THE STUDY OF THE SWELLING PROPERTY OF BlTUMINOU3 COAL
by
Wei Fun Sung
Submitted in Partial
Fulfillment
of the Requirements for the Degree of
Bachelor
of Science
at the
MASSACHUS~
INSTITUTE
OF TECHNOLOOY
May, 1917
Signature
of Author
Certified by
J. B.c Howard, Thes:ts Supe~isor
Accepted by
J~::hn --
De
mental Committee on
uate Theses
Und
ARCHIVES
...
~ ~-.~." .,,--.---
''':'.~
...
...,..~.,-,.-'
~..
~~l,.t,"::
, I
i
1994
ACKNOWLEDGEMENl'S
.
;
f
I would like to thank my thesis
for his advice and his patience
this
!~upervisor, Professor
Jack Howard,
in granting me extra time to comPlet~
18per.
Other people whose help
Ted Bush,for his assistance
am
encouragement I deeply appreciate
in collecting
their plrt in the typing effort.
include
samples, and other friends) for
!!!!. study
of the Swelling Prol)ert,y~
Bituminous
£E.!!.
page 1
1. Summary
2.
Introduction
2
2.1 General Background
2
2.2 Objective
2
and Motivation
4
3. Bacl$ground Material
3.1 Coal Plasticity
.5
3.2 Rheological Property of Coal
6
3.) Physical structure of Char Particles
9
3.4 Multiple Reaction Model
12
3•.5 Mode of Transport of Volatile
14
).51 Bubble Initiation
16
3•.52 Bubble Transport
18
3.53 Bubble Death
19
3.6 Particle Size Trend Prediction and Temperature
Trend
24
:Prediction
4. Experimental Appan,tus
am
Procedure
26
4.1 Apparatus
26
4.11
26
Laminar Flow Reactor
4.12 Microstar Light Microscope & TEM 200
28
4.13 TZG J
28
4.2 Procedure
30
4.21 Preparation of Closely Size-Graded Coal Particles
)0
4.22
31
Preparation
of Char Sample
4.23 Preparation of Particle Images For Size Analysis
32
5.
4.24 Determination of Average Farticle Sizes of SamPles
33
4.2.5 Determination of Fresh
J4
Feed
Agglomeration
"Results And Photographs
36
6. Discussion
66
6.1 Error Analysis
66
6.11 Determination of Particle Size
66
6.12 Constant Residence Time and Heat Transfer Limitation
67
6.2 "Treatment
of Tar Comensation
on Char Products
69
6.3 structure of Coal Residue
71
6.4 Relationship Between Swelling Ratio and Particle Size
74
6.5 Relationship Between the Swelling Ratio and Temperature
76
6.6 Agg;1.omeration
77
7• .Conclusions
78
8. Recommemations
79
9.
Appendix
81
1.
SUMMARY
The purpose of this
of. Pittsburgh
NOe
study \tI~ to determine the swelling property of
8 seam coal under different
The experimental variables
experimental conditioDSo
were the average initial
particle
and the peak temperature of the laminar I1.ow reactor
coal particles
employedto obtain paticulate
samples for this
of the
sample increases with the average initial particle
particulate
square methcxiwas us~ to eorrelate
between the average swelling ratio
..
study.
The study has shown that the average swelling ratio
A least
size of
siz80
the linear relationship
and the average initial
particle
size
for unagglomerated particu:la te samples formed at a constant peak
temperature
J
and the correlation
"'M. satisfactory
e
The study has also shown that there is a close relationship
between
the rate of thermal decomposition of coa.l and the swelling ratio
particulate
samples 5 namelyJ they both peak at a certain
Attempts .were madet.o correlate
of the
temperature.
the average swelling ratio
of the samples
with the average temperature of th$ Ja.mina.r flow reactor at a constant
average initial
particle
size.
The correlation
WA~
not
probably due to a lack of information on the reactor
very
gooil,
average. temperature
correspom1ng -to the average maximum
swelling of the particulate
as well as a lack of data obtained at the low temperature of the
laminar flow reactor.
samples,
2
2.
INTRODUCTION
2.1 General Background
Recently,
there
has been a growing cOJlJllerc1al interest
During the past years,
of coal and coal derived fuels.
has been directed
procedures
t
toward the developaent
in particular
and liquids,
i.e.
for natural
and liquefaction.
of the material.
of coals -:.ia Oc6 to 1.9 whereas,
grading can be accomplished to a certain
elevating
volatile
which is thermal
processes for upgrading.
The typical
for
atomic hydrogen
example, it
is 4.0
The task of up-
extent by coal pyrolysis.
decomposition accomplished by
the te.lJlpera.ture, the coal is converted. to a hydrogen rich
fraction
and a carbon rich solid residue.
react with hydrogen gas rapidly during or just after
(Anthony ani Howard,
describe -the rate
coals upon heating,
Anthony's
aa1n task of the
The
gas and about lea or 1.9 for erude 011.
In coal pyrolysis,
research
of improve:!. coal utilization
developaent is to investigate
the hydrogen to carbon ratio
to carbon ratio
intensive
processes for convertiDg coal to clean gases
gasification
coal utilization
in th$ .use ~. ~__
1976).
The residue will then
volatile
release
There have been many models developed to
of thermal decomposition and volatile
ani the most satisfactory
yields of
mcxlel developed is
Multiple Reaction Model.
2 ~2'Objective
And Motivation
Coal can be characterized
as plastic
whether it goes through a plastic
or nonplastic
depending upon
region upon thermal heating within
'2...
J
the experimental operating conditions of interest,
namely, rapid heating
o
~
.
rates of 103 a/see to 10 a/see, pressure ranges of 1 atm to 69 atm and.
o
0
temperature ranges of 400 C to 1000 C. It has been observed that some
coals swell under moderate and rapid heating,
is associated
as
'amountto
1929) •
wi:th plastic
coals.
and. .the swelling phenomenon
Someworkers have observed swelling
muchas a 4000 per cent increas.e in volume (Sinnatt,
The swelling of coal particles
will be a potential
1928
problem in i:.he
scaling up of environmentally and economically sound.pyrolysis processes,
especially
those based on the use of fluidized
Fluidized beds consists
phase.
particle
The properties
size,
i.e.
beds.
of two phases, a bubble phase and a particulate
of fluidized
the superficial
bed.Qf't strongly dependent on the
incipient
fluidization
velocity ...
the pres~ure drop across the bedlaM. the proportion of gas passing upward.
via .the bubble .phase and the particulate
coals,
particles
phase.
will swell and becomesticky
In the case of plastic
as they rise,
and both the
swelling and agglomeration of sticky partic les will change the behavior
of the bed.
the plastic
Therefore, it is desirable
coal under different
The primary objectives
~o study the swelling property of
experimental comitions •.
of this
study can be stated
1. To experimentally determine the effect
size on the swelling ratio
specific
(final
constant peak temperature,
of initial
diameter/initial
set of experimental conditions,
coal particle
diameter) under a
namely, inert
constant reaction
as follows:
atmosphere,
time and constant heating
rate.
2. To experimentally determine the effect
of temperature on the
4
swelling
ratio
under the following conditions,
constant
reaction
timeJand constant
A laminar flow reactor
particulate
initial
particle
The
in. a gaseous
of coal particles
is similar to that
of a fluidized
has exceedingly better
and the agglomeration of fresh
of feeding.
size.
study of swelling ratio.
reasons for the choice' were: The dispersion
laminar flOK reactor
atmosphere,
of the Badzioch type was used to obtain
samples for the present
medium of a flow reactor
namely, inert
control
bed, but a
of reaction
time •.
feed can be minimized with good techniques
Since the temJerature
is
of the. laminar flow reactor
the average and the peak reactor temperature 'Wereused to
constant,
evaluate data obtained in this study.
The heating rate
was in the range
0
Q
of 43200 C/soo to 64000 C/sec depending upon the peak temperature
(See Appendix A-S)
of the study 'Werethe sizes
coal particles
and the peak or the average temperature
Nine different
particle
size distributions
were examined which bait the following
diameter in pm)
(affective
Five different
o
6so
o.
and 600 C.
The reaction
:3 •..
used.
0
The major experimental variables
41.
not
I
No. 8
average particle
Searl
coal
sizEG
261, 202, 164, 14S, 122, 89., 71, 46 and
peak temperatures
The reaction
of the reactor.
of Pittsburgh
initial
of
were employed:
atmosphere was heliua.a.t
time was approximately
o
••
960, 8)0, 750,
a. pressure
of 1 atm.
1/3 secord.
BACKGROUND MATERIAL
During the past years,
behavior
of plastic
efforts
have been made to study the physical
coal at an elevated temperature with a rapid heating
5
rate.
ana
The commonlyobserved sequence of events is:
'solidification.
'plastic
More specifically,'
coals the coal particles
first;
decOIIlpositlon becanes appreciable,'
like
intumescence J
upon heating a bed of crushed
soften and fuse.
As thema.l
the bed swells and becomes foa.m~
(Brown am Waters t 1966; Chermin ani Van Krevelen, 1957; Gibson and
Gregory, 1971; Waters, 1962).
particles
resembles a boiling
Under rapid heating condition:», a bed of
liqu:1d (Anthony, 1974).
