United States
Environmental Protection
Agency
Industrial Environmental
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA-600/S7-84-068 July 1984
&ER& Project Summary
A Mathematical Model for a
Fluidized-Bed Coal Gasifier
M.J. Purdy, R.M. Felder, and J.K. Ferrell
A devolatilized Kentucky bituminous
coal and a New Mexico subbituminous
coal have been gasified with steam and
oxygen in a pilot-scale fluidized-bed
reactor. The reactor was operated at
pressures of 570-840 kPa (80-120
psia), molar steam-to-carbon feed
ratios of 0.6 to 1.9, and average bed
temperatures of 795-1010°C (1460-
1850°F). The coal feed rate ranged from
14 to 33 kg/hr (30-73 Ib/hr).
The experimental results provided a
basis for the formulation and evaluation
of mathematical models of the gasif ier.
A simple three-stage gasif ier model and
a two-phase bubbling-bed gasifier
model were developed. The simple
model assumes instantaneous devola-
tilization of coal at the top of the
fluidized bed, instantaneous combus-
tion of carbon at the bottom of the bed,
and steam/carbon gasification and
water gas shift reaction in a single
perfectly mixed isothermal stage. The
bubbling-bed model compartmentalizes
the reactor into an incipiently fluidized
emulsion phase and a solids-free bubble
phase. The solids are assumed to be
well-mixed as in the simple model, but
plug flow of the gases is assumed.
Model options allow for consideration
of a jetting region at the gas inlet of the
bed and elutriation of fines.
Parameters were estimated with each
model for each of the two feedstocks.
The main difference in the optimal
values was in char reactivity, for
which that of the New Mexico coal was
roughly an order of magnitude greater
than that for the Kentucky char. Using
the optimal parameter values, the
models were used for all experimental
runs.
Model predictions and experimental
results showed good agreement in all
cases. Taking into account departures
from isothermality in the bed, jetting at
the gas inlet, and particle size distribu-
tions in the feed coal did not provide
significant improvements in the ability
of the model to correlate the data,
except for elutriation rates, which are
highly sensitive to the concentration of
fines in the feed. Sulfur gas formation is
better predicted by equating sulfur and
carbon conversion than by using pub-
lished kinetic correlations.
The effects of various operating
parameters and phenomena on reactor
performance were determined using
the models. As expected, carbon
conversion and make-gas production
both increase with bed temperature,
steam-to-carbon feed ratio, and solid-
phase space time. Both also go up with
pressure; but, above about 1.7 MPa,
the increases are negligible. At the
temperatures studied, the water/gas
shift reaction falls short of equilibrium
for pressures lower than 2.1 MPa
(confirming experimental results), but
the reaction is close to equilibrium at
pressures above this value.
This Project Summary was developed
by EPA's Industrial Environmental
Research Laboratory. Research Triangle
Park, NC. to announce key findings of
the research project that is fully docu-
mented in a separate report of the same
title (see Project Report ordering
information at back).
Introduction
As a part of a continuing research
program on the environmental aspects of
fuel conversion, the U.S. EPA has
sponsored a research project on coal
gasification at North Carolina State
University (NCSU). The overall objective
of the project is to characterize the
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gaseous and condensed-phase emissions
from the gasification/gas-cleaning pro-
cess, and to determine how emission
rates of various pollutants depend on
adjustable process parameters.
The facility used for this research is a
small coal-gasification/gas-cleaning
pilot plant, including a continuous
fluidized-bed reactor, a cyclone separator,
a venturi scrubber, and absorption and
strippng towers and a flash tank for acid
gas removal. Process control, data
acquistion, and data logging systems, and
an extensive analytical laboratory com-
plete the facility.
In experiments conducted to date, a
devolatilized Western Kentucky bitumin-
ous coal, a New Mexico subbituminous
coal, a North Carolina peat, and a Texas
lignite have been gasified with steam and
oxygen. The experimental results are
summarized in several EPA reports.
