Byoung-Hwa Lee1, Viet Thieu Trinh2, Chung-Hwan Jeon1,2. 1. Pusan Clean Energy Research Institute, Pusan National University, 2, Busandaehak-ro 63 beon-gil, Geumjeong-gu, Busan 46241, Republic of Korea. 2. School of Mechanical Engineering, Pusan National University, 2, Busandaehak-ro 63 beon-gil, Geumjeong-gu, Busan 46241, Republic of Korea.
Abstract
Torrefaction is an appealing pretreatment method for improving the fuel properties of kenaf biomass before its utilization in thermochemical processes. This study evaluated and compared the impact of torrefaction on thermal behavior and kinetics during pyrolysis and gasification. Thermogravimetric analysis experiments were conducted at temperatures of 300-1173 K at several heating rates under N2 and CO2 atmospheres. The raw and torrefied kenaf (RK and TK) during CO2 gasification in the low-temperature region (<900 K) was found to exhibit a tendency that was similar to that of N2. However, TK during CO2 gasification resulted in a lower maximum mass loss rate, delayed initiating temperature, and lower devolatilization index due to lower reactivity. In addition, the gasification reaction of CO2 and char was observed to occur in the high-temperature region (> 900 K), thus improving conversion efficiencies. The activation energy for TK in a CO2 atmosphere depending on the conversion was calculated using the distributed activation energy method. The activation of RK during CO2 gasification was higher than that of N2. However, TK during CO2 gasification exhibited a lower activation energy compared to that of N2, indicating its potential as a better feedstock during the CO2 gasification process and the ability to save energy.
Torrefaction is an appealing pretreatment method for improving the fuel properties of kenaf biomass before its utilization in thermochemical processes. This study evaluated and compared the impact of torrefaction on thermal behavior and kinetics during pyrolysis and gasification. Thermogravimetric analysis experiments were conducted at temperatures of 300-1173 K at several heating rates under N2 and CO2 atmospheres. The raw and torrefied kenaf (RK and TK) during CO2 gasification in the low-temperature region (<900 K) was found to exhibit a tendency that was similar to that of N2. However, TK during CO2 gasification resulted in a lower maximum mass loss rate, delayed initiating temperature, and lower devolatilization index due to lower reactivity. In addition, the gasification reaction of CO2 and char was observed to occur in the high-temperature region (> 900 K), thus improving conversion efficiencies. The activation energy for TK in a CO2 atmosphere depending on the conversion was calculated using the distributed activation energy method. The activation of RK during CO2 gasification was higher than that of N2. However, TK during CO2 gasification exhibited a lower activation energy compared to that of N2, indicating its potential as a better feedstock during the CO2 gasification process and the ability to save energy.
Gasification aims to produce
biomass as a gas, which is converted
to syngas for liquid biofuel production.[1] The produced gas may also be used directly to generate heat and
power through combustion.[2] Integrated gasification
combined cycle systems have higher thermal efficiency compared to
direct combustion of biomass. Currently, most gasification plants
use coal as a resource, and replacing coal with biomass would be beneficial
as biomass is converted into value-added products. However, the direct
utilization of biomass as a gasification feedstock is limited by its
high moisture content, low grindability, low energy content, and low
bulk density.[3] Therefore, biomass gasification
has been investigated extensively to date, and increasing gasification
efficiency through feedstock upgrade using pretreatment methods such
as torrefaction is an important research topic.Torrefaction
is also known as mild pyrolysis and in recent years
has been preferred for the improvement of the characteristics of biomass
as fuel before thermochemical processes. Biomass is heated at 473–573
K in inert gas to produce high-quality solid fuel.[4,5] After
drying during the torrefaction process, hemicellulose and some cellulose
in biomass are thermally decomposed and biochar is produced.[6,7] This biochar has a higher calorific value and improved grindability
compared to raw biomass and is more effective for application in advanced
gasification and combustion technologies.[8] Owing to the aforementioned advantages, many studies have focused
on evaluating the fuel properties of torrefied biomass, and research
is gradually expanding in terms of the gasification kinetics of torrefied
biomass.[9,10] Gasification kinetics are crucial and have
an essential impact on the design, process control, and efficiency
of gasification.[11] The design and optimization
of gasifiers for industrial-scale applications require in-depth understanding