The intumescence
believed to be the fomation of gas bubbles inside the coal
is gen~lly
mass.
fusion,
After a significant
18rt of coal has decomposed, the mass solidifies
into coke and it has a much higher melting point than the original
1927) c
(Audibert,
Here the main concern is the physical behavior of
bituminous coal particles
different
upon heating,
experimental variablesCi
ioe. swelling property,
Hence5 it
is of interest
some of the s~udies on the physical properties
contributed
coal
to the present understaniing
of plastic
of swelling
under
to review
coals which have
of bituminous coal
upon heating •
.'.1 Coal .Plasticity
The chemical complexity of coals is partly
petrographic
cOllponents of the organic part.
due to heterogeneous
Neave1 (1915) has made a
sttxly on the effect
of marcerals on coal plasticity',
and he
that the plasticity
of bituminous coal is primarily
attributed
presence of marcerals
concluded
to the
axinite and vitrinite.
Early work done by Audibert (1927) has shown that the plastic
is transient,
ani the rate
of heating greatly
affects
state
the point of initial
ius'ion or plastic
state.
He has concluded that the initial
is always higher for higher heating rates,
melting point
and is independent of, coal
/
rank.
The rate
fluidity
(1956)
lor heating also has a significant
and duration' of the" plastic
region.
Vall Krevelen's .study
increasing heating rate.
the plastic
the effect
o
cl-.in •..
are associated
Whenheated at a constant rate
region lies between 420°C ani~500oc.
of heating on coal flUidity
In too same literature,
F~
for heating rates
Van Krevelen (1956)
that the developllent and decaying of fluidity
Walters (1962)
relationship.
has also performed a similar
between rates
and decaying of fluidity.
of fluidity
the fluidity
'-2
Figure ..
'j-la'illuStrates
o
from 0.7 C/min to
has also. determined
{See F!gure
study on the _
demonstrates the typical
decomposition at a heating rate
1Diic:a.tes that the rate
of plastic
of O.OSoC/sec.
of thermal decomposition ani the developnent
and rate of thermal
and it strongly
with the
and ~he rate of thermal
decomposition upon heating both depend on heating rates.:
3-1b).
.
':ot.p'iastic .
has concluded that the broadenirig;~of duration
region and the increase of maximum fluidity
7.2
impact on the maximum
coals
behavior
of 3DC/min,
of thermal decCIIPQSitoD
controls
c
3.2 Rheological Property of Coal
Since
tem~ture
tempera.tur~ relationship
is aa experimental varlable,
in. pyrolysis
In Water's investigation
number of plastic
coals,
'the ~iscosity-time-
should be studied.
(1962) of rheological
he observed that plastic
properties
of a
coals behave like a
1
\
I
!
;
\I
t
/
I
-'
.....
o•
~
o
o•
~
.\t'\
.. oo..
o
o
~
o
•
o
.-t
o
o•
(001% -'+Jl)
~VH
o
o
~.....
N
o
o
.-t
o
o
o
.....
SISX'IOHA-!
o
o
CD
~
o
(~Ul/~a~ap
o
o
o
.::2-
.~~)
:!lJ,W NOIJ,VIDH Hm:!lSfiD
o
o
C\l
8
Figure 3-2
Fluidity (full
line)
decomposition
(broken line) curves
(heating rate, 3°C/min)
(Waters, 1962)
and.
9
Newtonian fluid under normal stress
Based on this
observation,
during the ear~y stage of fusion.
he applied 'the Andrade equation for the
liquid viscosities
4{
exp(E/RT)
= . A.
ani found that- the plastic
relationship
well.
The activation
energies of flow for coals, E's.
and were fOUDdto be in the range or. 50
The values are high for Ol.'dinary Newtonian fluids
The AIXiradeequation is applicable
thermal decomposition is negligible
in that
19JQ.}\ '
region of the early stage of fusion obeys the
determined experimentally,
kcal/mole.
(ADirad~,
region am not significant.
thermal decomposition is active,
composition of coal particles;
only to plastic
there is a drastic
100
(Waters.,i962).
regions where the
because' the chemica.l changes
At the plastic
-
were
at
coal
region, where the
change in the chemical
hence the Andrade equation will no longer
be valid.
Recognizing the deficiency
the following PRMviscosity
of the equation,
Lewellen (1975) postulated
temperature relationship.
'1( = I1f 1(dri/ dt)-1
where d~dt
, -.,~~.~
.~.~.,
..
:Parameter.
is rate. pf pyrol)'Sis,
".
The value of
close relationship
physically
3.3
justifies
empirically
determined
6
used in his study was 3 x 10
between the fluidity
and the rate
sec/rse.
The
of thermal decomposition
the above relationship_
Physical Structure
A.
-1(.
and ~ is an
of Char Particles
rigorous X-ray study of the internal
of coals was madeby Hirsch (1954).
structure
of a wide range
Hirsch has developed a mexiel
10
to characterize the structure of coals.
Accordingto h1s model,
I
bi tum1nous 1s classified
characteriz~
as having a
liquid
fC
the near absence of pores.
by
structure
The striking
difference
(Woodset al.,
1967,
high large~scale porosity
Feldmazmet al •• 1m).
can be explained by the formation and motion of
Umer a hot 'stage
bubbles inside the coal pLrt1cle during pyrolysis.
microscope, the }articles may be seen to soften,
while large bubbles of gas repeatedly
beCOID8.
roUDl.
L-U'
bre&k through the particle
.
swell
surface
continues (Ergun et ale. 1959' Woodset a1•• 1967.
as pyrolysis
Spa.ckman and Berry, 1968).
entrapped
which 1s
But. an examina.tion of
char produots of thermal decompositlonrev~led
within the char pu:ticles
n
gas bubbles
Large-scale
(Woods et
porosity
1967.
al.,
is presumably formed 'Qy
Feldmann et
al.,
1971)•.
The development of cenospheres, ~hlch occurs when plastic coals
are heated at B10derate or rapid rates in the absence of air,
the extreme case of large scale porosity
1926, 19271 Simatt
Schora,
1967.
eenosphere
et al.,
Lightan
am
represents
1924,
(Newall am Sinnatt,
1921. S1nna.tt, 1928, 1929. Masonand
street..
1968. street at
al., 1969).
The
is essent1ally a hollow and swollen char particle (see-
Figure 5-Ja),with a reticulated
ribs and windows.
are transparent
structure containing -b,o major parts,
The ribs an brownish-black
brCll.nlsh thin fUms.
substanceS!'a.nd
A more detailed
the windows
examination of
cenospheres in the ..windows revealed:. :bhe .presence-of' minute torms •. '(See
Figure 3-:3).
In the Newall Jt.M Sinna.tt study (1924) ~ it vas observed
that the
formation of ceneshperes .under a mcxierate'heating" rate ill the abs'ence
11
"
"
~~.~."'.;
.
"
.' ......
~
. "'"
..
,:
'
....
."
."
~
'.~"
. '.-
....
\.
.J"
t~ ..
,,;,
.
~,
,
t
"i:
11
..
•
,'J
,
,"
,:.
• ;j
..
'.J
...--"
__•.
..
.J '
I
;
.
-1'
i
I'
-
Figure )-3
Cenosphere formed at 650 C (360x)
(Newall and S1nnatt, 1924)
Showing minute forms
J
12
of air is temperature depement.
The ribbed windowstructure
be clearly detected until 570°0 to 600°0 was reached.
in
could not
With an increase
temperaturs, the detection of cenoshperes Is easler~ and the network
structure increases in ~ize
0
The increase in size of the network structure
causes the rib and windowstructures
nearly colorless at high temperature.
~
0
to becomethinner.
However, when the coal particles
were heated to 800 or 900 C, the distinct
not be detected,
the particles
-
ribbed wlmow structure eould
become oplque am. shrank in size.
In another study of effects
structure
The windowsbecome,
of different
of cenosJileres. by Sinnatt,
atmospheres upon the
McCullochand Newall (1927), it
was observed tha.t cenos.phares formed in the presence of h~ogen
essentially
nitrogen.
structurally
were
identical with those formed in the pre~ence of
Whenan at.mosphere of steam was used, the formation of ribs and
windows was partially
inhiblted.c
In general f the poresi ty of the fine stmcture of char iBcreases
with an increase in temperature.
But, the accessibility
of these pores
to the penetrant molecules does not follow the same trena.
coals, the accessibility
In plastio
of pores to the penetrant molecules displays
C
tJ
a sharp minimum in the Plastic region of the coal (600 0-1000 C) because
C
Q
of an absence of continous, ~res, and increases below 500 .0 to 600 C.'
(Franklin,
1949&, 1949b, :Som and Spencer, 1958, Van Krevelen, 1961; Evans,
1970) •
3.4 Multiple Reaction Model
There are many kinetic models developed
to descrlb&l" the temperature
1)
dependent behavior of coal pyrolysis.
The Multiple Reaction Mexieldeveloped
by Anthony (1974) has been proven to be in good agreement with the
experimental data.
rate
assumption of the model is that 'the overaU.
The first
yield is the sum of a large number of parallel
of volatile
first
order reaction~~
dV =
dt
~
dt =
Cb
~ ,dV~
?'dt,.
,
..
ki(V •
I
In the above expression,
..; V. ) ~
•
subscript
i denotes
no subscript
denotes overall reactions.
of volatiles
evolved at time t,
V at infinite
species.
reaction
and
weight t'ractlon
and V* is the totallfei~ht'fractlon
c
E and k are the activation
i
i
factor respectively
particular
V is the total
Vi and V*
1 are similarly
time.
Q
in the above rate
of
defined for each reacting
.
energy and the preexpontential
constant
of Arrhenius type.
o
k
i
is to be determined expo....rimentally.
The second assumption of the _m6:ielis that
Distribution
(j
with mean activation
a Ga~sian
energy of E.and standard d-ev1a.t.loo
is used to determine the activation
energy distribution
of each
'r
..
r"
r,
~.
reaction.
