Limitation of thermogravimetry for oxy-combustion analysis of coal chars
Limitation of thermogravimetry for oxy-combustion analysis of coal chars
Piotr Babinski 0 1
Marek Sciazko 0 1
Ewelina Ksepko 0 1
0 Institute for Chemical Processing of Coal , 1 Zamkowa, 41-803 Zabrze , Poland
1 & Piotr Babinski
A kinetic study of the oxy-combustion of chars obtained from two Polish steam coals was conducted. A comparative study was focused on the data analysis concerning oxy-combustion of coal chars collected from two thermobalances, which differed in construction, design of crucibles, sample size and gas flow direction. The influence of individual factors such as temperature, O2 concentration, the dimensions of the crucibles and the dimensions of the char bed on the reaction rate was analysed. On the basis of these results, a global kinetic model was elaborated showing the influence of all factors, particularly mass transfer conditions, on reaction rates. The developed model can be extended to other mass transfer conditions or fluidised bed conditions and can be applied to other fast reactions to ensure they occur in the chemical reaction kinetics control regime during TG tests. It was concluded that the gas-solid fuel contact characteristics are crucial for the measured reaction rate and for the interpretation of kinetic data.
Diffusion effects; Kinetics; Oxy-combustion; Char combustion
APTGA Atmospheric pressure thermogravimetric
HPTGA High-pressure thermogravimetric analyser
Recently, great attention has been focused on carbon
dioxide emissions from the power sector due to the
significant impact of the greenhouse effect. To reduce the
emissions of greenhouse gases from fossil fuel-fired power
generation, the oxy-combustion of coal seems to be a
promising future technology combined with retrofitting of
existing boilers to allow an O2-enriched atmosphere for
In the process of oxy-combustion of fossil fuels, a high
purity of oxygen (above 95%) and a stream of recycled
CO2 from the flue gas are used to control the combustion
temperature. The process product is a gas consisting mostly
of CO2 and water vapour. The considerable concentration
of CO2 in the gas enables direct referral to sequestration,
which is followed by condensation of water vapour [
The oxy-combustion process comprises several
consecutive processes and reactions. When a coal particle is
introduced into the combustion chamber of a fluidised bed,
it is heated with a high heating rate (up to 1000 K s-1).
This step involves drying and pyrolysis of the coal particle,
and the evolution of volatile matter consisting of
combustible gases, while char is produced. The volatiles burn
in homogenous reactions, and the char reacts with oxygen
(heterogeneous reaction). The reaction of carbon from char
with O2 is the slowest step of the whole process [
Therefore, the present work focuses on the coal char
oxycombustion, because its reaction rate is crucial for boiler
design. Since the oxy-combustion of coal char is a
heterogeneous reaction, it can proceed under three different
reaction-controlling regimes: chemical kinetics, mixed
internal diffusion–chemical kinetics and external diffusion
]. Oxy-combustion in a fluidised bed boiler occurs at a
temperature of 1073–1173 K where diffusion limitations
3, 4, 10
]. The scaling-up of this process requires an
extensive computational analysis, which is critical for
proper boiler design. Herein, a kinetic analysis is
fundamental for oxy-combustion process modelling, where the
kinetic equations are implemented using modelling
On the other hand, thermogravimetric analysis is a
commonly used technique to investigate the kinetics of fast
heterogeneous reactions such as the combustion of solid
fuels, the oxidation of oxygen carriers [
5, 6, 11–19
]. It is
well known that kinetic parameters should be obtained
under a chemical reaction-controlling regime
5, 6, 13, 14, 17–19
], which is important for the study of
Some researchers have proposed specific approaches to
finding the transport limitations in TGs during combustion
or gasification of fuels [
11, 12, 20
]. They have found a
number of parameters which are crucial for shifting the
regime from chemical kinetics to diffusion, especially
crucibles and their dimensions, fuel bed mass and gas flow
direction. The interpretation of these results involves a
numerical analysis which is difficult to apply to other
The aim of the paper is the identification of diffusional
limitations for the crucibles used in thermobalances, which
influence the kinetic analysis of fast reactions, such as, for
example, oxy-combustion. As a result of the study,
suitable and generalised models for oxygen transport to the
coal char particles in TG crucibles were developed.
Moreover, the models can be extended for application in
fluidised bed processes.
Two char samples obtained from Polish lignite (Turo´w)
and hard coal (Janina), which are extensively used for
combustion in Polish power plants, were investigated. The
chars were prepared using a laboratory stand for the
pyrolysis of solid fuels. First, ca 150 g of coal sample of
size 1–3.15 mm was placed in a cylindrical batch reactor.
The reactor was heated up to 1273 K at a heating rate of
5 K min-1 under nitrogen. Subsequently, the reactor was
flushed with N2 to cool the sample to room temperature.