The primary function of the NCSU gasi-
fication reactor is to provide a reproducible
synthesis gas for studies of the potential
environmental impact of coal gasification
processes. The development of correla-
tive and predictive models of the gasifier
was felt to be an indispensable adjunct to
planning and implementing the overall
experimental program. As part of the
study, two gasifier models were developed
and used to correlate the data for
gasification of the bituminous char and
the New Mexico subbituminous coal—
one simple, the other relatively complex.
This report summarizes the principal
features of both models, and reports the
model correlations of the gasification
data for both feedstocks studied.
Model Description
The three-stage well-mixed reactor
model and the bubbling-bed model are
described.
Three-Stage Well-Mixed
Reactor Model
The first stage of the modeling studies
was to formulate the simplest possible
model which incorporates the principal
gasification reactions and the gross
physical characteristics of the reactor,
and to determine the degree to which the
gasifier performance could be correlated
by this model. A well-mixed fluidized-bed
model was used for this purpose. The
model assumes instantaneous devolatili-
zation and oxidation, followed by gasifica-
tion in a perfectly mixed bed. The model
takes as input the average reactor bed
temperature and pressure; the bed
dimensions; feed rates of coal, steam,
oxygen, and nitrogen; solids holdup in the
bed; and ultimate analysis of the feed
coal. It calculates carbon conversion and
make-gas flow rate and composition.
Devolatilization is presumed to occur
instantaneously where the coal enters
the bed. The extent of devolatilization and
composition of the volatile products are
taken from rapid pyrolysis data obtained
in a separate study at NCSU and additional
data for a western subbituminous coal
close in composition to the one used in
this study.
After devolatilization has occurred, the
following reactions are presumed to take
place:
C + H20 = CO + H2 (1)
C + 2H2 = CH4 (2)
2C + H2 + H2O = CO + CHU (3)
CO + H2O = C02 + H2 (4)
C+1/2O2 = CO (5)
C + O2 = CO2 (6)
S + H2 = H2S (7)
H2S + CO2 = COS + H20 (8)
Reactions 5 and 6, the oxidation steps
required to supply heat for the remaining
reactions, are assumed to occur instanta-
neously in a zone of negligible volume
separate from the gasification zone. All
oxygen in the feed gas is taken to be
consumed to form CO and CO& with the
combustion product distribution being
governed by the relation:
C + a02 = (2-2a)CO + (2a-1 )C02
where a, the combustion product distri-
bution coefficient, is an adjustable model
parameter. A value of a = 0.5 indicates
that all CO is formed, while a = 1.0
indicates that only C02 is formed.
Reactions 1, 2, and 3 are the reactions
with which the Institute of Gas Technol-
ogy correlated gasification kinetics data.
These kinetic expressions, summarized
in the body of the report, include as an
adjustable parameter a char reactivity
coefficient, f0, which has values ranging
from 0.3 (for low-volatile bituminous coal
char) to about 10 (for North Dakota
lignite).
Reaction 4 is the water/gas shift
reaction. A model option allows the
assumption of shift reaction equilibrium
or the use of kinetic rate equations. The
rate expression used contains an adjust-
able parameter, fwg, which accounts for
the varying catalytic activities of different
chars.
The rate of Reaction 7 is estimated by
assuming that the sulfur conversion
equals the carbon conversion, and that all
converted sulfur forms hydrogen sulfide
by Reaction 7. The flow rate of COS is
then determined by assuming equilibrium
of Reaction 8.
In summary, the model has three M
adjustable parameters: the intrinsic char \
reactivity factor, f0; the C0/C02 combus-
tion product distribution parameter, a;
and the water/gas shift reactivity factor,
fwg. The other coefficients of the various
rate and equilibrium equations are
prescribed by the model. Details of these
equations and of the model computation-
al procedure are given in the report.