of reliable kinetic data and characteristics during gasification.[12,13] Although several researchers have studied the effect of torrefied
fuel on gasification kinetics and thermal behavior, this subject has
not been systematically investigated. Tran et al.[5] reported that temperatures of torrefaction had a significant
effect on the CO2 gasification of forest residues, and
the gasification activation energy of the three samples varied from
260 to 290 kJ/mol. Chew et al.[10] evaluated
the impact of torrefaction on the gasification behavior and kinetics
of three oil palm biomasses: empty fruit bunch, methyl-furans, and
palm kernel shells. They reported that torrefied oilpalm biomass
showed reduced gasification reactivity relative to the nontorrefied
analogues due to the removal of volatile matter from biomass after
torrefaction. In addition, biomass reactivity during CO2 gasification was affected by the gasification temperature, biomass
type, and pretreatment method. Zhang et al.[14] investigated the distribution of solid products and the effects
of torrefaction conditions on char gasification reactivity, as well
as cogasification with coal and torrefied solids. They noted that
char produced by torrefied biomass showed faster conversion compared
to char produced by raw biomass during CO2 gasification.Kenaf, which grows in Korea, is an important source of herbaceous
biomass. The life cycle of kenaf among herbaceous biomass is relatively
short and production costs are relatively low. Owing to the price
competitiveness, kenaf is expected to replace woody biomass.[15] Therefore, we investigated the characteristics
of kenaf in terms of various aspects, such as the effect of torrefaction
and how kenaf compares with woody biomass.[16,17] Furthermore, we investigated the torrefaction-improved features
such as grindability, hydrophobicity, and carbonization. However,
to date, studies on the gasification kinetics of torrefied kenaf (TK)
biomass, which are essential for large-scale application development,
are lacking. In addition, the applicability of N2 and CO2 atmospheres for TK has not been studied and compared comprehensively.
Therefore, this study aims to examine the effect of torrefaction on
the CO2 gasification behavior and kinetics of kenaf compared
to N2 pyrolysis. In addition, we evaluated and compared
the CO2 gasification kinetics of raw kenaf (RK) and TK
biomass using the distributed activation energy method (DAEM). This
study elucidates the kinetics and thermal behavior of the gasification
process for TK.
Results and Discussion
Thermal Analysis
Figures and 2 show the mass
loss (TG, thermogravimetry) and mass loss rate (DTG)
curves for RK and TK under pyrolysis (N2) and gasification
(CO2) at a heating rate of 10 K/min. The effects of ambient
gas on thermal decomposition of RK and TK were investigated by comparing
and evaluating the TG and DTG results in N2 and CO2 atmospheres. Water evaporation, devolatilization, and char
reaction are evident in Figure . The 300–400 K region was associated with surface
moisture and adsorbent water in the sample. In the N2 atmosphere,
the devolatilization of RK started at approximately 450 K and reached
the maximum mass loss rate at 586 K. The mass loss rate decreased,
and there was no change in mass when the temperature was over 900
K, indicating that the thermal decomposition was complete. The decomposition
of hemicellulose and cellulose occurred mainly during the initial
region of the thermal decomposition, and that of lignin occurred in
the latter region. This is similar to previous results showing that
there are two thermal decomposition regions for lignocellulose biomass.[18] In the CO2 gasification experiments
shown in Figure ,
the mass loss tendency of RK and TK in the CO2 atmosphere
was similar to that of N2 when the temperature was less
than 900 K. However, the maximum mass loss rate of CO2 was
less than that of N2 because of the greater heat capacity
and lower reactivity of CO2. Nevertheless, an additional
mass loss was clearly observed at temperatures exceeding 900 K in
the CO2 atmosphere, indicating that the CO2 gasification
reaction occurred in the remaining char. These results are consistent
with the findings of previous studies.[19,20] Char produced
by thermal decomposition still contains a large amount of carbon,
and incomplete carbonation during the process of thermal decomposition
in conjunction with CO2 facilitates the gasification reaction
of the remaining char.[20,21] Hydrogen and oxygen-related compounds
are gradually compressed in the char matrix with increasing temperature,
and the fixed carbon content of the remaining char increases, resulting
in an inevitable gasification reaction between CO2 and
fixed carbon.[22]
Figure 1
Mass loss and mass loss
rate curves for RK under pyrolysis (N2) and gasification
(CO2) at a 10 K/min heating
rate.
Figure 2
Mass loss and mass loss rate curves for TK under
pyrolysis (N2) and gasification (CO2) at a 10
K/min heating
rate.