Combining the two assumptio~s,
am
lf
_
Anthony showed that
y*y; y
= .~~
k
dt
J
assuming k is identical
i
f(E)dE
for all
reactions,
.
o
The experimentally determined values of Eo' 0", k
i
*
and V have been founi
14
13
.
to be .54.8 kca1/mole, 17.2 kca1/mole, 1.67 x 10 /sec and 0.462, respectively,
No. 8 bituminous seam coal
for~ Pittsburgh
A1thought Anthony's mcx1.e1
successfully
described the temperature
dependent behavior of bituminous coal pyrolysis
3-4).
Suuberg (1977) also observed a similar
with particle
sizes
between volatile
size.
"(SeeF!gure
trend of yolati1e
0
yie]ds
To explain the ~pparent deviation
mechanism has been postulated,
4
0£
sizes,"
namely, reaction
generated by coal decomposition with the remaining char
to form solids and gases during the volatile
formed by the secondary
re",ction is deposited
thereby decreasing the total
1974)•
is a decreasing
yields from the Multiple Reaction Model at la,r,ge particle
a secondary reaction
particle
there
in his study using the captive heating technique to
.obtain " the volatile :yields
volatile
8
yield. with an increase in particle
trend of volatile
1976).
(A~thon7.and :H~ard,.
:escape•. Theqsolid
inside the remaining particle,
w:eight loss of the volatile
With increased. particle
size,
the volatile
(Ant"hony
J et ale,
must travel
farther
before escaping and thus has more time to react with the char particle.
is increased. and the
Consequently the extent of secondary reaction
volatile
yield is reduced.
secondary reaction
pressure
of volatile
~te
Lewellen (1975) assumed that ~he rate
is a first order reaction
and is proportional
of
to the
inside the coal particle.
of secondary reaction:
~ = kdP
where kd is the reaction rate constant of Arrhenius type.
3.5
Mcdeof Transport of Volatile
The macroscopic evidence af~the formation and motion of bubbles inside
15
PYROLYSIS YIELD AS FRACTION OF ORIGINAL COAL MASS
0
•
\..-)
0
0
•
g
0
•
\.n
0
0
•~
0
0
-...J
•
0
0
I:I:j
f
l\)
.I:~~
~~
c'~
t+
~~
gl
~..,.
a....,a
2~
....,rn
•
,,-..
..,.
N
~
0
!
~
~
I-t
g
f,;j
0
a
t:::J
I-t
>
~
t=J
:0
,,-..
:3:
I-t
a
~o
::r::S
Bid
~..,
-.....at:
~~
.;:-~
........
~
..,.
ti:
(J)
..
0
\..-)
~
.
oJ01
!
~
~
{Jl
1
........
0)
00
16
the plastic
coal particle
leads to the assumption that bubble transport
is an important mexieof transport
of v.olatile froll plastic
coals during
I
coal pyrolysis
An analytical
c
model/has been developEd by Lewellen (1975)
to describe the behavior of bubbles inside the plastic
the sequence of bubbles inside the coal particle
coal.
He pictured
as: (1) init1ation
of
bubbles, (2) growth of bubbles and (3) bubble death.
3.51 Bubble Initiation
Twomechanismsof"bubble initiation
proposed.
One is analogous to initiation
cavity at the liqu:id-solid
interface
analogous to bubble initiation
bubble initiation,
(41 ).
1977).
mechanism. Instead
distribution
function for
He assumed that the function
volumetric rate of bubble generation
the distance
(~I
dt)
to the nearest surface tQ which volatiles
could otherwise escape ( d
). ani the initial
min
(ao)
the second is
solution to describe the behavior of
bubble generation in the coal particle.
viscosity
used the first
he adopted a probability
depends on four variables t
t
in boiling water (Attar,
of developing an. exact analytical
coal have been
of bubbles from a vapor filled
(Lewellen, 197.5)
Lewellen's study of bubble initiation
particle
inside the plastic
radius of the bubble
•
Lewellen!s Probability
Distribut ion Function of Bubble Generation:
Figure 2-5 shows the concepts of bubble generation •. ~
is the initial
bubble size probability
distribution
is an empirical bubble generation constant.
concepts of bubble generation).
function. and ~
(See Figure
3-5
for
17
o
0
coal J8rllcle
viscosity -11
of
rate of volatile
generation
= (d~/dt
Figure
.'.
4
)-5
...
-'pot~'nt).al.'.
bubble
at.
~r;s"cf) ".
.
Concepts of bubble generation
(Lewellen, 1975)
.•
't
'
:
.
18
3•.52
Bubble Transport.
Lewellen's lengthy developnent of bubble growth (1915) assumes the
following physical conditions
1. The coal particle
of a plastic
is
coal particle.
homogeneous, isotropic
2. The coal :Particle 1s isothermal for all
3. The particle
is subject to no extemal
4. The coal particle
and spherical."
tble.
forces other than pressure.
has two homogeneousconstituents,
phase and a particle
' ..
a. ,,:olatile
phase.
Based on the above assumptions and other assumptions. i ..e. ideal
behavior of volatile,
negligence of the density
compare:lto that of the particle
volatile
and particle
and outer shell
phase, incompressibility
of bubble surface
the rate
In addition
an analysis
I
phase
of both
phase, and constant surface tension
performed to determine
on Table 3-1).
of volatile
for the inner
of momemtum
transport
of bubble growth,
a..
lias
(See EquationJ-2
to the hydrcxlynamicconsideration
of the
bubble growth, Lewellen (1975) also developed a mcx:lelto describe the rate
of increase of mass of volatile
inside the coal" particle
instantaneous trans port of nellly generated volatile
which in turn will increase the rate
the mass flux of volatile
on the total
transport
of bubble arowth.
this
plus the surface area of the coal partic~.
of secondary reaction
to the bubbles,
In his study,
is assumed to be equally distributed
surface area available,
flux per unit area, F.
due to
is,
the surface areas of bubbles
Equation 3-3 show the mass
Lewellen (1975) has also considered the effect
of the rate
of mass accumulation inside the bubble.
_...
,I
19
He assumed that
only solids
formEd from secondary reactions.
By a
simple mass balance, the net mass flux to a bubble is determinEd.
Equation of 3-4 on Table 3-1) e
Equation ;3-13 on Table 3-1 shows the.: expression
of the se60ndary reaction. rate'cbflstant.
total
(See
rate of the secondary reaction
Equation 3-12 describes
per ~icle.
bubble growth and concepts of secondary reaction
the
The conceptsof
chemistry are shown on
Twomechanisms of bubble death have been prop~ed by Lewellea (1975),
namely, dea.th through escape and death through inter5~ction.
3-8 for concepts of bubble death).
instantaneous
For' death through escape, an : .
expulsion of bubble contents
fro'Illthe coal particle
assumed when the bubble wall reaches a critical
surface
of the particle
contracted
distance
and the volume of the particle
by an amount equal to the bubble volume.
for coal particles
tlat
are in their
In death through intersection,
volumes of the individual
plastic
(~p)
is.
fl.'l)m
the
is instantaneously
Th:is 1s onl:? true
region am lave high fluidity.
the walls of two bubbles touch ea~h other and'
the two bubbles combine into one.
will depend on the locations
(See Figure
The location
of the newly formed bubble
of the bubbles before they intel:5act ~
bubbles.
the
(See Equation 3-7, 8, 9, 10 on Table
3-1) • The size of the newly fomed bub'ble will be detennined from the
equilibrium
condition;
(See Equation 3-ll
The total
that
is, the rate
of the bubble growth is zero.
on Table~3-1) •
volume of the coal particle
volume of the particle
phase plus the total
at any time is the sum of the
volume of the bubble phase or
20
~---
Ii'
'~
--
",."
--- ---
i
.2t
volatile specie~""~
~nttre' ~bble .
solids deposi-
.
."
\
tion at bubble
surface
through
thermal decom- /
position of
volatiles
/
diffusional
,
/
"-
.
.
and hydrodynamic
transport of gases within bubble
Figure 3-7
Concepts of secondary reaction chemistry.
(Lewellen,1975)
DEATH
THROUGH
INTERSECTION
-
-
DEATH
THROUGH
ESCAPE
bubble on
'verge of
0
, .)iUJt~l~~;?
-on ,~~ge ~~f .
. intersecti'on
escape
"bubbles)
bubble
intersect --
'escapes
- -ii1s~n~n~pu~ ..--_:
equilibration-
I
"0
1
1
:
-1nstantane"ous: --'
"equilibration..- _:
.new
bubble"
center
~at
'of
.mass of orJ.ginal
bubbles
Figure 3..;8
Concepts o:f bubble ~death '(Lewellen, 1975)
.
"
2)
~
I
i
,....
Po.
~.I
.....
:1
,
I
f
C""\ or4
cd
I
I
I
t
I
i
I
I
I
I
J
I
I
i
N
•
rr\
rr\
I
C"l
..:t
I
rr\
;
i
--t
I
1
I
i
I
!
i
I
f
~I
I
I
I
I
I
I
I
I.
i
•
[
!
24
the volatile
total
phase.
The size of the coal particle
volume assuming the coal particle
is calculated
from the
is a sphere.
3.6 Particle Size Trend Prediction AndTemperatUreTrend Prediction
In Lewellen's simulation
particle,
(1975) of bubble transport
he incorporated" Anthony's Multiple Reaction l-fodel for the
estimation of the rate of volatile
PRMviscosity
reaction
as lRrticle
5
of coal particles
size increases.
o
on Table 3-1 to predict
and the extent or- secondary
0
particle
temperature of 1000 C.
of 10'00'0'°C/sec f pressure of 10 atm,. init!U hbb~
x 10'-6 cm, M-', =
3
x 10'-6sec / psc a.?ld ~
= 6x
10'10'-2
em
Cl
J-9~
It is clearly
swelling ratio
size,
ani the volatile
increases with particle
is nearly linear
in too particle
size range of 120'
pm
shown that the
to 230'
yield ..
pn,
and it
size range of 230 pm.
increasing. trend is primarily due to an increase in the fraction
Of the'"1lumberof. generat.ed bubbles trapped in the particle
a longer distance
particle
of.
