based on the
corona discharge, and was found to be capable of responding
to the high frequency temperature fluctuations encountered
in such plasma jet flows. The corona probe was utilised
in developing the*post-arc injection reactor, and in
121
establishing its running conditions. It was concluded
that this reactor was capable of producing a well
defined reaction environment suitable for kinetics
investigation.
The progress of the oxidation reaction of titanium
tetrachloride was followed by measuring the chlorine
concentration and temperature variation with distance.
In attempting to analyse such data kinetically, it was
discovered that the chlorine reassociation was much
slower than had been supposed, and it was necessary
to investigate this in order to allow the determination
of the true rate of the oxidation reaction.
The rate of the chlorine reassociation process was
best described by an expression which is independant of
the reactant concentration. This is probably a result
of the high dilution of the reactants by an inert gas.
The oxidation reaction was also best described by an
expression which lacked dependence on the reactant
concentration, and in view of this, no attempt at
inferring reaction mechanism was. made. The activation
energy in each case was deduced, though the lack of
dependence on concentration may not apply in more
concentrated systems.
The major contributions of this work, apart from
determining the activation energies of the relevant
reaction steps, probably lie in the development of the
corona probe and the discovery of the slow rates of
chlorine reassociation in the oxidation reaction of
titanium tetrachloride. The former is an instrument
122
which ought to be used more generally for the assessment
of gas temperature distribution especially in systems in
which mixing of temperature dissimilar streams is
encountered. The latter throws doubt on every previous
kinetic investigation of this reaction in slow systems
at these temperatures, and leads to the derivation of
the true rate of the oxidation reaction. These contri-
butions lay open paths for more detailed study of this
and similar systems.
123
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129
Read Input Data
Curve Fit
Ci(t) and T(t) RMINGM-16-o-SMINXN
Calculate
dCi(t) and dT(t)
dt dt
APPENDIX 1
COMPUTER PROGRAMMES
Print
Ci(t)= a bt ct2
TT(t) = at+bit+clt2
I End
Fig. A.1 : Flow Diagram for Exagramme Rate.
130
Pram Rat 2
C THIS PROGRAM CALCULATES THE RATE OF A FUNCTION BY C FITTING A SECOND ORDER POLYNOMIAL TO THE DATA POINTS C AND COMPUTES THE DERIVATIVES. C IT IS SHOWN HERE COMPUTING THE CONCENTRATION RATE. C INPUT DATA: PARAMETER VALUES TIME NO. OF DATA a POINTS
C OUTPUT: COEFFICIENTS OF THE SECOND ORDER POLYNOMIAL C AND THE DIFFERENCE BETWEEN THE FITTED DATA POINTS C AND THE COMPUTED ONES. C A SECOND OUTPUT INCLUDES A LIST OF THE INPUT DATA C POINTS AND THE RATE.
PROGRAM MAIN(INPUT,OUTPUT,TAPE5=INPUT,TAPE6=OUTPUT) REAL TICL4(150),AR(150),T(150),TIME(150),AR2(3),AR3(
*3,3),HOLD1(3),HOLD2(3),HOLD3(3) REAL AR1(4,3),R(150) READ(5,1) N
10 FORMAT(10X,8HTI0L4(I),10X *10Xt10HRATE CALC.) DO 9 1=1,N R(I)=HoLD2(2)+2.0*HOLD2(3 wRITE(6,11) TICIA(I),AR(I
11 FORMAT(10X,G12.4,6X,G12.4 9 CONTINUE
STOP END
t6HOXYGEN110X,10HTEMPRATURE,
)TIME(I) ),T(I),R(I) ,4X,G12.4,8X,G12.4)
SUBROUTINE RMINGM(A,N,M,B,C) C THIS PROGRAMME IS WRITTEN BY MR.HORSNELL.IT IS PART C OF THE OPTICS LIBRARY, AND IS INCLUDED WITH KIND C PERMISSION.
REAL A(NtM),B(M),C(MtN) DO 1 J=1$1,1 DO 1 K=1„M T=O. DO 2 I=1,N,
2 T=T+A(ItJ)*A(I,K) 1 C(JtK)=T
CALL SMINXN(C,M) DO 3 J=1,N DO 5 K=1111 T=0. DO 4 I=1„M
4 T=T+C(K,I)*A(J,I) 5 B(K)=1 DO 3 K=1914
3 A(K,K)=B(K) RETURN END
SUBROUTINE SMINXN(AtN) REAL A(N,N) INTEGER IN(50) IA=0 DO 1 J=ltN
1 IN(J)=0 DO 8 I=ltisi T=O. - DO 3 J=1,N IF(IN(J).EQ.1) GO TO 3 DO 2 K=1,N IP(IN(K).EQ.1.0R.T.GE.ABS(A(Jt K))) GO TO 2 IR=J
132
IC=K T=ABS(A(J,K))
2 CONTINUE 3 CONTINUE IN IF(IR,EQ.IC) GO TO.5 DO 4 L=1 pN P=A(IR:,L) A(IRIL)=A(IC,L)
4 A(IC,L)=T IA=1
5 T=A(IC,IC) A(IC,IC)=1. DO 6 L=1,N
6 A(IC,L)=A(IC,L)/T DO 8 K=1,11 IF(K,EQ.IC) GO TO 8 MA(K,IC) A(KIIC)=0. DO 7 L=1,N
7 A(K,L)=A(K,L)_A(IC,L)*T 8 CONTINUE IF(IA.EQ.0) RETURN M=N/2 DO 9 I=l,M
DO 9 K=1,N T=A(K I) A(K,I=A(KIL)
9 A(K,L =T RETURN END
133
TRIANG
SOLVE
Read Input Data
Multiple Linear
Regression GLSP
Print
Kt E
•
End
Fig. A.2 : Flow Diagram for Programme Main.
134
Pro;; gamma
C THIS PROGRAM SOLVES THE SYSTEM OF EQUATIONS SHOWN C IN CHAPTER 7. THE CASE SHOWN HERE IS THAT FOR C OBTAINING THE LEAST SQUARE FIT FOR RUNS G2 AND G3, C IN CHAPTER 8. C DATA= COMPOSITION TEMPERATURE RATE C M AND N MUST BE SPECIFIED AFTER THE DIMENSION
STATEMENT. C M= NUMBER OF' DATA POINTS ' C N=NUMBER OF PARAMETERS TO BE FITTED
C EQUATION: RATE=K*EXP(E/RT).
C OUTPUT= PRE-EXPONENTIAL TERM ACTIVATION ENERGY C AND THE STANDARD ERRORS IN THE FITTED PARAMETERS C AND THE VALUE FOR THE RATE COMPUTED USING THE FITTED C PARAMETERS AND THE INPUT TEMPERATURES.
PROGRAM MAIN(INPUTOUTPUT,TAPE5=INPUT,TAPE6=OUTPUT) DIMENSION A(50,10),B(50,11),X(10,11),U(50,11),SUM(11),