The coal sample and obtained char samples were crushed
and sieved to a particle size smaller than 200 lm and were
The proximate analyses of the coal and char samples
were performed by a gravimetric method using a LECO
TGA701 analyser. The ultimate analysis that followed
sulphur analysis was conducted using CHN TruSpec LECO
and LECO SC632 apparatus. Pore structure was analysed
by nitrogen adsorption at 77 K and CO2 adsorption at
273 K, using Micromeritics 3Flex apparatus. A Malvern
Instruments Mastersizer 2000 particle analyser with a
dispersion Hydro 2000G mouthpiece was used for analysing
the particle size distribution of coal chars.
The tested samples were significantly different in terms of
metamorphism degree, as indicated by the volatile content,
elemental composition of coals and particularly the oxygen
content (Table 1). The pyrolysis of coal led to an increase in
elemental C content to approx. 80% and to the reduction of
the hydrogen, oxygen, sulphur and nitrogen contents. The
analysis results obtained from the coal chars indicate that the
chemical compositions of the chars are similar, even though
they come from coals with a different degree of
metamorphism. The pyrolysis resulted mainly in the removal of
moisture from the coal samples, and in a separation of the
volatile components, producing lignite char with zero
content, and approximately 0.5% for hard coal char. In other
words, the pyrolysis of the coal has increased the degree of
metamorphism of the parent coals and conformed them
chemically to one another. Although the technical and
chemical analyses show that the properties of chars are
similar, there are some significant differences in their
structure. This has the greatest impact on the char particles’
reactivity. For example, the pore structure of the char has a
greater impact than its chemical composition. A smaller
specific surface area (determined by the BET method), of the
order of few m2 g-1, is shown by the sample of hard coal
char and a significantly larger surface area by the lignite
char. The surface area of the micropores, determined by
adsorption of CO2 at 273 K, confirmed the greater surface
area of the lignite char micropores (Table 2).
Oxy-combustion tests were conducted in two
thermobalances, namely an atmospheric pressure Netzsch STA 409
PG Luxx (APTGA) thermobalance, and a TA Instrument
pressurised thermobalance TG-HP150 s with Rubotherm
magnetic suspension balance (HPTGA). The dimensions of
the TGA’s furnace and crucibles, and also the experimental
conditions, differ in these two thermobalances. The
differences are presented in Tables 3 and 4.
The reaction furnaces of the two TGAs in which the
crucibles are placed are of the tubular type. For each of the
thermobalances, a specific method of crucible mounting is
applied. In the APTGA, the crucible is placed on a long rod
which is a carrier for the crucible and is connected to the
mass measuring system placed below the reaction furnace.
On the other hand, HPTGA has a completely different type
of crucible mounting. In this case, the crucible is suspended
on a weighing hook which is connected to the permanent
magnet (magnetic roller) of the upper part of the reactor.
The permanent magnet is maintained by a magnetic field
from an electromagnet, which is a part of the electronic
measuring system of the balance. Gas entering the APTGA
is introduced at the bottom of the furnace and flows
upwards washing the crucible. Therefore, the gas cannot
interfere with the stationary gas layer in the crucible in any
way. In the case of the HPTGA, the gas is introduced into
the upper part of the furnace and it flows vertically
downwards. Therefore, the gas could influence the gas
layer in the crucible. In Tables 3 and 4, the dimensions of
the individual furnaces of the thermobalances are shown
together with dimensions of the crucibles used. The gas
flow values and the properties of the char beds are also
The experiments were conducted at isothermal
conditions by applying the temperature of 450 (only for the
lignite char), 500, 550, 600, 700, 800, 900 and 1000 C. In
the APTGA an alumina crucible was used, and in the
HPTGA a quartz crucible with porous bottom was used.
Reaction gases with defined composition and specific
volume flow were fed into the reaction furnace. The
gaseous mixtures with a suitable molar fraction of oxygen yO2
in CO2 equal to 0.2 were introduced into both TGAs.
Moreover, a protecting gas of ca 25 N cm3 min-1 of Ar
was dosed into the APTGA. For APTGA the char sample
mass was m0 = 5 mg, while for HPTGA it was 10 mg.
Comparison of the flow conditions showed that the flow
rate of the gas through the furnace was approximately eight
times higher for HPTGA than it was for APTGA. All these
parameters could have a significant effect on the results
obtained from the thermogravimetric analysis.
Analysing the presented data, it can be concluded that
the height of the char bed in both cases is comparable to the
diameter of the particles. Therefore, considering the
properties of the char bed it can be assumed that it is a
monolayer of particles, almost evenly distributed at the
bottom of the crucible. In addition, the ratio of the char bed
diameter to its height is very large: for the lignite char and
hard coal char for the APTGA crucible, it amounts to 22.9
and 27.4, respectively. The corresponding values for the
HPTGA case are 55.8 and 66.8. For this reason, it can be
assumed that the char bed is a single char tablet with height
hb. The crucible diameter is designated dN, and the
crosssectional area (footprint) is AN. This assumption is used to
describe the reaction rate in crucibles for both
Results and discussion
After the initial coal pyrolysis stage, the combustion of
coal chars proceeds in several consecutive and parallel
processes. Inside a real industrial boiler, a single particle is
raised in the reacting gases flowing upwards and is
surrounded by a laminar gas layer, as shown in Fig. 1a.
