Catalytic coal gasification, using alkali metal salts as catalyst (primarily potassium carbonate) to accelerate coal gasification rate and to produce a high-value methane-rich gas, enables the operation of pressurized fluidized bed gasifier at lower temperatures. This process establishes thermodynamically favorable conditions for methane production. Within the same reactor, endothermic steam gasification reaction and exothermic methanation occur, resulting in reduced reaction temperature (973 K) and an increased thermal efficiency. Catalytic coal gasification is poised to become a more promising technology for converting coal to synthetic natural gas (SNG) in the future.

Numerous studies have been conducted on lab-scale experimental results, such as catalyst properties, processes, and reactors, which are thoroughly reviewed by our previous work (Li et al. 2021). However, knowledge regarding the reactions and hydrodynamics with large scale gasifier is limited, particularly in the context of commercialization. Consequently, this review concentrates on catalytic mechanisms, kinetic modeling, and reactor modeling.

The process of chemical reactions can be profoundly understood through the catalytic reactions mechanisms. These mechanisms not only aid in modifying the structure of catalysts to enhance their activity but also provide a theoretical foundation for establishing kinetic model. Figure 1 illustrates a typical catalytic reaction mechanism for various catalysts, including Na (Bai et al. 2023), K (Kopyscinski et al. 2014), Ca (Zhang et al. 2021) and Fe (Mahamulkar et al. 2016). Several comprehensive reviews have identified the primary catalytic mechanisms, which include electron transfer mechanism, oxygen transfer mechanism, electrochemical mechanism, and free radical mechanism (Lobo and Carabineiro 2016; Sams and Shadman 1986; Wood and Sancier 1984; Wen 1980; McKee 1983). These mechanisms are described in detail across different chemical reactions.

Mechanism for varoious catalysts. a Na/Ca (Bai et al. 2023) b K (Kopyscinski et al. 2014) c Ca (Zhang et al. 2021) d Fe (Mahamulkar et al. 2016)

2.1 Catalytic C–O₂ reaction mechanism

It is widely acknowledged that the catalytic C–O₂ reaction in coal gasification primarily proceeds through two mechanisms: the electron transfer mechanism and the oxygen transfer mechanism. Many researchers have focused on elucidating the processes catalyzed by alkali metal carbonates, particularly through the electron transfer mechanism. This mechanism suggests that the introduction of catalysts leads to a redistribution of electrons within the graphite structure, which weakens the C–C bonds and alters the length and integrity of the C-O bonds. Consequently, the electronic properties of graphite may be modified by the formation of intermediates, thereby affecting the reactivity of the surface carbon atoms. In contrast, the oxygen transfer mechanism involves metal oxides acting as oxygen carriers to facilitate the transfer of oxygen from the gas phase to the carbon surface. For this mechanism to operate, the metal must be capable of existing in two valence states to sustain a redox cycle on the carbon surface. During the alkali metal-catalyzed C–O₂ reaction, alkali metal atoms act as oxygen adsorption sites, altering the ionization capability of the surface carbon atoms. This leads to the formation of active intermediates, such as oxides and peroxides (M₂O_1+n), which weaken the C–C bonds and facilitate the desorption of gaseous oxidation products at lower temperatures. The process can be further described as follows (R1 to R3):

2.2 Catalytic C–H₂O reaction mechanism

The catalytic C–H₂O reaction is underpinned by various mechanisms, including redox mechanism, intermediate compound mechanism, free radical mechanism and mixed mechanism.

2.2.1 Redox mechanism

The redox mechanism is illustrated by the following reactions (R4 to R6):

Evidence supporting this mechanism includes the detection of metal K products, the inhibitory role of CO, and the change in reaction rate when D₂O is used instead of H₂O.

2.2.2 Intermediate compound mechanism

Numerous intermediate compounds are proposed to exist during catalytic coal gasification. The C_nK mechanism as intermediate compounds are described by reactions R7 to R10:

To account for the gasification rate, which is solely related to the catalyst amount after accounting for its reaction with ash, and independent of the forms of carbon (e.g., active coal char and amorphous carbon) and the preparation methods (e.g., impregnation, dry mixing, and ion exchange), the K-Char-O mechanism is proposed, as shown in reactions R11–R13:

This mechanism was verified by comparing the structure of char with and without K₂CO₃ using XRD and laser Raman techniques (Zhang et al. 2016). The degree of graphitization and condensation of coal char was found to be inhibited by the addition of catalysts, which leads to a redistribution of electrons and weakening of the π-bonds in coal char. In the case of Na₂CO₃, Na-char was identified as a reactive intermediate (Tsubouchi et al. 2017).

Other intermediate compounds have also been proposed, such as C(O), determined as the instantaneous reaction rate of gas products by infrared micro-flow and thermal conductivity technologies (Hong et al. 2013). Additionally, K⁺-O-C formed by the reaction of carbon with K₂CO₃ verified using ¹³C-labeled methyl groups and nuclear magnetic resonance. Other compounds include KOH and K–O–C*, formed by K–O or it reacted with steam (Wu and Wang 2018).

A new active site/intermediate mechanism is often used for Ca-catalyzed gasification. The commonly observed intermediates include CaCO₃, CaO, and Ca oxygen complexes (Cazorla-Amoros et al. 1995; Lizzio and Radovic 1991; Kapteijn et al. 1986). This mechanism successfully explains the changes in gas composition, particularly the ratio of CO/CO₂ and H₂/(2CO₂ + CO), as carbon conversion progresses (Zhang et al. 2021). The typical mechanisms are shown as reactions R14-R16:

In the case of Fe-catalyzed gasification, the active centers include Fe(O), C(O), Fe₃O₄, and FeO (Popa et al. 2013a). The reactions are shown in R17-R19:

Some authors have suggested that FeO and Fe₃O₄ are active centers, with the detailed mechanism shown in reactions R20-R22:

For K–Ca composite catalysts, one proposed mechanism involves Ca reacting with acidic minerals to protect K. This was verified by TG, DSC, and XRD analyses comparing Ca(OH)₂ with CaCO₃ (Tang et al. 2013). Another mechanism involves the formation of a low-melting eutectic bimetallic oxide that reacts at the edge recession of carbon (Pereira et al. 1990, 1992), which is beneficial for the formation of C(O) or C-O-K. This was confirmed by detecting calcium species through XRD, TG/DSC, SEM, and XANES (Hu et al. 2013; Jiang et al. 2013, 2012; Wang et al. 2010). For Na–Ca composite catalysts, the mechanism is similar to that of K–Ca, involving Ca reacting with minerals to protect Na, as supported by Raman, SEM–EDS, and thermodynamic equilibrium calculations. In the case of Ca–Mg composite catalysts, a channeling reaction model is more suitable due to the majority of mineral particles being inserted into the char, resulting in the formation of more pores. Mg occupies more active sites than CaO, leading to a predominantly inhibitory effect. For Na-Fe composite catalysts, the vaporization of sodium is inhibited by the addition of Fe, and the formed Na₂CO₃ is beneficial for catalytic coal gasification. The dispersion of Fe is inhibited by Na (Jiang et al. 2019). Another explanation for the increased Fe mobilization and the formation of intermediates (α-NaFe₂O) suggests that Na-Fe has high catalytic activity (Monterroso et al. 2014). The proposed mechanism is shown as reactions R23 to R24:

2.2.3 Free radical mechanism

The concentration, stability, and chemical environment of free radicals in coal have been extensively studied using electron spin resonance spectrometry (ESR). These properties are closely related to coal rank, maceral type, heat treatment temperature, and the presence of impurities. The predominant stable radicals are aromatic n-radicals. An irreversible and inhomogeneous broadening of the free radical resonance line has been observed, which is attributed to interactions between unpaired electrons and electric fields associated with metal cations that have reacted with the carbon structure in situ ESR. In terms of the free radical mechanism, unpaired electrons in the K₂CO₃-C mixture interact with carbon atoms to form K-C bonds, subsequently weakening C–C bonds. This process involves the rupture of aromatic rings, leading to the formation of aliphatic rings with heightened reactivity (Wood and Sancier 1984).

2.2.4 Mixed mechanism

However, none of the aforementioned mechanisms can fully explain the composition of the product gas during catalytic steam coal gasification. By modifying the oxygen transfer mechanism and intermediate mechanism, a new redox reaction mechanism has been proposed (Wang et al. 2009a):

Herein, the productions of CO and CO₂ are limited by reactions (R27) and (R28).

2.3 Catalytic C–CO₂ reaction mechanism

Various mechanisms facilitate the catalytic C–CO₂ reaction in coal gasification, including the redox reaction mechanism, intermediate compound mechanism, electrochemical mechanism, and carbon dioxide activation mechanism, among others.

2.3.1 Redox reaction mechanism

The redox reaction mechanism involves the reaction between alkali metal carbonates and carbon, resulting in the formation of alkali metals. These metals are then oxidized by CO₂ to produce alkali metal oxides, which subsequently revert to alkali metal carbonates. This cycle is represented by reactions R30 to R32:

To support this mechanism, the presence of the metal (M) should be detected. However, based on in situ XRD, TPD, and ¹³C labered experiments, the metal (M) was not observed. Instead, changes in catalyst forms were observed, such as carbonate decomposition and conversion to hydroxide (isotope-labeled carbon), the formation of metal-rich nonstoichiometric oxides (Knudsen cell mass spectrometry), thermodynamically stable alkali metals (TGA and thermochemical calculations), evidence of a redox cycle (XPS, Knudsen cell mass spectrometry, and IR spectrometry), highly mobile species as liquid films (SEM, EDAX, CAEM), reactions at the edges of aromatic arrays (CAEM), and surface K⁺ phenolate ions (NMR).