The increasing trend of the swelling ratio
then i.1'lcreasesmonotonically above the particle
The linearly
.alma of
The results
his simulation are presented in Figure
decreases with p!--rticle size.
and
The conditiom.of his simulation were:
temperature of 298 C, final
particle
heating rate
generation of one coal plrticle,
prediction with the equations listed
the trend of swelling ratio
initial
inside the coal
each particle
has to travel before escaping.
size increases beyond 230.pm, t~
b'ecomesmore significant,
~ a -result~'of -
and a greater
effect
As the
of the secondary reaction
loss of bubble mass results.
In
turn the bubble volume is reduced' because of the smaller ;rate' of bubble growth.
Therefore,
instead of a linear
increase,
monotonic increase in swelling ratio
above 230'
m.
the trend shows a non-linear but
as the particle
size
increyee
a.
25
0.4
:z;
0
H
E-tCl)
0.3
~.~
~
tf)<
<0
0
E3...:J
r:l<
0.2
HZ
>tH
tf)a
HO::;
~O
Hrz.
00
0::;
0.1
~
..
0.75
---Coo
800
-. - 1000
PARTICLE DIAMETER (MICRONS)
Figure 3-9 Predicted trends in volatile yield and
particle swelling with particle size using
PRM viscosity calculation.
(Lewellen,-1975)
26
The author is not aware of any analytical
predict
effect
the effect
of temperature on swelling ratio.
on temperatUre on the- swellwg ratio
determined experimentally.
rate
solution
particle,
Therefore, the
of bituminous coal has to be
However, since it is believed that the
of bubble generation inside the coal particle
upon the viscosity
developed to
is part~lly
dependent
and the rate,~of 'thermal decomposition of the coal
it was speculated that the swelling-temperature
relationship
'"
would be similar to the fluidity-time-temperature
decomposition rate-time-temperature
Section 3-1)
4.
4.1
I
na.'Ilely, all
EXPERIMENTAL
relationship
or the-.:tMrmal
in pyrolysis
of them peak at a certain
(see'
temperature.
APPARATUS AND PROCEWRE
Apparatus
The laminar flcrill'reactor
constructed
needed for this
for used in previous research.
study had already been
A Microstar Light Microscope
and a Transmission Electron Microscope 200 (TEM200) were used to
photograph the representative
for the counting of particle
Flow Reactor
A simplifi~
diagram of the reactor
carried
employed in this
A s;aall stream of helium carrier
the sample particles
into the reaction
tube.
gas
study is shown
(5 - 10 cc/min)
through a water-cooled feed tube, 1/16 inches
A vibrator
was placed midwaybetween the
top of the feed tube and the top of the reaction
of the feed tube.
and a TZG3 was used
sizes.
4.11 Laminar
in Figure 4-1.
i.d.,
sample particles,
tube to avoid plugging
The main gas (helium) was fed into the reaction
tube
••
\
27
CARRIER
- GAS
..
..
..
•
MAIN
FLOW-:;
STRAIGHTENER
. GAS
:
REACTION ..
TUBE
I'
\
."t .. -
:.sAMPLE
,.
QUENCH
~A~ER ~,
o~
.•
.
'~'-
PROBE
CERMIC
VIAL
F~e
4-1 Laminar flow reactor
28
through an expansion chamber to insure uniformity
There was also a flow straightener
prevent a spiral
placed at the end of the feed tube to
flow in the reaction
tube.
The flow rate
was set to insure a laminar flow in the reactor
of interest.
(See Appendix A-3).
ion tube was constructed
the reaction
in the gas flow.
tube at the temperature
The one inch i.d.,
tube was not vertically
8 inch long reaction zone with the insertion
probe showed no appreciable
collect
of
The
tube overlapped. with the sample probe,. and the
zone was only eight inches long.
Appendix A-2).
long react-
uniform (See Appendix A-i).
sample probe was water-cooled to quench the reaction;
zone without the insertion
22 in'.
of 99.8% aluminum. The temperature profile
lOKer part of the reaction
reaction
of the main ~
deviation
therefore8
the
The temperature profile
~f the
of the water-cooled. sample
from that
of the water-cooled
of the 8 inch reaction
sample probe.
(See
A ceramic vial was connected to the sample probe to
the char samples for size determination.
4.12 l*1icrostar Light Microscope & TEM200
See the manuals of the Microstar Lig~t Microscope and the TEM200
for a description
of the apparatus and methcxls of operation.
4.13 'I2G :3
The TZG:3 was used to determine the average particle
samples of interest.
The TZG:3 employed in this
Twomeasuring relationships
number were incorporated
between the iris
size of -tkt.
study is shown in Fig. 4-2
diameter and the counter
in the TZG:3, namely, the linear
and exponential
29
1 2
Figure 4-2
TZG 3
3
30
relationship
linear
between the iris diameter and the counter number.
mode of operation is used for narrow particle
size distributions.
and the exponential mode of operation;,"is used for wide particle
distributions.
The
size.
For each measuring mo:le, there are two measuring ranges,
the standard range (1.2 mmto 27.7 mm)and the reduced range (0.4 mmto
9.2 mm). The TZG:3 also has two modes of recording the relationship
between the counter number and the iris
curve and the cumulative curve.
altogether.
In this study,
a standa:rd linear
ation,
diameter, namely.the distribution
There are eight modes of operation
only two modes of operation were used:
modeof"operation
both using the distribution
and a reduced linear mode of opercurve.
The method of operating of the TZG:3 is very simple.
of operation is chosen, the diameter of the iris
with the rotary
erest
until
is adjusted manually
switch to cover the area of the particle
the two areas coincide.
After the mode
image of int-
To recom the size of the particle
image on the counter number, the foot switch is pressed.
mark on the image and releases
This makes a
the numberc
4.2 Procedure
4.21 Pre:pa.ration of C.losely 5ize-Graded c.oal P.articles
In order to examine the swelling property of different
sizes
of Pittsburgh
needed.
SeamCoal, closely
size-graded
particle
coal particles
are
The molecalar sieve method was employedto narrow the particle
size distributions.
{See Appendix A-4 for the relationship
between
31
u .S.
Standard mesh # and particle
size).
Nine different
closely
graded coal samples were obtained and each sample was transferred
crucible
and stored separately
with silica
in a s~all
dessicator
partially
sizeto a
filled
gel to prevent contamination from air moisture.
4.22 Preparation
of Cbar Sample
After the proper size range had been chosen, approximately 20 mg of
the coa.+sample was spread carefully
_ belt
of the reactor.
on the center portion. of the feed
The length of the spread was usually 3-4 inches
long, and the width of the spread was approximately t/8 to t/16 of an
inch.
The exact amount of the coal charged to the reactor was determined
by the w:eight difference
cruciblec
between the initial
and final
weight of the
The feed tube was closed during the process of feeding to
prevent partic les from ~ntering the reaction
the reaction run.
After the charging of the reactor,
laminar flow reactor was sealed,
sample probe.
tube prior to the start
of
-the top of the.
and a ceramic vial was connected to the
Then th~ "flow velocity
of the main gas was set at 2 ft/sec.
The top of the reactor was pressurized. slightly
above one.atmosphere
with the feed tube closed to prevent back flow of the main gas in the
rea~tion tube.
•
The final
the feed tube and tuming
J'
belt
was set at tln./min.
steps were turning on the vibrator,
on the feed belt.
The velocity
opening up
of the feed
Each run lasted about 6 minutes.
.
At the end
of each run, the ceramic vial was disconnected from the sample probe and
weighed before transferring
the char sample to a glass bottle
The weight of sample collected
was calculated
for storage.
from the weight difference
between the initial
and final
weight of the ceramic vial.
4.23 Preparation of .particle
Images for Size Analysis.
After the sample had been collected,
uniformly on a microscope slide,
a portion
of it 'Was"spread
and examined under the light
microscope •
. (The procedure for char products produced at the peak temperature
'Wasslightly
different
cation used was
sentative
4X
or
sample sites
The number of particles
samples.
from the above.
10X',
depending upon the particle
'Werephotographed using Type
Therepr~-
.52 ".~o1aroidfi1m •..
th~ ~r1ginal
size was needed to complete the anal~~.
The orig~l
samples were photographed in a similar
particle
size distributions
manner, except for the
of 4ltpm - 53pm and 53
that the ave--rageparticle
not be accurately
sizes.
was the main interest,
particle
felt
The magnifi-
photographed was about 200-300 for most of the
Since the swelling ratio
average particle
See Section 6.2.).
6s<f C
of
pm -
63
It was
size of these two size distributions
determined using the light microscope.
was used to prepare particle
pm.
could
So the TEM200
images for the size analysis.
Before the sample could be examined under the"TEM200, it had. to be
placed on a grid of mesh #200.
film of collodion.
While the coating was drying, the sample of interest
'Wassuspended in the distilled
a drop of the liquid-solid
grid.
The grid was coated with a very thin
'Water.
After the coating had been dried,
suspension was placed on top of the coated
The water was allowed to evaporate before the sample was placed
inside the TEM200 to be photographed.
ped and the pi"ctures were printed.
Finally, the plates were develo-
The plate magnification
used here
))
was 2600.