Mass loss and mass loss
rate curves for RK under pyrolysis (N2) and gasification
(CO2) at a 10 K/min heating
rate.Mass loss and mass loss rate curves for TK under
pyrolysis (N2) and gasification (CO2) at a 10
K/min heating
rate.Figure shows the
thermal decomposition behavior of TK in both N2 and CO2 atmospheres. Evidently, the first strong shoulder on the
first half of the devolatilization peak found in RK is not observed
for TK, indicating a significant reduction of hemicellulose content.[23] In addition, most of the weight loss occurred
from 500 to 700 K with the maximum rate and temperature of mass loss
at 8.3 mg/min and 599.8 K in N2 and 6.44 mg/min and 599.4
K in CO2, respectively, which was almost identical to the
behavior of the cellulose region.[24] Furthermore,
the maximum mass loss rate of TK was significantly more pronounced
than that of RK, and the second shoulder was generally associated
with the thermal decomposition of lignin; hence, this observation
shows that lignin content increases after the torrefaction process.
Yan et al. also reported that the lignin fraction of lignocellulosic
biomass was significantly increased as a result of torrefaction.[25]Figures and 2 show that the maximum mass loss
rate and temperature of the DTG peaks in the CO2 gasification
region for RK and TK occurred at 3.72 mg/min and 1086.8 K and 6.18
mg/min and 1117.9 K, respectively, indicating that the increased lignin
content in char resulted in a greater reaction with CO2.
Analysis of Crucial Thermal Parameters at
Different Heating Rates
The TG and DTG curves for RK and
TK under pyrolysis (N2) and gasification (CO2) at heating rates of 5, 10, and 20 K/min are shown in Figures and 4, respectively. The heating rate showed a significant effect on the
behavior of the TG and DTG curves and the maximum rate of decomposition.
At higher heating rates, a shorter reaction time and thermal progression
delay of the sample was observed with respect to heat transfer, indicating
that the peak moved into the high-temperature region.[18] In addition, the maximum mass loss rate during the thermal
decomposition increased, and the conversion rate decreased on increasing
the heating rate at the same temperature owing to the thermal hysteresis
phenomenon caused by heat resistance.[26] This is attributable to the delay in the heat transferred to the
internal bulk sample, resulting in the central temperature of the
particle being lower than the surface temperature. The increased heating
rate increased this temperature difference; furthermore, the sample
interior was not supplied with sufficient energy to decompose on time.
The higher CO2 gasification reaction of carbon was also
observed to occur more significantly at temperatures exceeding 900
K and at a higher heating rate, as mentioned in section .
Figure 3
Mass loss and mass loss
rate curves for RK under pyrolysis (N2) and gasification
(CO2): (a, b) effect of heating
rates.
Figure 4
Mass loss and mass loss rate curves for TK under
pyrolysis (N2) and gasification (CO2): (a, b)
effect of heating
rates.
Mass loss and mass loss
rate curves for RK under pyrolysis (N2) and gasification
(CO2): (a, b) effect of heating
rates.Mass loss and mass loss rate curves for TK under
pyrolysis (N2) and gasification (CO2): (a, b)
effect of heating
rates.To compare and evaluate processes
quantitatively, the key thermal
parameters of pyrolysis (N2) and gasification (CO2) heated at several heating rates are described, which include the
initiating temperature (Tin), peak temperature
(Tpeak), maximum mass loss rate (Rmax), and devolatilization index (Di), as summarized in Table and Figure . In this study, the Di was used
to investigate the release behavior of the volatile materials, as
shown by He et al.[27] and in eq below:
Table 1
Effect of Heating Rates on Key Thermal
Parameters for RK (a) and TK (b) under Pyrolysis (N2) and
Gasification (CO2)a
heating rate
(K/min)
Tin (K)
Tpeak (K)
Rmax (mg/min)
ΔT1/2 (K)
Di (10–8 mg/ min-K3)
residual
(%)
(a) RK
N2 (pyrolysis)
5
346.86
586.07
4.08
119.60
16.77
18.95
10
368.83
596.66
7.81
113.92
31.17
15.70
20
377.98
609.63
15.24
115.82
57.08
18.83
CO2 (gasification)
5
379.13
587.74
4.06
104.31
17.49
4.87
10
394.89
596.19
7.32
100.65
30.90
4.07
20
403.75
605.90
13.57
101.08
54.88
4.72
(b) TK
N2 (pyrolysis)
5
537.01
588.60
4.14
25.80
50.74
32.59
10
546.10
599.85
8.30
26.87
94.28
34.77
20
555.70
612.23
16.37
28.27
170.23
35.65
CO2 (gasification)
5
543.96
589.23
3.79
22.63
52.19
5.66
10
547.91
599.46
6.44
25.78
76.03
3.94
20
560.26
609.20
12.73
24.47
152.43
6.71
Tin,
Initial devolatilization temperature at a conversion of 10%; Tpeak, Maximum peak temperature; Rmax, Maximum mass loss rate; ΔT1/2, Temperature interval when R/Rmax is 1/2; Di,
Devolatilization index.
