Gasification of the Char Residues with High Ash Content by Carbon Dioxide

Abstract

To increase the carbon conversion of char in gasification, this paper aimed to reveal the gasification behaviours of char residues. Char residues with different ash contents in this work were prepared from Shenmu char and Tejing char. Those char residues were gasified by different CO₂ gas mixtures at different temperatures. The gasification process of char residue was different from the end stage of the gasification process of the corresponding raw char: the gasification rate of the char residue increased at first and then decreased, whereas the gasification rate of the corresponding raw char kept decreasing during the end stage of gasification. The highest gasification rate was achieved at a lower conversion in the gasification of char residue than in the gasification of the corresponding raw char. Catalytic minerals, high temperature, and high CO₂ partial pressure benefited the gasification of gasified char residues. The char residues that contained more catalytic minerals were more reactive in gasification and were less sensitive to changes in temperature and CO₂ partial pressure. The Modified Random Pore Model (MRPM) and Random Pore Model (RPM) were used to predict the gasification kinetics of the chars, and the MRPM describes the gasification processes of gasified char residues well.

1. Introduction

As a major energy resource, coal supplies 27% of world energy [1]. Combustion for thermal power generation is the most common usage method for coal [2], which leads to serious problems: incomplete combustion of coal causes waste of energy resources, black carbon emission causes a significant greenhouse effect [3,4], toxic gas (nitrous oxides, sulphur oxides, etc.) emission pollutes the environment [5], and the removal of the ash residue costs a lot of work.

In order to solve problems caused by the direct combustion of coal, many methods have been proposed, and the most used method is gasification [6,7]. Coal gasification includes the reactions of coal with oxygen (O₂), steam, carbon dioxide (CO₂), air, or a mixture of these gases at a high temperature, and these reactions produce combustible gases like carbon monoxide (CO), hydrogen (H₂), and methane (CH₄) [2]. The gaseous products of coal gasification are easy to completely combust. The pollutants (black carbon, toxic gas, and ash) are only produced during the coal gasification process and are rarely produced during the combustion process of the gaseous products. Since gasification only occurs in gasification factories whereas combustion can happen anywhere, the pollutant treatment in gasification is much easier than that in coal combustion.

Nowadays, most large commercial coal gasification plants adopt entrained flow gasifiers because entrained flow gasifiers only need several seconds to convert coal slurry into products due to their high operating temperature. Though the operating temperature in entrained flow gasifiers is normally 1873 K, the unreacted carbon content in the slag remains high (approximately 40% mass) [8]. This is because the unreacted carbon is enveloped in molten ash in entrained flow gasifiers, which means the unreacted carbon cannot be gasified by increasing gasification temperature, nor by adding gasification stages [8]. Molten slag not only causes issues with equipment maintenance, related operation time, and operation costs, it is also hard to remove. For those reasons, everything that flows out of an entrained flow gasifier needs to be cooled down to a temperature below the melting point of ash (about 1473 K) immediately to change the molten slag into solid slag, which causes a great waste of energy [9].

In order to ensure the energy efficiency of coal gasification, as well as to make slags easy to remove, the gasification temperature should not be higher than the melting point of ash. When the operating temperature is limited, the number of gasification stages should be increased to ensure the conversion of the carbon in coal. A typical schematic of multistage gasification is illustrated in Figure 1.

As shown in Figure 1, coal is pyrolyzed in the pyrolysis column at first to obtain gas fuel and light liquid. Since pyrolysis can be a batch process, green energy (wind energy and solar energy) is suggested to be used to pyrolyze coal. In this way, the coal pyrolysis process can be not only a part of coal gasification, but also a method that transforms green energy to chemical energy to make energy easy to store.

After the pyrolysis stage, the char goes to the gasification stage. Since the ash content of partially gasified char residue is high and the processing capacity of the gasifier needs to be large, fluid bed gasifiers are chosen as the gasifiers in the multistage gasification system. The number of gasification stages is set at two in Figure 1 to make the schematic easy to describe, whereas it depends on the demand of coal gasification in the industry. The most commonly used gasifying agents in the gasification stage are steam and CO₂.

For a specific amount of char, the gasification rate is normally slow when the carbon content in char is low, so partially gasified char residue with a low carbon content (normally not lower than 50% mass) can hardly complete gasification via steam and CO₂ with a reasonable gasification rate. For that reason, the last stage of the multistage gasification system normally uses O₂ or air as the gasifying agent to ensure the gasification rate [10,11]. The CO₂ produced in the intensified gasification stage flows back to the last gasification stage (“Gasification 2” in Figure 1) to work as a gasifying agent. The heat generated during the oxidation in the intensified gasification stage is used to provide the heat demanded in “Gasification 2”. The partially gasified char residue in the intensified gasification stage can also be sent back to the last gasification stage to act as both feed and a heat carrier, which is the same as the coke between the heater and gasifier in the flex coking process in the petroleum refining industry [12]. In addition, since the intensified gasification stage is independent, which makes its temperature easy to control, the porous solid and the salts that have surface activity in the ash can be used as promoters in hydrate-based CO₂ capture processes [13,14,15], which can further increase the economic value of the multistage gasification system.

Since char oxidation is much faster than char gasification by steam and CO₂, the reaction rate in the last gasification stage (“Gasification 2” in Figure 1) is slowest among the reaction rates in the reactors in the multistage gasification system, which makes the last gasification stage the rate-limiting stage. In order to increase the reaction rate in the last gasification stage to enhance the performance of the multistage gasification system, it is necessary to understand the gasification behaviour of char residues with high ash content.

For that reason, gasification of partial gasified char residues with different ash contents at different temperatures under different gasification agent partial pressures was carried out in this work. The gasification of pyrolyzed char was investigated and compared with the gasification of partial gasified char residue to better understand the gasification behaviour of char residue. The gasification of raw char was investigated and compared with the gasification of pyrolyzed char to investigate the effect of pyrolysis on char gasification. Two raw chars which have different ash compositions were used to make the char samples in this work so that the effect of minerals on the gasification behaviour could be investigated by comparing the gasification behaviour of chars made from different raw chars. Apparent activity energy and apparent reaction order were used to describe the effects of temperature and CO₂ partial pressure on the gasification rates. CO₂, steam, and oxygen are all important gasification agents, which makes the gasification of chars by CO₂, steam, and oxygen important for the development of the coal gasification industry, but the range of a paper is limited, so this work only focuses on the gasification of char with CO₂, and the gasification of chars by other gasification agents will be investigated through further study.

To better describe the kinetics of the gasification of different char samples, the gasification kinetics were modelled by the Random Pore Model (RPM), which is the most frequently used in gasification modelling. Since RPM hardly fits well with gasification in which the maximum gasification rate appears at a carbon conversion higher than 0.393 [16], the Modified Random Pore Model (MRPM) was also used in this work to better describe the kinetics of the gasification [17]. The reason why those models were chosen is discussed in detail in Section 2.5.

2. Experiments and Modelling

2.1. Experimental Materials

The experimental gases used in this work are shown in

Table 1. The experimental gases used in this work.

Experimental Gas	Purity	Application
Argon (Ar)	High purity > 99.99%	Carrier and purging gas
Carbon dioxide (CO2)	High purity > 99.99%	Reactant gas

.

Shenmu raw char and Tejing raw char were supplied by Sinosteel Anshan Research Institute of Thermo-energy (China). The proximate analysis provided by the supplier is shown in

Table 2. Proximate analysis (mass%).

Char Sample	Moisture, Mad	Ash Content, Ad	Volatile Matter, Vdaf	Fixed Carbon, Cad
Shenmu raw char	6.57	7.58	9.68	77.98
Tejing raw char	0.87	17.66	9.94	73.51

Note: ad—air dry; d—dry; daf—dry ash-free.

.

2.2. Char Sample Preparation

The char samples used in the gasification experiments included raw chars, pyrolyzed chars, and partially gasified char residues. Their preparation methods were as follows.

• Raw char

The raw chars were crushed by a jaw crusher and screened for sizes of 500–600 μm, which is in the range of the typical size of char particles for the fluidized bed [18].

• Pyrolyzed char

Since the gasification temperatures in this work were not higher than 1373 K, 1373 K was chosen as the pyrolysis temperature to ensure that the difference between gasification temperatures did not lead a difference in the char structures at the beginning of gasification. The size range of the raw char particles used in the preparation of the pyrolyzed chars was from 500 μm to 600 μm.

The preparation of pyrolyzed chars was carried out in a horizontal tube furnace, which was also used for the preparation of partially gasified char residues. The experimental set-up is shown in Figure 2. It consists of gas cylinders, mass flow controllers, a horizontal furnace, an aluminium oxide (Al₂O₃) furnace tube, a temperature measuring system, an infrared (IR) analyser, and a data recording system. The Al₂O₃ tube has an inner diameter of 50 mm and length of 1000 mm, and the length of the isothermal zone is 200 mm. The temperature was measured by a type R thermocouple with its tip above the sample. The gas flow rate was controlled by Aalborg Mass Flow Controllers with the uncertainty of the gas flow rate of 1%.

The preparation procedure was as follows:

• A raw char sample was placed in an Al₂O₃ crucible in a horizontal Al₂O₃ furnace tube, and an Ar gas flow of 1.00 NL/min was used to purge the air from the furnace tube for 20 min.
• Then, the sample was heated to a final pyrolysis temperature of 1373 K under a continuous Ar flow of 1.00 NL/min and held for 1 h before cooling to room temperature. Based on the work of Li et al. [19], the heating rate was about 15 K/min.