It was soon discovered that the particle
44
fIn - 53 pm
and 53
fIn -
much smaller than the
4¥ pm
had particle
distributions
63 pm had a ~ge
or 53 pm.
size distributions
fraction
of particle
Although all
particles).
sizes
other particle
sizes much smaller than the lower limit
the mesh # used (probably due to adhesion of smaller particles
larger
of"
compared to the rest
of
to the .
they could be ignored since the weight fraction
them was expected to be negligible
size
of
of the particle
size distribution.
The problem became more pronounced as the particles
decreased in size.
At 44
53
pm
and 53
for the present study.
size analysis
The
it was a serious
4t and
lOX magnification
sizes
of the images.
of
~izes
used for the light
images photographed were 4
Therefore, the calibration
particle
were used for part-
in these size dj,stributions.
mean that the particle
first,
pm,
63
App~oximately3D particles
4.24 Determination of A.verageparticle
sizes.
pm -
It was decided -to ignore part-icle sizes smaller than )0 pn ."
problem.
icle
pm -
i
Samples.
microscope does not
or lOX their
original
of TZG3 was needed to determine the
The method of calibration
was as follows:
a very accurate reference system was photographed for each mag-
nification
, then, the iris diameter of the TZG3 was matched with one
particular
length of the magnified scale for each mode of operation of
interest,
and finally,
the length of the iris
The magnification factor was then calculated
length of iris
diameter was recorded.
by taking the ratio
diameter recorded to the co:rresponding reference
of the
length.
Each counter number of TZG3 was then calibrated
ponding iris
A-7) •
diameter by the same magnification
by dividing the corresfactor.
(See Appendix
This procedure was performed four times for different
tion and modes of operation
was no need to calibrate
simply the product
the TZG3.
For the case of TEN200. there
The magnification
of the magnification
and the magnification
After all
of TZG3.
of particle
factor
was
images on the plate
of the enlarger.
the particle
TZG3. the arithmetic
magnifica-
images of a char sample 'Wererecorded by
averages of swelling ratio
'Werecalculated
for each
sample,
4.25 Determination of f:resh Feed Agglomeration.
At' an early stage,
of coal particles
it was realized
that the fresh feed agglomeration
might account for the large increase
char products of small particles.
in volume of
Most of the fresh agglomeration
could not be detected under the microscope because agglomerated
particles
fused to form one particle ~ In. order to determine the extent
of agglomeration of coal particles.
the following experinient was
perfonned.
Approximately 0.) mg of particles
41
pm
were carefully
spread unifonnly on a microscope slide.
amount of coal particles
between the initial
sample sites
with average diameter of
on the slide
The
was determined by the difference
and final' weight ofuthe slide.
The ~presentative
were then photographed, and the number of particles
approximately equal to )0
pm
or greater
were counted.
Then the
'.of diameter
35
average number of particles
dividing
the total
gra phed. si tes.
by multiplying
per unit area of spread was calculated
number of pu-ticles
The total
counted by the area of the photo-
number of pu-ticles
area of spread.
on ~he slide
Similarly,
initial
diameter of 41
number of J::6rlicles
by dividing the total
by the weight of the particles
the experiment was carried
on the slide.
at a peak temperature of 650 'C.
in the char product.
of. average initial
The' same analysis
study was the determination
cles,
and 71
pm
average particle
were discarded ~rom the analysis.
pm
of the uncertainty,
size of 41
pm,
46 )1m,
But •.:there was also some question
average particle
(See Figures 5-.5a, b,c. ) e
data obtained for char particles
sizes of 89
were discarded.
of the
were agglomerated since some char products appeared to be
agglomerations of two. or more particles.
particle
pm
of unagglomerated parti-
as to whether the char prcxlucts obtained from the initial
size of 89
and 71
the agglomeration
Since the main interest
of the swelling ratio
data olr'~ined for initial
was performed
sizes of 46fm
particle
o
5 respectively.
It was found
by assuming the weight
formed at a peak temperature of 650 CJ it was found that
was.approximately 60 and
with
f)'
Fm
for the char }Srlicles
number of
out for the char particles
that the agglomeration was more than 200 particles.
loss was negligible
was determined.
per unit area of spread
The total
per unit mass of the sample was calculated
particles
on the slide
the average number of particles
by the estimated total
by'
pm
at peak temperatures
of 650
with initial
o. ".
c,
0
.
Because'
average
0
830 C, and 960 C
s'.
RESUL'lS AND PHarOGRAPHS
Table 5-1
Average Swelling Ratio of Char Particles
Peak temp.
(Oc)
600
650
7;0
830
960
Avg. temp.
550
600
700
780
900
Inlt. avg.
pttt. size
Final avg. particle size/lnit. avg. part. size
Do (pm)
D/D'~'0 '. , 'D/D 0
Din 0
"D/D' ..... .. : .. •
0
Q
267
1.286
1.289
1.060
1.011
202
1.080
1.568
1.045
0.954 .
164'
1.075
1.176
0.896
0.965
122
0.997
1.109
89
0.982
1.1.50
*
1.817
71
46
41
4.920
4.058
*
6.41
No data collected.
Agglomerated
char products.
.
.. 0•.
909
0.821
0.865
1.083
14.5
*
DID
0.848
0.906
0.869
1.465
*
*
*
*
*
3.789
*
1.158
*
2.180
1.90)*
*
2.816
*
. 2.410*
4,24 .
3.774
*
37
Table 5-2
Results of the Least Square Method for The.
Relationship
(.
between Swelling Ratio and Particle Size
Peak temperature 00
(Average temperature)
600
Derived correlation
X 10-3 D
DID o
= 1.548
(600)
DID o
=
750
DID = 1.305
X 10-3 D
p(DO = 6.158
X 10-4 Do + 0.842"
(550)
650
(700)
1.330
00"
830
,(780)
960
DID
(900)
o
= 3.878
X
0
+ 0.819
10-3 D 0 + 0.832
X 10-4 D
+ 0.723
o
+ 0.786
..
Table 5-3
Relationship
Results of the Least Square Method forrrh£
between Swelling Ratio and Average Temperature
Initial average
particle size
Do (pm)
S - (DID
A = (llr)
)
2
X 10
4
X 10
"
267
S -
11.607
202
S ~
13.886 A
164
S =-
11.14 A - 115.364
122
S
11.355
a
A
-109.685
-
A -
137.696
123.613
38
Peak ..T ~m,Pera"ture (OC.)
1 (0)
2 (~)
. :3
(0)
;(@)
I
.
..
,
I
200
100
DO.-
Figure
S-la ..'Relationship
(pm)
between swelling ratio
and! particle
size.
39
l,
1.4
..
I
Peak Te:aperature
..........
:3 (0)
750
4 (X)
830
5. (t)
960
(OC)
..
1.2
0
~
~
'-""
0
-
H
f-:t
~-<
:1
C1
~
J%1'
::;:
4
. 1.0
v)
5
0.8
'" c
• I."'
0.6
•.
t)
~':::
..l
100"
'-; .. I
t.d
-
.h.-
t
I
11117
'.200
'.~'
,-:.--')00
..
DO' (pm)
Figure 5-11)" ":ReJ.at10rislup
between
sweiiing ratio
and particle
size
40
33
Average Initial Partlcle:~~e
1 (Ii)
267 pm
2 (D)
202
I
JL_~ __
'L- ..,
-L--L
7.9
pm
;1--,_~,
9.4
-...L.----L-_..t.--..!..._..t--..--,1<l.9
~.4
RECIPROCAL OF AVERAGE TEm'ERATtJRE
Figure
5-2CL
A
C tiT
4
) x 10
Relationship between swelling ratio
and average temperature
.41
33
Average Initial Farticle Size
164 pm
102 pm
•
1,- .....
t
I
9.4
RECIPROCAL
F~e
OF AVERAGE TEMPERATUF.E
5-2b
~
. -. -.lc.4
10.9
.
4
(1/T) x 10 .
--.---
Relationship between swelling ratio
and average temperature
42
,,
,.....,
It ~
><
.... 2s::: ~ •
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45
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Figure 5-5C
Char part icles formed at 96d C •
.
'(Do=8Cfrm,
lOX)
Showing possible agglomeration.
46
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55.
Figure 5-8a
Opaque particles
and cenospheres
0
formed at 750 c. (n0:.267
4X)
JAm,
><
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59
Figure
5-9c
Opaque particles
formed at 830°C.
and cenospheres
(Do=l6l+fm, 4X)
.
•
Figure 5-l0c
Cenospheres and char particles
0
at 960 C. (Do=122f m, 4X)
Showing open and closed
window structure.
formed
62
63
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r-t
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64
••
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Figure 5-llg
Agglomerated opaque particles
and cenospheres
fomed at 9600 c. (Do=41j<mt 4x) .
66
6.
DISCUSSION
6.1
Error Analysis
: .. 6.1l~D.etenniila..tion
The greatest
.of'Parld.cle ~Size
poss.ible source of error in determining the swelling ratio
of .qha.r parliC+BS"comesfr~the
has uniform cross sectional
assumption ''that. each coal. particle
area for all possible
the assumption is not very good.
improved if a lJa:ie number of particles
distribution
particles,
is used.
all possible
The situation
size
It i~ hoped that by counting a large number of
particle
whenthe particles
cress sectional
assume a spherical
areas are cov~ed so
cross sectional
<area of the
configuration.
The measuring process employed using TZG:3 has several
sources of error.
a sphere"
can be
of a narrow particle
that the average of them is the representative
particles
i.e.
counted had random configurations,
A"large portion of coal particles
therefore
orientations,
possible
The most important one :is the error in matching
the area of a circular
iris with the area of a noncircular
image by equating the area of the particle
with the area inside the iris
particle
image outside the iris
not convered by the particle
image.'