The catalytic mechanisms of Ca, Ni, and Ce are similar to those of alkali metals, but the active centers are found to be CaO (He et al. 2020), Ni-Oads, or CeO₂vacO (Jiao et al. 2020). The CaCl₂ is transformed into CaO, following an oxidation–reduction mechanism. The active centers are CaCl₂ and CaCO₃. For Ni, both Ni and NiO actes as active centers (He et al. 2020).

2.3.2 Intermediate compound mechanism

The intermediate compound mechanism is depicted in R33 to R36

Research on active intermediates has been summarized by Jiang et al. (2017), including loosely bonded metal–oxygen complexes, intercalated metal–carbon complexes, and tightly-bonded metal–oxygen complexes supported by thermogravimetry (TG) (Wigmans et al. 1983), phenolate groups detected by solid-state ¹³C NMR (Mims et al. 1982; Mims and Pabst 1983), C-O-K phenolate-type groups inferred using molecular orbital calculation, TPD, and IR (Chen and Yang 1993), Na₂O-Na₂O₂ cycles based on isotope labeling and temperature programmed desorption/reduction (TPD/R) (Saber et al. 1988; Kapteijn and Moulijn 1983), sodium clusters (Na_n-C) and cluster-containing oxygen (Na_n(O)-C) based on pulse reaction, isotope labeling, and TPD/R (Suzuki et al. 1992), potassium phenolate species and a covalently bound carbonate group (dimethyl carbonate) based on DRIFTS, K-C complexes detected by K vapor, or C₄₈K and C₆₀K (C_nK) metals observed in blue and red flames, hydrides based on the thermochemical stability of LiH, reduction of alkali carbonates, and H/C ratio.

Three mechanisms for K₂CO₃-catalyzed coal gasification are detailed shown in Fig. 2. As shown in Fig. 2a, –COK is initially formed at the surface of carbon with the interaction of K₂CO₃, producing CO₂. If there is less oxygen in the carbon (graphite), –COK changes to K-C, producing CO, and subsequently decomposes to K. If there is an abundance of oxygen on the carbon surface, –C-O-K is formed. This is supported by weight loss, CO and CO₂ production, and a comparison of K₂CO₃ loading on graphite and coal (Jiang et al. 2017). As shown in Fig. 2b, there are three intermediates: K₂O₂-C, K₂O-C, and K₂-C, which can transform between each other through cooling with or without H₂O and heating to release CO, CO₂ and H₂. The K₂-C generated at higher temperatures has a strong ability to absorb oxygen from H₂O. The phenomena of H₂ yield, initial reaction rate, and the ratio of H₂/(2CO₂ + CO) can be well explained (Zhu et al. 2015). As shown in Fig. 2c, there are three intermediates: K₂O₂–C, K₂O–C, and C(O). With the addition of H₂O, K₂O–C reacts with H₂O to produce H₂, CO is produced through C(O), and CO₂ is produced from K₂O₂–C (Wang et al. 2009a). The first two mechanisms are similar and more reasonable to explain the gas composition and the formation of K metal. The third mechanism, however, cannot explain the formed K metal. Other potassium salts (KCl and KOH) behave similarly to potassium carbonate (Qiu et al. 2022).

The typical catalytic mechanism for K₂CO₃. a Jiang et al. (2017) b Zhu et al. (2015) c Wang et al. (2009a)

In the case of Ca-catalyzed gasification, one mechanism involves the formation of a hyperoxide intermediate (CaO⋅O) (Zeng et al. 2019; Sears et al. 1980), as depicted in reactions R37-R39. Another mechanism suggests that CaO is first carbonated and then exchanges oxygen with the free active sites on coal char in two steps (Cazorla-Amoros et al. 1992), as shown in reactions R40-R42. The high catalytic activity is attributed to the organic calcium species produced in lignite, which connect with aromatic fused rings through O–Ca bonds and attract electrons on the condensed rings toward them, altering the delocalization of electron distribution. This results in a higher likelihood of aromatic C–C bond disintegration, as indicated by XPS analysis (Lin et al. 2021).

For Fe-catalyzed gasification, the mechanism is presented in reactions R43 to R46 (Domazetis et al. 2012), with [Fe–C], [Fe–C-OH₂], and [Fe–C–O] as intermediate active products.

2.3.3 Electrochemical mechanism

Electrochemical mechanisms involve electron transfer mechanisms and oxygen transfer mechanisms. Above the melting point of alkali metal carbonates, a molten electrolyte forms on the carbon surface. The following reaction occurs at the anode:

Concurrently, alkali metal cations migrate to adjacent cathodes through the carbon surface, facilitating the CO₂ reduction reaction and electron transfer:

The active site in this process is CO₃²⁻, which is similar to O²⁻. Evidence for this mechanism includes the formation of peroxide ions (O²⁻) during the Na₂CO₃-catalyzed gasification process. The oxygen activity in a carbonate-eutectic melt changes, which can be monitored using a solid electrolyte sensor. Voltammetric sweeps in an electrochemical cell with a molten sodium carbonate electrolyte have been observed. If there is no clearly defined cathode and external path for electron transfer, the catalyst mechanism cannot be considered electrochemical.

2.3.4 Carbon dioxide activated mechanism

Recently, a new catalytic mechanism without forming intermediate compounds has been proposed, named carbon dioxide activated mechanisms (Mei et al. 2021), as shown in reactions R50 to R52

The carbon dioxide is first activated at the surface of the catalyst (e.g., Na₂CO₃) and forms CO and O*. The O* then attacks the carbon matrix to form CO*, and finally converts to CO. This mechanism was verified by comparing the reactions between C–CO₂ and Fe–CO₂, TGA, XRD, and in situ heating with a microscope were used to detect mass change rate, phase transformation, and particle size change.

2.3.5 Other mechanisms

For Fe-catalyzed gasification, the increased reaction rate may be due to increased active sites and CO₂ molecular stability, as calculated by DFT (Wang et al. 2021).

For Na–Ca catalyzed gasification, with the addition of Na₂CO₃, the aggregation of Ca was inhibited, and the dispersity increased, based on elemental mapping analysis of char residues (Liu et al. 2022; Yu et al. 2023; Gao et al. 2017). This was also verified by Mei et al. (2019), who found that Ca inhibits the reaction between Na, Si, and Al, as detected by FT-IR and FactSage. At high temperatures, Na reacts with Ca and Si to form sodium silicate and calcium silicate phase.

For Ca-Mg catalyzed gasification, the sintering of CaCO₃ can be effectively inhibited by the formation of tiny MgO particles, which then increase the dispersion of Ca. This was verified by comparing the gasification performance of DCa and DCa-Mg char (Yu et al. 2020).

2.4 Catalytic carbon monoxide methanation mechanism

It is commonly believed that Ni is the most effective catalyst for methanation. There are two mechanisms for catalytic methanation (Gao et al. 1990). One is the carbide mechanism, where carbon monoxide dissociates to form active carbon, which is then hydrogenated to methane. The other is the oxygen-containing complex mechanism, where an oxygen-containing complex (e.g., CH₂O) forms on the catalyst surface and is then reduced to methane. Many researchers have supported carbide mechanism. During the catalytic carbon monoxide methanation process, the activation of carbon monoxide is important. With the introduction of water, the rate of carbon monoxide hydrogenation to methane decreased, but the rate of carbon conversion to methane increases (Kimura et al. 1985). The influences of mixed components including H₂O, H₂, CO₂ and CO on the methane generation rate were also investigated. At low reactivity of gas-phase carbon species, methane is formed by the reaction of carbon and hydrogen rather than carbon monoxide or carbon dioxide. At higher reactivity, methane is formed by gas phase carbon oxides produced by carbon deposition (Mims and Krajewski 1986).

The mechanism of K₂CO₃ for catalytic carbon monoxide methanation is as follows (Otake et al. 1984):

where, * refers to adsorption vacancy on surface; (A) refers to adsorption active site of A.

The rate-determining step involves the hydrogenation of (CH), and the dissociation of carbon monoxide and hydrogen on the adsorption vacancies formed by alkali metal K, leading to the formation of reactive intermediates for methane production (Otake et al. 1984).

Based on these findings, the following reaction mechanism has been proposed (Meijer et al. 1992):

where, * is alkali metal in its reduced state; CO–* is adsorbed CO on the site. C' is activated carbon. The formation of methane depended on whether C' reacts with hydrogen or dissociated into carbon.

The mechanism of catalytic carbon gasification consists of three steps, carbon dissolution, carbon bulk diffusion, and surface reaction. Carbon exchange is a critical intermediate pathway during catalytic gasification process (Domazetis et al. 2012). Moreover, the formation of oxygen-containing functional groups is also vital for the catalytic process (Mei et al. 2021). Hence, further investigation into the mechanism of catalytic carbon monoxide methanation is warranted.