• Partially gasified char residue

The experimental set-up for partially gasified char residue preparation is shown in Figure 2. Pyrolyzed chars were gasified to prepare the partially gasified char residues. CO₂ was used as the gasification agent. Since the most commonly used operating temperature for fluidized bed gasification is about 1173 K [20,21], the partially gasified char residues were prepared at 1173 K. The preparation procedure was as follows:

• A pyrolyzed char sample was placed in an Al₂O₃ crucible in the furnace tube, and the tube was purged by Ar at 1.00 NL/min for 20 min to remove the air.
• The sample was heated to a final temperature of 1173 K under continuous Ar flow of 1.00 NL/min at a heating rate of about 15 K/min.
• When the temperature reached 1173 K, the purging Ar was switched to 1.00 NL/min CO₂. An online CO and CO₂ gas analyser was used to monitor the composition of the outlet gas, and the ash content in the partially gasified char residue was estimated according to the compositions of the inlet and outlet gases. When the ash content in the char reached the desired value (30 ± 2 or 50 ± 2 mass%), the CO₂ gas was switched to 1.00 NL/min Ar, and the furnace was cooled to room temperature.
• The actual ash content in the partially gasified char residue was confirmed by the char weight after gasification according to Equation (1):

$$A_{\mathrm{c}}=m_{\mathrm{r}\mathrm{c}}{A}_{\mathrm{r}\mathrm{c}}/m_{\mathrm{c}}$$

(1)

where m_rc and m_c denote the masses of the raw char and the char after gasification, respectively. A_rc and A denote the mass fractions of ash in the raw char and the partially gasified char residue, respectively. In this work, A_c was controlled at 30% mass or 50% mass, because the ash content of the char residue discharged from a fluidized bed is normally less than 50% mass [8,22,23]. The chars used in this work are summarized in

Table 3. Char samples in this work.

Sample Number	Char	Pyrolysis Temperature (K)	Gasification Temperature (K)	Ash Content (mass%)	Apparent Density (g/cm3)
RC1	Shenmu raw char	NA	NA	7.3	0.49
RC2	Tejing raw char			17.4	0.50
PC1	Shenmu pyrolyzed char	1373	NA	9.0	0.43
PC2	Tejing pyrolyzed char			19.2	0.49
GC1-30	Shenmu partial gasified char residue	1373	1173	30.4	0.39
GC2-30	Tejing partial gasified char residue			31.9	0.42
GC1-50	Shenmu partial gasified char residue	1373	1173	49.2	0.41
GC2-50	Tejing partial gasified char residue			51.4	0.67

.

In Table 3, RC1 and RC2 are the raw char samples made from Shenmu raw char and Tejing raw char in Section 2.2, respectively. PC1 and PC2 are the pyrolyzed char samples made from RC1 and RC2 in Section 2.2, respectively. GC1-30 is the partial gasified char residue containing about 30% mass ash which was made from PC1 in Section 2.2. GC1-50 is the partial gasified char residue containing about 50% mass ash which was made from PC1 in Section 2.2. GC2-30 is the partial gasified char residue containing about 30% mass ash which was made from PC2 in Section 2.2. GC2-50 is the partial gasified char residue containing about 50% mass ash which was made from PC2 in Section 2.2.

The gasification of the raw char sample was compared with that of the corresponding pyrolyzed char sample to investigate the effect of the pyrolysis of char on the gasification behaviour of char. The gasification of the pyrolyzed char sample was compared with that of the corresponding partial gasified char residue sample to investigate the gasification behaviour of partial gasified char residue. Gasification results for the partial gasified char residue samples with different ash contents were compared to investigate the effect of ash content on the gasification behaviour of partial gasified char residue.

After the char samples were prepared, the mineral compositions in the ashes of the char samples were analysed by XRD and XRF to lay a foundation for the discussion in Section 3, and the results of XRD and XRF are shown in

Table 4. The mineral phases in the ash of the char samples from XRD analysis.

Sample	Composition
RC1	SiO2, CaSO4, CaO, Al2O3, Fe2O3, Fe2(SiO3)3, CaCO3, Al2(SiO3)3
RC2	SiO2, CaSO4, CaO, Al2O3, Fe2O3, FeCa(SiO3)2, CaCO3
PC1	SiO2, CaSO4, CaO, Al2O3, Fe2O3, Fe2(SiO3)3, CaAl(SiO3)2(AlO2), Al2(SiO3)3
PC2	SiO2, CaSO4, CaO, Al2O3, Fe2O3, FeCa(SiO3)2, CaAl(SiO3)2(AlO2)
GC1-30	SiO2, CaSO4, CaO, Al2O3, Fe2O3, Fe2(SiO3)3, CaAl(SiO3)2(AlO2), Al2(SiO3)3
GC2-30	SiO2, CaSO4, CaO, Al2O3, Fe2O3, FeCa(SiO3)2, CaAl(SiO3)2(AlO2)
GC1-50	SiO2, CaSO4, CaO, Al2O3, Fe2O3, Fe2(SiO3)3, CaAl(SiO3)2(AlO2), Al2(SiO3)3
GC2-50	SiO2, CaSO4, CaO, Al2O3, Fe2O3, FeCa(SiO3)2, CaAl(SiO3)2(AlO2)

and

Table 5. The ash chemical compositions of different chars from XRF.

Element	RC1	RC2	PC1	PC2	GC1-30	GC2-30	GC1-50	GC2-50
MgO	0.9	8.4	1	8.7	1	8.7	1	8.7
Al2O3	17.6	15.8	21	15.8	20.6	15.7	20.6	15.7
SiO2	43	36	41	35.5	39.2	34.9	39.1	34.9
P2O5	0.4	0.1	0.5	0.1	0.5	0.1	0.5	0.1
SO3	6.5	6.5	7	6.9	4.1	6.3	4.2	6.4
K2O	0.1	0.6	0.1	0.6	0	0.5	0	0.5
CaO	20.8	17.2	22.6	17.7	22.3	17.8	22.4	17.8
TiO2	0.5	0.6	0.6	0.6	0.5	0.6	0.5	0.6
MnO	0.2	0	0.2	0	0.2	0	0.2	0
Fe2O3	4.9	5.2	5.6	5.2	5.5	5.5	5.5	5.5

, respectively. Since the chars made from Tejing raw char have more catalytic minerals than those made from Shenmu raw char, the effect of minerals on the gasification behaviour can be investigated by comparing the gasification behaviours of the char made from Tejing raw char and the char made from Shenmu raw char.

2.3. Gasification

The experimental set-up for the gasification is shown in Figure 3. It consists of gas cylinders, mass flow controllers, a vertical electric tube furnace, an Al₂O₃ tube reactor assembly, a temperature measuring system, an infrared (IR) CO-CO₂ gas analyser, and a data recording system. The reactor assembly consists of an inner tube and an outside sheath made of alumina, connected using fittings. The inner and outside diameters of the inner tube are 8.0 mm and 12.0 mm, respectively. The inner and outside diameters of the outside tube are 18.7 mm and 25.4 mm, respectively. The reactor assembly was inserted into the tube furnace so that the char sample held at the lower end of the inner tube was located in the isothermal zone of the furnace, which was determined by the temperature profile of the furnace measured in advance. The temperature was measured by a type R thermocouple in an alumina sheath, which was installed so that its tip was just above the sample. The gas flow rate was controlled by the Aalborg Mass Flow Controllers, of which the uncertainty of the gas flow control was ±1%. The outlet gas was filtered by a filter to remove the dust from the reaction system before being directed to the gas analyser.

A char sample of 0.05 g was weighed and loaded at the bottom of the inner tube and supported by alumina wool, which was fixed using an alumina pin. (The alumina wool was disposable so that the ash adhering to it was removed after the experiment and did not affect the next experiment). Then, the inner tube was assembled with the outside tube and fixed with fittings. The reactor assembly was fixed on the loading mechanism and first purged by 1.00 NL/min Ar for 20 min to remove the air inside the reactor. Then, the reactor was lowered into the furnace. The purging with the Ar stream remained while heating the sample to the experimental temperature. After the sample temperature reached the experimental temperature and became stable, the purging gas was switched to 1.00 NL/min reactant gas of the desired composition. During the gasification process, the concentrations of CO₂ and CO in the outlet gas were measured by the CO-CO₂ infrared gas analyser. After gasification ended, the gas was switched back to the Ar stream, and the reactor was cooled down to room temperature by lifting the reactor assembly from the furnace. Then, the reactor was disassembled, and the sample was taken out of the reactor for further analysis.

2.4. Data Treatment

The instantaneous char gasification rate (dx/dt, s⁻¹) and the char conversion at time t (x_t) can be calculated as shown in Equations (2) and (3):

$$dx/dt={\displaystyle \frac{{dn}_C/dt}{m_0·(100\%-w_{ash,0})/M_C}}$$

(2)

$$x_t=1-{\displaystyle \frac{{\int }_0^t{dn}_C}{m_0·(100\%-w_{ash,0})/M_C}}$$

(3)

where dn_c/dt (mol∙s⁻¹) is the molar reaction rate of the carbon in char during a gasification process, m₀ (g) is the mass of the sample put into the reactor, w_ash,0 is the ash content (mass%) in the char sample before gasification, M_C (g∙mol⁻¹) is the molar weight of carbon, and t is gasification time. The char gasification by CO₂ is shown in Equations (4)–(6):

$$\mathrm{C}+{\mathrm{C}\mathrm{O}}_2=2\mathrm{C}\mathrm{O}$$

(4)

$$v_{CO}={\mathrm{v}}_{total,0}\times {\displaystyle \frac{y_{CO}}{100 mol\%-y_{CO}/2}}$$

(5)

$${dn}_C/dt={\displaystyle \frac{v_{CO}\times P}{\mathrm{R}T}}$$

(6)

where v_CO (NL/s) is the volumetric flow of the CO in the off gas of the reactor, v_total,0 (NL/s) is the volumetric flow of the inlet gas of the reactor, y_co (mol%) is the concentration of the CO in the off gas of the reactor, and P and T are standard pressure and temperature because the mass flow controllers and the gas analyser are calibrated to the Standard Temperature and Pressure (STP) condition. R is the universal gas constant.

The fixed carbon in char residues reacted with CO₂ and converted into carbon monoxide. The potassium oxide, magnesium oxide, calcium oxide, and iron oxide in the ash of the char residues promoted the gasification of fixed carbon through intermediate catalytic reactions. The other components in char residues did not significantly react with CO₂.

Calculated by HSC Chemistry 5.11, the equilibrium constant of the reaction between CO₂ and the material of the experimental equipment (aluminium oxide) was smaller than 5.843 × 10⁻⁷² in the range of the experimental condition in this work, so the reaction between CO₂ and the experimental equipment can be ignored in data treating. For that reason, high temperatures and CO₂-rich environments have no obviously negative effect on the gasification equipment, such as corrosion.