Bubbling-Bed Model
The two-phase bubbling-bed model
divides the reactor into two main sections:
a bed region, and a freeboard region
above the bed. Consideration of a jetting
region at the gas inlet of the bed is a
model option that can add a third section
to the model.
The NCSU gasifier uses a top coal
feeding system, with the feed particles
falling through the hot exiting gas stream
before entering the bed. In the freeboard
region, the particles (heated by the gas
stream) are dried and devolatilized. In
addition, the fines in the coal feed stream
may be eluted by the exiting gas stream.
The model of the freeboard section
accounts for all of these phenomena.
If elutriation is considered, the amount
of fines blown out of the reactor is first ^
calculated by assuming that all particles m
with terminal velocities less than the gas
velocity at the top of the reactor are
eluted. The blowover solids are assumed
to be devolatilized at the gas exit
temperature.
After the blowover calculation, the flow
rate and size distribution of the remaining
coal are determined. The devolatilization
products for this stream are calculated,
assuming equilibrium yields at the
temperature at the top of the bed. The
devolatilization products are assumed to
be evenly evolved along the length of the
freeboard region.
Heat transfer from the gas to the coal
particles is calculated for each class of
particle sizes using a single-sphere heat
transfer correlation. It is assumed that
there are no radial temperature gradients
within particles. The latent heat of
devolatilization is neglected. The heat of
vaporization of moisture is included in the
model, with an average value of 37.7
kJ/gmol being used for all conditions. It is
assumed that the heat required to
vaporize the moisture in the feed coal is
taken from the gas phase.
Particles are assumed to have constant
volumes in the freeboard region, so that
the particle densities decrease as drying
and devolatilization proceed. No gas-
phase reactions are considered in this
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region. The model contains an option to
consider a jetting region at the gas inlet of
the bed. The jet penetration height and jet
angle are calculated using earlier correla-
tions.
The gases in the fluidized bed are
assumed to be in plug flow, while the bed
solids are assumed to be well-mixed with
respect to composition and size. Mass
transfer between the jet and emulsion
phases is determined using a mass
transfer coefficient correlation.
The region between the jet penetration
height and the top of the bed is assumed
to be a two-phase fluidized region,
consisting of an incipiently fluidized
emulsion, and a solids-free bubble phase.
Both gas phases are assumed to be in
plug flow, while the solids are assumed to
be perfectly mixed throughout the jet and
fluidized-bed regions. The assumption of
well-mixed solids throughout the bed is
supported by experimental results. Mass
transfer rates between the two phases
are calculated using earlier correlations.
For both the jet and fluidized regions,
the temperature may be determined
three ways: (1) a specified isothermal
value; (2) an imposed temperature profile;
and (3) a profile calculated assuming
adiabatic reactor operation. For all, the
solids and gases at any height are
assumed to be at the same temperature.
The following reactions are assumed to
occur in the emulsion phase:
C + H20 = CO + H2
C + 2H2 = CH4
2C + H2 + H20 = CH4 + CO
C + O2 = C02
2C + O2 = 2CO
S + H2 = H2S
CO + H20 = C02 + H2
2CO + 02 = 2C02
2H2 + 02 = 2H2O
CH4 + 2O2 = CO2 + 2H20
H2S + CO2 = COS + H20
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
The jet and bubble phases are solids-free,
so that only Reactions 15-19 may occur.
Reactions 9-11 are gasification reac-
tions, with rates given by the previously
discussed kinetic expressions. Carbon
combustion Reactions 12 and 13 are
described by an earlier rate equation. The
combustion rate expression yields the
rate of carbon consumption, but does not
specify the gaseous products. The
combustion product split between CO
and CO2 is therefore calculated as
outlined in the context of the simple
three-stage model. The C0/C02distribu-
tion coefficient, a, can be determined
from an earlier correlation or left as an
adjustable parameter.