2.5 Comments for different mechanisms

Based on literature research, evidence supports the redox mechanism and the formation of intermediate compounds. However, few studies have explored the kinetic performance in relation to these mechanisms. Future research should focus on the relationship between reaction mechanisms, kinetic models, and methanation formation mechanisms, especially for coal-to-SNG technologies. A sound mechanism should explain the gas product compositions (H₂, CO, CO₂, etc.) and the changing process of the catalyst more reasonably, using methods such as TG, XRD, NMR, SEM, EDAX, CAE, IR, DFT, and thermochemical calculations.

Reaction kinetics, a pivotal aspect of catalytic coal gasification, offers a theoretical guidance for the design and scale-up of reactor. Numerous kinetic models for coal gasification have been proposed, such as volume reaction model, shrinking core model, random pore model, grain model, and integrated model. In the context of catalytic coal gasification, a fundamental approach to establishing kinetic model involves introducing a correction coefficient to account for the effect of catalysis. To date, several kinetic models for catalytic coal gasification have been proposed and applied, such as modified volume reaction model, modified shrinking core model, modified random pore model, extended random pore model, active extended position model, and active site/intermediate mechanism model. The common used types are Langmuir–Hinshelwood (L–H, Eq. (1)) and Power Law models (Eq. (3)).

where, x is carbon conversion; t is reaction time, s; k_1i are constant, i refers to 1, 2, 3, 4, 5 and 6; \(P_{{\text{i}}}\) is partial pressure of gas i, such as H₂O, H₂, CO and CO₂, Pa.

To explain the increased reaction rate at low carbon conversion values, Schumacher et al. (1986) modified the L–H equations by adding two terms in the numerator to account for contribution of hydrogasification (Eq. (2)).

The Power Law model (PLM) is shown in Eq. (3).

where, k₃ is constant; a_3j is reaction order, j refers to 1, 2, 3 and 4.

The L–H model can be used to reflect the adsorption and desorption of reactants and products. The PLM can be used to determinate the reaction order, which is closely related to the contact extent between carbon atoms and the catalyst (Leonhardt et al. 1983). A negligible difference was found in catalytic activities of potassium carbonate prepared by dry mixing and impregnation methods, suggesting that the catalyst has high mobility and the reaction order is zero. The minerals in coal significantly affect the reaction order (Huhn et al. 1983). A uniform reaction order can adequately describe low-ash coal but is unsuitable for high-ash coal. This is mainly due to complex interactions between the catalyst and the coal during gasification process, such as catalyst deactivation and changes in the reaction surface area. Therefore, the reaction order cannot be described by a single model alone.

3.1 Volume reaction model (VRM)

The assumptions of the Volume Reaction Model (VRM) encompass the following aspects:

1. (1)

   Active sites are uniformly distributed across the coal surface.

2. (2)

   The coal–gas reaction takes place at these active sites.

3. (3)

   The reaction rate is directly proportional to the surface area of the coal, which progressively diminishes as conversion increases with reaction time.

4. (4)

   The gasification reaction takes place uniformly at particles surfaces.

5. (5)

   As the reaction moves forward, although the particle size appears constant, the density decreases.

This is illustrated in Fig. 3a and is described by Eq. (4)

where, k₄ is constant.

Kinetic models. a Description of volume model, shrinking core model and random pore model. b Comparison of results

Kim et al. (2014) introduced a Modified Volume Reaction Model (MVRM) as shown in Eq. (5)

where, α₅ and β₅ are model parameters that reflect the change in carbon conversion over time.

Although this model is widely used due to its simplicity, it fails to capture the maximum reaction rate. The MVRM can be utilized to model the reaction rate as a declining line and an S shaped curve over time.

3.2 Shrinking core model (SCM)

The Shrinking Core Model (SCM) posits several assumptions regarding the process of coal gasification:

1. (1)

   The active sites on the coal particles decrease in size as gasification proceeds.

2. (2)

   The particles are uniform, non-porous grains with size constant. The reaction initially takes place on the particle surface, after which the reaction zone moves deeper into the solid, leaving a product layer behind.

3. (3)

   The reaction surface shrinks over time, and the size of the un-reacted core diminishes gradually until it is entirely consumed.

4. (4)

   Gaseous reactants react with the un-reacted core after diffusing through the ash layer.

This is illustrated in Fig. 3a and the reaction rate is given by Eq. (6):

where, k₆ is reaction rate constant.

To account for the influence of catalyst capacity, amount and stagnation, Zhang et al. (2003) proposed a Modified Shrinking Core Model (MSCM) by introducing an effective factor \(f\) into SCM, as shown in Eq. (7):

where, k₇ is reaction rate constant; \(f\) is effective factor; \(C_\text{A}\) is concentration of reactant in gas phase; \(C_{i}^{*}\) is concentration of reactant on reaction interface at equilibrium.

This model can describe the reaction both inside and outside the char but, like the VRM, it fails to capture the maximum reaction rate.

3.3 Grain model (GM) or Integrated model (IM)

The GM model posits that the reaction predominantly takes place on the outer surface of the char particle, specifically with the agglomeration of smaller, uniform-sized spherical grains. This is because gasification reactions within the pores are hindered by mass transfer limitations. Concurrently, as the reaction unfolds, the gasification rate diminishes as the size of the coal particles reduces, subsequently leading to a decrease in their total external surface area.

The reaction rate in the Grain Model (GM) is given by Eq. (8):

where, k₈ is reaction rate constant; m is reaction order.

This model combines the advantages of both the VRM and the SCM but it is unable to describe the maximum reaction rate.

3.4 Random pore model (RPM)

The Random Pore Model (RPM) posits that reactions occur at the interfaces of internal pore surfaces of char particles. During coal gasification, it is assumed that the cylindrical pores of varying diameters expand as their internal surfaces worn away by the progression of the reaction, ultimately coalescing and resulting in a peak reaction rate.

This is illustrated in Fig. 3a and the reaction rate in RPM is given by Eq. (9):

where, k₉ is reaction rate constant; \(\phi\) is structure parameter.

To account for the increasing active surface area and sites, Wang et al. (2006a) introduced a Modified Random Pore Model (MRPM) by incorporating a catalytic factor (\(\exp [x(c - x)]\)).The expression is shown in Eq. (10).

where, A₀ is initial constant gasification rate, primarily determined by the reaction temperature; c is an empirical constant that reflects catalytic ability.

To enhance the accuracy of predicting reaction rates at high carbon conversion (above 70%), Liu et al. (2003) also modified RPM using a structural factor (\({\text{exp( - }}\varphi \tau {)}\)) in Eq. (11).

where, k₁₁₀ is reaction rate constant.

To elucidate why the reaction activity of Ca was high at low carbon conversions and that of K was high at high carbon conversions, Zhang et al. (2010) proposed an extended random pore model (EPRM) to consider the impact of catalyst type and loading. The model is presented in Eq. (12):

where, k₁₂₀ is constant; θ and p are empirical constants that reflect changes of pore structure and surface area, respectively.

This model could be employed to simulate the maximum reaction rate and is more appropriate for catalytic coal gasification.

3.5 Active extended position model (AEPM)

The assumptions of the AEPM were shown as follows:

1. (1)

   The gasification reaction occurs specifically at the active sites. This process involves three distinct stages: generation, expansion, and extinction. It’s important to note that the formation of active sites is not instantaneous.

2. (2)

   The rate at which active sites are generated is directly proportional to the number of sites. During the gasification of char, the production of active sites is simultaneous with the progression of the gasification reaction itself.

3. (3)

   It is hypothesized that active site expansion, which is believed to be spherical, occurs in all three spatial dimensions (x, y, z). The growth in each direction is proportional to time, with the expansion rate remaining constant throughout the process.

4. (4)

   The generation of active sites during gasification reactions is a process that is both time and spatially dependent.

To represent the number of active sites and reaction surface area, Wang et al. (2006b) proposed the Active Site Extended Position Model (ASEPM) model, as shown in Eq. (13):

where, x_c is carbon conversion at critical stage; k₁₃₁ and k₁₃₃ reflect the effect of temperature; k₁₃₂ and k₁₃₄ reflect the effect of catalyst type.

This model has divided the reaction rate into two parts, which may not be convenient for practical application.

3.6 Active site/intermediate mechanism model (ASIMM)

The assumptions of the ASIMM were shown as follows:

1. (1)

   The effective carbon concentration varied as carbon conversion progressed.

2. (2)

   The K–O–C* complex was not observed. Therefore, it is hypothesized that the concentration of effective carbon [C] remains constant until the peak of the gasification rate, after which it decreases linearly with increasing carbon conversion.

3. (3)

   The pathway for the formation of carbon monoxide (CO) differed from the pathway for the formation of carbon dioxide (CO₂).

Recently, Wu et al. (2016) and Tang et al. (2015) developed an Active Site/Intermediate Mechanism Model (ASIMM) (Eq. (14)) to describe the maximum gasification rate and gas composition for K₂CO₃ catalyzed steam gasification of ash-free coal, based on the active site/intermediate mechanism.

where, α₁₄ and β₁₄ are catalysis factors; k₁₄₁ and k₁₄₂ are reaction rate constant; \(\theta_{a} (t)\) and \(\theta_{b} (t)\) are the dimensionless concentration of moles numbers of K–O–C * and K–O–C(O).