The activation energy (E) of the chars at conversions of 0.5, 0.7, and 0.9 was used to discuss the effect of temperature on gasification. The effect of temperature on the gasification of chars can be assessed by the activation energy of the gasification of different chars according to Arrhenius law [17,24,25,26,27]. The calculated activation energy of this paper is apparent activation energy, which is based on a number of assumptions, including that the specific surface area was the same at the same conversion for gasification at different temperatures [17,24,25,26,27]. The calculation of the activation energy of the reactions was based on the rate of reactions for unit (initial) mass of char samples [17,24,25,26,27]. In this case, the value of the specific surface area of a sample does not affect the calculated value of the activation energy, because the ratios of the rates at different temperatures are used, and the ratios of the rates for unit mass of a sample are the same as those for unit surface area [17,24,25,26,27]. When the rate of reaction is controlled by the intrinsic kinetics of the reaction, the values from the experimental data are the true values, while the values are apparent if the rate of reaction is affected by diffusions.

The activation energy of the gasification of different chars by CO₂ was obtained by correlating the gasification rate at conversions of 0.5, 0.7, and 0.9 (r_0.5, r_0.7, and r_0.9), respectively, to understand the effect of temperature on the gasification at different stages. The char gasification in this work was dealt with as a gas-solid non-catalytic heterogeneous reaction, and the gasification rate can be described as Equation (7) (some ash components have catalytic activity in the gasification processes, but the catalytic activity is assumed not to change during reaction processes) [17,24,25,26,27]:

$${\displaystyle \frac{dX}{dt}}=k(T)·f(X)·P_{{\mathrm{C}\mathrm{O}}_2}^n$$

(7)

where dx/dt is the apparent reaction rate. n is the apparent reaction order. f(X) describes the changes in the physical or chemical properties of the sample as the gasification proceeds. $P_{{\mathrm{C}\mathrm{O}}_2}$ is the partial pressure of the CO₂ in gas phase. T is temperature. $k\left(T\right)$ is the apparent gasification rate constant, and it can be expressed as Equation (8) [17,24,25,26,27]:

$$k(T)=k_0·{\mathrm{e}}^{-{\displaystyle \frac{E}{\mathrm{R}·T}}}$$

(8)

where k₀ is the pre-exponential factor, and E is activation energy. The gasification rate at the same conversion with the same gas composition is proportional to the apparent reaction rate constant due to constant f(X) and Pⁿ, and Equation (7) can be expressed as [17,24,25,26,27]:

$$\mathrm{r}={\displaystyle \frac{dX}{dt}}=k_0·e^{-{\displaystyle \frac{E}{R·T}}}·f(X)·P_{{\mathrm{C}\mathrm{O}}_2}^n$$

(9)

Let $K=k_0·f\left(X\right)·P_{{\mathrm{C}\mathrm{O}}_2}^n$:

$$r={\displaystyle \frac{dX}{dt}}=K·{\mathrm{e}}^{-{\displaystyle \frac{E}{\mathrm{R}·T}}}$$

(10)

where K is a constant at the same conversion and with the same gas composition. Equation (16) can be expressed as follows:

$$lnr=(-{\displaystyle \frac{E}{\mathrm{R}}})·{\displaystyle \frac{1}{T}}+\mathrm{l}\mathrm{n}K$$

(11)

The E of chars can be obtained by correlating the rate of gasification at the conversion following Equation (11). Taking the gasification of PC1 as an example, the ln(r_0.5), ln(r_0.7), and ln(r_0.9) of PC1 at different temperatures are shown in Figure 4. r_Exp is the reaction rate obtained from the experiment and r_Fit is the reaction rate obtained by correlating r_Exp following Equation (11). By fitting the experimental data in Figure 4, the activation energy was obtained by fitting r_0.5, r_0.7, and r_0.9 of PC1 with 1/T, respectively. Based on Figure 4, the activation energies obtained by fitting r_0.5 (E0.5), r_0.7 (E0.7), and r_0.9 (E0.9) are 86.1, 89.7, and 96.3 kJ/mol, respectively. The activation energies of the other chars at conversions of 0.5, 0.7, and 0.9 can be obtained similarly.

The effect of CO₂ partial pressure on the gasification of chars can be assessed by the apparent reaction order (n) of the gasification of different chars according to Equation (9). A higher apparent reaction order indicates a stronger effect of the CO₂ partial pressure on the gasification of chars. The apparent reaction order of the gasification of different chars by CO₂ was obtained by correlating the gasification rate at the conversions of 0.5, 0.7, and 0.9 (r_0.5, r_0.7, and r_0.9), respectively, to understand the effect at different stages of reaction. According to Equation (9), the gasification rate at the same conversion at the same temperature is proportional to Pⁿ due to constant k(T) and f(X). Let $KK=k_0·{\mathrm{e}}^{-{\displaystyle \frac{E}{\mathrm{R}·T}}}·f(X)$:

$$r={\displaystyle \frac{dX}{dt}}=KK·P^{\mathrm{n}}$$

(12)

where KK is a constant at the same conversion and at the same temperature. Equation (12) can be expressed as follows:

$$lnr=lnKK+n·\mathrm{l}\mathrm{n}\mathrm{P}$$

(13)

The apparent reaction order of chars can be obtained by correlating the rate of gasification at the conversion following Equation (13). Taking the gasification of PC1 at 1073 K as an example, the ln(r_0.5), ln(r_0.7), and ln(r_0.9) of PC1 under different CO₂ partial pressures are shown in Figure 5. r_Exp is the reaction rate obtained from the experiment and r_Fit is the reaction rate obtained by correlating r_Exp following Equation (13). By fitting the experimental data in Figure 5, the apparent reaction order was obtained by fitting r_0.5, r_0.7, and r_0.9 of PC1 with lnP, respectively. Based on Figure 5, the apparent reaction orders obtained by fitting r_0.5 (n0.5), r_0.7 (n0.7), and r_0.9 (n0.9) are 0.49, 0.47, and 0.46, respectively. The apparent reaction orders of the other chars at the conversions of 0.5, 0.7, and 0.9 can be obtained similarly. The lower apparent reaction order of the char residue after most of the carbon was gasified can be attributed to the decrease in the gasification rate.

2.5. Modelling

Kinetic modelling of gasification is of significance in understanding the gasification process and process design. As discussed in the literature [17,24,25,26,27], the Volumetric Model (VM), Grain Model (GM), Random Pore Model (RPM), and Modified Random Pore Model (MRPM) are mostly used in the simulation of gasification.

VM is the model which was first used to describe the gasification process [28]. In the Volumetric Model, gasification is assumed to occur in the whole solid particle, and the sizes of solid particles do not change during the gasification, but the density of particles changes uniformly as gasification progresses [28]. Limited by the assumption of the VM, the VM cannot describe the change in the surface area of the char particle during the gasification process, so it can only predict a monotonal decrease in the reaction rate with carbon conversion, which is inconsistent with the real gasification process [17].

In the GM, a porous particle is assembled by uniform nonporous spherical grains (with unreacted core behaviour) [29,30]. The gasification reaction initially occurs on the external surface of grains and then gradually moves inside; as the gasification proceeds, only the ash layer remains [29,30]. Compared with the VM, the GM takes the effects of the external surface area of char particles and the accumulation of the ash on the external surface into consideration. However, the internal surface of char is ignored in the GM, so the GM can only predict a monotonal decrease in the reaction rate with carbon conversion [17].

In the RPM, the solid particle is assumed to be porous, and gasification occurs on the internal surfaces of these pores [17,24,25,26,27]. The pores in the solid char particles are assumed to have cylindrical structures with non-uniform size; they are enlarged and merge together with the progress of the gasification reaction so that the RPM can predict the initial stage of increasing gasification rate observed in the experiments, which makes the pore models superior to the VM and the GM. For that reason, the RPM was used to describe the gasification processes of different chars in this work. The RPM introduces the parameter ψ, which represents the pore structure of the char particles before gasification, into the calculation of f(X). ψ is the key kinetic parameter that affects the gasification rate, which is obtained by fitting experimental data. Both the carbon conversion at which the maximum gasification rate appears (X_M) and the ratio of the maximum gasification rate to the initial gasification rate increase with the increase in ψ. The RPM considers the competing effects of pores growing during the initial stage of gasification and the destruction of the pores due to the coalescence of neighbouring pores during the reaction. In the RPM, the f(X) in Equation (7) can be expressed as Equation (14) [17,24,25,26,27]:

$$f\left(X\right)=(1-X)\sqrt{1-\psi ln(1-X)}$$

(14)

Limited by Equation (14), the carbon conversion at which the maximum gasification rate appears (X_M) in the RPM cannot be higher than 0.393 [17,31]. In addition, gasification with a similar X_M can have different ratios of the maximum gasification rate to the initial gasification rate, but the ratio of the maximum gasification rate to the initial gasification rate cannot be adjusted without changing X_M in RPM, because there is only one structure parameter ψ in the gasification rate equation of RPM.

In case the X_M in this work is higher than 0.393, as well as in case gasification with a similar X_M has significantly different ratios of the maximum gasification rate to the initial gasification rate, the MRPM, in which f(X) can be written as Equation (15), is also used in this work to describe the kinetics of gasification [17]:

$$f\left(X\right)={(1-X)}^{\mathrm{q}}\sqrt{1-\Psi ln(1-X)}$$

(15)

where q is a dimensionless power law constant. Ψ and q are the key kinetic parameters that affect the gasification rate, which are obtained by fitting experimental data. Both X_M and the ratio of the maximum gasification rate to the initial gasification rate increase with the increase in Ψ, whereas they both decrease with the increase in q. By adjusting the values of q and Ψ at same time, the two limitations in the RPM can be overcome. It needs to be noted that the prediction accuracy of the model can be technically increased by introducing more parameters, as well as introducing a correcting function, because the more parameters (or correcting functions) are in the model, the easier it is to adapt different relationships between the gasification rate and carbon conversion. However, according to the experimental data in Section 3.1 and Section 3.2, the relationship between gasification rate and carbon conversion does not follow a specific function type, and it varies significantly with changes in char type and gasification condition. For that reason, a limited increase in the number of the parameters (or correcting functions) in the model cannot ensure a significant increase in the prediction accuracy of the model. In addition, the increase in the number of the parameters (or correcting functions) makes the fitting of the model much more complex. Since this work only focuses on the gasification of char by CO₂, the MRPM meets the requirements of this work. To make models easy to use, only the RPM and MRPM were used in this work, and no additional parameters or correcting functions were introduced into the models.