The equating process is purely dependent upon personal judgement, ,
thereby making consistency and care essential
measuring.
Hopefully, by emploY)!)3alarge number'of particles
counting, the errors will cancel each other.
of the process, several
Was
in the process of
particle
To test
the consistency
sizes were measured twice,
found tl'at the average particle
sizes differed
in size
by 2
pm
and it
to
67
5 fIB-
other errors
intrcxluced in this measuring process involved. the
of the TZG3.
sensitivity
number.::
o:(~
.~
.
It was mentioned earlier
:3 was calibrated
that the (:o~ter
using a magnified reference scale.
the operation of the stamdard linear distribution
of the counter number is 12 pm and. 4
pm
For
curve, the sensitivity
of 4 X and
for maginification
lOX:-respectively. For the operation of the reduced linear distribution
of the counter number is 4
curve, the sensitivity
for magftificatlon of 4X and lOXrespectively.
lhear
and l.~"pm
"Since the standard"
for 4X has an error of 12 pm in counting,
distribution."~e
it was us~
pm
only for particle
sizes greater
than 200
.."
pm.
6.12 Constant Residence Time And Heat Transfer Limitation
Constant residence time for all
interest
is required.
gas velocity
velocity
travel
down the reaction
so that the coal particles
The flow rate of the main gas was adjust"ed for
to achieve a constant ~in
s"tudy, it was assumed that
traveled downthe reaction
is the velocity
will
tube with the main gas at approximately
peak tem~ratures
all particle
tube with a velocity
of the main gas.
assumption, final ~ettling
~ . 0"
60.0,\
700., 800 and
factor.
0
gas velocity.
sizes of interest
of 2 ft/sec,
To determine the validity
velocitj:es
for initial
sizes of 270. 200 and 180 pm were calculated
correction
of
in the laminar flow region above the final settling
equal velocity.
In this
size distributions
This can be accomplished by using a constant main
of the coal particles,
different
particle
900 C using Stoke's
which
of the
coal particle
for temperatures of
Law and the Ladenburg wall
It was found that the final
particle
settling
68
velocit.ies
were greater
greater than 200 pm.
270 pm, the final
by a factor
than t.he main gas velocity
(See Appendix A-6). For the particle
settling
velocity
size of
the residence
time for an
size of 267 pm is probably smaller t.han 1/3 second.
The higher value of the final
gas velocity
sizes
exceeds the main gas velocit.y
of 1 to 0.5; therefore,
average particle
for particle
particle
has an important effect
settling
velocity
on the particle
t.han of the
temperature.
The main concern here is the developnent of an effecti ve thermal
bOundary layer which is higher than the effective
thermal boundary
.
,
'
layer of a stagnant flow due to a difference
between the gas
and the particle
thermal boundary
velocity.
layer incr~~~~because
from stagnant
and deviate
As the effective
of increasing
flCTIf,the temperature
size.and deviation
of the particles
from the main gas temperature.
'Wayof measuring the lB.rticle
deviation
particle
will decrease
Since there
temperature,
the extent of the temperature
from "that of tpe main gas due to non-stagnant .flow and large
size can not be determined. ,.But a hint of the existence
temperature deviation
large particle
different
the rest
of -the' gNater
from the main gas due to non-stagnant
size distributions
flow and
ca.llect'Gd at the same peak temperature.
at a peak temperature
average particle
size
of 267
pm
of the char prcxiucts were round•.
The difference
particle
size oan be Mta1nad. by examining the char products of
was discovered. that,
the initial
is no diI:ect
o
•
of 600 OJ char products of
were not round although
(See
Figure ....
S-6b Jd)
is probably due to the incomplete fusion of char
prcxlucts of the initial
average particle
size
of 267
pm
because of
It
a lower particle
temperature'.
6.2 Treatment of Tar Condensation on Char Products
.The experimental
of char particles
procedure for the preparation
formed at the peak temperature
from the preparation
of the rest
of .tar occured at the surface
of particle
images
•
of 650 C differed
of the char samples because condensation
of these particles.
Before char products were examined under the microscope, it was
noticed that. the color of the inside wall of the ceramic vial became
more'intense
than its
original
each run for peak temperatures
color
(light
brown) at the end of
o
tJ
of 650 C and 750 C.
o
'Wentup to 830 C.
of the color decreased as the peak temperature
the peak temperature
of
960 "C and
But the intensity
6000 C, the color of the inside wall
of the ceramic vials remained the same.
It 'Was?lso observed'that
char pa.-rticles prcduced at the peak temperatures<of.~50and
tendency to stick
000
of 600, .8JO_and
examination of the char particles
revealed
a dark brown, tar-like
that at 650 C, some particles
substance,
visible
o
A microscopic
formed at the different.
was less intense
(See Figure 5-4b).
960.c.
o
in. the 'samples. (See Figure 5-4a).
Oy the particles
b
arrl that
were ccated with
tar droplets
The coating
peak
of tar
were present
at the surface
at the peak temperature
tar coating at the surface
o
of 750 C.
0
At 600, 830 and 960 C, there was little
char samples collected
..750.C .had:':
to the ceram1c wall than' ..other char proclucts
formed at the peak temperatures
temperatures
the
0
I)
a greater
At
of the !articles.
had a very :thin layer
or no
(Nearly all
of film which could not
70
be detected
unier the microscope.
demonstrated by the dtlfraction
Most o£ the tar coating
The presence of this
effect
cooling.
,observed under the microocope.)
was one side:! a.t the surface
This was explained as caused by tar
condensation
too
Whenthe main gas carried
thin film was
of the particles.
in the main gas upon
evolved tar to the ceramic vial
through the water-cooled. sample probe, it condensed out and then
deposited
at t.he surface
of the particle,
vial and "the wall of the water-cooled
the surface
sample probe.
of the ceramic
As the temperature
the 'amount of ,tar, present .in,the' main gas- increased
increased,
a' greater",eXtent of tper'W\al1ecomposition
So when the main gas was cooled,
increased
with temJeratvre._
a certain
point,
of coal at a high temperature.
the amount aftar
condensed also
But when the tem~rature
the cracking
of tar
due to
to solids
take place,
and therefore
decreased.
So when the main gas was coolei,
increased
to
and gases started
the amount of tar present
to
in the main gas
the amount of tar
condensed
decreased as the rate of tarcra.:c.k\n.,9 increased with temperature.
La.u
(1977) experimented with cracking of propane in the laminar flow reactor.
He <>bserved that
the cracking of propane started
the peak temperature
cracked increased
peak temperature
of 750• C,.aM that
with an increase
reached 960°C,
the amount of propane being
in the peak temperature.
98% of the original
His observed cracking phenomena coincided
condensation
phenomenaat the surface
Since. some of the condensed tar
particles
to take place at
material
Whenthe
was cracked.
well with the abserved tar
of the char particles.
at the surface
formed at the peak temperature
of the char
o
of 650 C
If(:aS,
dark brown, the'
71
distinction
detected
between the char phase and tar phase couJd not be readily
in the particle
images.
For fear of interference
of condensed
tar during size cou..'lting, it was decided to suspend the char particles
o
.
formed at the peak temperature of 650 C in a benzene so tv.tion on a
microscope slide
to wash out the tar.
before photographing.
of destruction
not disappear
Then they were dried carefully
The only concern of this
of cenospheres,
at the peak temperature
(See Figure
light
to be either
Host coal particles
of.
of coal is complex, when the
microscope, no complexity
examined were opaque under the
TEM200, but they were a felf exceptions •.. It: was
less than 1
%
of the coal partic les examined appeared
dark brown or. silver under the light
dark brown particles
particles
5-3b ).' .Since the.tar condensation
was. not applied: to them.
were examined under the light
that
if
of Coal Residue
microscope
observed
partially
0
Although the physical structure
was observed.
was dissolved
of 750 C.was not s.1gnificanh, and less ~:lnt..ense...iIJ
the benzene .treatment
particles
did
when a few drops of benezene were ca.:r:efully added to them
too much benezene was added.
6.3 Structure
method was the possibility.
but it was found tl'at the cenospheres
Sometimes. however, the window structure
color,
..
microscope.
were suspected to be mostly tar,
to be tletal.
The silver
particles
The
and the silver
did not appear to go
through any :physical change under these experimental conditions.
The structure
of the char products appeared to be more
heterogeneous than the original
coal particles.
The heterogeneity
Wlt~
72
caused by the fact that.:portions
of coal particles
were transparent.
A
microscopic examination of unagglomerated char products formed at the
o
of 600 C revealed
temperature
the occurence of transparent
(See Figure .5-6b,f,g,h, j).
formation of cenospheres.
cenospheres which could be detected
peak temperature
the particles
under the light
was nots igilificant.
microscope at this,
as shown in Figure 5-Ja..
windOlfstructure
usually
exhibited
Cenospheres having the distinct
a much largetincrease
and rourxi, and some had minute vesicles
were op:a....que
(See Figure 5-6d).
surface.
of 267
at this
fIR'
peak, temperature,
5-6a,:b, c,
But, for the initial
most of the particles
d,
and
ribbed window
(See Figure 5-6f).
than the average char particles.
fewer than % of
ribbed window structures,
even a fewer number of cenospheres had the distinct
structure
But the: number of
On the average,
examined had detectable
coal particles,~h~'
were not round.
ribbed
in volume
Meat of the pu-ticles
at .their
particle.'
average particle
size
There waS some swelling.
but it was not very significant
•. (See Figure
e, f,: i, j).