This model was formulated based on catalytic mechanism, considering the maximum gasification rate and gas composition, and holds promise for practical application.

3.7 Comparison of different types of kinetic model

Selecting the appropriate model type is the first step in establishing a kinetic model. For K₂CO₃-catalyzed steam gasification, RPM generally exhibits better performance than VRM and SCM (Li et al. 2014a), as shown in Fig. 3b. SCM and RPM can adequately describe both non-catalytic and Na₂CO₃-catalyzed processes (Popa et al. 2013b). For CO₂ gasification, MVRM demonstrates significantly superior performance over VRM and SCM (Kim et al. 2014). When using GM, IM, and RPM models for the Na₂CO₃-catalyzed process, there is minimal difference (Zhang et al. 2017). The SCW model outperforms RPM model (Li 2014). For ash-free coal mixed with 20 wt% K₂CO₃, the ERPM shows better performance than IM, VRM, RPM, and SCM. Compared to SCM and RPM, ASIMM model exhibits a stronger ability to reflect catalytic deactivation and changes in char structure (Tang et al. 2015). If the catalyst is more likely to adhere to the surface of coal particle, the RPM model is more suitable. If not, the SCM model is preferred (Zhang et al. 2017). During catalyst coal gasification, char particles may not always maintain a spherical shape, making the IM more suitable. If there is a maximum reaction rate during catalytic coal gasification, it is essential to establish a more appropriate kinetic model to describe the process more accurately.

The second step in establishing a kinetic model involves selecting relevant influencing factors. Common factors considered in the kinetic models include temperature, pressure, reactants (eg., H₂O), products (eg., H₂, CO and CO₂), catalyst loading, coal structure factors (such as pore length, surface area, and void fraction), and coal properties (ash content). The reaction rate is lineally dependent on potassium in low-ash coal but shows no correlation with high-ash coal (Leonhardt et al. 1983). Several kinetic models have been proposed to predict both catalytic and non-catalytic reaction process (Li 2014; Kopyscinski et al. 2013).

However, no universal kinetic model exists to describe the effects of catalyst type and coal rank. Some studies have attempted to account for catalyst loading (Li et al. 2014a). For industry application, additional factors must be considered due to the complex interactions among existing gases, such as H₂, CO and CO₂. The most critical aspect of industry application is selecting the appropriate coal or catalyst, which is essential for balancing cost and efficiency. However, kinetic model rarely take into account these effects, particularly when comparing different types of catalysts and coals. Moreover, ash can also deactivate the catalyst, an aspect that is often overlooked in the kinetic model. Some studies have been conducted using ash-free coal. If more cost-effective technologies for deashing and high catalyst activity can be developed, this approach could hold greater promise for the future.

4.1 Catalytic steam gasification

The most important reaction in catalytic coal gasification was carbon with steam to from CO or CO₂, shown as CR1. The proposed kinetic models for steam gasification were shown in Table 1.

4.1.1 Catalyst

The kinetic performance of carbon reacting with steam is summarized in Table 1. There were minimal difference among the catalysts Na, K, Rb and Cs (Meijer et al. 1994). The activity order for the catalysts was K₂CO₃, Na₂CO₃, Li₂CO₃, KCl, NaCl and CuO. There was no activity observed for the catalysts CaO and Fe₂O₃ (Kayembe and Pulsifer 1976). Occasionally, the activity of 5 wt% Na₂CO₃ was significantly higher than that of K₂CO₃. Regarding catalyst loading, the reaction rate increased with the amount of catalyst loading from 0 to 15 wt% (Meijer et al. 1994).

4.1.2 Temperature and pressure

The reaction rate consistently increased with temperature. The chemical reaction rate remained almost unchanged with the increase in pressure when it exceeded 1.5 MPa, as the active sites were saturated (Schumacher et al. 1986; Li et al. 2014a).

4.1.3 Inhibition of product

As the ratio of H₂/H₂O increased, the gasification rate decreased rapidly (Li 2014; Meijer et al. 1994). This may be due to the loss of contact with the catalyst, alkali evaporation, and active sites blocking, which were confirmed by TPD experiments. With the ratio of CO/H₂O increased, the gasification rate also decreased rapidly (Meijer et al. 1994). The gasification almost not happened with adding 5% CO at 1000 K. This was because there were fewer sites available and chemisorptions. The inhibition role of CO was much higher than that of H₂ (Li et al. 2014a). As the ratio of CO₂/H₂O increased, the gasification rate also decreased.

4.1.4 Activation energy and pre-exponential factor

The addition of catalyst typically reduced the activation energy, but it changed little with the addition of H₂, CO, CO₂ (Meijer et al. 1994) and K concentration (Huhn et al. 1983). With the addition of alkali catalysts (Meijer et al. 1994) and eggshells (Fan et al. 2017), the activation energy decreased from 256 to 160–190 kJ/mol and from 134.2 to 107.6 kJ/mol, respectively. With the addition of 10 wt% K₂CO₃, the activation energy decreased from 196 to 169 kJ/mol (Schumacher et al. 1986) and from 254.2 to 144.5 kJ/mol (Kayembe and Pulsifer 1976), respectively. The degree of reduction was closely related to the catalyst type and coal properties. For the same amount of NaOH, Na₂CO₃, CH₃COONa, NaNO₃ and without catalyst, the activation energy varied from 70.87, 87.92, 102.84, 108.39, and 117.74 kJ/mol. The activation energy decreased to 38.2 to 42.9 kJ/mol with adding 10 wt% black liquor, which was consistent with the literature results (Karczewski and Porada 2023).

The pre-exponential factor increased with the amount of catalyst loading. With the addition of 10 wt% K₂CO₃ (Schumacher et al. 1986) and eggshells (Fan et al. 2017), the pre-exponential factor decreased from 2.41 × 10⁸ to 1.32 × 10⁴ and from 464.1 to 39.65, respectively. However, these findings were not consist with the work of Schumacher et al. ( 1986), which showed that the pre-exponential factor increased from 3.1 to 6.7 × 10⁷ with the addition of 10 wt% K₂CO₃. These discrepancies may be due to different coal types. For the same amount of NaOH, Na₂CO₃, CH₃COONa, NaNO₃ and without catalyst, the pre-exponential factor varied from 1.21 × 10³, 1.68 × 10⁴, 9.98 × 10⁴, 1.29 × 10⁵ and 6.74 × 10⁴.

To further validate the kinetic model established for fluidized beds, the activation energy and pre-exponential factor were compared across various reactor types. The results obtained from the fluidized bed type TGA showed minimal deviation from those previous studies conducted in an atmosphere of 3% oxygen-balance nitrogen using K₂CO₃ as catalyst (Samih and Chaouki 2017). This finding was also corroborated by Li et al. (2014), who compared the outcomes of pressurized fixed bed and fluidized bed reactors.

4.2 Catalytic water gas shift reaction

The water gas shift reactions were described as follows:

Water gas shift gasification reaches equilibrium for most catalyst at temperatures ranging from 950–1000 K (Meijer et al. 1994) and 868–1030 K (Meijer et al. 1994), as indicated in Table 2.

4.3 Catalytic carbon dioxide gasification

Catalytic carbon dioxide gasification was shown as following:

4.3.1 Pressure, temperature and catalyst

Common used kinetic model for catalyzed carbon dioxide gasification are presented in Table 3. The rate of chemical reactions significantly changes with increases in pressure and temperature when these values are low (Schumacher et al. 1986). The activity order of catalyst is Na, K, Rb and Cs (Meijer et al. 1994), which is closely related to the dispersion. The reaction rate of Na is approximately 8 times that for Cs (Meijer et al. 1994). The rate of steam gasification is about three times that of carbon dioxide gasification.

4.3.2 Activation energy and pre-exponential factor

The addition of a catalyst typically results in a decrease in activation energy. For example, the addition of 10 wt% (Ding et al. 2015), 3 wt% Na₂CO₃ (Zhang et al. 2015), and 16 wt% K₂CO₃ (Li and Cheng 1995), reduces the activation energy from 252.1 to 220.6 kJ/mol, 206.78 to 66.65 kJ/mol, and 122 to 52 kJ/mol, respectively. Despite the same adding amount (7 wt%), the activation energies for K₂CO₃, Na₂CO₃, dolomite and CaCO₃ differ significantly, measuring 82, 127, 151 and 185 kJ/mol, respectively. However, some researchers have found the activation energy increases from 144.9 to 163.9 kJ/mol with the addition of 10 wt% K₂CO₃ (Schumacher et al. 1986). The activation energy of ash-free coal with 20 wt% K₂CO₃ is twice that of the uncatalyzed reaction. The activation energy decreased from 207.53 to 112.22 kJ/mol with catalyst loading changing from 0 wt% to 9 wt% KCl (Qiu et al. 2022). The activation energy obtained from kinetic model could be also verified by isoconversion method at various carbon conversion and loading methods (grinding, impregnation and high pressure method) (Yang et al. 2022). The activation energy decreased from 218.1 to 197.1 kJ/mol with adding 5 wt% Fe (Wang et al. 2020). These inconsistencies may be attributed to the varying properties of the catalysts and substrates.

