CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
•
MATHEMATICAL
r.mDELING
,,
IN Ttffi KINETICS OF COAL GASIFICATION
A graduate project submitted in partial
satisfaction of the requirements for the
degree of Master of Science in
Engineering
by
Ping-Fu Cheng
January, 1976
..
2
The graduate project of Ping-Fu Cheng is approved:
California State University, Northridge
December, 1975
3
TABLE OF CONTENTS
Page
1.
ABSTRACT
4
2.
INTRODUCTION
5
3·
4.
ONE STAGE COAL HYDROGASIFICATION
13
RESULTS AND DISCUSSION
20
5·
CONCLUSION
26
6.
NOMENCLATURE
27
7.
REFERENCES
29
APPENDICES
A Equilibrium. constant. calculation
31
B Viscosity of gases
35
C Viscosity of steam and water
36
D Computer program
37
..
4
ABSTRACT
MATHEMATICAL MODELING
IN THE KINETICS OF COAL GASIFICATION
by
Ping-Fu Cheng
Master of Science in Engineering
January, 1976
Mathematical modeling is developed for the gasifi1
cation of coal.
The coal char reaction with steam and
hydrogen are treated as two simultaneous reactions
taking place at 1800°F-1400°F and J0-70 atm •.
The model
can estimate the gas composition of product and the reactor size at different levels of carbon conversion in
a moving-bed reactor.
However, at high temperature more
steam was consumed, with more methane product as the
temperature is raised.
5
INTRODUCTION
The purpose of the work reported here is to develop
mathematical modeling for the gasification of coal.
The
model can estimate the product gas composition and reactor size at different levels of carbon conversion in
a moving-bed reactor.
Gas manufactured from coal was first produced in the
late 18th century by heating coal in the absence of air.
The first coal-gas company, which distributed its product
for lighting, was chartered in London in 1812; the first
U.S. company was chartered in Baltimore in 1816.
In recent years, hydrogenation of coal has shown
substantial potential for au5tnenting supplies of natural gas and crude petroleum.
Coal gasification in-
volves not only heating the coal, as in distillation,
but also the subsequent reaction of the solid residue
with air, steam, or various mixtures of them.
volatilization step releases a certain
a~ount
The deof gas that
has a fairly high BTU. content because methane and other
hydrocarbons contained in the coal are among the first
components to emerge as the coal decomposes.
The gasi-
fication sten produces a gas that is essentially a mixture of hydrogen and carbon monoxide with some of the
gases distilled from the coal.
The amount of the gas in
the final product varies with the gasification process.
6
A number of research programs are now under way all
over the world to test and develop efficient and economical production of high-heating-value gas from coal.
Only a few studies were concerned with reaction kinetics.
Many problems associated with coal hydrogasification
must be solved before the process can become economically feasible.
One of these concerns the properties
of coal that affect the hydrogasification rates.
From
a reaction-kinetic point of view, carbon in coal consists roughly of two types which differ greatly in associated with the volatile·matter, and a portion of residual carbonaceous matter with relatively low reactivity.
_Under the high temperatures and pressures required
for hydrogasification, coal tends to soften and agglomerate, preventing free flow through the reactor.
Pre-
treatment of coal, therefore, has usually been required
in moving-bed or fluidized-bed reactor operation.
In studying the kinetics of coal hydrogasification
Wen, Huebler, and Abraham (1),(2),(3) assumed that the
·coal char reactions with steam
a~d
hydrogen may be
treated as two simultaneous reactions taking place without interfering with each other.
The initial reaction
rates (highly reactive portion) in a semiflow test were
analyzed and found to be proportional to the amount of
unreacted carbon remaining in the particles as well as
..
7
the effective partial pressure of hydrogen.
Also, the
initial rate of hydrogasification of coal is very rapid
in comparison to the relatively slow second-phase reaction.
The relatively slow second-phase reactions
considered to take place at the solid-gas interface.
Diffusional resistance was the major controlling factor at low gas velocities.
Correlations for different
controlling regimes are also studied:
(a)
Gas-Film Diffusion-Controlling.