Figure 5
Effect
of heating rates on (a) Rmax and (b) Di for raw and torrefied kenaf.
Effect
of heating rates on (a) Rmax and (b) Di for raw and torrefied kenaf.Tin,
Initial devolatilization temperature at a conversion of 10%; Tpeak, Maximum peak temperature; Rmax, Maximum mass loss rate; ΔT1/2, Temperature interval when R/Rmax is 1/2; Di,
Devolatilization index.Owing to the thermal hysteresis, the Tpeak, Rmax, and Di increased as the heating rate increased, as observed in both atmospheres,
and the Di value for TK was higher than
that of RK at all heating rates. For comparison between N2 and CO2 atmospheres, the Di value for CO2 at 5 K/min was slightly higher than that
of N2, but the Di value for
CO2 at 10 and 20 K/min was 5% less than that of the N2 atmosphere, implying that the CO2 devolatilization
performance dropped below that of N2 as the heating rate
increased. In addition, Di and Rmax values for TK under CO2 were
significantly lower than those of RK under N2, indicating
that gasification results in less reactivity with lignin-like compounds
produced by torrefaction, which is consistent with the results obtained
by other studies.[28] In addition, the residuals
for CO2 decreased by approximately 74% for RK and 84% for
TK because the gasification reaction of the remaining char with CO2 and the reduction ratio for TK was higher than that of RK.
Kinetic Parameter Analysis
Figure shows conversion
as a function of temperature for reaction stages I and II in the N2 and CO2 atmospheres for RK and TK. The model-free
activation energy was analyzed using the DAEM. Stages I and II indicate
the low-temperature (< 900 K) and high-temperature regions (>
900
K), respectively. In addition, the reaction during stage II only represented
CO2 because there was no reaction during stage II for N2. Thus, the kinetic analysis for stage II was only carried
out in the high-temperature region, as shown in Table . The model-free activation energy using
the DAEM at each conversion was obtained from the slope of the linear
regression method. The activation energy of RK for N2 was
estimated using a conversion of 0.1 and 0.7 because the correlation
factor was very low when the conversion exceeded 0.8.[29] The estimated squares of the correlation coefficient, R2, corresponding to linear fitting almost exceeded 0.99. The
activation energy calculated according to conversion is shown in Figures and 8. The activation energy changed as the reaction progressed
during pyrolysis and gasification. This phenomenon occurred because
the material was not a pure compound but a mixture of other elements
with complex chemical bond structures. Figure shows the variation of activation energies
according to conversion for RK and TK under pyrolysis (N2) and gasification (CO2) in stage I. The conversion graph
in the reaction during stage I for N2 and CO2 appears similar for both RK and TK. The activation energy according
to conversion for RK was higher in the case of CO2 compared
to that of N2, yielding average values of 222.42 and 183.29
kJ/mol, respectively. This indicates that the reactivity of CO2 is lower than that of N2. In the case of TK, the
activation energies for CO2 were higher as the conversion
ratio increased to 0.6, and activation energies for N2 increased
significantly when the conversion ratio exceeded 0.6. This shows a
higher activation energy of lignin derived from hemicellulose and
cellulose by torrefaction during the final stage of the reaction,
a tendency that was also observed in a previous study.[27] However, the activation energies for CO2 did not change significantly even after the conversion ratio
exceeded 0.6, indicating varying patterns in the CO2 atmosphere.
Thus, with respect to TK, the average activation energy for CO2 is lower than that of N2, whose average values
are 218.29 and 251.87 kJ/mol, respectively. These results show that
the energy needed for gasification in the case of TK is lower than
that needed for pyrolysis. Figure shows the variation of activation energies according
to the conversion ratio for RK and TK under a CO2 environment
during stage II. The activation energies for stage II (197.94 and
197.62 kJ/mol for RK and TK, respectively) under a CO2 atmosphere
were similar for both the samples. The activation energy gradually
decreased as the conversion ratio increased. Furthermore, all samples
showed kinetic compensation effects with simultaneous increase or
decrease in activation energy and pre-exponential factors for N2 and CO2, as shown in Table . This behavior was consistent with the findings
of previous studies.[30,31] These results suggest that the
energy required in the gasification system using TK as feedstock is
less than that of RK, which implies that energy can be saved in the
system.