In the applications of the RPM and MRPM, $k\left(T\right)$ can be obtained by curve fitting of the dx/dt—t relation using Origin 9.6. The pre-exponential factor (k₀), apparent reaction order (n), and apparent activation energy (E) can be obtained according to Equations (7) and (8). The change in conversion X with time t can be calculated as Equation (16):

$$X={\int }_0^{t}k\left(T\right)·f\left(X\right)·P_{{CO}_2}^n$$

(16)

Average relative deviation (ARD) and goodness of fit (GF) are calculated in order to evaluate the deviation between model results and experimental data. They are calculated by Equations (17) and (18) as follows:

$$ARD={\displaystyle \frac{\sum _{\mathrm{i}}^{\mathrm{n}\mathrm{n}}\left|\frac{\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e} - \mathrm{C}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}}{\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}}\right|}{\mathrm{n}\mathrm{n}}}·100\%$$

(17)

$$GF={\displaystyle \frac{\sum _i^{nn}{(\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}-\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e})}^2}{\sum _i^{nn}{(\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}-\sum _i^{nn}\mathrm{E}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{l} \mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}/nn)}^2}}$$

(18)

where nn denotes the total number of experiments. A smaller ARD shows better prediction accuracy of the model. The GF is used to present how well the model shows the effect of each factor on the kinetics of gasification. A value of GF close to 1 means that the model can predict the effect of a factor on the kinetics of gasification satisfactorily. Due to the limitation in the experimental numbers, no efforts have been made to use independent experiment data for model validation.

3. Results and Discussion

The char-CO₂ reaction is one of the major reactions in the industrial processes of coal gasification [17,25,26,32,33,34,35,36,37,38]. The kinetic data on the reaction of CO₂ with char residue are needed in the analysis of the gasification process of char residue, as well as in the modelling and design of the gasifier. This section focuses on the gasification of the chars with different ash contents by CO₂. The ash content of the char residue discharged from a fluidized bed can be less than 50% mass [8,22,23], so the ash contents of the partially gasified char residues used in this work were selected to be 30% mass and 50% mass.

In order to lay a foundation for the investigation on the char-O₂ gasification, thermodynamic equilibrium data of the Boudouard reaction were calculated by HSC Chemistry 5.11 and are shown in

Table 6. The equilibrium conditions of carbon gasification by CO₂.

PCO2,Feed (atm)	C + CO2(g) = 2CO(g)
	T (K)	K	PCO2,eq	PCO,eq	T (K)	K	PCO2,eq	PCO,eq
0.2	1123	16.62	0.002	0.198	1323	253.7	0.0002	0.1998
0.4			0.009	0.391			0.0006	0.3994
0.6			0.020	0.580			0.0014	0.5985
0.8			0.035	0.765			0.0025	0.7975
1			0.054	0.946			0.0039	0.9961
0.2	1173	35.97	0.001	0.199	1373	440.8	0.0001	0.2000
0.4			0.004	0.396			0.0004	0.3997
0.6			0.010	0.590			0.0008	0.5992
0.8			0.017	0.783			0.0014	0.7986
1			0.026	0.974			0.0023	0.9977
0.2	1223	72.91	0.001	0.199	1423	735.4	0.0001	0.1999
0.4			0.002	0.398			0.0002	0.3998
0.6			0.005	0.595			0.0005	0.5996
0.8			0.009	0.791			0.0009	0.7991
1			0.013	0.987			0.0014	0.9986
0.2	1273	139.5	0.0003	0.1997	1473	1183.0	0.0000	0.2000
0.4			0.0011	0.3988			0.0001	0.3998
0.6			0.0025	0.5975			0.0003	0.5997
0.8			0.0045	0.7955			0.0005	0.7994
1			0.0071	0.9930			0.0008	0.9991

.

According to Table 6, the equilibrium partial pressure of CO₂ is very low, and it is negligible compared with that in either the inlet gas or the outlet gas in each experiment in this work under corresponding conditions. For that reason, no char-CO₂ gasification was controlled by thermodynamic equilibrium in this work, and the driving force characterized by ΔP_CO2 (=P_CO2 − P_CO2,eq) can be assumed to be the same as P_CO2 in the outlet gas. For example, for the gasification of RC1, the P_CO2 in the off gas at the peak gasification rate was 0.995 atm at 1173 K, corresponding to P_CO2 = 1.0 atm in the inlet gas, meaning that the gasification reaction did not reach equilibrium in the experiments due to the very short contact time between the gas and char particles.

It can be seen from Table 6 that carbon gasification by CO₂ is thermodynamically favoured, with the equilibrium constant being much higher than unity. Increasing temperature favours more complete conversion of CO₂ to CO. The performance of the gasification with CO₂ is affected by the temperature, CO₂ partial pressure, and the properties of carbonaceous materials [8,24,39,40,41,42]. In this paper, the effects of temperature and CO₂ partial pressure on gasification with CO₂ were investigated. The gasification of raw chars, pyrolyzed chars, and partially gasified char residues were investigated to make a comparison of the reactivity of different chars. The operating conditions used in this chapter are summarized in

Table 7. The operating conditions of the gasification by CO₂.

Sample	Temperature (K)	Reactant Partial Pressure (atm)
RC1, RC2	1173, 1273, 1373, 1473	1
	1173, 1273, 1473	0.2, 0.6
PC1, PC2	1173, 1273, 1373	1
	1273	0.2, 0.6
GC1-30, GC2-30, GC1-50, GC2-50	1123, 1223, 1273, 1323, 1373	1
	1273	0.2, 0.4, 0.6, 0.8

.

3.1. Effect of Temperature on the Gasification of Different Chars

3.1.1. Raw Char

In this part, the effect of temperature on the gasification of raw chars with a gas flow of 1.0 NL CO₂/min was experimentally investigated in the temperature range from 1173 to 1473 K (1473 K is higher than the pyrolysis temperature in this work and is only for comparison purposes), and the relationships between gasification rate and time at different temperatures are shown in Figure 6.

In Figure 6, for both RC1 and RC2, the gasification rate increased at first and then decreased with the progress of gasification. This was likely caused by the change in the inner surface area of char particles during gasification, which is illustrated in Figure 7 [8]. The char gasification mainly occurred on the inner surface of char particles. The consumption of carbon caused by gasification enlarged the size of the pores in chars during the initial stage of gasification, increasing the inner surface area of char particles [8,43]. But as char particles further gasified, as shown in Figure 7, the pores in char particles collapsed and merged, which led to decrease in the inner surface area of char particles. In addition, the pores were blocked and the particle surface was partly covered by the ash, which also decreased the area of the surface for gasification to occur, so the gasification rate decreased. The change in the inner surface area with conversion was qualitatively evaluated based on theoretical evaluation [8].

In Figure 6, the peak gasification rate is reached later for RC1 than for RC2. This may be because RC1 had a smaller reaction rate. The higher the temperature was, the earlier the gasification reached its maximum value; for example, it took 790 s for RC1 to reach the maximum gasification rate at 1173 K but only 30 s at 1473 K. A higher temperature led to a higher gasification rate, which accelerated the consumption of carbon and decreased the time for the gasification to reach the highest rate.

To further discuss the effect of temperature on the rate of raw char gasification, the relationships between gasification rate and conversions at different temperatures are shown in Figure 8.

In Figure 8, the gasification rate increased with the increase in temperature: the maximum gasification rate of RC1 increased from 3.48 × 10⁻⁴ s⁻¹ at 1173 K to 6.44 × 10−³ s⁻¹ at 1473 K, which was a significant increase of 17.5 times. Correspondingly, the maximum gasification rate of RC2 increased by 4.2 times. For the same temperature increase, the gasification rate of RC1 at 0.5 and 0.9 (X = 0.5 and X = 0.9) conversion increased by more than 18 times, while that of RC2 increased by approximately 4 times.

As shown by Figure 8, the gasification rate of RC2 was higher than RC1 at the same temperature, which was more significant at lower temperatures. The maximum gasification rate of RC2 was 6.41 times that of RC1 at 1173 K, which became 1.79 times at 1473 K. This was caused by the difference between the minerals in RC1 and RC2. According to the XRF analysis, the contents of potassium and magnesium (which can accelerate gasification) in the ashes of RC2 are much higher than those in the ashes of RC1; the contents of Ca and Fe oxides (which can accelerate gasification) in the ashes of RC1 and RC2 are similar, and the contents of alumina and silica (which can inhibit gasification) [9,44] in RC2 are much lower than those in RC1. It can be concluded that the minerals in RC2 had a stronger effect in promoting the gasification reactions than those in RC1.

Figure 8 shows the change in gasification rate with carbon conversion of RC1 and RC2 at different temperatures. Although Figure 6 shows that some of the peak values of dx/dt were quickly reached, Figure 8 shows that it reached the maximum with up to 30% conversion. For both RC1 and RC2, the conversion at which the maximum gasification rate appeared changed with the change in temperature, which indicates that pore structure development was different at different temperatures. This was because the raw chars had not been completely pyrolyzed, so their structures changed significantly during the heating stage before gasification occurred.

3.1.2. Pyrolyzed Char

The effect of temperature on the gasification of pyrolyzed chars was investigated using PC1 and PC2, with a gas flow of 1.0 NL/min CO₂, in the temperature range from 1173 to 1373 K. The experimental results are shown in Figure 9 and Figure 10.

Figure 9 presents the change in gasification rate of PC1 and PC2 at different temperatures with time. Like the case of raw chars, the gasification rate curves of both pyrolyzed chars at different temperatures show peak values along with progress of gasification, which appeared in long periods of time when the gasification was slow. However, from the curves showing the change in gasification rate with carbon conversion (Figure 10), it is found that the maxima of all of the curves appear at about 24% carbon conversion. This is very different from the case of raw chars RC1 and RC2, where the peaks appear with different conversions and move to a short gasification time under fast gasification conditions. This is a good indication that pore structure development was the same at different temperatures for either PC1 or PC2.

From Figure 10, the gasification rate increased with the increase in temperature. The gasification of PC2 was faster than that of PC1 at the same temperature, and it reached its peak rate and completed earlier than PC1. The difference between the gasification rates of PC2 and PC1 became less significant as the temperature increased: the maximum gasification rate of PC2 was 3.38 times that of PC1 at 1173 K, which decreased to 2.56 times at 1373 K. The difference in the performance of PC1 and PC2 is consistent with that in the performance of RC1 and RC2.

3.1.3. Partially Gasified Char Residue

The effect of temperature on the gasification of partially gasified char residues was investigated using samples GC1-30, GC1-50, GC2-30, and GC2-50, with a gas flow of 1.0 NL/min CO₂ in the temperature range from 1123 to 1373 K. Since the gasification of partial gasified char residue is the primary research object in this work, more experimental temperatures were used in this section than in Section 3.2.1 and Section 3.2.2. The experimental results are shown in Figure 11 and Figure 12.