With the addition of 7 wt%, the pre-exponential factors for K₂CO₃, Na₂CO₃, dolomite and CaCO₃ were determined to be 1.46 × 10³, 2.07 × 10⁵, 7.89 × 10⁵, and 4.53 × 10⁷, respectively. Upon adding 10 wt% Na₂CO₃ (Meijer et al. 1994) and 3 wt% Na₂CO₃ (Zhang et al. 2015), the pre-exponential factors decreased from 1.63 × 10¹¹ to 1.16 × 10¹¹ and from 20.02 to 0.54, respectively. However, an increase in the pre-exponential factor was observed from 1.6 × 10⁴ to 1.9 × 10⁸ with the addition of 10 wt% Na₂CO₃ (Schumacher et al. 1986). These inconsistencies may be attributed to the differing properties of the coal substrates used.

Some model parameters were also detected. The structure parameter φ in RPM model were detailed analyzed for Fe based catalyst. The φ was not affected by the gasification temperature, but little with catalyst. The φ for the dry mixing method was much larger than that of wet impregnation (Guo et al. 2021).

4.4 Catalytic methanation

The kinetic models of methanation (CR4) were listed in Table 4. The reaction is described as follows:

Common used kinetic model for catalyzed methanation were shown in Table 4. Limited research has been conducted on the kinetic model of methanation. The partial pressure of the product and equilibrium constant were considered in the H₂-CO-H₂O system (Kimura et al. 1985). A kinetic model based on dual-site mechanism was proposed (Otake et al. 1984). The effect of catalyst loading on the kinetic model was also taken into account (Li 2014).

Due to the complexity phenomenon involving mass transfer, heat transfer, momentum transfer, chemical reactions, and hydrodynamics behaviors (such as bubble fromation and bed expansion) in bubbling fluidized bed, it is very challenging to fully describe the entire catalytic coal gasification process through experiments alone. Consequently mathematical models have been proposed as a valuable tool for elucidating and describing this processes, particularly for scaling up the process.

Five typical mathematical models are employed, including molecular models (MD) or density functional theory (DFT), empirical models, computational fluid dynamics (CFD) models, Aspen Plus models, and artificial neural network (ANN) models, as shown in Fig. 4. Molecular models or DFT are micro-scale models used to reveal reaction mechanism. Empirical models and computational fluid dynamics (CFD) models are meso-scale model used to simulate hydrodynamics and chemical reactions. Macro-model Aspen Plus are used to simulate the flowsheet. The artificial neural network (ANN) models, as an all-scale model and a typical machine learning model, are used to simulate the complex processes that cannot not easily simulated by the above models. These models are discussed in the following sections.

Mathematical model for catalytic coal gasification

5.1 Molecular models (MD) or density functional theory (DFT)

Developing a molecular model or DFT offers several advantages, such as a deeper understanding of coal properties, the catalystic reaction mechanism, and the design the catalyst, as well as the development of new technologies. The typical structures representations of a molecular model or DFT are shown in Fig. 5a. The frist step was to model the coal structure. The complexity of coal structure necessitates a high degree of accuracy in modeling, which should integrate data from solvent extraction, liquefaction, pyrolysis, and spectroscopic techniques such as Raman, FTIR, NMR, STM, XRD and XPS, as well as instrument equipment detection, including TPD, TGA, and isotope tracing experiments. Consequently, coal models with varying numbers of nitrogen, sulfur, hydrogen, σ, and π bonds are constructed. Some catalyst are tested in CO₂ and H₂O gasification process, such as alkali and alkaline earth metals, transition metal, and composite metal. These catalysts are also integrated into the coal structure model. After optimizing structure, the energy and transition states for CO₂ and H₂O gasification are caculated and searched (Fig. 5b). Based on the above information, along with bond orders, the reaction path and catalytic reaction mechanism are finally determained and proposed.

Molecular model/DFT. a Model structures b Typic results (Bai et al. 2023)

5.1.1 Alkali and alkaline earth metals

The C–C bonds could be weaken at the carbon edge by adding –O-M (Li, Na, K, Ca, and Cu), which was benefical for the desorption of carbon–oxygen complex, adsorbing gasification agent molecules, and facilitating CO desorption (Huang and Yang 1999). This was consistent with the catalyst activity.

Regarding Na-catalyzed CO₂ gasification, the active centers were free Na₂CO₃ (Bai et al. 2023), nucleophilic planar semiquinone structures (Lei et al. 2021), and C–O–Na (Caldero et al. 2015), The used coal model was six- membered carbon ring polycyclic aromatic hydrocarbons with two carbon edge models, unclosed active carbon and H closed carbon edge (Caldero et al. 2015), two graphite models (armchair-edge and zigzag-edge) with two catalytic active centers (CNa and C–O_n–Na) (Zhao et al. 2018), and ethyl benzene (Dong and Feng 2022). The increased catalytic activity was due to the formed nucleophilic structure between Na and C atoms at the edge. as evidenced by the results of reaction kinetics through TGA (Lei et al. 2021). Na would spontaneously adsorb at the defect site to inhibit the reconstruction of the carbon matrix, making the carbon layer more easily oxidized, and increasing the dissociation of carbon dioxide and the generation rate of CO (Caldero et al. 2015; Lu et al. 2022). However, during the desorption process, the C–C bond was almost unaffected, and the catalytic effect on armchair-edge structure was due to the stability of the intermediate (Zhao et al. 2018). There was little difference in the calculated reaction energies by B3LYP, M06 and coupled-cluster (Caldero et al. 2015). The reaction activation energy for methane formation reactions through 1-phenylethanol cracking decreased to 4.64% and 9.12% for Na⁺ and Ca²⁺, respectively (Dong and Feng 2022).

Regarding K-catalyzed CO₂ and H₂O gasification, the active center was the C-O-M structures, which could be infered from high temperature TPD experiments (Chen et al. 1993; Chen and Yang 1997). The coal model used consisted of Zigzag and Armchair edge structures of carbon. By altering the charge of adjacent carbon atoms, the C-O-M structure exhibited catalytic activity and produced more off-plane oxygen. Additionally, there are two important factors affecting catalyst activity: the dissociation ability of the catalyst cluster model for CO₂ and H₂O, and the mobility of the O atom. However, these structure had little impact on the strength of adjacent C–C bonds between C (O) groups, thus not affecting CO desorption.

For Ca-catalyzed CO₂ gasification, the active center was the intermediate structure of “C-O-Ca-C”(Bai et al. 2023), as shown in Fig. 5b. Two possible pathways were compared: direct gasification and the formation of a surface complex. Based on reaction rate constants and NBO analysis, when CaO intereated with the active size of two serrated edge horizontally, the catalyst role of Ca²⁺ was to increase the amount of C(O) and promte the dissociative adsorption of CO₂ due to the charge distribution of the edge-activated carbon atoms. This facilitated O adsorption on carbon atoms, resulting in an increased reaction rate. There was no change in the reaction activation energy during the desorption process, as there was no difference between catalystic and non-catalystic processes (González et al. 2013).

5.1.2 Transition metal

Regarding Fe-catalyzed CO₂ and H₂O gasification, the active center was identified as [C-O-Fe], [Fe–C], [Fe ← OH₂], and C-Fe-CO based on the analysis of total organic oxygen to total carbon ratio, surface Fe concentration from XPS, weight loss from TGA, H₂ and CO gas yields, and the existing forms of Fe from XRD (Domazetis et al. 2007, 2008a, b, c; Zhao et al. 2021, 2020). The C-O-Fe structure could be readily formed through preoxidation, which effectively decreased the activation energy (Zhao et al. 2021). The effect of catalyst on armchair edge was higher than that on zigzag edges. The adsorption of CO₂ and desorption of CO were promoted by the addition of Fe due to its active d electrons.

Fe (III) formed various complexes with one or more Fe atoms as the core with hydroxyl groups in solution, which would further interact with oxygen-containing functional groups in lignite. These oxygen-containing functional groups would be decomposed during coal pyrolysis, generating CO₂ or CO. Concurrently, Fe (III) was gradually reduced to Fe⁰ and formed Fe–C or Fe–O–C complex structures. These complexes centered on a single or several Fe atoms, bonded to C or C–O. In the subsequent gasification process, FeO first adsorbed on the edge of polycyclic aromatic hydrocarbons, and then formed carbonyl groups that coordinated with Fe, ultimately leading to the formation of coordinated carbonyl groups and the production of CO. Fe also occupied the vacancies left by C atoms, forming Fe–C bonds and becoming a part of the carbon ring.

The simulation of hydrogen abstraction, hydrogen formation, and carbon monoxide formation was conducted using single-point self-consistent field DFT and semiempirical. The iron-catalyzed steam gasification process was understood to occur in three primary steps: water adsorption on [Fe–C] complex, hydrogen abstraction, and oxygen transfer. Among these steps, the initial adsorption of water was identified as the most critical. Water molecules were adsorbed on the [Fe–C] complex to form [Fe ← OH₂] species, which then produced hydrogen gas (H₂). Carbon monoxide (CO) was produced from the [Fe–C–O] complex after oxygen inserted in the [Fe–C] site, rather than direct Fe adsorption. The adsorption of CO₂ parallel to the surface of iron was found to be more favorable due to a net adsorbate–substrate interaction and robust hybridisation (Wang et al. 2021).