Under this
conditions, the rate of reaction between hydrogen and
char should be insensitive to temperature and the correlation should be made in terms of gas mass velocity.
(b)
Chemical Reactivity-Controlling.
Under this
condition the rate of reaction will be proportional to
the surface area of residual char.
With spherical par-
ticles, the unreacted char is present as a spherical
core of diminishing radius (the shrinking core model).
The reaction rate will be proportional to the surface
area of this core and the rate will be sensitive to
temperature and insensitive to gas velocity.
(c)
Ash Diffusion-Controlling.
This occurs when
the unreactive ash formed in the reaction provides the
chief resistance in the rate process.
If this condi-
tion prevailed, the reaction rate correlation would be
insensitive to temperature and gas velocity.
..
8
It is possible the reaction rate may be controlled
by one, two, or even all three of these mechanisms.
The effect of major parameters on the rate of reaction is also discussed by Wen et al.
For the differ-
ent ratio of methane-hydrogen mixture feed at the same
temperature indicates that the driving force in the
second-phase reaction has been successfully accounted
for by the effective hydrogen partial pressure (PH2 -Pli2 ).
Further, several possible effects, the diffusivity of
gas feed, the particle size and shape of coal char, the
equilibrium constants of ·reaction are reported as a
function of temperature in gasification .
.However, Johnson (4) investigated coal char hydro.gasification rate in a thermobalance reactor at pressure
up to 70 atm., and temperature up to 2000°F with variety
of gases and gas mixtures.
Usually, the thermobalance
is an apparatus capable of continuously weighing a coal
sample -- which is particularly useful in obtaining
fundamental gasification information because gasification rates can be measured at constant, well-defined
environmental conditions.
Most of the information used
to formulate the kinetic models developed in his study
was based on data from several hundred tests conducted
with the thermobalance.
The models developed in Johnson's study for the
..
9
quantitative description of coal char gasification kinetics assume that the overall gasification occurs in
three independent stages: (1) devolatilization (2) rapid
rate methane formation and (J) low-rate gasification.
Further, a feed coal char
ass~~ed
to contain two types
of carbon volatile-carbon and base carbon.
Base carbon
remains in the coal char after devolatilization is completed, this carbon gasified in either the rapid-rate
methane formation stage or the low-rate gasification
stage.
The rates of reaction are ·found to be a func-
tion of temperature, pressure, gas composition, in
addition of prior history.
A number of earlier papers concerned with the kinetics of coal gasification was discussed as follow:
Gadsby, Hinshelwood, and Sykes (5) showed that the
differential rate of gasification of carbon by steam,
in a fixed bed at low temperature, could be correlated
by an expression of the Langmuir type expression:
k1P1/(1+kzpz+kJP1), where P1 and P2 are partial pressures of steam and hydrogen respectively, and where k1,
kz, and kJ are constants dependent only upon temperature.
Good straight-line plots of log k1, log kz and log kJ
versus reciprocal temperature were obtained over the
temperature range 1256 to 1472°F.
By means of the
Gadsby-Hinshelwood-Sykes expression, calculation of the
..
10
integral gasification rate for a fixed bed at low temperature is a straight forward task.
May, Mueller, and Sweetser (6) of Esso Research
and Engineering Co. give fluid-bed and fixed-bed gasification data for a coke prepared from high-volatile Pittsburgh-Seam bituminous c-oal.
They determined values of
reaction rate constants for the Gadsby- HinshelwoodSykes expression from fixed-bed experiments covering
the temperature range 1600 to 1800°F.
They found that
the water-gas shift reaction may account for a substantial fraction of the steam reacted; the over-all rate
of steam conversion will not have the form given by
Gadsby-Hinshelwood-Sykes expression, and advanced expression is reported in r;Iay' s report.
Also, parallel
, work has been done by Zielke and Gorin (9) (10), who
used a similar type of fluidized system and the
coke as May et al.
sa~e
However, treatment of the data is
different, their emphasis being on reaction mechanisms
rather than on providing design correlations.