According to Figure 11 and Figure 12, the gasification process of partially gasified char residue was not just like the end stage of the gasification process of the corresponding raw char (or pyrolyzed char), though the conversion at which partially gasified char residue achieved its highest gasification rate was lower than that of the corresponding raw char (or pyrolyzed char). The gasification rate of the partially gasified char residue with high ash content still increased during the initial stage of gasification, then decreased. This is clearer from the gasification rate vs. carbon conversion plots in Figure 12. According to the ash contents of the chars in Table 3, more than 0.4 of carbon was consumed during the preparation of the partially gasified char residues. According to the experimental data in Figure 8 and Figure 10, the point at which maximum internal surface area was obtained was smaller than 0.4 (X_M < 0.4), so this point was passed after the preparation of the partially gasified char residues. For that reason, the formation of a new peak in the gasification rate curves should have not observed. The formation of a new peak in some curves can be attributed to the partial destruction of the carbon structure formed by partial gasification during sample preparation in some experiments.

From Figure 12, the gasification rate increased with the increase in temperature. The maximum gasification rate of GC1-30 increased from 2.30 × 10⁻⁴ s⁻¹ at 1123 K to 7.36 × 10⁻³ s⁻¹ at 1373 K, while that of GC2-30 correspondingly increased from 1.06 × 10⁻³ s⁻¹ to 1.36 × 10⁻² s⁻¹. These were increases of 31 and 12 times in gasification rate, caused by the increase in temperature. For GC1-50 and GC2-50, the corresponding increases were 43 and 15 times, respectively, which is more significant than for GC1-30. The gasification rates of GC1-30 and GC2-30 at 0.5 and 0.9 carbon conversion also increased significantly as a result of the increase in temperature. An increase of up to 52 times was observed in the case of GC1-50 at 0.9 carbon conversion.

It can be seen from Figure 11 and Figure 12 that the gasification rate of char samples made from Tejing char was much higher than that of char samples made from Shenmu char when partially gasified to the same ash content under the same gasification condition. This result is consistent with the gasification of raw chars and pyrolyzed chars in Section 3.1.1 and Section 3.1.2.

It can also be seen from Figure 12 that the gasification rate of GC1-50 was slower than that of GC1-30 at the same temperature, which indicates the accumulation of ash from 30% mass to 50% mass inhibited the gasification, whereas the gasification rate of GC2-50 was faster than that of GC2-30 at the same temperature, which indicates the accumulation of ash from 30% mass to 50% mass benefited the gasification. Opposite experimental results were caused by the difference between the ash composition of the chars made from Shenmu char and Tejing char. As discussed in Section 3.1.1, the ash of chars made from Tejing char contains significantly more minerals that promote gasification, whereas the ash of chars made from Shenmu char contains significantly more minerals that inhibit gasification. For that reason, the ash accumulation in the chars made from Shenmu char inhibits gasification, whereas the ash accumulation in the chars made from Tejing char promotes gasification.

3.1.4. The Effects of Temperature on the Gasification of Different Chars

The activation energies of the chars at the conversions of 0.5, 0.7, and 0.9 were obtained through the method shown in Section 2.4 and are summarized in

Table 8. The activation energy of char gasification by CO₂ at different conversions.

Sample	Conversion	E (kJ/mol)	K (s−1)	ARD	GF
RC1	0.5	155.8	1.90 × 103	14.0%	0.99
	0.7	155.9	1.41 × 103	10.3%	0.99
	0.9	154.9	6.00 × 102	11.8%	0.99
PC1	0.5	86.1	3.61 × 100	1.6%	1.00
	0.7	89.7	3.48 × 100	5.0%	0.99
	0.9	96.3	2.53 × 100	14.1%	0.94
GC1-30	0.5	201.2	3.28 × 105	8.4%	0.96
	0.7	209.1	4.53 × 105	5.0%	0.98
	0.9	213.1	2.38 × 105	3.6%	1.00
GC1-50	0.5	186.8	3.29 × 104	11.1%	0.98
	0.7	169.7	3.34 × 103	10.8%	0.99
	0.9	133.6	2.67 × 101	13.9%	0.97
RC2	0.5	98.6	3.17 × 101	30.2%	0.86
	0.7	106.8	4.49 × 101	36.2%	0.82
	0.9	123.4	6.63 × 101	46.7%	0.62
PC2	0.5	72.0	2.34 × 100	7.0%	0.98
	0.7	76.4	2.38 × 100	2.3%	1.00
	0.9	83.1	1.67 × 100	2.3%	1.00
GC2-30	0.5	134.5	1.65 × 103	16.3%	0.90
	0.7	143.8	2.53 × 103	9.6%	0.97
	0.9	138.8	5.01 × 102	6.8%	0.98
GC2-50	0.5	152.1	7.96 × 103	7.8%	0.97
	0.7	149.5	3.80 × 103	3.7%	1.00
	0.9	130.1	2.01 × 102	7.9%	0.96

. It can be seen from Table 8 that the average relative deviation (ARD) of the gasification rate of the chars made from Shenmu char is smaller than that of the gasification rate of the chars made from Tejing char, which indicates that the gasification rate of the chars made from Shenmu char fits Equation (11) better than that of the chars made from Tejing char.

According to Table 8, the ARD of the gasification of raw chars, especially RC2, is generally larger than that of other char samples. The temperatures used in the gasification experiments were higher than the temperature of raw char preparation from coal (773 K to 973 K), so some volatiles were lost while heating a sample to its gasification temperature before gasification commenced, which caused a structure change in the char. This change in the structure of raw chars may have been affected by the gasification temperature, making the results less reliable.

It can be seen from Table 8 that the gasification of both pyrolyzed chars by CO₂ has significantly lower activation energy. That may be because pyrolyzed chars lost some highly reactive substance during the pyrolysis process, which made them less reactive than raw chars, and because they had less catalytic minerals than partial gasified char residues.

From Table 8, for PC1, PC2, GC1-30, and GC2-30, the activation energy increased with the increase in conversion. This trend in activation energy change is attributed to the preferred consumption of carbon of higher reactivity as catalysed by the catalytic components in ash. The activation energy of GC1-50 and GC2-50 decreased with increasing conversion. A possible reason could be that under this high ash content condition, further gasification of the carbon caused collapse of the pore structure, and more contacts between carbon and catalytic ash components were formed. This promoted the gasification of the final carbon residue.

3.2. Effect of CO₂ Partial Pressure on the Gasification of Different Chars

3.2.1. Raw Char

The effect of CO₂ partial pressure on the gasification of the raw chars was experimentally investigated by changing CO₂ partial pressure from 0.2 to 1.0 atm in a CO₂-Ar gas mixture. Though the most commonly used operating temperature for fluidized bed gasification is about 1173 K [20,21], the gasification rate normally decreases with the decrease in temperature. In case the gasification rate at 1173 K was too slow under low CO₂ partial pressure, experiments at 1273 K were also carried out. In addition, 1473 K is higher than the pyrolysis temperature in this work, and the experiments at 1473 K are only for comparison purposes. The experimental results are shown in Figure 13.

Figure 13 presents the change in the gasification rate with time for both RC1 and RC2. It seems that there is a trend of the peak gasification rate appearing for a longer time with the decrease in CO₂ partial pressure. Although both increasing temperature and increasing CO₂ partial pressure increased the gasification rate, they affected the rate of reaction in different manners. Increasing temperature enhanced the intrinsic kinetics, making gas diffusion a more significant factor controlling the rate of gasification. Conversely, increasing CO₂ partial pressure increased the pressure/concentration item of the rate equation; the gas diffusion from bulk gas to the reaction interface increased proportionally with the increase in CO₂ partial pressure, but the effect on the intrinsic kinetics was much less due to a reaction order less than unity, which is discussed in more detail later. As a result, more CO₂ was diffused into deep pores for gasification to take place, so the reaction was more uniform between the outer and inner parts of char particles. For intrinsic kinetics-controlled gasification, uniform gasification allowed appropriate development of the pore structure, and the peak gasification rate appeared later. By contrast, if the gasification was controlled by external diffusion of gas, carbon was only consumed from the external surface of the char particles, and the maximum gasification took place at the commencement of experiments.

As in the case of the effect of temperature, with the increase in temperature, the time for complete gasification decreased, with increasing CO₂ partial pressure corresponding to the increase in gasification rate. The gasification rate increased with increasing CO₂ partial pressure for both RC1 and RC2 and at all temperatures employed. Taking the gasification at 1273 K as an example, the maximum gasification rate of RC1 increased from 5.19 × 10⁻⁴ s⁻¹ under 0.2 atm CO₂ to 1.13 × 10⁻³ s⁻¹ under 1.0 atm CO₂, while that of RC2 increased from 2.31 × 10⁻³ s⁻¹ under 0.2 atm CO₂ to 4.66 × 10⁻³ s⁻¹ under 1.0 atm CO₂, which were increases by 1.12 and 1.0 times, respectively. The gasification rate of RC1 at 0.5 and 0.9 of carbon conversion increased by 1.10 and 1.19 times, respectively. The corresponding increase for RC2 was 1.04 and 1.56 times, respectively. Obviously, the increase in the rate was not in proportion to that of CO₂ partial pressure.

3.2.2. Pyrolyzed Char

The effect of the CO₂ partial pressure on the gasification of the pyrolyzed chars was examined using PC1 and PC2 by changing CO₂ partial pressure from 0.2 to 1.0 atm and keeping a gas flow of 1.0 NL/min. According to the experimental data in Section 3.2.1, the gasification at 1173 K was very slow when CO₂ partial pressure was low, which made the experimental time much longer than the real reaction time in industry could be; for example, the experimental time of RC1 at 1173 K under 0.2 atm CO₂ was about 42,000 s. On the other hand, since the refresh rate of the online CO and CO₂ gas analyser is once per second, the uncertainty of the conversion at which the peak gasification rate appears would be high if the gasification is too fast, so it is better that the gasification rate is not too high. For those reasons, the experimental temperature was set at 1273 K. The experimental results are shown in Figure 14.

In Figure 14, the gasification rate changed with time, similar to the case of the effect of temperature; that is, the peaks appeared later when the reaction rate was lower, but at a similar carbon conversion for both char samples and different CO₂ partial pressures.