Oxygen from the bulk gas enters the laminar layer
surrounding the char particle by convection, and then the O2
transport occurs by diffusion. Therefore, the process can be
divided into several stages as follows:
O2 transport to the particle and within the particle,
which consists of:
O2 convection to the gas film surrounding the char
O2 diffusion in the laminar gas layer surrounding
O2 diffusion in the pores of the char particle.
In the TGA, char particles are not carried in the gas but
they form a fixed bed of thickness hb at the bottom of the
crucible. The mass transfer differs from that in the fluidised
bed, which may affect the oxy-combustion reaction rate.
Figure 1 shows schematically the flow patterns in the
fluidised bed and in the crucibles used in TGA.
The overall oxy-combustion reaction rate is a result of
all existing resistances, and it can be shown as Eq. (1):
1 1 1
robs ¼ rR þ rD
where robs is the observed overall reaction rate, rR is the
chemical reaction rate, and rD is the O2 transport rate.
In the chemical kinetic regime, the chemical reaction is
the slowest step of global reaction, and the main
rate-determining step is a chemical reaction rate. Thus, the
condition robs = rR is valid, and the reaction can be described
using nth-order kinetics as in Eq. (2):
robs ¼ rR ¼ kR f ðXÞ COn2 ð2Þ
where kR is a chemical reaction constant, CO2 is the O2
concentration on the surface of the char particle (in the
kinetic regime on both the inner and outer surface of
particle), n is the reaction order with respect to O2
concentration, and f(X) represents the reaction model.
The reaction rate in this analysis is represented as the
rate of C element loss from the char in moles, in a specified
time interval, i.e. dNC/dt as calculated from Eq. (3):
¼ dt MC
; mol s 1
where dm/dt is the reaction rate from DTG and MC is the
molar mass of carbon (12 g mol-1).
lnðrRÞ ¼ R T þ lnðA0Þ
The mean value of the reaction rate from a conversion
range of 0.2–0.8 was used in this paper, and only one
concentration of oxygen was applied. Therefore, the
reaction model f(X) and the O2 concentration are both included
in the reaction rate constant which is equal to the reaction
rate (rR = kR). The Arrhenius equation is shown in Eq. (4):
where Ea is the activation energy and A0 is a
With increasing temperature, the main resistance to the
reaction may be O2 transport to the char particle surface
(diffusion regime). In these conditions, when the
temperature is increased, the reaction rate is not significantly
increased, because of the small increase in O2 transport
rate. Therefore, the overall reaction rate may be equal to
the rate of O2 transport, or in other words robs = rD.
Therefore, specific O2 transport models can be applied for
different apparatus and for different types of solid–gas
The transport model of O2 in the APTGA crucible
In the APTGA crucible, the gas flows vertically upwards
and it flows around the crucible. Subsequently, it joins the
uniform gas flow which takes place over the crucible.
Figure 2 shows a schematic representation of the APTGA
crucible, with the directions of reactant transportation and
their local concentrations indicated (Fig. 2a). The potential
distribution of the O2 concentration as a function of
crucible height is shown in Fig. 2b.
At the top of the crucible, the O2 concentration is the
same as in the bulk gas and is equal to the initial
concentration of O2 directed to the furnace, CO2;1. In the crucible
Fig. 2 Model approach of O2
transport in the crucible of the
a schematic with selected
concentrations and the molar
fraction of O2, with dimensions
and directions of flow of the
reactants, b distribution of O2
concentration as a function of
above the bed of char considered as a tablet, there is a
stationary layer of gas with height hD equal to the height of
the crucible hN minus the thickness of the char layer hb.
When oxy-combustion of the char takes place, the
concentration of O2 on the surface of the char bed, CO2;2,
decreases as a result of the reaction. Combustion of one
mole of O2 results in the formation of one mole of CO2.
Therefore, for each mole of O2 flowing towards the particle
there is one mole of CO2 which diffuses in the opposite
direction, as described by Eq. (5):
NO2 ¼ N_ CO2 ; mol s 1
Fick’s first law defines the equimolar countercurrent
diffusion rate, which is proportional to the concentration
gradients of the components and inversely proportional to
the length of the diffusion path which is the height of
stationary gas layer. As a consequence, for O2 diffusion, it
can be mathematically expressed as in Eq. (6) [
_ dCO2 ; mol m 2 s 1
NO2 ¼ DO2 dhD
where dCO2 is the O2 concentration gradient between two
points along the length of the diffusion path dhD and DO2 is
the molecular diffusion coefficient of CO2 in O2.
After separation of variables, integration and taking into
consideration the surface of the char bed (the crucible
area), this is modified as follows:
_ DO2 AN CO2;1
NO2 ¼ hD
where AN is the surface of the char bed in the crucible
calculated according to the equation AN ¼ p dN2=4.
The molecular diffusion coefficient is dependent on both
the temperature and the pressure value, and it can be
calculated from the Fuller–Schettler–Giddings equation
shown as Eq. (8) [
where vO2 and vCO2 are the molar volumes of both gas
components, (i.e. O2 and CO2), MO2 and MCO2 are the
molar masses of O2 and CO2, Pt is the total pressure, and
T is the temperature.