Blackwood and McCarthy (11), who gasified wood charcoal in fixed beds at temperatures between 1382 and
1526°F and at pressures up to 50 atmospheres, found that
the Gadsby"-Hinshelwood-Sykes expression had to be modified by addition of two terms, so that the rate was
given as (k1p 1 +k4PiPz+k5P1 2 )/(1+kzpz+k 3p 1 ).
Also,
11
Blackwood (12) postulated that the formation of methane,
both in the reaction between carbon and steam and in the
reaction between carbon hydrogen is controlled by oxygen
groups, such as chromone or benzopyran (C6H4·Co·cH·o,
/o•CH4C6H4- CH -:::;:::::;- CH), in the carbon structure. He believed
that methane arises in steam gasification from the reaction of steam with adsorbed hydrogen, liberating methane and carbon monoxide.
Dent and co-workers (13) conducted extensive studies of coal hydrogenation at elevated pressure and at
temperatures in the range' of interest here.
Dent found
that carbon reactivity toward hydrogen is strongly dependent upon the history of the carbon's thermal-environment.
Material which has been strongly coked in the
absence of hydrogen is unreactive, and little of such
material can be converted by hydrogen to methane at substantial methane concentrations.
On the other hand,
coal which is heated slowly in hydrogen under pressure
can be almost quantitatively converted to methane at a
substantial concentration.
Initial production of methane
occurs at around 950°F, and final conversion of carbon
to methane is accomplished at around 1700 to 1750°F.
Coal which is rapidly heated in hydrogen under pressure
yields less methane than coal slowly heated.
Dent ex-
plained this general behavior as reflecting a competi-
..
12
tion bet·ween hydrogenation reactions and reactions tending toward graphitization of the surface of carbon residue.
Once carbon surface becomes graphitized, hydrogen
is a poor reagent for restoring activity.
Dent shoWed
that catalysts make possible higher concentration of
methane.
The kinetic studies are important for the rational
design of
gas.
coTh~ercial
systems to convert coal to pipeline
The available information which can be applied to
the development of such systems.is relatively limited,
particularly oecause the'data reported from many studies
conducted with integral contacting systems reflect, in
part, undefined physical and chemical behavior peculiar
to the specific experimental systems used.
Although
some differential data have been obtained with various
carbonaceous materials, they cover only narrow ranges
of conditions.
A mathematical model which is applicable to many
gasification processes and a wide range of conditions
was developed in this report.
A CDC 3170 computer is
used for simulating the gasification process under different conditions.
..
13
ONE-STAGE COAL HYDROGASIFICATION
Coal Char + Steam + Hydrogen
First Phase
Second Phase
= Product
initial rapid reaction
solid-gas interface
In both first and second phase, the steam-char reaction and. the
hydrogen~char
reaction are considered
simultaneously.
C + H20
~
CO + H2
C + 2H2
~
CH4
of course, the actual reactions are much more complex than indicated by the above simple schemes.
How-
ever, these two reactions are believed to be sufficient
to characterize the two greatly different rate periods
observed in coal hydrogasification.
' First Phase Reaction
Steam-Char Reaction.
The rate of the steam-char
reaction in the first phase is represented by:
[
dXH20
dt
J = k1(f-x)
1
Where k1 is the rate constant in min-1, and f is the
fraction of carbon that will react according to the
( 1)
..
14
frist-phase reaction, PH2 o is the partial pressure of
steam, PH2 is the partial pressure of hydrogen, KE1 is
the equilibrium constant for steam-char reaction (see
Appendix).
The first-phase reaction of steam-char is
a volume reaction, whose rate is proportional to the
amount of the unreacted portion of the volatile carbon
still in the particle.
The rate of the steam-char re-
action is not affected by the partial pressure of steam,
(5,
this agrees with results of previous investigators.
6,?,8)
Hydrogen-Char Reaction.
The hydrogen-char reaction
in the first phase may be represented by:
[
k2
dXH2
dt
J
1
= k2(f-x)(PH2 -PH2 )
( 3)
=
1+PH2 exp(-10.4520+19976/T)
( 4)
where k2 is the rate constant obtained in (atm-min)- 1
and f is the fraction of carbon that reacts .according
to the first-phase· reaction.