Char particles
of agglomerated coal particles
namely" round and opaque.
to unagglomerated coal particles,
no cenospheres detected
appeared similar
for agglomerated coal particles.
There were
(See Figure
5-
lIb) •
Whenthe peak temperature
increased
in char products was a significant
detected.
structures.
o
to 650 C, the IIlost drastic
increase
change
in the number of cenospheres
Most of tm c enospheres formed had distinct
ribbed window
The size of cenospheres andwindows also increased.
(See Figure 5-7a, b, c, d, e, f. h).
The fomation
of cenosphereswas most
13
significant
at the initial
particle
this sample had detectable
had detectable
cenospheres.
It is difficult
expla..nQtjon for the significant
experimental errors, i.e.
This 15 a muchhigher
surface.
of the char particles
It is probably due to
difference.
were spherical,
%
to conceive of an .~
the peak tem~rature
I
Most of the particles
vesicleS at the particle
More than half of
of the char sample formed at this peak
On the average, approximately 30
temperature.
pm.
ribbed windowstructures.
percentage than that of the rest
run.
size of 202
was off for this
and there were also minute
The swelling of the particles
at
.
this peak temperature appeared to be more significant
particles
particular
than the char
o
formed at the peak temperature of 600 C. Both agglomerated
and unagglomerated char particles
beha.ved similarly
temperature.
d)
(See Figure 5-llc,
at this
peak
o
At atempe:ra.ture of 750 C, the formation of cenospheres was
observed.
But, the number of cenospheres that could be detected
reduced, and the sizes of cenospheres were also reduced.
5-Ba, b,
Cs
d, e) c
There was an increase
in the o~ity
Approximately 10 % of the char products ~
structures
at this peak temperature.
formed were not as round as char particles
temperature of 650°C. Miinute vesicles
peak temperature.
particles
(See Figure
of particless
ribbed
~lfindOW
but there were no cenosph~es
behaving like the one shown,on Figure 5-Ja.
this
detectable
was
Most char particles
formed at the peak .-
cou]d still
be detected
at
Both agglomerated and unagglomerated char
behaved similarly.
(See
Figure 5-lle) It,::' The.shI:ink~g
14
of the unagglomerated char :(articles
Whenthe peak temperature
were oplque.
5-Ja..
of the char particles
c).
structures~were
tl
particles
At the peak temperature
o
of 830 C, a small portion
(See Figure 5-9a,
o
of 960 C, some of the ribbed window
open, i.e. there were contin"o\l~ pores.
Minute vesc1les could also be det~ed
The agglomerated:am
at these
bemving like the one
had ribbed window structures.
At the peak temperature
b, c).
o
reached 8)0 C and 960 C,. mast of the particles
There were no detectable
shown in Figure
b,
was observed at this peak temperature.
two ~empera.tures.
The unagglomerated
formed at. these ~wo peak temperatures
(See Figur~. 5-l0a,
at th~two
unagglomerated char particles
-
pe~
temperatures.
behaved similarly.
char particleS
.....
were smaller. than the original
coal particle.
In brief,
the detection 'of .the ce!lospheres was_highly temperature
dependent under the employed experimental c a'lditions •
in this study coincided with Newall and Sinnatt's
The trend observed
~b~ervation.
(See
Section 3.3). The 1UUlber of cenospheres~c:1etected and the size of
cenospheres peaked with a certain
detection
temperature.
The exact point of the maximum.
of cenoshperss is not known at present,
be in the peak tem~rature
o
but it. is suspected to
0
range of 600 C to 750 C.
The minute forms observed. by Newall and. Sinnatt
not be detected
under the light
(1924) could
microscope since the magnification
used. in this study was not high enough.
6.4 Relationship Between Swelling Batio And Particre. Size
Table 5-1 shows the effect
of particle
size on the average swelling
7S
ratio at the constant peak temperature for all particle
size distributions
~mployedin the study • Too data here do not always f?howan increase in the
swelling ratio
in particle
ratio
of char samples free of agglomeration with an increase
sizec
But it is reasonable to conclude that the swelling
increases with an increase in particle
and the initial
between the swelling ratio
Lewellen (1975)
is nearly linear
size.
The relationship
particle
with the initial
size predicted by
size in the
particle
range of 120 pm to 230 pm.
(See Figure 3-9).
swelling ratio vs. particle
size at constant peak temperature' was performed.
for samples that were free of agglomeration
was us ed for this
analys is c
and the graphical results
is interesting
The results
0
Data fancU.ysis--of"_
The least
are tabulated
square metl?od
in Table
5-2
are presented in Figure 5-la and 5-lb.
to note that the slopes of DIDO
VSe
It
DOfor peak temperatures
000
650 and 750 C were very similar to that of Le':orellen'sPlrticle
of 600,
size trend prediction
in this
( 1.6 x 10-3).
The experimental conditions employed
study were not .similar to that of Lewellen's simulation,
significance
of the coincidence is uncertain.
d.e~reases as the peak temperature increases.
high peak temperature, the plrticle
ratio.
Tm slope of the curve
This implies that,
size has less effect
Curve J and Curve 4 on Figure 5-1b intersect
unlikely and it is probably caused by the scattering
the 'linear relationship
size fits
between the ~welling ratio
the data well.
at the
on the swelling
at 16.5'pm.
of data.
This is
In general,
and.the.particle
The deviation. of data from the corresponding
value detennined by the least
corresponding value.
so the
square method is within 5
%
of its
There are a few exceptions which have approximately
76
10 %. deviation.
Due to_~icle
initial
agg+omeration...no ,accurate data were obtained for
average particle
the swelling ratio
sizes
89 pm.
less t~
But it is expected tb1.t
will be nearly constant for very small particle
since. the bubbles generated' inside the coa.l particle
transported
linearly
as the particle
study (1975), the sw~lling ratio will not'
with particle
in swelling ratio
sizes above 230 pm.
with the initial
particle
size increases above 230
have been done for average particle
validity
sizes
Since not enough experiments
greater than 230 pm. the
of Lewellen's predicted trend remains uncertain.
Table 5-1 also shows the effect
of unagglomerated char particles
particle
The increase
size will be less significant
pm.
6.5 Relationship Between Swelling Ratio
ratio
will be instantaneously
to the surface and escape.
Accoming to lewellen's
increase
sizes
size.
Ani. Temp!rature
of temperature on the average s.welling
at ~he constant initial
The table shows that the_swelling ratio
peak temperature of"'650° C.
The swelling ratio
temperature when the peak temperature increases
average
peaks at the
increases
with the peak
o
0
from 600 C to 650
c,
and
+
peak temperature of
65(l C
Ii
Increasing the peak temperature from 6000C
0
~~ 650 C always increases the swelling ratio;
0
increasing the peak temperature from 650 C to
swelling ratio.
discussed
in most cases however,
960°c
causes a decrease in
The observed trend agrees well with the predic'ttd trend
in Section 3-6.
The swelling-temperature
to the thermal decomposition. rate-time-temperature
i.e.
both peak at a certain
with
1/T
(reciprocal
temperature.
relationship
relationship
is similar
iB i>yrolysis,
It 'Wasdecided to correlate
of the average temperature of the reactor)
In{D/D )
o
at a constant
initial
.
was
60
particle
0
size.
0
0 C to 900 C.
The results
The ave1;agetempera,!!urerange for the corre.1ation
The least square method was used for this correlation.
of the correlation
in Figure 5-2a, b.
are tabulatea. on Table
and plotted
As-is evident f.'romFigure 5-2atl a linear
exists between the In(D/DO) and l/T at the initial
267 and 202 pm. But the correlation
sizes ..of 164 am 122
particle
5-3.
counting or scattering
pm.
of data.
obtained to draw any correlation
particle.
was not satisfactory
relationship
sizes of
fC?rthe initial
This is probably due to errors in size
Since -insufficient
da;ta were
and the
o •", , ,"
average temperature for average temperatures -below 600 C ~ the empirica.l
relationship
between the swelling ratio
between -the swelling ratio
and the temperature is still
undefined.
There were two assumptions: made'in correlating
with the average temperature.
First,
the swelling ratib .
the nonunifo:rmity of heating
rate at different average or peak temperatw:es has little
effect
or no
on the swelling.~property of_the coal samples. - Secondly, the
average or peak temPerature of the reactor
swelling ratio
o
0
does not lie
corresponding to the maximum
in the average temperature
range of
-,
600 C to 700
c.
the validity
of the above correlation
Since the assumptions were not tested
general, the swelllng ...te~perature
is still
relationship
experimentally,
uncertain.
But in
is similar to
the thermal decomposition rate ...-:tirqe-temperature .relati:.,onshipor the
fluidity-time-temperature
6.6 Agglomeration
relationship
in pyrolysiS
~f bituminou~ coal.
78
Although the swelling ratio
of agglomerated' char particles
...". ~;...,
o
displays a maximum
at the peak temperature of 6.50 C, it does not
necessarily
suggest that the agglomeration of coal is tem:t:erature
;
of
dependent~ Since the agglomeration
char :p!.rticles is caused
mainly by the agglomeration of raw coal particles
the reactor tube, the effect
of the peak temperature of the reactor
on the agglomeration of char particle
maximum
swelling ratio
before entering
should be insignificant.
The
o
.observed at the peak temperature of ,650 C is
probably due to the more intensive swelling of agglomerated coal .
~
at the peak temperature of 6.50 C than that _of agglomerated
Particles
coal particles
at other temlEratures.
It is evident frOJ1\Table
the extent of agglomeration 6f char particles
size decreases.
No correl
increases. as .the particle
has been made to establish
QtIOt'l.