Gas phase combustion occurs accord-
ing to Reactions 16-18. The reactions are
very fast, and are assumed to go to
instantaneous completion. If oxygen is
insufficient for complete combustion, the
reactions probably compete for oxygen at
different rates. However, the reactions
are expected to have a small overall effect
on the modet predictions. So, for simpli-
city, the three reactions are assumed to
compete equally for available oxygen.
The water/gas shift reaction is con-
sidered to occur in both the bubble (jet
phase in the jetting region) and emulsion
phases. In the emulsion phase, the
reaction occurs predominantly on the
char surface, which acts as a catalyst. A
model option also allows for the assump-
tion of shift reaction equilibrium.
Hydrogen sulfide formation by Reac-
tion 14 can be calculated two ways: by
using earlier kinetic rate equations, or by
assuming equality of the sulfur and
carbon conversions with all sulfur being
converted to H2S. The latter assumption
is based on experimental data.
The elutriation rate from the bed is
determined following the size reduction
calculations. The size distributions of the
elutriated solids and the bottoms exit
solids are then calculated, and the solids
elutriated from the bed are added to the
solids blown out at the top of the reactor
to form the total elutriate flow.
Details of the computational procedure
for the model are given in the report. Also
given are tabulations of the physical
property data and correlations used in
formulating both models.
Results
Results are given separately for the
well-mixed stage model and the bubbling-
bed model.
Well-Mixed Stage Model
The coal reactivity coefficient, f0, the
combustion product distribution coeffi-
cient, a, and the water/gas shift reactivity
parameter, fwg, were evaluated by using
a Pattern Search routine to minimize a
function of the sum of squared deviations
between predicted and measured values
of gasifier performance variables, includ-
ing carbon conversion, dry make-gas flow
rate, and mole fractions of hydrogen, car-
bon monoxide, and carbon dioxide in the
make-gas. The runs with the best mass
balance closures were chosen to provide
the data base for the parameter estima-
tion. For the Kentucky bituminous char,
the parameter values obtained were:
fo = 0.276
a = 0.828
fwa = 1.29x10"5
The value of a, given above, indicates
that 66% of the carbon oxidized forms
C02 and 34% forms CO. An earlier
equation predicts a = 0.57 at 760°C and a
= 0.52 at 1100°C, while several gasifica-
tion studies have assumed a = 1.0.
The value of fwg = 1.29 x 10~5 indicates
that the shift reaction rate is approximate-
ly five orders of magnitude less than the
rate typically obtained in catalytic shift
reactors. An earlier study used a shift
reactivity value of 1.7 x 10~4 in modeling
the gasification of a bituminous coal by
the Synthane process. The larger earlier
value many be attributed to differences in
the coals used in the studies.
Using the optimal parameter values,
the model was run for all char runs.
Plots of predicted vs measured values of
carbon conversion, dry make-gas flow
rate, and sweet gas heating value are
shown in Figures 1 -3. (The sweet gas is
defined as the dry make-gas with the
C02 and H2S removed.) The close proxim-
ity of the points to the 45 degree line is
gratifying in view of the simplicity of the
model.
The same optimization procedure used
to determine the optimal parameters for
char was used to find the optimal
parameter values for the New Mexico
subbituminous coal, using fast pyrolysis
product data to calculate the devolatiliza-
tion gas product distributions. The
resulting parameter values were:
fo = 4.20
a = 1.00
fwa= 1.2x10-"
The char reactivity parameter for coal is
much larger than that obtained for the
Kentucky char. The combustion coeffi-
cient does not differ greatly for the coal
and the char; however, the shift reactivity
parameter is an order of magnitude
greater for the coal than for the char. A
possible reason for the greater shift
reactivity of the New Mexico coal
(compared to the char) is the different ash
contents of the two materials: the coal
had a feed ash content of 22.6%, while
the ash content of the char was only
10.7%. The minerals in the ash fraction of
coal serve as catalysts for the shift
reaction. In addition, during gasification,
the coal was converted to a greater extent
than the char, giving an even larger
difference in ash contents. The shift
reactivity parameter obtained in this
study for a subbituminous coal agrees
well with the earlier value used for a
bituminous coal (fwg = 1.7 x 10"4).