PH~ is the partial pres-
sure of hydrogen in equilibrium with reacting char and
methane.
KE2 is the equilibrium constant for hydrogen-
char reaction.
The rate of hydrogen-char reaction at
any time is proportional to the volume of the unreacted
portion of the volatile carbon and to the effective
..
15
partial pressure of hydrogen.
Second Phase Reaction
The second phase reaction is heterogeneous and occurs at the surface of the particle.
The reaction causes
the reacting surface to shrink and to leave an ash layer
as the particle moves through the reactor.
Steam-Char Reaction.
The steam-char reaction in the
second phase is probably occurring at the surface, the
rate of the steam-char reaction in the continuous-flow
moving-bed reaction is probably controlled by gas diffusion and may be characterized as:
rdXH20]
(Kg)H20
*
~ 2 =
Dp
(1-f)(PH2o-PH20)
where
(Kg)H 2o=
and
(N Re )Livi
number, log
1.7x1o-5(NRe)~~
=
Dp~
(5)
20
(6)
is the particle Reynold's
me~~.
Hydrogen-Char Reaction.
As discussed by liJen and
Huebler ( 3 ),( 4), the reaction under experimental conditions in the
pilot-pl~~t,
continuous flow reactor may
be affected by gas diffusion since the gas flow rates
employed were extremely low and there was evidence that
considerable gas channeling, predominantly along the
vessel wall, occurred in this type of reactor.
Under
such circumstances, the reaction rate of the secondphase reaction may be characterized by:
..
16
=
(?)
(8)
Over-all Reaction Rate:
dX
-=
(9)
dt
for x <f
(11)
for x>f
(12)
(13)
Moving-Bed Reactor Design
For a small diameter, long shaft type reactor, the
assumption of plug flow for both solids and gases is
valid.
Below is a carbon for differential volume, dV:
(14)
(15)
Since reaction 1 & 2 occur simultaneously in the
17
same reactor, an equation of the preceding type must
hold for each reaction individually.
These expressions
are:
vpB
-F
VfB
=
F
~J
J
dXH20
dXH 2o
dt
(16)
dXHz
(17)
dXH2
dt
As direct integration is not possible, it is necessary to re'.vri te the two equations ( 16) and ( 17) in difference form and accomplish the integration by a stepwise numerical approach using a computer.
small element of volume L:::. V the
Thus in a
conversions~
XH2 o and
b.. XHz are:
llXHzO
=
t.XH
.. 2
=
a v fB
F
a v fB
F
dXHzO
dt
(18)
dXHz
dt
(19)
The method of solution of equations
(1~)
and (19)
will be illustrated by starting at the entrance to the
reactor., where XHzO and XH2 are both zero, and carrying
out several stepwise calculations.
with
assume
18
Choose an interval of
= EPSI
where EPSI is a very small number.
The conversions at
the end of the interval are, according to (18) and (19)
Now more accurate values of DX11 and DX21 can be
obtained by substituting ·these values of the conversion
in the rate equations.
dX'H20
DX11 =
dt
dX'H2
dt
=
DX21
The average values of the rate in the first incre-
vpB
ment of A(-p-) may be taken as the
arith~atic
average
of the rates entering and leaving the increment.
DX1
=
DX10 + DX11
2
DX2
=
DX2o + DX21
2
using these revised values of the average rates,
the conversions at the end of the first increment are,
again according to (18) and (19)
XH2 o
=0
+ EPSI x DX1
19
XH2 = 0 + EPSI x DX2
This stepwise procedure can be repeated until the
steady state value of XH2 o+XH2 is reached.
A_program
for computing with this procedure is given in appendix.
20
RESULTS AND DISCUSSION
In hydrogasification, the most prominent variables
are coal rate, hydrogen:steam ratio, maximum temperature
attained by the solids and vapors, total pressure, hydrogen partial pressure, partical size and density, gas
viscosity, and heat capacity of the feed gas.
The com-
position of the effluent gas is determined by the feed
gas rate, but the gas yield depends on many variables,
some of which interact.