5.1.3 Composite metal

Four potassium-modified composite metals (KCo, KNi, KFe, KCe) were investigated using DFT. These metals adsorbed CO₂ initially, with oxygen being captured by the metal surface and reacting with carbon intermediates (C*) to produce CO. The transition metals (Co, Ni, Fe, Ce) were treated as the crystal phase, with a single carbon atom representing coke. These representations were validated through crystal phase analysis using XRD (Jiao et al. 2020). Two proposed active centers were the M-Oads (where M refered to Co, Ni, Fe) and the CeO₂vacO, The negative structure was considered to be electrophilic B₂O₃ (Lei et al. 2021).

Further work should focus on the synergistic effect of composite catalysts and the interactions between multiple atmospheres containing H₂O, CO₂, H₂, and CO. Additionally, the development of more complex coal strucrture model should be pursued (Tang et al. 2023).

5.2 Empirical model

The empirical model features fast execution, minimal computing resources, and a distinct physical representation. Figure 6a displays the typical components for empirical model. Adhering to two phase principle, the gasifier is hypothetically segmented into various sections based on the flow pattern, including grid zone, bubble zone, and freeboard zone. The model’s credibility is contingent upon the hydrodynamic correlations employed, which were proposed through experimental methodology. The majority of model parameters possess physical significance, serving as a critical aspect for accurate predictions, especially when substantial discrepancies are present between experimental outcomes and model-predicted data. The typical results for catalystic coal gasification in bubbling fluidized bed are shown in Figs. 6b and c. Figure 6b demonstrates that catalyst loading can substantially influence gas composition, potentially elevating the methane volume fraction to over 20%. Figure 6c delineates the impact of catalyst loading on several aspects: carbon monoxide produced by combustion (CO_C), carbon monoxide produced by steam gasification (CO_G), carbon monoxide consumed by water gas shift reaction (CO_S) and carbon monoxide consumed by methanation (CO_M). More effects were obversed on CO_G and CO_S.

Empirical model. a Model structure b Effect of catalyst loading on gas composition (Li et al. 2014b) c Effect of catalyst loading on carbon dioxide for different reactions (Li and Song 2022a)

Table 5 summarizes empirical models for coal gasification in bubbling fluidized bed. One important consideration is the description of the flow patterns within bubble fluidized beds, which include plug flow, complete mixing flow, and bubble coalescence. The performance of bubble coalescence model was found to be superior to that of plug flow model and complete mixing flow models (Haggerty and Pulsifer 1972). The carbon conversion predicted by the bubble coalescence model was higher than that predicted without considering the enhanced mass transfer rate of smaller bubbles (Ciesielczyk and Gawdzik 1994). The gas and particle phases were assumed to be in plug flow and completely mixed flow, respectively (Ma et al. 1988). Due to homogeneous combustion reaction and solid heat transfer, the temperature of emulsified phase quickly equilibrated with solid temperature, where as the temperature of the bubble phase increased more gradually.

The model are typically divided into three components: hydrodynamics models, chemical reaction models, and heat transfer model. Hydrodynamics models consider factors such as bubble size and velocity, particle and gas velocity, particle volume fraction, minimum fluidizing velocity, bed expansion ratio, terminal discharge height (TDH), elutriation rate, etc. Special characteristics are also taken into account in jetting fluidized beds, including jet diameter and height, mass and heat transfer between annulus and jet. Chemical reaction models incorporate kinetic constant, char reactivity factor, combustion product distribution coefficient, and steam gasification produce distribution coefficient, etc. Heat transfer model include heat transfer mechanism and species diffusion. Simulated results encompass fluidization state, gas and particle velocity, particle concentration and hold-up, bubble size and velocity, steam conversion, carbon conversion, gas composition (O₂, CO, CO₂, H₂ and CH₄), gas heating value and production rate, particle and gas temperatures, bed temperature, bubble and emulsion temperature, heat transfer rate, heat transfer coefficient distribution, among others.

Simulate the entire gasification behaviors within fluidized bed through a single model can be challenging; thus, the gasifier is often divided into different zones. A three-zone model (i.e., grid zone, bubbling zone, and freeboard zone) for a jetting fluidized bed coal gasifier has been established (Bi and Kojima 1996; Bi et al. 1997; Luo et al. 1998). The high-pressure Winkler gasifier was segmented into different cells by considering drying as an unsteady heat conduction process, and its performance was predicted for both atmospheric laboratory and pressurized commercial scale gasifier (Hamel and Krumm 2001).

The model also accounts for certain unique phenomenon, such as particle size distribution, pressure, and 'net flow', which are challenging to replicate through experimentation. Investigations into the particle size variations resulting from processes such as combustion, gasification, and elutriation within a pressurized gasification environment have been conducted (Chejne and Hernandez 2002). The reduction in particle size was modeled using a shrinking model, and the separation of particles by cyclone followed by their return to the furnace was also considered (Souza-Santos 1989, 2007). The impact of pressure on phenomenon of transfer, hydrodynamics behaviors (including minimum fluidization velocity, bed expansion, and bubble size), physical properties, and the kinetics of both homogeneous and heterogeneous reactions, as well as the heat transfer coefficient, were all incorporated into the model (Chejne et al. 2011; Li et al. 2014b). The 'net flow' resulting from devolatilization and gasification significantly affects gasifier performance (Yan et al. 1998, 1999; Yan and Zhang 2000; Ross et al. 2005). Without accounting for 'net flow', the carbon monoxide consumption rate in the bubble phase is minimal, whereas it reverses in dilute phase. Whether the water–gas shift reaction reaches equilibrium has a profound influence on the gas composition. The discrepancy between predicted and experimental bed temperature, when not considering homogeneous combustion reaction (NHCR, 30–70 K), is much greater than when HCR is taken into account (7–14 K) (Yan and Zhang 2000). This is due to the fact that homogeneous combustion reactions produce more heat than carbon combustion. Consequently, the carbon conversion predicted by HCR is lower than that by NHCR, since part of the oxygen is consumed by the homogeneous combustion reaction. The predicted temperature in the upper section of the distribution plate closely matches the experimental data from the Babcock & Wilcox gasifier, thanks to effective gas–solid mixing (Souza-Santos 1989, 2007). The concentrations of oxygen, carbon monoxide, and carbon dioxide in the dilute phase exceed those in the bubble phase. In the case of the Institute of Gas Technology (IGT) gasifier, volatiles are released and then mixed with oxygen at the feed inlet, leading to an increase in the dilute phase temperature but a decrease in bubble phase temperature. The temperature difference resulting from heat generation via the water–gas shift reaction and tar cracking is approximately 10 K (Souza-Santos 1989, 2007).

The aforementioned models were developed for coal gasification without catalyst at low operational pressures. The significant differences between the non-catalytic and catalytic coal gasification model are closely related to the catalytic reactions, particularly the methanation reaction. Moreover, the operational pressure for catalytic gasification to produce methane is high (3.5 MPa), which can lead to substantial differences in hydrodynamics within the reactor compared to the non-catalytic process. An empirical model was formulated by integrating pressurized hydrodynamics with catalytic chemical reactions to simulate the catalytic coal gasification process. This model took into account several critical parameters related to pressurized hydrodynamics, including jet diameter and height, bubble size and velocity, and bed expansion. The model successfully predicted the effects of operation conditions, such as catalytic loading amount, oxygen flow rate, and steam flow rate on gas composition, carbon conversion, and methane yield (Li et al. 2014b, 2014c; Li and Song 2022a).

Further research should focus on revealing the interactions between different chemical reactions and the interactions between chemical reactions and hydrodynamics. To better guide industrial operations, an operational map should be provided, which includes various operational conditions effect on gas composition, temperature, and pressure. More importantly, the key factors should be identified to assist with operations, especially when restoring normal conditions following any disruptions.

5.3 Computational Fluid Dynamics (CFD)

Computational fluid dynamics (CFD) can offer real-time insights into the dynamic changes occurring within fluidized bed, particularly in terms of particle and gas flow behavior. The Navier–Stokes (N-S) equation can be directly solved using CFD, which expands its applications beyond empirical models (Singh et al. 2013).

The CFD model structure for coal gasification in a fluidized bed is illustrated in Fig. 7a, which primarily involves mesh and module selection. Initially, the gasifier must be partitioned into an appropriate mesh. If the mesh is too coarse, the calculation may fail to converge. Conversely, if the mesh is too fine, the computation time could significantly increase. Thus, researchers often face a challenge in balancing the level of detail with computational efficiency. The subsequent step involves selecting the appropriate module. Turbulence models, for instance, can influence particle velocity. The multiphase model is chosen based on the number of particles being simulated. The drag model is a crucial factor affecting gas–solid fluid dynamics. Researchers are particularly interested in the local particle and gas movement to identify backmixing or dead zones. The location of the highest temperature is invaluable in reactor design to prevent slagging. Typical output parameters in CFD simulations include flow patterns, gas and particle velocities, solid phase volume fraction, pressure distributions, jet growth, bubble rise, gas composition (O₂, H₂, CO, CH₄, and CO₂) and their distributions, carbon conversion, reaction rates, temperature distributions for gas and particle phases, and the mass of the feed, along with the effects of operating conditions (oxygen concentration, water content, temperature, and pressure). Some representative results of gas velocity and gas volume for catalytic coal gasification in a jetting fluidized bed are provided in detail in Figs. 7b and c, respectively.