There are also other mathematical relations enabling
calculation of the molecular diffusion coefficient, and these
are widely shown elsewhere [
]. The molecular diffusion
coefficient is a parameter which is characteristic for the set
of two gases, and it is independent of the components’
concentrations. As can be seen, the diffusion coefficient is
proportional to the temperature to the power of 1.75 and
inversely proportional to the total pressure. As a result, it
can be concluded that the reaction steps of oxy-combustion
in the reported TGA system are:
O2 diffusion in a stationary gas layer in accordance
with Fick’s first law (from the inlet of the crucible to
the surface of the char bed).
Chemical reaction on the surface of char particles.
The slower of the two above stages will be the
ratelimiting step. In the extreme case where the global rate of
the reaction is determined by the rate of O2 diffusion in the
crucible, the concentration of O2 on the surface of the char
bed will be CO2;2 ¼ 0. This means that the diffusion
resistance of O2 between the inlet of the measuring crucible
and the surface of the char bed is the largest. Each oxygen
molecule diffusing to the bed surface will immediately
react when it makes contact with the nearest carbon atom.
Therefore, the model of diffusion in the crucible can be
simplified to Eq. (9):
_ DO2 ANCO2;1; mol s 1
NO2 ¼ hD
Oxygen transportation model in the HPTGA crucible
The gas flow in the pressurised thermogravimetric analyser
(HPTGA) is directed downwards, resulting in interference
with the gas layer in the crucible (Fig. 1c). Furthermore,
the crucible has a porous semipermeable bottom, which
might result in some partial gas flow throughout the
In Fig. 3 the schematic of the crucible from the HPTGA
is shown. The directions of reactant transportation and their
local concentrations, together with the potential
distribution of the O2 concentration as a function of the height of
the crucible, are shown for the established convection–
There are two gas layers in the crucible: convection
(turbulent gas layer) and diffusion (stationary gas layer). In
the upper layer with height hcon, the gas flowing into the
crucible can cause turbulence and hence transport of
oxygen by convection. In the bottom part of the crucible, there
is a gas diffusion layer at the char bed surface with height
hD, where the transport of O2 takes place by equimolar
countercurrent diffusion, in accordance with Fick’s first
]. Therefore, the steps of the oxy-combustion
reaction in the analysed HPTGA system are:
Transport of O2 to the mouth of the crucible.
Convection of O2 to the surface of the diffusion layer.
Diffusion of O2 through a stationary gas layer in
accordance with Fick’s first law.
Chemical reaction on the surface of the char.
Assuming that the transport of O2 in the convection zone
is carried out over the height of hcon to the planar surface of
AN, the transport rate of O2 is represented by Eq. (10) [
where L is the length of the surface on which the
penetration of mass is followed (in this work the model
presented is the diameter of the crucible dN), Sh is the
Sherwood number, Re is the Reynolds number, and Sc is
the Schmidt number.
Sherwood’s number for O2 transport to the flat surface is
calculated from Eq. (12) [
Sh ¼ 0:664Re1=2Sc1=3
while the Reynolds number is calculated from Eq. (13):
Turbulent gas layer
Stationary gas layer
where ug is the rate of gas entering the crucible, lg is the
viscosity of the gas, and qg is the gas density.
The Schmidt number is calculated from Eq. (14):
Sc ¼ qglDgO2 ð14Þ
Above the surface of the char bed is a layer of stationary
gas with height hD, where the transport of O2 occurs by
equimolecular countercurrent diffusion, in accordance with
Fick’s first law. This is expressed by the relation described
in Eq. (15):
_ DO2 AN CO2;2
NO2 ¼ hD
CO2;3 ; mol s 1
Since the oxy-combustion reaction is faster than the
transport rate of O2, on the surface of the char bed, the
concentration of O2 CO2;3 is close to zero and is therefore
negligible with respect to further calculations. As a
consequence, Eq. (15) can be simplified to Eq. (16):
_ DO2 AN CO2;2; mol s 1
NO2 ¼ hD
Calculating the flow rate of O2 in the HPTGA crucible is
problematic because there are some unknown factors, such
as the heights of the convection and diffusion layers from
Eq. (8) and Eq. (14), respectively. The concentration of O2
at the interface between the two layers CO2;2 is also
unknown. Assuming that conditions are stationary, the
transport rate of O2 in the convective layer must be equal to
the diffusion rate of O2 in the stationary gas layer.
Therefore, Eq. (10) and Eq. (16) are related by Eq. (17):
However, the concentration of O2 at the interface
between these two gas layers is still not known. Hence, a
further assumption is made, i.e. that O2 transport resistance
in the convection layer and O2 diffusion in the stationary
gas layer are equal. This means that the differences in
concentrations in both layers are equal, and this condition
can be written in the form of Eq. (19):
Furthermore, substituting Eq. (19) and Eq. (20) into
Eq. (16), the equation for transport rate of O2 through the
whole crucible in HPTGA is obtained:
Sh DO2 AN CO2;1 ; mol s 1
This association allows the calculation of the O2 stream
in the HPTGA crucible, and it also indirectly enables
calculation of the thickness of the diffusion convection layers.