The ranges of calculation con-
ditions are given in Table 1.
TABLE 1
Summary of Gasification Conditions Studied
1400 to 1800
Temperature, °F
Pressure, atrm.
JO to 70
Average char diameter, ft
O.OOJ
Gas feed rate/char feed rate,
SCF/lb of carbon
Hydrogen;stea~,
%
Volatile matter in coal,
55·5
25 to 75
%
251'a
From Figure 1, the reaction C + H20 ¢CO+ H2
was significant at higher temperature, and increased
with temperature.
At 1600°F, 40% of the feed steam
decomposed, but at 1800 F, 65% was consumed.
Carbon
oxides formation was related directly to the steam feed
and to the steam decomposition.
..
....~
.
:;s
~
60-
50
-·-
E-1
{/)
>-t
21
40
/',------------
/"/
1800°F
1600°F
1400°F
/
/.
p::)
Q
rx1
E-1
/c
JO
/
~
rx1
:>
z
/
20
0
(.)
z
0
p::)
~
•
/
/'
/
/
-
-
·--
--
/
./
10
/
<1!
(.)
...--. ___....-·-·-·-
I
5
1
3
REACTOR VOLU'iVIE, ft /lb-mole Carbon Feed
FIGURE 1 Effect of t·emperature on Steam-Char
reaction
0
*
z
lZl
60
~
:r:
50
0
0
0::
1800°F
1600°F
1400°F
>-t
p::)
Q
40
rx1
E-1
~
~
z
./
/
JO
/
--- --
0
(.)
z
20
~·
0
~
~
<1!
(.)
/
---·
---->
_,
----- - - - ,,
~---
11
-·-
10
I
I
I
4
I
6
I
I
I
2
8
1
7
9
5
J
REACTOR VOLUNIE, ftJ/lb-mole Carbon Feed
FIGURE 2 Effect of temperature on Hydrogen-Char
reaction
0
..
22
The hydrogen consumed in different reactor volumes
by hydrogen-char reaction is plotted in Figure 2.
The
hydrogen consumed increases with decreasing temperature
because methane formation from hydrogen is a function
of the hydrogen partial pressure driving force (PH2 -PH2 ).
At higher temperature the hydrogen partial pressure
driving force is smaller than that at lower temperature.
It has also been shown that the equilibrium hydrogen
partial pressure is related by carbon-hydrogen-methane
equilibrium.
The equilibrium constant for Hydrogen-Char reaction
is much larger at lower temperature, but it is difficult
to carry the reaction out since no catalyst is added.
At higher temperature where a catalyst would probably
not be required the equilibrium constal'lt for the reaction is unfavorable for the synthesis of methane from
its elements.
Figure 3 shows at
50 atm. the total carbon conver-
sion by steam and hydrogen at different temperatures.
It appeared at equilibrium, the higher temperature can
reach the higher coal conversion.
And the low temper-
ature reaction is rapidly in early stage of reaction.
The hydrogen:steam ratio has an important bearing
on the quality of product gas.
Figure 4 shows that
sa.'ne volume of reactor converted more carbon at hydrogen
23
~
.
60-
I
?'.
,.,::?"
Q
P:l
8
A::
!.'it
>
:z;
0
0
//.
50
/
/
40
/
/
/
0
~
/
30
0
./
/ ./
/
:z;
p:::
<I!
----------
/
I
/
•
./
•
./
-·-
1800°F
1600°F
1400°F
20
10
2
3
5
7
9
REACTOR VOLUff!E, ft3 /lb-mole Carbon Feed
FIGURE 3 Temperature effect on carbon conversion
rich ratio.
However, the recovered hydrogen usually is
recycled to achieve higher hydrogen steam ratio.
If
operated as a fixed-bed process, it presents an adaptation of Lurgi pressure gasifier modified for hydrogen
recycle to the upper portions of the bed to minimize
hydrogen requirements in hydrogasification.
Thermody-
namic analyses of coal gasification show in hydrogasification at 50 atm. 1700°F, the effect of increasing
the hydrogen to steam inlet molar ratio is to approacl:
24
60
/
.50
.