CFD model. a Model structures b The solid velocity vectors fields for catalytic coal gasification (Xia et al. 2016) c Contours of the gas volume fraction vs time (Xia et al. 2016)

Based on the treatment of fluid and particles within different coordinate systems, CFD models can be categorized into three types: Euler-Euler, Euler-Lagrangian, and Lagrangian-Lagrangian. In the Euler-Euler model, both fluid and particles phase are simulated within the Euler coordinate system, also known as two-fluid model (TFM) or continuous medium model. Here, the particle phase is treated as a continuous medium with dynamic properties akin to those of the gas phase. A particle concentration higher than 10% is typically required, with the kinetic theory of granular flow (KTGF) being a commonly used model. The Euler-Lagrangian mode handles fluid movement in Eulerian system and particles movement in the Lagrangian system, also known as the particle trajectory model or discrete phase model (DEM). In industrial process, the number of particles can reach up to 10¹²–10¹⁵, which exceeds the capacity for direct calculation in CFD. Furthermore the computational time for the Euler-Lagrangian model significantly increased with the number of particles. The recently developed computational particle fluid dynamics (CPFD) model can handle large fluidized bed by simulating packed particles. In the Lagrangian-Lagrangian model, both fluid and particles phases are depicted using Lagrangian coordinates, also known as the fluid pseudo-particle model.

Additionally, several new models were proposed. To more effectively capture the behavior of rotating rough particles, which cannot be simulated by the KTGF, the kinetic theory of rough spheres (KTRS) was developed. This new theory incorporates translational and rotational granular temperatures (Wang et al. 2014). Furthermore, to combine the benefits of CFD-DEM — which provides detailed particle-scale information — and the computational efficiency of CFD-TEM for larger-scale fluidized gasifiers, a multiphase particle-in-cell approach was proposed. This method maintains detailed information on mesoscale bubble sizes (Liu et al. 2021). Leveraging the strengths of both CFD and experimental correlations while mitigating their respective limitations, a novel model was introduced. In this model, CFD is used to simulate hydrodynamic parameters within the gasifier, while chemical reactions are solved in the VMG-Sim framework using three plug flow reactors (Esmaili et al. 2014). Table 6 summarized various CFD models applied to coal gasification in bubbling fluidized bed.

The selection of an appropriate phase in CFD is crucial. Coal and quartz sand should be treated as two separate phases (Armstrong et al. 2011a, b). The bubble and sand particle size have a significant effect on back-mixing, especially for pyrolysis gas combustion. Good back-mixing could be obtained at a sand particle size of 0.8 mm. The gasification rate is largely affected by bubble-induced horizontal fuel mixing (Hu et al. 2019). Another study focused on the effect of the local bubble behaviors (β_gas-inlert, gas-inert solid phase momentum exchange using different drag models) on heterogeneous reaction rate, gas phase temperature, and gas compositions. With a high β_gas-inlert, the mixing content of coal and inert solid phase increases, resulting in a high content of H₂ and CO (Parvathaneni et al. 2023). Bubble containing various combustible gas (H₂, CO, and CH₄) were mainly found in the lower part of the gasifier (Liu et al. 2021). Some hydrodynamics models in CFD have also been tested, such as drag models and specularity coefficients in the bubble zone, and particle restitution coefficient (Sahu et al. 2019). The mass transfer rate of bubble to clouds and clouds to emulsion were specially simulated by CFD (Esmaili et al. 2014). The distribution of carbon, ash and sand was well simulated (Xie et al. 2013).

Chemical reaction rates in CFD are typically modeled using the Arrhenius–Eddy dissipation reaction rate for homogeneous reactions, along with the Arrhenius-diffusion reaction rate and Arrhenius kinetic-rate for heterogeneous reaction. Gasification rate predicted by a two-dimensional KTGF are mainly affected by the Arrhenius rate of combustion, diffusion rate, heterogeneous reaction rate, and turbulent mixing rate for homogeneous reaction (Yu et al. 2007). Steam gasification in a jetting fluidized bed primarily occurs in the distribution plate area and around the jet, while carbon dioxide gasification and the water–gas shift reaction take place in the upper main bed and on both sides of the transition zone, respectively (Gao et al. 2006). The water gas shift reaction and steam methane reforming reaction had much effect on gas composition (Sahu et al. 2019).

Here were some typical results of effect of operation conditions. As pressure increased from 0.1 to 0.3 MPa, carbon monoxide and hydrogen concentrations significantly raised, whereas methane and carbon dioxide concentrations underwent only slight changes. With temperature increased, the concentration of hydrogen and methane decreased due to reactions with oxygen (Cornejo and Farías 2011). High concentrations of carbon dioxide and hydrogen, and low carbon monoxide concentration were mainly due to errors in the steam gasification product coefficient, inaccuracies in the kinetic equations, and limestone desulfurization (Wang et al. 2009b). Methane deviations were a result of ignoring carbon reactions with hydrogen (Yu et al. 2007), using an unsuitable correlation of volatile matter, and neglecting tar decomposition reactions (Cornejo and Farías 2011). Adding limestone did not noticeably alter the gas composition (Armstrong et al. 2011a, b).

The structure of a gasifier could be also optimized using CFD. The tapered section (characterized by a tapered angle 3–11) and gas agent velocity were specially considered for their effects on the LHV and HHV of the gas product, as well as the CCE of the gasifier. The tapered angle had a positive impact on H₂, CO₂, and CCE, while it had a negative effect on CH₄, LHV and HHV. The maximum of CO yield could be obtained at tapered angle of 7. As the gas agent velocity increased, the CO₂ and CCE increased, while the CO, LHV and HHV decreased. The CH₄ and H₂ remained almost constant (Askaripour 2020).

The aforementioned work primarily concentrates on non-catalytic coal gasification. In catalytic coal gasification, understanding the detailed hydrodynamics is much more critical due to the complex interactions between coal and the catalyst. A CFD model incorporating the KTGF approach has been proposed to examine the effect of a pair of embedded high-speed air jets on hydrodynamics, including gas volume fraction, jet height, gas and solid velocity, particle concentration distributions, and bed expansion (Xia et al. 2016). Under optimal operational conditions, the maximum temperature can be kept below the ash softening temperature to prevent slagging.

Further research should focus on revealing the detailed hydrodynamics of methane formation. This includes studying the suitable bubble size distribution, achieving efficient back-mixing without the formation of dead zones to prevent high temperatures and slagging. Additionally, the impact of local hydrodynamics on chemical reactions needs to be investigated, particularly when introducing oxygen, steam, or syngas, and determining the optimal positions for their introduction. These factors are crucial for industrial operations.

5.4 Aspen

The sequential module method and the equation-oriented method are commonly used methods in Aspen to simulate coal gasification, assuming all chemical reactions are in equilibrium based on the principle of Gibbs minimum free energy. However, this assumption is not suitable for predicting bubble fluidized beds, as reactions are not in equilibrium at low operating temperature. The typic model structures of Aspen was shown in Fig. 8a, which mainly consit of component definition, selection of physical property methods, and selection stream and Block.

Aspen simulation. a Model structures b Simulation process for catalytic coal gasification by Aspen (Jang et al. 2013) c Simulation results compared with Exxon (Jang et al. 2013) d Simulation results of different chars (Jang et al. 2013)

The essential components of the Aspen model mainly include conventional components and unconventional components (coal, fly ash, and bottom ash), which require the introduction of parameters based on proximate analysis, elemental analysis, and sulfur analysis of coal. The RKS, RKS-BM, and PR-BM equations are commonly used as physical property methods (Liu et al. 2011; Yan and Rudolph 2000; Jang et al. 2013; Sánchez et al. 2016).

In Aspen simulation, the gasifier is typically divided into units for dry, pyrolysis, gasification, and slag separation. In the dry process, the coal was dewatering. In the pyrolysis unit, coal is decomposed into a mixture of conventional streams (carbon, hydrogen, ash, etc.), which react with oxygen and transforms into the gas phase. Ash is assumed as an inert substance. The RSTOIC or RYIELD reactor modules are used to simulate this process (Sánchez et al. 2016). The pyrolysis components are then introduced into gasification unit, where they react with gasifying agent (oxygen and steam), and the outlet gas composition is calculated by chemical reaction equilibrium and phase equilibrium, which is simulated by RGIBBS reactor. The combustion-gasification process of char (carbon) reacts with gasification agent to produce syngas is depicted through a four-stage process comprising a CSTR for the emulsion phase and a PFR for the bubble phase (Sánchez et al. 2016). A pressurized ash agglomerating fluidized bed gasifier was further divided into jet, bubbling and freeboard zones to better simulate gas composition, yield and heat value, carbon conversion, cold gas efficiency, bed temperature, ratio of H₂/CO; and the effect of H₂O/coal and O₂/coal on gasification performance. In addition, a split module is used to simulate the separation process of slag and crude synthesis gas. The hydrodynamics processes of interval fluidized bed coal gasification process is simulated using user-written models, such as entrainment and elutriation rate, particle size distribution, and solid circulation (Yan and Rudolph 2000). Table 7 summarizes the Aspen models for coal gasification in bubbling fluidized bed.