The gasification rate increased with increasing CO₂ partial pressure for both PC1 and PC2. The maximum gasification rate of PC1 increased from 5.72 × 10⁻⁴ s⁻¹ under 0.2 atm CO₂ to 1.23 × 10⁻³ s⁻¹ under 1.0 atm CO₂, while that of PC2 increased from 1.67 × 10⁻³ s⁻¹ under 0.2 atm CO₂ to 2.69 × 10⁻³ s⁻¹ under 1.0 atm CO₂. These are equivalent to increases of 1.15 and 0.61 times, respectively. The gasification rate of PC1 at 0.5 and 0.9 carbon conversions increased by 1.25 and 1.19 times, respectively, and the corresponding increases for PC2 were 0.68 and 0.94 times, respectively. This was because a higher CO₂ partial pressure led to a higher driving force for the reaction to take place and a higher gas diffusion rate. There is not much difference between the gasification rates of PC1 and RC1 under the same experimental condition, while the gasification rate of PC2 is obviously smaller than that of RC2 under the same experimental condition, which indicates pyrolysis has a greater effect on Tejing char than Shenmu char.

3.2.3. Partially Gasified Char

The effect of CO₂ partial pressure on the gasification of partially gasified char residues was investigated at 1273 K with a CO₂-Ar gas mixture of 1.0 NL/min to make a contrast with the data in Section 3.2.2. Since the gasification of partial gasified char residue is the primary research object, we used more experimental CO₂ partial pressures in this section than in Section 3.2.1 and Section 3.2.2. The CO₂ partial pressure was changed in the range from 0.2 to 1.0 atm. Figure 15 presents the change in gasification rate of the partially gasified char residues with time.

The gasification rate increased with increasing CO₂ partial pressure for all four partially gasified char residues. Comparing the maximum gasification rates at the peaks of the curves, it can be seen that the increase in gasification rate was not proportional to that of CO₂ partial pressure. The increments become smaller and smaller with the increase in CO₂ partial pressure. Furthermore, it can be noticed that the increase in gasification rate was more remarkable for chars from Shenmu char (GC1-30 and GC1-50) than for those from Tejing char (GC2-30 and GC2-50). By increasing CO₂ partial pressure from 0.2 atm to 1.0 atm, the maximum gasification rate of GC1-30 and GC1-50 increased by 0.91 and 1.26 times, while that of GC2-30 and GC1-50 increased by 0.35 and 0.42 times.

It can also be seen from Figure 15 that the gasification rate of GC1-50 was slower than that of GC1-30 under the same CO₂ partial pressure, whereas the gasification rate of GC2-50 was faster than that of GC1-30 under the same CO₂ partial pressure. The opposite experimental results were caused by the difference between the ash composition of the chars made from Shenmu char and Tejing char, which was discussed in Section 3.1.1.

3.2.4. The Effects of CO₂ Partial Pressure on the Gasification of Different Chars

The apparent reaction orders of the other chars at the conversions of 0.5, 0.7, and 0.9 were obtained through the method in Section 2.4 and are summarized in

Table 9. The apparent reaction order of char gasification by CO₂.

Sample	Conversion	n	KK (s−1)	ARD	GF
RC1	0.5	0.47	8.67 × 10−4	3.7%	0.97
	0.7	0.51	6.31 × 10−4	7.6%	0.90
	0.9	0.64	2.76 × 10−4	19.6%	0.56
PC1	0.5	0.49	1.01 × 10−3	2.0%	0.99
	0.7	0.47	6.56 × 10−4	2.2%	0.99
	0.9	0.46	2.31 × 10−4	0.7%	1.00
GC1-30	0.5	0.40	2.19 × 10−3	1.9%	0.99
	0.7	0.38	1.33 × 10−3	3.1%	0.97
	0.9	0.47	4.49 × 10−4	2.6%	0.98
GC1-50	0.5	0.50	8.20 × 10−4	2.2%	0.99
	0.7	0.46	3.90 × 10−4	4.6%	0.95
	0.9	0.39	8.14 × 10−5	5.2%	0.94
RC2	0.5	0.41	3.70 × 10−3	3.8%	0.97
	0.7	0.51	2.45 × 10−3	9.0%	0.94
	0.9	0.79	8.39 × 10−4	16.7%	0.87
PC2	0.5	0.34	2.33 × 10−3	0.3%	1.00
	0.7	0.44	1.71 × 10−3	0.8%	1.00
	0.9	0.59	6.59 × 10−4	4.9%	0.97
GC2-30	0.5	0.24	5.31 × 10−3	8.6%	0.69
	0.7	0.29	3.14 × 10−3	13.6%	0.56
	0.9	0.57	1.04 × 10−3	5.5%	0.93
GC2-50	0.5	0.33	5.30 × 10−3	2.4%	0.98
	0.7	0.48	3.05 × 10−3	5.0%	0.94
	0.9	0.61	1.06 × 10−3	5.2%	0.96

. It can be seen that most of the values of apparent reaction order were close to 0.5. Those with significant deviation from 0.5 had relatively bigger ARD and GF. This means that the gasification of chars by CO₂ has an order of 0.5, which normally means that the gasification involves dissociative adsorption of CO₂ at the reaction sites.

Table 9 compares the apparent reaction order of different chars at different carbon conversions. Overall, the apparent reaction order of gasification of the same char by CO₂ was lower than that by H₂O, which indicates that the gasification rate by CO₂ was less sensitive to the change in the reactant partial pressure [45]. Relatively speaking, the order of gasification of the chars made from Shenmu char was more stable with the progress of gasification than in those made from Tejing chars. For the latter chars, there seemed to be a trend of increase in the apparent gasification order with the progress of gasification.

3.3. Kinetic Modelling of the Gasification of Different Chars

As discussed in Section 2, the preparation temperature of raw char is much lower than the experimental temperatures in this work, so the structure and carbon content of the raw chars changed significantly during the heating stage before gasification began. For that reason, the structures and carbon contents of the raw chars at the beginning of gasification at different gasification temperatures were different, so raw chars were not used to model the gasification kinetics.

In this section, the gasification of different chars by CO₂ is simulated by different models. The performances of the models on the prediction of the gasification kinetics are compared. The activation energy (E) and the reaction order (n) obtained by kinetic modelling are used to evaluate the effects of temperature and partial pressure of gasification agents. The RPM and MRPM were applied in the work, and the reasons for the choice of the RPM and MRPM are provided in Section 2.5.

For the RPM and MRPM, separate evaluation of the diffusion resistance by the ash layer was not possible because the pore structure and porosity of the layer could not be determined. This was only a part of the diffusion resistance; external diffusion and internal diffusion through the char pores may also affect the reaction kinetics. As a result, the effect of diffusion through the ash layer cannot be evaluated separately via experiments either. More sophisticated modelling would incorporate the effect of stepwise diffusion into the model and set the structure variables as model parameters, which is beyond the scope of this paper. For the above reasons, the effect of diffusion was only qualitatively derived from the experimental and modelling data in this work, and the absence of the quantitative description of the effect of diffusion might contribute to the average relative deviation of the models in this work.

The experimental data were firstly used to fit the model parameters for each experimental condition. The model parameters for all experimental conditions were obtained by fitting the model parameters for each experimental condition. Finally, the calculation results using the model parameters for all experimental conditions were compared with the experimental data.

The gasification rate of chars by CO₂ was fitted by the RPM and MRPM to obtain the model parameters, and then the K × Pⁿ item was fitted with temperature and the partial pressure of CO₂ to obtain the kinetic parameters of the gasification by CO₂. Taking pyrolyzed chars, for example, the fitting results are shown in Figure 16, and the model parameters obtained from fitting the experimental data are shown in

Table 10. Model parameters from fitting kinetic data (gasification rate vs. conversion) of CO₂ gasification of pyrolyzed chars.

Char	Model	T (K)	P (atm)	ψ	Ψ	q	K∙Pn (s−1)	ARD	GF
PC1	RPM	1173	1.0	3.414	NA	NA	2.50 × 10−4	9.2%	0.95
		1273	0.2				5.08 × 10−4	8.6%	0.96
		1273	0.6				8.28 × 10−4	9.0%	0.95
		1273	1.0				1.11 × 10−3	8.9%	0.96
		1373	1.0				2.13 × 10−3	1.2%	1.00
	MRPM	1173	1.0	NA	18.64	1.316	1.58 × 10−4	2.3%	1.00
		1273	0.2				3.21 × 10−4	2.3%	0.99
		1273	0.6				5.23 × 10−4	2.4%	1.00
		1273	1.0				7.01 × 10−4	2.2%	0.99
		1373	1.0				1.36 × 10−3	8.9%	0.95
PC2	RPM	1173	1.0	2.552	NA	NA	8.95 × 10−4	12.3%	0.94
		1273	0.2				1.57 × 10−3	13.8%	0.94
		1273	0.6				2.28 × 10−3	3.3%	0.99
		1273	1.0				2.74 × 10−3	2.8%	0.99
		1373	1.0				5.52 × 10−3	8.7%	0.98
	RPM	1173	1.0	NA	9.27	1.265	6.79 × 10−4	6.7%	0.98
		1273	0.2				1.20 × 10−3	6.6%	0.99
		1273	0.6				1.74 × 10−3	5.6%	0.98
		1273	1.0				2.09 × 10−3	7.1%	0.97
		1373	1.0				4.23 × 10−3	4.0%	0.99

.

It can be seen that the ψ of PC1 and PC2 in the RPM are lower than the ψ of the chars made from peanut shell, maize cob, wheat straw, rice lemma, pine sawdust, and bamboo sawdust (between 8.26 and 2140) [17,46], whereas they are higher than the ψ of the chars made from the heartwood of Pinus elliottii [25]. This indicates that the changes to the internal surfaces of PC1 and PC2 during gasification processes are greater than those to the internal surfaces of the chars made from peanut shell, maize cob, wheat straw, rice lemma, pine sawdust, and bamboo sawdust, but they are not as great as those for the internal surfaces of the chars made from the heartwood of Pinus elliottii. The ψ of PC1 and PC2 in the MRPM are lower than the ψ of the chars made from peanut shell, maize cob, wheat straw, rice lemma, pine sawdust, and bamboo sawdust (between 5.3 and 1870) [17], whereas the q of PC1 and PC2 in MRPM are higher than the q of the chars made from peanut shell, maize cob, wheat straw, rice lemma, pine sawdust, and bamboo sawdust (between 0.234 and 0.837) [17]. This indicates that the changes in the internal surfaces of PC1 and PC2 during gasification processes are greater than those in the internal surfaces of the chars made from peanut shell, maize cob, wheat straw, rice lemma, pine sawdust, and bamboo sawdust, which is consistent with the result found in the RPM.