----
-
.-·-·-
~
.
Cl
1:<1
E-t
P::
40
z0>
JO
z
20
1:<1
0
0
Ill
11::
<l!
0
-·-
2.5% steam 7.5% H2
.50% steaTU .50% H2
7.5% steam 2.5% H2
10
0
2
1
4
3
.5
6
7
8
9
FIGURE 4 Effect of Steam:Hydrogen ratio on coal
gasification at 1600°F and 70 atm.
60
..
.,/
.-
/
.50
\R
.
Cl
1:<1
~
g:
z
0
0
z
0
40
JO
/
.I
/
•
./
I
. . -f(f-
/
/
/
/
/
/
/
/
/
0-
/
/
/
.-
-·-
70 atm.
.50 atm.
JO atm.
20
I:Q
0::
<
0
10
0
1
2
3
.5
7
8
REACTOR VOLUTVIE, ft3 /1 b-mole Carbon Feed
FIGURE .5 Effect of total -pressure
on carbon
0
converted at 1600 F
9
25
a balance in thermal and hydrogen requirements at equilibrium.
The effect of total pressure on the coal gasification is shown on Figure 5.
The plot shows that as the
total pressure increases from JO atm. to 70 atm. at
same reactor volume more carbon is converted at higher
total pressure.
This result also agreed with an earlier
report (20).
It must be mentioned that at high temperature more
steam was consumed, with more methane product as the
temperature is raised.
..
26
CONCLUSION
The calculation of results are based on an idealized
model of the gasification process which consists of two
stages: initial rapid reaction and solid-gas interface.
The initial rapid reaction is related to the amount of
volatile matter, and the solid-gas interface seems to
be controlled by gas diffusion rate.
The
ste&~-char
reaction and the hydrogen-char re-
action are considered as independent and simultaneous.
At high temperature more steam is consumed, with more
methane product as the temperature is raised.
But, the
hydrogen-char reaction is unfavorably affected by high
temperature.
Therefore, the catalytic effect on coal
gasification will be considered in further study.
..
27
NOMENCLATURE
Dp = average char particle diameter, ft.
f
= fraction
of carbon in the coal char which poten-
tially can react with hydrogen and/or steam according to the first-phase reaction
F
k1
=
coal char feed rate, lb./hr.
= steam reaction rate constant in the first phase,
min. -l
k2 = hydrogen reaction rate constant in the first
phase, (atm.-min.)-1
KgH 2o = effective mass transfer factor for steam,
ft./hr.-atm.
KgH 2
=
effective mass transfer factor for hydrogen,
ft./hr.-atm.
KE1
KE2
=
=
equilibrium constants for steam-char reaction
equilibrium constants for hydrogen-char reaction
PcH
* 4 =partial pressure of methane, in equilibrium with
coal char and hydrogen, atm.
PH 2 = partial pressure of hydrogen, atm.
* 2 = partial pressure of hydrogen in equilibrium with
PH
coal char and methane, atm.
PH2o = partial pressure of steam, atm.
PH
* 2o = partial pressure of steam in equilibrium with C,
CO, C02 and H2, atm.
T
= temperature
°F.
28
v = volume of the reactor, ft.3
X = fraction of carbon converted
XH2
XH20
= fraction of carbon converted by hydrogen
= fraction of carbon converted by steam
fB =
bulk density of coal char in bed, lb./ft. 3
t == time, hr.
)1.= viscosity of the gas, 1 b •/ ft . - hr .
..
29
REFERENCES
(1)
\'Ven,
c. Y.
&
Abraham, 0. C., "A Kinetic ·Study of
the Reaction of Coal Char with Hydrogen-Steam
Mixtures" Advan. Chem. Ser. 69, P.253 (1969)
(2)
Wen, C. Y., Huebler, J., Ind. Eng. Chem. Proc.
Design Develop. 4, P.142 (1965)
(3)
Wen, C. Y., Huebler, J., Ind. Eng. Chem. Proc.