The model was used to correlate the
New Mexico coal run data using optimal
parameter values. In general, the agree-
ments between model predictions and
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100
80 -
60 -
I
Q.
40 -
20 -
roo
Experimental, percent
Figure 1. Predicted vs. experimental carbon conversion for Kentucky char, well-mixed model.
experimental measurements were excel-
lent. Comparisons of predicted and
measured reactor variables are shown in
Figures 4 and 5.
For each run, the water/gas shift
equilibrium ratio was calculated from
both experimental measurements and
model predictions of the gas composition.
A plot of the predicted vs experimental
values of this ratio is given in Figure 6.
The substantial degree of scatter may be
attributed to the simplicity of the model,
and equally to the fact that the mole frac-
tions which are the constituents of Kwg
are interdependent, so that an experi-
mental error in one of them affects the
values of the others.
The significance of this plot emerges
when it is compared with Figure 7, which
shows the values of KWg predicted
assuming shift equilibrium. This assump-
tion leads to overprediction of Kwg and
lends support to the conclusion that the
shift reaction should not be assumed to
proceed to equilibrium.
Bubbling-Bed Model
The two-phase bubbling-bed model of
the gasifier contains the same three
parameters as the well-mixed model. In
addition, a fourth parameter—the char
abrasion constant (Ka)—is required to
calculate the particle size reduction due
to abrasion in the fluidized bed. All are
properties of the material being gasified.
The parameters are independent of
processing conditions, and (once deter-
mined) are applicable to any set of reactor
conditions.
The two-phase bubbling-bed model of
the gasifier is much more complex than
the well-mixed model. It also requires a
much larger program and more computer
time for completion. As a consequence of
the model's size and limited available
computing time, the optimization proce-
dure was less detailed than that for the
well-mixed model. To speed the optimiza-
tion computations, the step sizes used in
searching for the optimal set of param-
eter values were increased from those A
used in optimizing the well-mixed model ™
parameters, and smaller data bases were
used.
The optimal parameter values for the
bituminous char were
fo = 0.80
a = 1.00
fwa= 1.5x10'4
ka = 3.0x10""
The values of f0, a, and fwg are all higher
than the corresponding values determined
for the well-mixed model. The differences
may be due to the gas/solid contacting
assumed in the two models. In the two-
phase model, a large fraction of the gas
passing through the bed is in the bubble
phase and does not contact the coal. The
well-mixed model does not allow for such
gas bypassing, and as a consequence
may underpredict the reactivity param-
eter values.
Using the optimal parameter values,
the model was run for the conditions of all
Kentucky char runs for which acceptable
mass balance closures were obtained.
The model predictions for carbon conver-
sion and gas production are plotted
versus the experimental results in the
report. The plots show good agreement
between the model predictions and the
experimental measurements, but similar A
to and not significantly better than those ™
shown in this summary for the well-
mixed stage model.
Parameter estimation for the New
Mexico subbituminous coal yielded the
following results:
fo = 8.60
a = 1.00
fwg = 2.2x 10""
ka = 4.5x 10"4
The char reactivity factor for the New
Mexico coal is roughly 11 times greater
than that for the Kentucky char. This
agrees with the experimentally observed
trend, and with the results of the well-
mixed model (f0 ratio of 15). The combus-
tion product coefficient is the same as
that determined for the Kentucky char,
and indicates that CO: is the sole product
of the carbon/oxygen reaction. Similar
values were obtained for the shift
reactivity factor, while the greater
abrasion constant value for the New
Mexico coal indicates that it is more fri-
able than Kentucky char.