Analysis of experimental data
The developed O2 transport models in the crucibles have
been applied to the analysis of the experimental data from
oxy-combustion of coal char using both TGAs. The aim of
this study was to demonstrate that the differences in the
obtained results can be explained by the difference in the
effective rate of O2 transport to the surface of the char bed.
Figures 4 and 5 show the reaction rate curves r = dNC/
dt as a function of conversion for the oxy-combustion
Fig. 4 Reaction rate versus X for oxy-combustion of: a lignite char
and b hard coal char, obtained in the APTGA
experiments from the APTGA and HPTGA
The presented data indicate a significant increase in the
reaction rate up to a temperature of approximately 600 C,
after which the reaction rate progression is less significant.
Comparing the oxy-combustion of the investigated two
chars, it can be concluded that the reaction proceeds at a
higher rate for lignite char which has the higher BET
surface area (17.3 m2 g-1) compared to hard coal char with
lower surface area (3.8 m2g-1). Another aspect of this
analysis is also extremely important, i.e. the clear
difference between the reaction rates obtained depending upon
the measuring apparatus used. Higher reaction rates are
achieved in HPTGA than are obtained in APTGA.
For the calculation of the reaction rates, the mean value
of the reaction rates with a conversion ratio of 0.2–0.8 was
used. This range is indicated as a blue field in Figs. 4
and 5. The range of conversion degree is characterised by
the smallest changes in the reaction rate, and it can be
considered as representative for further analysis.
Figure 6 presents a comparison of the experimental data
with the results of the model analysis for both TGs.
Analysing the data, it can be seen that in the low-temperature
range (up to 550 C for lignite char and up to 600 C for
hard coal char) the reaction rate increases significantly,
followed by a slowdown of the reaction rate above these
temperatures. Under low-temperature experimental
conditions, the chemical reaction kinetics is the rate-limiting step
which determines the overall reaction rate. With increasing
temperature (greater than 550 C for lignite char and
greater than 600 C for hard coal char), the diffusion rate
of O2 in the crucibles becomes the main resistance, and O2
transport is the rate-limiting step. To confirm this thesis,
the results of the model analysis and the experimental
results are compared, as shown for both TGs in Fig. 6a, b.
In Fig. 6 the model data for the oxy-combustion
chemical reaction are shown extrapolated up to a
temperature of 1000 C. The extrapolation of the results was
based on data obtained from the estimation of kinetic
parameters using Eq. 4. Data from the 450–550 C range
for the lignite char and from the 500–600 C range for hard
coal char were used to estimate the kinetic parameters of
chemical reactions in the kinetic regime, i.e. the activation
energy Ea and the exponential coefficient A0. These
parameters were used to calculate the rate of
oxy-combustion chemical reaction up to 1000 C where the
ratedetermining step above approximately 600 C is the
extrapolated value. The results of the kinetic parameter
estimates are presented in Table 5.
As can be seen, the results from both thermobalances
correlate with each other at a very high level, with
correlation coefficients above 0.99. As a result, the following
values were obtained for lignite and hard coal chars,
Ea ¼ 145 kJ mol 1 with lnðA0Þ
¼ 6:87 ln mol s 1 ; and Ea
¼ 134 kJ mol 1; with lnðA0Þ ¼ 4:38 ln mol s 1 :
Figure 6 presents the results of the O2 transport rate
models in the crucible in accordance with Fick’s first law
for APTGA and a mixed convection–diffusion model for
HPTGA. The overall observed reaction rate for
oxy-combustion in the crucible from TGA is the sum of the
chemical reaction resistance and the O2 transport resistance
in the crucible, and it can be represented by the previously
shown Eq. (1).
The presented model analysis indicates the very
significant impact of the crucibles and the type of balance used
on the reaction rate for coal chars. Among other things, this
includes the type of crucible and its dimensions, and the
direction of the reaction gas flow which is crucial for the
type of gas–solid fuel contact. The results of the analysis
are essential for the correct interpretation of the results
obtained from oxy-combustion experiments using TG.
They allow for clear distinction between the impact of the
coal char properties on the reaction rate from the influence
of the crucible and the apparatus conditions in which the
measurement is performed. At temperatures higher than
600 C, the oxy-combustion reaction rate is mainly
influenced by the measuring apparatus, and also the shape and
dimensions of the experimental crucible. The latter factor
is responsible for the shifting of oxy-combustion to the
diffusion regime. This conclusion gives rise to the
comparison of the results obtained from the two TG
The analysis evidently shows that in the kinetic regime
the differences between TGAs are negligible. The obtained
reaction rates do not significantly differ, and therefore, the
results of the experimental studies in the two different
apparatuses are comparable with each other. This means
that if adequate working TGA conditions are maintained
for the reaction in the kinetic regime, the experimental
results should lead to similar reaction rates. However, in
the mass transfer-limiting regime the experimental results
primarily depend on the apparatus in which they were
obtained. Hence, in this regime the apparatus and its
specification mainly determine the reaction rate.