Design Develop. 4, P.147 (1965)
( 4)
Johnson, J. L., "Kinetic of Bituminous Coal Char
Gasification with Gases Containing Steam & Hydrogen" Advan. Chem. Ser. 131, P.145 (1974)
(5)
Gadsby, J., Hinshelwood, C. N., Sykes, K. W.,
Proc. Roy. Soc. A187, P.129 (1946)
(6)
May,
w.
G., Mueller, R. H., Sweetser, S. B.,
Ind. Eng. Chem. 50, P.1289 (1958)
(7)
Mayer, L., Trans. Faraday Soc., 34, P.1056 (1938)
(8)
Pexton, S., Cobb, J. W., World 78, P.619 (1963)
(9)
Zielke, C. W. and Everett Gorin, Ind. Eng. Chem.,
Vol.47, No.4, P.820 (1955); Vol.49, No.3, P.396
(1957)
(10)
Goring, G. E., Curran, G. P., Zielke, C.
w.,
and
Everett Gorin, Ind. Eng. Chem. Vol.45, No.11,
P.2586 (1953)
(11)
Blackwood, J, D. and McCarthy, D. J., Aust. J.
Chern., 19, P.797 (1966)
..
(12)
Blackwood, J.D., Nature Vol.182, P.1014 (1958)
(13)
Dent, F. J., International Conference on Complete
Gasification of Mined Coal, Liege, Paper B1, P.113
(1954)
(14)
Von Fredersdorff, C. G., Ind. Eng. Chern. Vo1.52,
No.?, P.595 (1960)
(15)
Gray, D., Cogoli, J. G., Essenhigh, R. H., Advan.
Chern. Ser. 131, P.72 (1974)
(16)
Harry Perry, Scientific American, Vol.230, No.3,
P.19 (1974)
(17)
Feldmann., H. F., Mirna, J. A., Yavorsky, P.M.,
Advan. Chern. Ser. 131, P.108 (1974)
(18)
Zahradnik, R. I., Grace, R. J., Advan. Chern. Ser.
131, P.126 (1974)
(19)
Anthony, D. B., Howard, J. B., Meissner, H. P. and
Hottel, H. C., Rev. Sci. Instrum., Vol.45, No.8,
P.992 (1974)
(20)
Goring, G. E., Curran, G. P., Tarbox, R. P., and
Everett Gorin, Ind. Eng. Chern., Vol.44, No.5,
P.1051 (1952); P.1057 (1952)
(21)
Sergeant, G. D., Smith, L. VJ., Fuel, Vo1.52, P.58,
(1973)
( 22)
Squires, A. M. , Trans. Instn. Chern. Engrs. , Vol. 39,
P.3.(1961)
(23)
Chopey, N.P., Chern. Engr., P.?O, March4, (1974)
30
31
APPENDIX
EQUILIBRIUM CONSTANT
CALCULATION
Often the Gibbs free energies of formation 6G 0 f and
enthalpies of formation ~H~ are available for 25°C, and
the values Cp for the reactants and products are known
over a range of temperature.
With this information it
is possible to calculate 6 G0 at any temperature in the
range where the Cp data are valid, and of course from
AG 0 the equilibrium constant may be calculated using
AG 0
= -RT
ln K.
The enthalpy of reaction at temperature T is given
by
6HT
= AH 0
+
T-
JA CpdT
(A-1)
0
where AH 0 is the hypothetical enthalpy of reaction at
absolute zero.
Since the equations used to represent Cp
as a function of temperature are not valid down to absolute zero, AH 0 would not be the actual enthalpy change
at absolute zero.
However, if this equation is used
only to calculate AH in the temperature range where the
empirical equations for Cp are valid, no error is introduced. Since LlCp = 6a + (Ab)T + (&c)T 2 + • • • ·, it is
readily shown that
6H
= AH 0
+ (Aa)T + ·Hilb)T 2 + _3 (Ac)T3 + • • •
(A-2)
Substituting this value of AH into equation
o(G/T)
~T
- -H
- T2
which is the convenient form of the Gibbs-Helmholtz
(A-3)
32
equation, and integrating, it is readily shown that
AG
0
== AH 0 -(Aa)Tln
T-t(.6b)T 2 -~(Ac)T3+. • •+IT
(A-4)
where I is an integration constant.