Using the above values, the model was
used to correlate the results for New
Mexico coal. Parity plots of the main
reactor performance variables are shown
in the report. As for the bituminous char
correlations, good agreement was ob- ^t
tained between the model predictions V
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25
20 -
IS -
10 -
5 -
JO 15
Experimental, scfm (dry)
\
20
25
whereas the well-mixed model does not
require size distribution. The two-phase
model was run for several feed size
distributions to determine their effect on
reactor performance predictions. All
operating conditions were held constant
except feed size distribution. Results
show that feed size distribution has a
dramatic effect on the elutriation rate, but
a relatively small effect on carbon
conversion and gas production. The
make-gas shows a decrease in the
CO/COz ratio with increasing particle
size. The hydrogen content in the dry gas
increases with increasing particle size.
Figure 2. Predictedvs. experimental gas production rate for Kentucky char, well-mixed model.
and experimental results, but not signifi-
cantly better than with the simpler model.
Quantitative measures of goodness of
fit for both models lead to the conclusion
that no significant improvement in data
correlation is obtained by resorting to the
more sophisticated bubbling-bed model
—certainly not enough to justify the
considerably greater computation time
required to implement the latter model.
Studies were performed to determine
the effect on reactor performance of an
axial temperature profile in the bed;
jetting at the gas feed nozzles; and
particulate elutriation. For all, it was
found that relatively little error in
calculated carbon conversion and dry
make-gas flow rate is introduced if these
phenomena are neglected. Sulfur gas
formation is better predicted by equating
sulfur conversion and carbon conversion
than by using published kinetic correla-
tions.
The well-mixed stage and bubbling-bed
models were run for several sets of hypo-
thetical reactor conditions to determine
the effects of selected operating variables
on reactor performance. The variables
examined were temperature, pressure,
HgO/C feed ratio, solid-phase space time,
and feed particle size distribution.
The results are presented in detail in
the report. As expected, carbon conver-
sion and gas production increase with
bed temperature, steam-to-carbon feed
ratio, and solid-phase space time. Both
also increase with pressure; but, above
a pressure of about 1.7 MPa (250 psia),
the increases are negligible. Another
noteworthy result is that the water/gas
shift reaction falls short of equilibrium for
pressures lower than 2.1 MPa (300 psia),
as earlier results indicate, but the
reaction is extremely close to equilibrium
at pressures above this value.
The bubbling-bed model takes the feed
particle size distribution into account,
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400
300 -
I
l
i
200 -
100
100 200 300 400
Experimental, Btu/scf <
Figure 3. Predicted vs. experimental heating value for Kentucky char, well-mixed model.
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700
80 J
601 ^
s
S
Q.
1
40 -1
20 <-{
20 40 60
Experimental, percent
80
100
Figure 4. Predicted vs. experimental carbon conversion for New Mexico coal, well-mixed
model.
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10
Experimental, scfm (dry)
Figure 5.
Predicted vs. experimental gas production rate for New Mexico coal, well-mixed
model.
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0.8
0.7 -
I
1
I
I
0.6 -
0.5 -
0.4 -
0.3
0.3 0.4
Experimental.
Figure 6. Predicted vs. experimental Kwg value for New Mexico coal, well-mixed model.
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0.8
0.7 -
O
1
j
0.6 -
o.s -
0.4 •
0.3
0.3
0.4
0.6
Figure 7.
0.5
Experimental.
Equilibrium vs. experimental Kwg value for New Mexico coal.
M. Purdy, R. Felder. and J. Ferrell are with North Carolina State University,
Raleigh. NC 27650.
N. Dean Smith is the EPA Project Officer (see below).
The complete report, entitled "A Mathematical Model for a Fluidized-Bed Coal
Gasifier," (Order No. PB 84-209 469; Cost: $20.50, subject to change) will be
available only from:
National Technical Information Service
5285 Port Royal Road
Springfield. MA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Industrial Environmental Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
* USGPO: 1984-759-162-10634
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