In the thermogravimetric analysis, char particles are
deposited as a bed in the TG’s crucible. Therefore, there is
no way for gas to wash each particle separately as it does in
a fluidised bed, which has key implications for the kinetic
analysis of oxy-combustion. In a boiler, char particles
formed after the pyrolysis of coal are carried in the gas
stream. Therefore, there are no limitations on the type and
depth of the measuring vessel (crucible) affecting the O2
transport rate. Under such conditions, the model of char
oxy-combustion, and in particular the oxygen transport rate
model, must be modified. The transport rate of O2 to the
surface of the char particle, assuming that on the particle
surface the CO2;2 concentration is zero, is expressed by
rD;O2 ¼ N_ O2 ¼ kD;O2 ApCO2;1; mol s 1
where kD;O2 is the O2 transport rate constant over the
surface of the char particle.
For particles raised in a gas stream, the O2 transport rate
coefficient is calculated from Froessling’s equation
5, 6, 9, 18, 19, 21, 22
]. For particles with a spherical
geometry, this is expressed as follows:
kext;O2 dp ¼ 2:0 þ 0:6Re1p=2Sc1=3
where dp is the char particle diameter.
The existence of internal diffusion causes a consequent
resistance of both internal and external diffusion which is
different from the external resistance itself. A resultant
resistance can be calculated from Eq. (24):
ln(A0)/ln (mol s-1)
Data set: 450–550 C
where Deff,int is the effective diffusion coefficient for O2 in
the char particle pores and Rp is the pore radius.
The diffusion coefficient in the pores refers to single
pores; therefore, for the purpose of generalisation to the
whole porous particle, the following relationship is used:
where sp is the tortuosity of the pores and e0 is the porosity
of the particle.
Generally, it can be assumed that the pore diffusion rate
is in the transition area and is dependent on Knudsen
diffusion as well as on molecular diffusion [
Therefore, the diffusion coefficient in the pores is
calculated from Eq. (27):
1 1 1
Dint ¼ DO2 þ DK ð27Þ
where DK is the Knudsen diffusion coefficient and Dint is
the diffusion coefficient in the pores.
The internal rate of diffusion constant indirectly
determines the effect of particle size on the chemical reaction
rate, and essentially, it replaces the efficiency factor which
is determined by the Thiele modulus. This relationship
allows the calculation of internal diffusion resistance
independently of the kinetics of the chemical reaction, as is
the case for Thiele modulus calculations. Table 6 presents
the specific values of the gas diffusion parameters in pores
and dimensionless numbers for both chars.
Hard coal char has a lower diffusional limit because of
the lower porosity and specific surface area which results in
higher Knudsen diffusion coefficient values and finally
higher diffusion coefficients in the pores. Reynolds
numbers are higher for the lignite char particles because of the
higher particle diameter, resulting in a higher Sherwood
The results of the model analysis which show the
comparison of the conditions of HPTGA with a fluidised
bed boiler are presented in Fig. 7.
For fluidised or raised particles in the gas stream, O2
transport to the external surface of the particle is several
times higher than for a char bed placed in the crucible in
the thermogravimetric analyser. For the char used in the
study, the diffusion regime could not appear at
temperatures below 800 C. Therefore, the results of the
experiments in the temperature range above 600–700 C, i.e.
where the O2 transport rate in the crucible is a key process
for determining the oxy-combustion reaction rate, do not
reflect the boiler conditions. On the other hand, the O2
transport rate in the thermogravimetric crucible indicates
the magnitude of this influence during the analysis itself.
Figure 7 also shows the results of studies presented in the
literature, which were performed in research devices other
than the thermobalance. Figure 7 shows results from
Saastamoinen et al. [
] who investigated the
combustion of coal dust (obtained from Polish coal) using an
O2/CO2/N2 mixture in a flow reactor.
Fennel et al. [
] who investigated coal char
combustion in a laboratory fluidised bed reactor.
Lasek et al. [
] who examined the oxy-combustion of
various coal types in a fluidised bed reactor with
0.5 kg h-1 capacity.
Fig. 7 Comparison of the
reaction rate as a function of
inverse temperature for coal
char oxy-combustion (20% O2/
CO2, 0.1 MPa, particle size
A comparison of results both from this study and from
the literature indicates that in thermogravimeter the mass
transport rate is much lower than in a fluidised bed which is
resulting from the type and dimensions of the TG’s
crucible. The kinetic parameters of oxy-combustion such as an
activation energy, a pre-exponential factor and a reaction
rate with respect to the oxygen concentration should be
determined in the low-temperature range. Usually, it
should be below approximately 600 C for
oxy-combustion, while the reaction rate at temperatures above 800 C
should be determined by extrapolation based on the
Arrhenius equation. The practical result of the work, which
is crucial for its scientific interpretation, is that diffusion
effects are essential for the rate-determining step the
combustion reaction under standard laboratory conditions
where TG is used. Furthermore, they are also important in
real devices for coal combustion such as fluidised bed
boilers. It should be pointed out that the diffusion
limitation in TGA is not the same as that observed in the raised
particles in a fluidised bed and in industrial boilers.