Figure 6
Conversion ratio versus temperature for the pyrolysis and gasification
at different heating rates in the reaction during stage I (a, b) and
II (c).
Table 2
Activation Energy,
Pre-Exponential
Factor, and Correlation Coefficient According to the Conversion Ratio
in the Reaction during Stage I (a, b) and II (c)
conversion
ratio (α)
activation
energy (kJ/mol)
pre-exponential
factor (1/s)
R2
(a) RK (stage I)
N2 (pyrolysis)
0.1
180.73
9.54E+14
0.9971
0.2
182.05
6.44E+15
0.9987
0.3
186.63
1.25E+15
0.9965
0.4
188.11
7.09E+14
0.9981
0.5
183.71
1.35E+14
0.9990
0.6
180.20
3.59E+13
0.9996
0.7
181.59
2.76E+13
1.0000
0.8
0.9
average
183.29
1.36E+15
0.9984
CO2 (gasification)
0.1
206.72
2.038E+18
0.9891
0.2
215.26
2.332E+18
0.9903
0.3
232.05
2.827E+19
0.9900
0.4
243.50
1.124E+20
0.9915
0.5
235.08
7.365E+18
0.9940
0.6
218.63
1.122E+17
0.9953
0.7
205.72
4.064E+15
0.9961
0.8
192.57
1.123E+14
0.9827
0.9
122.65
6.40E+06
0.9412
average
222.42
2.18E+19
0.9923
(b)
TK (stage I)
N2 (pyrolysis)
0.1
175.49
3.14E+13
1.0000
0.2
172.59
5.26E+13
1.0000
0.3
176.67
2.17E+13
1.0000
0.4
178.12
1.85E+13
0.9999
0.5
184.13
4.09E+13
0.9998
0.6
216.38
1.37E+16
0.9981
0.7
320.37
1.04E+24
0.9976
0.8
385.15
2.24E+27
0.9985
0.9
457.93
1.19E+30
0.9948
average
251.87
1.32E+29
0.9987
CO2 (gasification)
0.1
242.74
4.058E+20
0.8916
0.2
235.62
1.461E+19
0.9421
0.3
228.24
1.216E+18
0.9778
0.4
219.78
1.082E+17
0.9927
0.5
213.80
1.742E+16
0.9965
0.6
223.37
5.263E+16
0.9916
0.7
234.20
6.463E+16
0.9795
0.8
195.55
3.159E+12
0.9993
0.9
171.30
2.623E+09
0.9862
average
218.29
4.69E+19
0.9730
(c)
RK and TK (stage II) – CO2 (gasification)
RK
0.1
314.70
1.57E+14
0.9823
0.2
226.02
7.93E+08
0.9990
0.3
204.75
3.42E+07
0.9999
0.4
194.54
7.13E+06
1.0000
0.5
184.82
1.79E+06
0.9994
0.6
175.27
4.93E+05
0.9982
0.7
166.52
1.56E+05
0.9971
0.8
159.29
5.95E+04
0.9965
0.9
155.58
3.31E+04
0.9960
average
197.94
1.75E+13
0.9965
TK
0.1
300.12
1.24E+13
0.9741
0.2
223.31
3.07E+08
0.9926
0.3
201.99
1.38E+07
0.9953
0.4
189.87
2.37E+06
0.9966
0.5
181.77
7.39E+05
0.9973
0.6
175.38
3.02E+05
0.9981
0.7
170.55
1.53E+05
0.9988
0.8
165.45
7.59E+04
0.9993
0.9
170.18
1.14E+05
0.9975
average
197.62
1.38E+12
0.9944
Figure 7
Variation of activation energies according to
conversion for raw
(a) and torrefied kenaf (b) under pyrolysis (N2) and gasification
(CO2) during stage I.
Figure 8
Variation
of activation energies according to conversion for raw
and torrefied kenaf under gasification (CO2) during stage
II.