Then, the pre-exponential factor (k₀), activation energy (E), and reaction order (n) were obtained by correlating the constant item K × Pⁿ in Table 10 with temperature and the partial pressure of CO₂. The correlation plots for the RPM and MRPM are shown in Figure 17 as examples, and the corresponding kinetic parameters are summarized in

Table 11. Kinetic parameters of CO₂ gasification of pyrolyzed chars by modelling.

Char	PC1		PC2
Model	RPM	MRPM	RPM	MRPM
E (kJ∙mol−1)	113.2	114.3	110.0	110.6
k0 (s−1)	43.8	30.8	85.1	69
N	0.4	0.41	0.31	0.31
ARD	15.2%	14.9%	5.9%	5.9%
GF-T	0.989	0.99	0.997	0.997
GF-P	0.920	0.925	0.971	0.971

.

The performance of the gasification of PC1 and PC2 by CO₂ can be predicted using Equations (7) and (8) with the parameters in Table 11, and the accuracy of the models in predicting the rate of gasification is summarized in

Table 12. The prediction accuracy of the kinetic models (gasification rate vs. conversion) of CO₂ gasification of pyrolyzed chars.

T (K)	PCO2 (atm)	Assessment Parameter	PC1		PC2
			RPM	MRPM	RPM	MRPM
1173	1.0	ARD	68.2%	59.0%	30.0%	25.3%
		GF	−2.5	−2.34	0.62	0.65
1273	0.2	ARD	9.2%	2.8%	14.2%	7.2%
		GF	0.95	0.99	0.94	0.98
1273	0.6	ARD	8.7%	2.8%	3.9%	6.0%
		GF	0.95	0.99	0.99	0.98
1273	1.0	ARD	10.8%	9.9%	5.4%	9.4%
		GF	0.85	0.89	0.97	0.95
1373	1.0	ARD	1.8%	9.0%	9.1%	4.0%
		GF	1.00	0.95	0.96	0.99

. GF-T was calculated by Equation (18) using the gasification data under 1.0 atm CO₂ in Figure 17, and GF-T was used to describe the model prediction accuracy of the effect of temperature on the kinetics of gasification. GF-P was calculated by Equation (18) using the gasification data at 1273 K in Figure 17, and GF-P was used to describe the model prediction accuracy of the effect of CO₂ partial pressure on the kinetics of gasification.

The simulation of the gasification rate of partially gasified char residues by CO₂ was also carried out using the same method with gasified chars.

Table 13. Model parameters from fitting kinetic data (gasification rate vs. conversion) of CO₂ gasification of GC1-30 and GC2-30.

Char	Model	T (K)	P (atm)	ψ	Ψ	q	K∙Pn (s−1)	ARD	GF
GC1-30	RPM	1173	1.0	0.564	NA	NA	6.31 × 10−4	7.0%	0.99
		1123	1.0				1.46 × 10−3	4.9%	0.99
		1273	0.2				1.90 × 10−3	7.5%	0.99
		1273	0.4				2.64 × 10−3	4.6%	0.99
		1273	0.6				2.95 × 10−3	5.3%	0.99
		1273	0.8				3.25 × 10−3	7.1%	0.99
		1273	1.0				3.59 × 10−3	7.2%	0.99
		1323	1.0				6.48 × 10−3	4.1%	0.99
		1373	1.0				1.02 × 10−2	11.7%	0.91
	MRPM	1173	1.0	NA	2.414	1.252	5.57 × 10−4	5.7%	0.98
		1123	1.0				1.29 × 10−3	3.3%	1.00
		1273	0.2				1.68 × 10−3	5.3%	0.99
		1273	0.4				2.33 × 10−3	0.9%	1.00
		1273	0.6				2.61 × 10−3	1.6%	1.00
		1273	0.8				2.87 × 10−3	3.6%	1.00
		1273	1.0				3.18 × 10−3	3.7%	1.00
		1323	1.0				5.72 × 10−3	7.3%	0.98
		1373	1.0				8.97 × 10−3	14.6%	0.90
GC2-30	RPM	1173	1.0	0.434	NA	NA	3.20 × 10−3	8.6%	0.97
		1123	1.0				5.98 × 10−3	21.0%	0.96
		1273	0.2				6.46 × 10−3	33.5%	0.94
		1273	0.4				6.79 × 10−3	17.9%	0.97
		1273	0.6				7.24 × 10−3	23.9%	0.94
		1273	0.8				8.36 × 10−3	13.8%	0.98
		1273	1.0				1.01 × 10−2	7.8%	0.97
		1323	1.0				1.26 × 10−2	9.9%	0.96
		1373	1.0				1.69 × 10−2	12.5%	0.87
	MRPM	1173	1.0	NA	5.902	1.457	2.34 × 10−3	4.7%	0.99
		1123	1.0				4.42 × 10−3	9.4%	0.98
		1273	0.2				4.78 × 10−3	18.0%	0.98
		1273	0.4				5.01 × 10−3	6.8%	0.99
		1273	0.6				5.34 × 10−3	12.3%	0.97
		1273	0.8				6.16 × 10−3	2.5%	1.00
		1273	1.0				7.41 × 10−3	9.1%	0.98
		1323	1.0				9.23 × 10−3	9.4%	0.97
		1373	1.0				1.24 × 10−2	20.4%	0.85

and

Table 14. Model parameters from fitting kinetic data (gasification rate vs. conversion) of CO₂ gasification of GC1-50 and GC2-50.

Char	Model	T (K)	P (atm)	ψ	Ψ	q	K∙Pn (s−1)	ARD	GF
GC1-50	RPM	1173	1.0	7.39 × 10−17	NA	NA	2.94 × 10−4	6.6%	0.99
		1123	1.0				6.09 × 10−4	8.7%	0.99
		1273	0.2				7.37 × 10−4	16.9%	0.97
		1273	0.4				1.06 × 10−3	13.7%	0.99
		1273	0.6				1.26 × 10−3	18.8%	0.97
		1273	0.8				1.46 × 10−3	18.9%	0.97
		1273	1.0				1.67 × 10−3	24.0%	0.96
		1323	1.0				2.98 × 10−3	17.9%	0.97
		1373	1.0				4.72 × 10−3	33.3%	0.94
	MRPM	1173	1.0	NA	4.759	1.72	2.38 × 10−4	7.6%	0.96
		1123	1.0				4.94 × 10−4	4.1%	0.99
		1273	0.2				5.98 × 10−4	5.7%	0.99
		1273	0.4				8.63 × 10−4	1.2%	1.00
		1273	0.6				1.03 × 10−3	4.8%	1.00
		1273	0.8				1.19 × 10−3	5.7%	0.99
		1273	1.0				1.36 × 10−3	9.3%	0.99
		1323	1.0				2.44 × 10−3	2.3%	1.00
		1373	1.0				3.92 × 10−3	11.9%	0.98
GC2-50	RPM	1173	1.0	5.78 × 10−16	NA	NA	2.75 × 10−3	4.2%	1.00
		1123	1.0				5.57 × 10−3	3.7%	1.00
		1273	0.2				6.30 × 10−3	34.7%	0.91
		1273	0.4				8.43 × 10−3	12.6%	0.98
		1273	0.6				8.83 × 10−3	14.6%	0.98
		1273	0.8				1.00 × 10−2	9.1%	0.98
		1273	1.0				1.12 × 10−2	3.7%	1.00
		1323	1.0				1.43 × 10−2	9.5%	0.97
		1373	1.0				2.24 × 10−2	12.5%	0.93
	MRPM	1173	1.0	NA	0.0133	1.209	3.06 × 10−3	13.8%	0.95
		1123	1.0				6.33 × 10−3	10.7%	0.99
		1273	0.2				7.26 × 10−3	17.8%	0.97
		1273	0.4				9.62 × 10−3	3.9%	1.00
		1273	0.6				1.01 × 10−2	2.6%	1.00
		1273	0.8				1.14 × 10−2	8.5%	0.99
		1273	1.0				1.27 × 10−2	10.7%	0.99
		1323	1.0				1.59 × 10−2	13.9%	0.94
		1373	1.0				2.48 × 10−2	25.1%	0.82

present the model parameters obtained from fitting. The kinetic parameters of the gasification of partially gasified char residues are summarized in

Table 15. Kinetic parameters of gasification of GC1-30 and GC2-30 by CO₂ from kinetic modelling.

Char	GC1-30		GC2-30
Model	RPM	MRPM	RPM	MRPM
E (kJ∙mol−1)	159.2	159.2	97.2	96.7
k0 (s−1)	11770	10374	86.1	59.9
N	0.34	0.34	0.24	0.23
ARD	11.5%	11.5%	6.8%	6.9%
GF-T	0.99	0.99	0.98	0.98
GF-P	0.97	0.97	0.74	0.74

and

Table 16. Kinetic parameters of gasification of GC1-50 and GC2-50 by CO₂ from kinetic modelling.

Char	GC1-50		GC2-50
Model	RPM	MRPM	RPM	MRPM
E (kJ∙mol−1)	162.0	164.4	119.3	117.2
k0 (s−1)	7016.3	7182.1	771.8	714.4
N	0.451	0.452	0.233	0.218
ARD	11.7%	11.4%	9.6%	10.3%
GF-T	0.99	0.99	0.98	0.98
GF-P	0.98	0.98	0.81	0.78

.

It can be seen from Table 10, Table 13 and Table 14 that the ψ of PC1 and PC2 in RPM are higher than the ψ of GC1-30 and GC1-30, respectively, and the ψ of GC1-30 and GC1-30 in RPM are higher than the ψ of GC1-50 and GC1-50, respectively. This indicates that the changes in the internal surfaces of PC1 and PC2 during gasification processes were smaller than those in the internal surfaces of GC1-30 and GC1-30, respectively, and the changes in the internal surfaces of GC1-30 and GC1-30 during gasification processes were smaller than those in the internal surfaces of GC1-50 and GC1-50, respectively, which is consistent with the experimental results in this work. This means that the pre-gasification decreased the change in the internal surface of char during gasification. It also needs to be noted that the ψ of GC1-30, GC2-30, GC1-50, and GC2-30 are all smaller than the ψ of the chars made from the heartwood of Pinus elliottii, which means the change in the internal surfaces of the partial gasified char residues during gasification processes is smaller than that in the internal surfaces of the heartwood of Pinus elliottii [25]. Since the ψ and q work together to make the modelling results fit the experiment results, and they do not monotonically increase (or decrease) with the increase in ash content, the ψ and q of char residues in the MRPM are not compared with each other or with the literature value, respectively.