In the kinetic analysis for the application of TG, one
must be extremely careful during interpretation of the
obtained raw results from TG. Summarizing, the TG
analysis is very useful for the development of a global
model. The reaction rate in the chemical kinetics regime is
independent of the apparatus in which the measurement is
carried out. However, each type of laboratory equipment,
such as a thermobalance, has its construction limitations
and differences in reaction rates are observed. Any
differences in the reaction rates depending on the apparatus
used are due to the presence of reactant gases
transportation and the type of gas–solid contact during the analysis.
oxy-combustion of coal in
entrained flow reactor [
fluidised bed reactor [
combustion in fluidised
bed reactor [
The proposed oxy-combustion reaction models in TGAs
were described in this paper by Eq. (9) for APTGA and by
Eq. (21) for HPTGA. They allow estimation of the impact
of O2 transportation on the reaction rate which is observed
in the apparatus. Furthermore, knowledge of this impact
allows both selections of the particular temperature range
where the influence of O2 transport is significantly reduced
and also the range where it is possible to determine the
kinetic parameters for the given chemical reaction.
Therefore, as a result, reaction rates for industrial boilers
can be determined by extrapolating the kinetic data using
the Arrhenius equation.
Two different arrangements of gas–solid contact in TGA
were investigated for the development of a global reaction
rate model of coal char oxy-combustion which explains the
differences in testing methods. The reason is that the
observed effect is related to the gas–solid phase contact,
which is associated with crucible dimensions and the
direction of the gas flow. The TGA testing device significantly
influences the experimental results presented in this paper.
The proposed model combines chemical reactions and
mass transfer kinetics of reagents to the reactive surface of
the particle and allows different data to be explained. The
kinetics of the chemical reaction is independent of the
apparatus, which gives the same model of chemical
reaction kinetics based on the Arrhenius equation for all the
global models. However, different devices have their own
transport limitations which result in specific mass transport
models, e.g. Eq. (9) for APTGA, Eq. (21) for HPTGA and
Eq. (22) for a fluidised bed.
The developed model can be used for oxy-combustion
process scaling-up purposes, by applying the global model
with chemical kinetics and the mass transfer model for a
fluidised bed boiler.
Acknowledgements This scientific work was supported by the
National Centre for Research and Development, as Strategic Project
PS/E/2/66420/10 ‘‘Advanced Technologies for Energy Generation:
Oxy-combustion technology for PC and FBC boilers with CO2
capture’’. The support is gratefully acknowledged. This work was
partially financed from the People Programme (Marie Curie Actions) of
the European Union’s Seventh Framework Programme FP7/
2007–2013 under REA Grant Agreement No.
PIRSES-GA-2013612699 entitled ‘‘Long-term research activities in the area of
advanced CO2 capture technologies for Clean Coal Energy
Generation—‘‘CO2TRIP and by the Polish Ministry of Higher Education and
Science, Decision No. 3111/7.PR/2014/2 as ‘‘Scientific work financed
from the funds for science in years 2014–2017, allocated for
completion of the international co-financed project’’, and also from
subsidy project 11.17.005.
Open Access This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://creative
commons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a link
to the Creative Commons license, and indicate if changes were made.
1. Stroemberg L. Combustion in a CO2/O2 mixture for a CO2 emission free process . In: 2nd Nordic mini symposium on carbon dioxide capture and storage , Go¨ teborg, 26 Oct 2001 .
2. Buhre BJP , Elliot LK , Sheng CD , Gupta RP , Wall TF . Oxy-fuel combustion technology for coal-fired power generation . Prog Energy Combust Sci . 2005 ; 31 : 283 - 307 . https://doi.org/10.1016/j. pecs. 2005 . 07 .001.
3. Lasek J , Glod K , Janusz M , Kazalski K , Zuwala J . Pressurized oxy -fuel combustion: a Study of selected parameters . Energy Fuels . 2012 ; 26 : 6492 - 9 . https://doi.org/10.1021/ef201677f.
4. Lasek J , Janusz M , Zuwala J , Glod K , Iluk A . Oxy-fuel combustion of selected solid fuels under atmospheric and elevated pressures . Energy . 2013 ; 62 : 105 - 12 . https://doi.org/10.1016/j. energy. 2013 . 04 .079.
5. Ma L, Mitchell R. Modeling char oxidation behavior under zone II burning conditions at elevated pressures . Combust Flame . 2009 ; 156 : 37 - 50 . https://doi.org/10.1016/j.combustflame. 2008 . 06 .015.
6. Roberts DG . Intrinsic reaction kinetics of coal chars with oxygen, carbon dioxide and steam at elevated pressures . Ph.D. thesis , University of Newcastle; 2000 .
7. Kordylewski W. Fuel combustion . Wrocław: Publishing House, Oficyna Wydawnicza Politechniki Wrocławskiej; 2008 . In Polish.