The Gibbs free-energy change for a reaction may be
calculated from equation (A-4) if (1) the heat capacity
of each reactant and product is known as a function of
temperature from 25° to the desired temperature; (2) the
heat of reaction 6H is known at one temperature so that
~H 0
may be evaluated; and (3) the value of
~G
is known
at one temperature so that the integration constant I
may be calculated.
TABLE A-1 Enthalpy and Gibbs free energies of formation
at 25°C
Substance
AH~ cal/mole
AG~ cal/mole
H20 (g)
-57797 ~· 9
-54635·7
CH4
-17889
-12140
co
c
-26415.7
-32807.9
o.
o.
(s)
H2
o.
o.
These data have been obtained from F. D. Rossini,
D. D. Wagman,
w.
H. Evans, S. Levine, and I. Jaffe,
"Selected Values of Chemical Thermodynamic Properties."
TABLE A-2 Molar heat capacity of gases at constant
pressure (cal/mole-degree C)
34
21,827.8
= J0,801.8-(2.29)(298.15)ln(298.15)
-t(-2.JOx10-3)(298.15) 2
- (-0.077x1o-7)(298.15)3+(298.15)I
I = -17.4
~G 0
= J0,801.8-5.26T logT+1.15x1o-JT 2
+0.01Jx10-7TJ-17.4T
KE1
= exp(-AG 0 /1.987T)
Char-Hydrogen Reaction
C(S) + 2H2(g)
KE2
=
~
CH4(g)
p~H4
*
PH2
2 .
at 298 degree K
dCp
= -17.889 kcal
= -12.140 kcal
= Cp,CH4 - 2Cp,H2
.L\H0
= (-14.2818)+16.6848x1o-JT-51.266x10-7T2
= .L\ H - LlCpT
AH
AG
=
- Cp,C
-17,889+14.2818(298.15)-8.J424x1o-3(298.15) 2
+17.089x1o-7(298.15)3
-12140
= -1.4JJx104
= -14JJ0-(-14.2818)(298.15)ln(298.15)
-i(16.6848x1o-3)(298.15) 2
- (-51.266x1o-7)(298.15)3+(298.15)I
I= -71.6
33
b
103
107
Gas
a
Hz
6.9469
-0.1999
4.808
co
6.3424
1.8363
-2.801
H20
7.1873
2.3733
2. 084
CH
3.422
X
17.845
C X
-41.65
*Cp graphite = 3.81 + 1.56 x 10-JT
The constants are applicable in the range J0015000K.
H. M. Spencer and J. L. Justice, J. Am. Chem.
Soc., 56, 2311 (1934); H. M. Spencer and G. N. Flannagan,
J. Am. Chem. Soc., 64, 2511 (1942).
Char-Steam Reaction
* x PHz
*
Pco
KE1
also,
=
PHzO
KE1 =exp(- G/RT)
at 298°K
AG
= -32.8079-(-54.6357)
= 21.8278 k cal
~H
= -26.4157-(-57·7979)
= 31.3822 k cal
~Cp
= Cp,H2+Cp,Co-Cp,HzO-Cp,c
~ 2.29-2.)0 X 10-3T-0.077 x 10-7T 2
AH 0
=
H-2.29(298.15)+(1.15x1o-3)(298.15) 2
+(0.026x10-7)(298.15)3
= 30,801.8
cal
..
6G 0
35
= -14330-(-142818)(T)ln(T)-8.3424x10-3(T) 2
+8.55x1o-7(T)3-71.615(T)
VISCOSITY OF GASES
TABLE A-3 Absolute viscosity of' gases in micropoises
Gas
j).,
poises
Estimated
uncertainty
+fp.'
po1ses
Temp.
increment
(~p)T'
poises/°C
Pressure
increment
(.0)-l)p
poises/atm
Air
181.92
o.oo6
0.536
0.1224
C02
146.63
0.07
0.450
0.0046
co
175·3
0.1
0.474
......
0.05
0.200
0.0118
Hz
88.73
I
American Institute of' Physical Handbook.