Conversion ratio versus temperature for the pyrolysis and gasification
at different heating rates in the reaction during stage I (a, b) and
II (c).Variation of activation energies according to
conversion for raw
(a) and torrefied kenaf (b) under pyrolysis (N2) and gasification
(CO2) during stage I.Variation
of activation energies according to conversion for raw
and torrefied kenaf under gasification (CO2) during stage
II.
Conclusions
The
effect of torrefaction on kenaf under N2 and CO2 atmospheres was examined using thermogravimetric analysis
(TGA) data at different heating rates. In the low-temperature region
(<900 K), the thermal effect on gasification for TK was similar
to that of pyrolysis. However, from the analysis of essential thermal
parameters, TK under CO2 gasification resulted in a lower
maximum mass loss rate, delayed initiating temperature, and lower Di at the different heating rates, indicating
that CO2 gasification has a lower reactivity. However,
in the high-temperature region (> 900 K), the gasification reaction
of CO2 and char occurred, resulting in high conversion
efficiencies in the CO2 atmosphere. In addition, torrefaction
led to a larger reaction of CO2 gasification with increased
char, which was confirmed by the residual char. The activation energies
were analyzed using the DAEM with distinctive stages I and II. TK
under a CO2 atmosphere in the entire region remarkably
exhibited a lower average activation energy compared to RK, which
opposes the tendency observed in the results of RK. The activation
energies for the CO2 reaction with char at high temperatures
had similar values for both samples. These results suggest that the
energy needed for TK under gasification is less than that needed for
RK and could thus contribute to saving energy in the system.
Materials and Methods
Materials
Kenaf
was used as fuel
(Hibiscus cannabinus L.), a sample
of which was pretreated by torrefaction. Then, 5 g of RK was added
to a sample crucible and N2 was passed through a tube at
1.5 cm3/min to form an inert atmosphere. TK was produced
in a fixed-bed furnace under inert N2 gas conditions at
523 K for a residence time of 30 min. The RK and TK samples were prepared
at a particle size of < 100 μm using a grinder, and the properties
of each sample are listed in Table .
Table 3
Fuel Properties of RK and TK
sample
RK
TK
proximate analysis (wt %, as-received)
moi.
9.18
1.96
VM
69.42
62.12
FC
17.91
30.48
ash
3.48
5.43
FR
0.26
0.49
ultimate
analysis (wt %, dry basis)
C
43.36
52.27
H
5.69
5.27
N
0.66
0.87
Oa
50.21
41.49
S
0.08
0.11
O/C
1.158
0.794
H/C
0.131
0.101
HHV (MJ/kg, AR)
17.4
20.8
Calculated by difference.
Calculated by difference.
Experimental Procedures
The experiments
of RK and TK during pyrolysis and gasification were conducted using
a thermogravimetric analyzer (SDT Q600, TA Instruments Co.) at three
heating rates (5, 10, and 20 K/min). The heating rate was selected
as a TGA experiment in which kinetic analysis can be performed using
the DAEM.[32] In a ceramic crucible, the
samples were distributed evenly in a thin layer (17 mg ± 2 mg),
and the mass and temperature of the samples were continuously recorded
on increasing the temperature at a set heating rate until the final
temperature of 1173 K. In the pyrolysis experiments, ultrapure N2 was injected into the thermogravimetric analyzer at a constant
flow rate of 100 mL/min, creating an inert gas environment; in the
case of gasification experiments, a constant flow rate of ultrapure
CO2 was continuously supplied.
Distributed
Activation Energy Model
In this study, kinetic analysis was
conducted using the DAEM and
a single-step reaction model based on the TGA data on the pyrolysis
and gasification of RK and TK to compare and evaluate the characteristics
of samples during thermal degradation.[33,34] Thus, converting
raw materials into products is assumed to be a single-step process.[35] The rate constant of the reaction (k) according to the Arrhenius method is expressed as follows:where k is
the reaction rate constant, A is the pre-exponential
factor (1/s), E is the activation energy (kJ/mol), R is the gas constant (8.314 J/mol-K), and T is the absolute temperature (K). For biomass conversion from solid
to volatile states, the rate equation is expressed as follows:The conversion ratio
(α) is calculated using eq where mi is the initial mass, m is
the
mass at time t, and mf is the final mass.By combining eqs and 3, we getRearranging eq into
a logarithmic form using the simplified DAEM for the Arrhenius equation
yields the following:From eq , the plot
of versus 1/T yields a straight-line
equation. provides the slope of the equation
and provides the intercept value, while the
value 0.6075 is kept constant for simplicity.