Hydrogen-rich synthesis gas can be obtained at a high steam-to-coal ratio with a low oxygen-to-coal ratio (Liu et al. 2011). Due to the low gasification reaction rate, the carbon consumed in gasification is less than that in the combustion chamber (Yan and Rudolph 2000). The used modules for catalytic coal gasification are slightly different from those of non-catalytic coal gasification. An Aspen model was established by modifying kinetic parameters based experimental data, and the predicted data were compared with the experimental results of Exxon catalytic coal gasification, shown in Fig. 8b. The simulated process was including three parts: gas and coal input, and catalytic char gasification. The predicted gas compositions (CO, CO₂, H₂, and CH₄) were in good agreement with the experimental data of Illinois #6 and Indonesian coals (Figs. 8c and d) (Jang et al. 2013). Further work should focus on coupling the catalyst recovery process. The 5E analysis (Environment, Efficiency, Energy, Economy and Exergy) and Life Cycle Assessment (LCA) could also be necessary for potential scale-up with various catalysts.

5.5 Artificial neural network (ANN)

Artificial neural network (ANN) has been widely applied to various chemical reactions processes due to their rapid calculation speed and high accuracy, despite the lack of detailed information. The complexities of chemical reactions and hydrodynamics within fluidized bed have led researchers to employ ANN model to simulate these processes (Patil-Shinde et al. 2014; Chavan et al. 2012; Li et al. 2018; Guo et al. 1997; Li and Song 2022b).

The establishment process of the ANN model is shown in Fig. 9a. The advantage of this model is its ability to handle complex non-linear relationships between input and output variables. Consequently, it is crucial to determine an appropriate performance metric. Input and output parameters are selected based on the understanding of the underlying processes. The second step involves data treatment. All data used must be normalized to prevent its impact on performance. Subsequently, the data are randomly divided into three parts: Training (75%), Testing (15%), and Validation (10%). This partitioning ensures that the simulation process has good predictive ability and helps to mitigate overfitting. The third step involves experimenting with different types of ANN, algorithms, and the number of neurons. The architecture of the ANN model is shown in Fig. 9b, consisting primarily of input layer, hidden layer and output layer. Input parameters encompass proximate analysis (fixed carbon (FC), volatile matter (VM), and ash (A)), ultimate analysis (carbon (C), hydrogen (H), oxygen (O)) and operation conditions (air flow rate (QA), oxygen flow rate (QO₂) steam flow rate (QS), coal feed rate (F), gasification temperature (T), and heating rate (HR)), specific surface area (SS), activation energy (AE), mineral matter (MM), gasification time (t), catalyst mole weight (M), catalyst loading amount (W), and ash discharge rate (ADR). Output parameters include syngas production rate (P), syngas generation rate (R), gas yield (Qg), composition of the product gas, carbon conversion (CC), active char ratio (ACR), active carbon-to-total carbon ratio (ATR), active carbon reaction rate (RC), low heating value of the syngas (LHV), and gasification reaction rates (RG). Types of ANN frequently utilized include artificial intelligence-based model (AIM), genetic programming (GP), multilayer perceptron (MLP), multivariate regression (MR), back propagation neural network (BPNN), feed-forward back propagation neural network (FFBP), cascade-forward back propagation (CFBP), multilay feed forward neural networks (MFNN), among others. The algorithm employed was error-back-propagation (EBP), Levenberg–Marquardt (LM), particle swarm optimization (PSO), genetic algorithm (GA), and back propagation (BP). Additionally, the activation functions used include tangent sigmoid and log sigmoid. The ANN models for coal gasification in bubbling fluidized bed were summarized in Table 8.

ANN model. a Establishement process b Model structures c Effect of catalyst type on carbon conversion (Li and Song 2022b) d Relative influence analyzation (Li and Song 2022b)

The MLP model outperforms MR for 18 steady-state gasifier operated in India and other countries with feed rate of 30–40 kg/h (Chavan et al. 2012). The GP and MLP showed good performance (Patil-Shinde et al. 2014). Regarding different gas compositions, the optimum numbers of neurons in the hidden layers varied significantly. Transfer functions should also be carefully considered. PSO demonstrated better performance than LM (Li et al. 2018). The challenging measurement of experimental data for (ACR) could be effectively simulated by using an ANN model (Guo et al. 1997). To account for the influence of catalyst, the catalyst mole weight (M) and catalyst loading amount (W) was introduced in the ANN model, as depicted in Fig. 9c (Li and Song 2022b). The CFBP showed better performance than FFBP, and GA outperformed LM. The ranking of different factors could be also predicted, which was very useful for further operation, as shown in Fig. 9d.

Further research should focus on the development of more widespread ANN models, particularly for industrial data applications. The ANN model can accommodate a greater variety of input and output data, which are essential for industrial operations. This model can be seamlessly integrated with molecular models or DFT, empirical models, CFD, and Aspen software. If certain components of these models are not easily adaptable, the ANN model may represent a favorable alternative.

5.6 Comparison of different models types

Molecular model or DFT are used to operate at the molecular or atom level to study chemical bonding and processes involving free radical generation. These models are invaluable for revealing reaction mechanisms and ultimately for establishing kinetic models. Empirical model, based on reliable calculation formulas derived from extensive experimental data, can easily describe the overall fluid flow and chemical reaction behaviors in bubbling fluidized bed gasifier with very fast calculation speed. However, these models may not provide a comprehensive description of hydrodynamics in the gasifier. CFD models can provide a timely representation of the flow behavior in bubbling fluidized bed by directly solving momentum equations through numerical discretization methods. However, this approach can be time-consuming and challenging to converge, particularly for large-scale fluidized bed with chemical reactions. Moreover, many adjustable parameters in CFD models depend heavily on empirical knowledge. Aspen Plus offers a complete physical property database and a suite of general unit operation models, including reaction modules, cyclones and slagging, which can efficiently evaluate gasification performance and optimize operating conditions. Howerer, the process caculated are often based on minimum Gibbss energy, which may be far from equilibrium in practical reactions within bubbling fluidized bed gasifiers. This is the "black box" approach that neglects mass transfer, momentum transfer, and heat transfer during the gasification process and reaction behavior. ANN models can quickly and accurately predict many performances metrics, although detailed information remains elusive. With the advent of big data, ANN model are becoming increasingly powerful.

This review has summarized and discussed mechanisms, reaction kinetic, and reactor models for catalytic coal gasification in detail. The K-char-O mechanism was identified as the most reasonable for coal gasification catalyzed by potassium species. Among the various kinetic models, the modified random pore model was found to be more suitable in most cases. The pre-factor was observed to vary with catalyst loading, whereas the activation energy is more closely related to the catalyst type. Gas composition, carbon conversion, and methane yield could be well predicted by an empirical model within an acceptable rang of error. The flow states of gas and solid in fluidized bed gasifiers could be well simulated by CFD models. The EXXON catalytic coal gasification process could be well simulated by the Aspen model. The catalyst type and loading had been successful introduced into the ANN model.

The most critical aspects of catalytic coal gasification in fluidized bed are the alignment of catalytic chemical reaction rate with appropriate hydrodynamics. Further work should focus on the synergistic effect of composite catalysts and the interactions between multiple atmospheres containing H₂O, CO₂, H₂, and CO using Molecular model or DFT. The development of more complex coal strucrture model should be pursued. Therfore, a more accurately kinetic model is needed. The interactions between different chemical reactions and the interactions between chemical reactions and hydrodynamics should be revealed by empirical model. To better guide industrial operations, an operational map should be provided, including the effect of various operational conditions on gas composition, temperature, and pressure. More importantly, key factors should be identified to assist with operations, especially when restoring normal conditions following any disruptions. The catalyst recovery process should be coupled with gasification process by Aspen. The 5E analysis and LCA could also be necessary for potential scale-up with various catalysts. With big industrial data, ANN model can accommodate a greater variety of input and output data, which are essential for industrial operations. This model can be seamlessly integrated with molecular models or DFT, empirical models, CFD, and Aspen software. If certain components of these models are not easily adaptable, the ANN model may represent a favorable alternative.

In the future, a simulation-based research approach will be developed to support the advancement of industries. Through molecular modeling or DFT calculations, a highly efficient catalyst will be designed. By understanding the intricate details of the catalytic mechanism, a precise kinetic model can be established. CFD will provide optimal hydrodynamic conditions. Empirical models will effectively elucidate the interactions between various chemical reactions as well as the interplay between chemical reactions and hydrodynamics. Based on the 5E analysis and LCA, the flowsheets for gasification and catalyst recovery will be outlined. ANN will accurately simulate the uncertain relationships among variables. By harnessing the strengths of these models, the progression of catalytic coal gasification is poised to accelerate with confidence. This review offers valuable insights for the development and scaling-up of reactors tailored for catalytic coal gasification, which can also be applied to the thermal conversion of other carbon-containing substances.