The performance of the gasification of GC1-30, GC2-30, GC1-50, and GC2-50 by CO₂ can be predicted using Equations (7) and (8) with the parameters in Table 15 and Table 16, and the accuracy of the models in predicting the rate of gasification is summarized in

Table 17. The prediction accuracy (gasification rate vs. conversion) of the models of CO₂ gasification of GC1-30 and GC2-30 chars.

T (K)	PCO2 (atm)	Assessment Parameter	GC1-30		GC2-30
			RPM	MRPM	RPM	MRPM
1173	1.0	ARD	59.8%	57.7%	34.0%	27.8%
		GF	−0.71	−0.73	0.67	0.64
1223	1.0	ARD	32.9%	31.1%	21.7%	9.9%
		GF	0.46	0.45	0.96	0.98
1273	0.2	ARD	11.8%	9.8%	29.9%	15.1%
		GF	0.97	0.97	0.93	0.97
1273	0.4	ARD	5.2%	3.4%	21.0%	10.3%
		GF	0.96	0.99	0.96	0.98
1273	0.6	ARD	5.1%	1.2%	29.6%	17.5%
		GF	0.99	1.00	0.92	0.95
1273	0.8	ARD	6.8%	3.1%	13.8%	2.5%
		GF	0.99	0.99	0.98	1.00
1273	1.0	ARD	6.6%	2.5%	11.1%	18.7%
		GF	0.98	0.99	0.90	0.91
1323	1.0	ARD	8.6%	11.4%	9.8%	9.8%
		GF	0.97	0.97	0.96	0.97
1373	1.0	ARD	10.9%	14.0%	11.7%	19.9%
		GF	0.90	0.90	0.87	0.85

and

Table 18. The prediction accuracy (gasification rate vs. conversion) of the models of CO₂ gasification of GC1-50 and GC2-50 chars.

T (K)	PCO2 (atm)	Assessment Parameter	GC1-50		GC2-50
			RPM	MRPM	RPM	MRPM
1173	1.0	ARD	52.6%	39.1%	32.7%	27.5%
		GF	−0.01	0.06	0.21	−0.01
1223	1.0	ARD	48.1%	35.0%	13.8%	11.1%
		GF	0.27	0.29	0.95	0.94
1273	0.2	ARD	18.6%	7.6%	42.3%	24.7%
		GF	0.97	0.97	0.89	0.95
1273	0.4	ARD	13.5%	1.9%	9.1%	8.2%
		GF	0.98	1.00	0.97	0.99
1273	0.6	ARD	18.7%	4.7%	13.9%	3.0%
		GF	0.97	1.00	0.98	1.00
1273	0.8	ARD	18.2%	5.2%	5.7%	12.5%
		GF	0.97	0.99	0.97	0.98
1273	1.0	ARD	21.9%	7.4%	9.9%	21.0%
		GF	0.95	0.98	0.95	0.93
1323	1.0	ARD	16.1%	4.4%	11.9%	10.6%
		GF	0.96	0.99	0.96	0.93
1373	1.0	ARD	34.9%	13.3%	12.4%	25.1%
		GF	0.94	0.98	0.93	0.82

.

In general, MRPMs are better than RPMs in both fitting and predicting the gasification rate of different chars by CO₂, especially when the ratio of the maximum rate and initial rate (r_max/r_o) changes with operating conditions. In addition, the MRPM correctly fits most of the experimental gasification rate curves of the chars with peak gasification rates, but the RPM sometimes fails in predicting the peaks. Since there is only one model parameter ψ in the RPM, r_max/r_o is fixed when the position of a peak X_M is fixed. In the MRPM, the introduction of an additional parameter q allows r_max/r_o to change even when X_M is fixed, which makes the MRPM more adaptable in fitting and predicting the gasification rate.

The parameter ψ in the RPM and parameter Ψ in the MRPM are related to the original pore structure of char particles, and the parameter q in the MRPM is related to the particle shape, all being the properties of the chars before gasification. These parameters do not change with the experimental conditions in models. The structure of the same char is assumed to be the same in the RPM and MRPM. For this reason, the X_M of the same char under different operating conditions is assumed to be the same in the RPM and MRPM [17,31,47,48]. But in the actual experiments, the structures of the samples taken from the same char were different when the gasification began. This is because there was a heating stage before the gasification started, and factors such as temperature, heating rate, and the heating time may affect the structure of the particles, which adds uncertainty to the model fitting.

In addition, chars are not homogeneous substances, which also adds uncertainty to the model fitting. For this reason, in the actual experiments, the X_M of the same char under different conditions can be different. Since the X_M of the same char in the models is limited as a unique value for different experimental conditions, the performance of the models in fitting the gasification rates of the same char with significantly different X_M values is not as effective as for those which have similar X_M values.

The values for the activation energies of different chars reacting with CO₂ obtained from the experimental data and by model fitting in Section 3.3 are summarized in Figure 18. The experimental values of the activation energy presented in Figure 18 are the average values of those obtained at 0.5, 0.7, and 0.9 carbon conversion. It can be seen from Figure 18 that the activation energies of the char samples in this work are in the range reported in the literature studies shown in

Table 19. Comparison of the activation energy values with those reported in the literature.

Reference	E (kJ/mol)
	VM	GM	RPM	MRPM
This work	-	-	91.5–162.0	93.6–164.0
[17]	128.4	129.1	129.8	163.7
[17]	144.4	145.4	146.4	132.8
[17]	163.5	163.6	163.3	153.2
[17]	183.5	181.2	180.3	149.5
[17]	140.7	141.2	143.3	144.7
[17]	171.5	171.1	168.1	162.7
[49]	-	-	125.7	-
[50]	197	-	-	-
[46]	-	-	203–238	-
[46]	-	-	232–249	-
[51]	-	-	125	-
[25]	183.9	184.5	184.3	-
[25]	245.3	246.2	246.1	-

.

It can be seen from Figure 18 that the activation energies (E) for the same char by the RPM and the MRPM are the same, and the reaction orders (n) for the same char by the RPM and MRPM are similar, which is consistent with previous research [17,24]. The activation energy values of the chars from Tejing char are smaller than those of the chars from Shenmu char for pyrolyzed chars or for circumstances in which their ash contents are made similar by partial gasification, which indicates chars from Tejing char are more reactive than chars from Shenmu char. This is consistent with the experimental data.

The activation energy values obtained directly from the correlation of experimental data showed larger deviation from those obtained from the RPM and MRPM. This may be related to the variation in the structure change during gasification. The chars made from the Tejing char have lower activation energies than those made from the Shenmu char when their ash contents are similar. The higher reactivity of the chars from Tejing char is attributed to differences in their ash content and mineral composition. As discussed previously, the ash from Tejing char has a significantly higher content of potassium, which is well known to be highly active in catalysing the gasification of carbonaceous materials.

The change in the activation energy of a char with the extent of partial gasification is complex, and no single rule can be applied to predict the change. The activation energy of PC1 in gasification by CO₂ is significantly smaller than that of partially gasified char residues GC1-30 and GC1-50, and the partially gasified char residues have similar activation energy values. The lowest temperature tested in the work was 1173 K, which is 13 K higher than the decomposition temperature of CaCO₃ [52]. According to the literature [52], CaO in the ash has significantly higher activity below the decomposition temperature due to its capacity to hold CO₂ on the catalytic sites. Although the nominal testing temperature of 1173 K is higher than the decomposition temperature of CaCO₃, due to the strong endothermic effect of the gasification reaction, the actual reaction temperature, as measured by thermocouple in the reactor, decreased to below the decomposition temperature of CaCO₃, which resulted in a faster gasification of PC1 than what was predicted by the models. As such, a lower apparent activation energy was obtained by modelling. The predicted rate of gasification of PC1 at 1173 K is only 50% of that measured in experiments (Figure 18), which confirms the significant effect of CaCO₃ formation on the catalytic activity due to the endothermic effect. The formation of CaCO₃ at temperatures below its decomposition temperature has been demonstrated in the literature [52].

It can be seen from Figure 18 that GC2-30 has the lowest activation energy for gasification by CO₂ among those of the chars made from Tejing char. In gasification by CO₂, the activation energy of PC2 is about the same as for PC1, which may have included the effect of endothermic reaction and CaCO₃ formation. The significantly lower activation energy values of GC2-30 and GC2-50 in comparison with GC1-30 and GC1-50 are attributed to differences in the mineral compositions of the ash, especially the difference in the contents of K₂O and CaO. Obviously, the rates and activation energy values of the gasification reactions are complex and affected by many factors, which is worthy of further detailed investigation.

The reaction order of different chars reacting with CO₂ obtained by direct fitting of the experimental data and by kinetic modelling, which were obtained in Section 3.3, are summarized in Figure 19.

Similar to activation energy, the order of gasification changes depending on the char, the gasification agent, and the ash content. The complexity of the ash composition of the char samples becomes more serious due to its change with the progress of gasification. A better understanding of the gasification kinetics would need detailed analysis of the ash composition and its change during gasification in further study.

4. Conclusions

This paper investigated the gasification of different chars to reveal the gasification behaviours of char residues; apparent activity energy and apparent action order were used to discuss the effects of temperature and CO₂ partial pressure on the gasification kinetics. The chars with different ash contents were prepared from Shenmu raw char and Tejing raw char, and they were gasified by different CO₂ gas mixtures at different temperatures. The gasification process of char residue was different from the end stage of the gasification process of the corresponding raw char: the gasification rate of the char residue increased at first and then decreased, whereas the gasification rate of the corresponding raw char kept decreasing during the end stage of gasification. The highest gasification rate was achieved at a lower conversion in the gasification of char residue than in the gasification of the corresponding raw char. Catalytic minerals, high temperature, and high CO₂ partial pressure benefited the gasification of gasified char residues. The char residues that contained more catalytic minerals (the char residues made from Tejing) were more reactive in gasification and were less sensitive to changes in temperature and CO₂ partial pressure. The MRPM fits the experimental results better, because the MRPM does not limit the conversion where the highest gasification rate is achieved.