8. Wall TF , Liu Y , Spero Ch , Elliott L , Khare S , Rathnam R , Zeenathal F , Moghtaderi B , Buhre B , Sheng Ch , Gupta R , Yamada T , Makino K , Yu J. An overview on oxyfuel coal combustion: state of the art research and technology development . Chem Eng Res Des . 2009 ; 87 : 1003 - 16 . https://doi.org/10. 1016/j.cherd. 2009 . 02 .005.
9. Smith IW . The combustion rates of coal chars: a review. 19th symposium on combustion . Proc Combust Inst . 1982 ; 19 : 1045 - 65 .
10. Czakiert T , Bis Z , Muskala W , Nowak W. Fuel conversion from oxy-fuel combustion in a circulating fluidized bed . Fuel Process Technol . 2006 ; 87 : 531 - 8 . https://doi.org/10.1016/j.fuproc. 2005 . 12 .003.
11. Gomez-Barea A , Ollero P , Arjona R . Reaction-diffusion model of TGA gasification experiments for estimating diffusional effects . Fuel . 2005 ; 84 : 1695 - 704 . https://doi.org/10.1016/j.fuel. 2005 . 02 . 003.
12. Salvador S , Commandre JM , Stanmore BR . Reaction rates for the oxidation of highly sulphurised petroleum cokes: the influence of thermogravimetric conditions and some coke properties . Fuel . 2003 ; 82 : 715 - 20 . https://doi.org/10.1016/S0016- 2361 ( 02 ) 00363 - 0 .
13. Babin´ski P, Łabojko G , Plis A , Kotyczka-Moran´ska M. Kinetics of coal and char oxy-combustion studied by TG-FTIR . J Therm Anal Calorim . 2013 ; 113 : 371 - 8 . https://doi.org/10.1007/s10973- 013-3002-x.
14. Babin´ski P, Tomaszewicz M , Topolnicka T , S´ cia˛ z_ko M, Zuwała J . Tlenowe spalanie we˛gla: badania kinetyki i mechanizmu spalania cis´nieniowego . Przem Chem . 2015 ; 94 : 450 - 6 . https://doi. org/10.15199/62. 2015 . 4 .2. (In Polish).
15. Ksepko E , Babinski P , Nalbandian L . The redox reaction kinetics of Sinai ore for chemical looping combustion applications . Appl Energy . 2017 ; 190 : 1258 - 74 . https://doi.org/10.1016/j.apenergy. 2017 . 01 .026.
16. Ksepko E , Babinski P , Evdou A , Nalbandian L . Studies on the redox reaction kinetics of selected, naturally occurring oxygen carrier . J Therm Anal Calorim . 2015 ; 124 : 137 - 50 . https://doi.org/ 10.1007/s10973-015-5107-x.
17. Vyazovkin S , Burnham AK , Criado JM , Pe´ rez-Maqueda LA , Popescu C , Sbirrazzuoli N. ICTAC Kinetics Committee recommendations for performing kinetic computations on thermal analysis data . Thermochim Acta . 2011 ; 520 : 1 - 19 . https://doi.org/ 10.1016/j.tca. 2011 . 03 .034.
18. Schulze S , Nikrtiuk P , Abosteif Z , Guhl S , Richter A , Meyer B. Heat and mass transfer within thermogravimetric analyser: from simulation to improved estimation of kinetic data for char gasification . Fuel . 2017 ; 187 : 338 - 48 . https://doi.org/10.1016/j.fuel. 2016 . 09 .048.
19. De La Cuesta D , Gomez MA , Porteiro J , Febrero L , Granada E , Aree E. CFD analysis of a TG-DSC apparatus application to the indium heating and phase change process . J Therm Anal Calorim . 2014 ; 118 : 641 - 50 . https://doi.org/10.1007/s10973-014-3734-2.
20. Ollero P , Serrera A , Arjona R , Alcantarilla S. Diffusional effects in TGA gasification experiments for kinetic determination . Fuel . 2002 ; 81 : 1989 - 2000 . https://doi.org/10.1016/S0016- 2361 ( 02 )001 26 - 6 .
21. Hottel HC , Noble JJ , Sarofim AF , Silcox GD , Wankat PC , Knaebel KS . Perry's chemical engineering handbook, Section 5 heat and mass transfer . 8th ed. New York: The McGraw-Hill Companies ; 2007 .
22. Saastamoinen JJ , Aho MJ , Hamalainen JP , Hernberg R , Joutsenoja T. Pressurized pulverized fuel combustion in different concentrations of oxygen and carbon dioxide . Energy Fuels . 1996 ; 10 : 121 - 33 . https://doi.org/10.1021/ef950107l.
23. Fennel PS , Dennis JS , Hayhurst AN . The order with respect to oxygen and the activation energy for the burning of an anthracitic char in O2 in a fluidised bed, as measured using a rapid analyser for CO and CO2 . Proc Combust Inst . 2009 ; 32 : 2051 - 8 . https://doi. org/10.1016/j.proci. 2008 . 06 .097.