5-1, tkat
the
of
relat~0!1ship between.~he extent.) agglomeration: and. the particle
size in
this studys
1c
CONCLUSION
1. At constant peak temperature~ the swelling ratio
with the average initial
particle
size.
A linear
increases
relationship
used to describe the reJa tionship between the swelling ratio
initial
particle
2.
sizes
of 89
At. constant initial
pm
to 267
can be
and the
p_
average particle
size,
the swelling-
temperature relationship
is similar to the thermal decomposition rate-time-
temperature relationship
or the fluidity-time-temperature
pyrolysis
of bituminous coal.
rate all peak at a certain
i.eo
swelling.
fluidity
relationship
in
and thermal decomposition
tellpe%.."?;ture.Based on the data obtained,
19
an empirical relationship
has been developed to correlate
ratio with the average temperature
.
of the reactor.~
The average
0
'0
temperature ranges were 600 C to 900 C.
swelling ratios
the swelling
and. the temperatures
is st ill
of information on the average reactor
the maximum swelling ratio,
But the exact correlation
of
undefined due to a lack
temperature corresponding -to
and insufficent,-.data
obtained'L.at'_low
temperatures.
8.
RECOMMENDATION
of the assumptions used in corre4ting',
The validity
'swelling. ratio
a.verage initial-
with the average_reactor
particle
study should first
reactor
particles
size were not tested
probably lies
experimentally .. Future
the maximumswelling ratio
of heating rates
on the swelling ratio
at constant peak temperature.
of the reactor
of coal particles,
of char
The peak temperature
corresponding to the maximumswelling of char particles
o
in the temperature region near 650 C. Therefore,
study should focus on the effect
near that region.
ratio
temperature at a cOnstant
determine the average or peak temperature of.the'
corresponding'to
and the effect
the average
But the effect
of char Iarticles
of peak tem];eratura ..on ...,oll1Dg ratio
of heating rate on the swelling
can not be investigated
of the laminar flow reactor
future
in the present
set up
since there is a one to one reJationship
between the heating rate and the peak temperature of the reactor.
Appendix A-S) •
ratio
Once the peak temperature
(See
of the maximumswelling
of char: pa.rtic~es is determined~ a correlation-
of the swelling
80
ratio with the average or peak temperature of the reactor
be madeat a constant initial
particle
'size.
size and peak temperature ,of the laainar flow reactor,
Besides particle
there are other experimental variables
such as pressure and reaction
~tmosphere which will have significant
ratio
can then
of char pa.rtic1es
effects
on the swelling
Therefore, future research can also include
c
the study of the dependence of the swelling ratio
graded bituminous coal particles
of closely size-
on the pressure and the atmosphere
employedin the reactor.
Since the extent of fresh feed. agglomeration is very significant
avera.ge initial
particle
not include particle
sizes. less than
sizes
between the coal particles
e 9 J.llll,
I
less than 89}lI1l.
future' researCh should
The non-stagnant flow.
and the main gas is also undesirable,
future research shouJd exclude particle
velocity greater than the velocity
for
hence
sizes which have final settling
of the min gas at the experimental
conditions of interest.
Too
examination of char particles
reveals only the surface structure
under the light
microscope '
of the char particles;,
it does not
provide ,information on the porosity inside the char particles.
Future
study can also focus on the study of porosity of char particles
of
bituminous coal formed under different
experimental variable.
is a large scale of porosity present inside the char particles,
be detected using a refractive
microscope.
If there
it can
The char particlcasmust be
imbedded in epoxy resin and polished before examining them under a
refractive
microscope.
81
APPENDIX
//
•
•
I
I ;
a
o
co
~
V'\
_ ,
l
~
o
V"\
V"\
82
Q)
OJ ()
eS~
~
~
.c:P-t
CJ
~~
~
-C'IS
f.4
Q)
t1J
,...
J.f OJ
O~
co
0'8
i
I
a'S
~P-t
tJ)'d
QJ
Q)&1
tJ)G)
r-I
r-I
~ ~
~!
"=""
-•
r-tp..
~tr.:l
II
t90
-
-
><
,.....
6
~
i
J
.....
~
J
\'l
/
."
/
C!I:J'
~j
~
~
:z:
o.
I
H
E-t
/'
~
..J~
\.,
-1
,
8
er4
tJO
CD
fof.
'~
er4
~
0
~
tJ
~
~
r-f
eM
r:il
ct-4
0
~
r:.
\
.,
0
Pi
0
E-t
Q)
~
,..CD
:s
~
.~
~
~~
I
j:
a
0
co
I
......
0
R
(:)
~
0
0
'-~
(DO) aHfll\i~dW3J.
...L-_L--.l
0
0
....
i
=:::
8.
g:
N
:z:
0
<
~
~
0
'H
'»
0
D..
I
'ECD
P4
Pi
<
8)
Appem.1x A-)
Helium Flow Rate Setting for the Laminar Flow Reactor
Peak temperature
0
SeeM
C
Helium
600
6248.5
700
5606•.5
800
5084
900
46.51
1000
4285.6
1100
3973.5
Appendix
A-4
~elationsh1p between Mesh # and Farticle Size
U.Sc Stamard
Mesh #
Particle Size
80
177
100
149
120
125
140
105
170
88
200
74.
2.30
6)
270
53
325
44
84.
60
~
~
~
~
&:J
j
"1 ,t~
...
X
I
0
e
........,
I
I
/'
f
\oN
~
/
j
50
,;'
1-
I'
I
Q
;
,
1
;
i
45
L
40
I
800.
600
p~~
Appendix A-5
TEMPERATURE
•
900
( °c )
Hea.-ting rate' of the '~m;na-r flow reactor
I
1000
85
Appendix
A~6
Determination of Final Particle Settling Velocity
vf - final settling velocity (rt/sec)
Average
270 Jum
200,.wn
180 }lDl
temperature
(Oe)
vf
vf
v
600
4.08
2.42
1.96
100
3.ao
2.30
1.83
800
3.48
2.10
1.68
900
3.37
2.03
1.62
f
86
Appendix
A-7
Calibration of TZG 3
Counter
number
standaxd
lOX
4x (fihl)
1
26.8 :10.9
2
39.0
3
.Reduced
4X9~')10X
Counter
number
standard
4Xjam) lOX
Reduced
4x/ /a",}lOX
9.5
3.8
25
320.5 130.6 108.3 43.5
15.9
13.5
5.4
26
332.7 135.6 112.4 45.1
51.4
20.9
17.6
7.1
27
344.9 140.5 116.6 46.8
4
63.6
25.9
21.6
8.7
28
357.3 145.6 120.7 48.4
.5
.75.8
30.8
25.6 10.3
29
369.5 150.4 124.9 50.2
6
88.0
35.8
29.7 12.0
30
381.7 155.4 129.0 51.8
7
100.2
40.7
34.0 13.6
.31
393.9 160.3 133.0 53.4
8
112.6
45.8
38.0 15.2
32
406.1 165.; 1;7.3 55.1
9
124.•8
,50.8 42.; 17110
;3
418.5 170.3 141.4 56.7
10
137.0
~5,7
46.3 18.6
J4
430.7 175.3 145.6 58.5
11
149.2
60.7
50.3 20.2
;5
442.9 180.3 150.0 .60.1
12
161.4
65.6
,54.6 21.9
;6
455.1 185.2 153.7 61.7
I;
173.8
70.7
.58.7
23.5
37
467~3 190.2 1.58.0 63.4
14
186.0
75.6
62.9 25.;
38
479.7 195.2 162.0 65.0
15
198.2
80.6
67.0 26.9
39
491.9 200.2 166.3 66.8
16
210.4
85.5
71.0 28.5
40
504.1 205.2 170.3 68.4
17
222.6
90.5
75.3 30.2
41
516.3 210.1 174.4 70.0
18
235.0 .95.7
79.3 31.8
42
528.5 215.1 178.7 71.7
19
247.2 100.7
8;.6 33.6
4;
.540.9 220.1 182.7 73.3
20
259.4 105.7
87.6 35.2
44
553.1 225.1 187.0 75.1
21
271.5 110.6
91.7 36.8
45
565.3 2)0.1 190.0 76.7
22
28).8 115.6
96.0 38.5
46
577.5 235.1 195.1 78.3
23
296.2 120.7 100.0 40.1
47
589.6
24
308.3 125.6 104.3 41.9
48
602.1 245.0 203.4 81.6
240.0 199.3 80.0
Appendix A-a
Nomenclature of Table )-1
&0
Initial bubble size.
ai,aj
Radius of bubble l,j.
Ai
Growth rate of bubble
bi,bj
Distance between the particle wall and the center of bubbles i.j.
dmin
Distance to the nearest surface through which volatUe can escape.
Ed
Activation energy of the secondary reaction.
F
Volatile
kO
Preexponential factor of the secondary reaction rate constant.
ka:
Secondary reaction rate constant.
Mo
Original eoal masst
Mp
Coal mass.
p~
PresstL.~ of surroundings.
a
nux
i
per unit surface area •.
Rate of ~ecoMa:ry reaction per unit area.
Rate of the secondary reaction per bubble.
R
Radius ot ];8.rllcle or universal gas constant •.
w
Total mass loss of ];8.rlicle.
w
Mean molecular weight of the bubble.
Spatial coordinates
of bubble i,j,k.
Bubble generation probability distribution function.
88
I\~D
Initial
.~
Viscosity.
o
~urface tension of bubble shell.
~
Density of particle phase.
~'.;'I
.
V: .
lIJ')
alL
bubble size probability
distribution
function •
Massof bubble i,j,k •
Rate of mass accumulation inside bubble 1.
6-
d.J..
~
Rate of volatile
generatioD per un!t mass of original
coal.
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Part 11-