Enhanced Accuracy of the Reaction Rate Prediction Model for

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Enhanced Accuracy of the Reaction Rate Prediction Model for Carbonaceous Solid Fuel Combustion Kevin Yohanes Lisandy,† Gyeong-Min Kim,† Jin-Ho Kim,† Gyu-Bo Kim,‡ and Chung-Hwan Jeon*,‡ †

School of Mechanical Engineering and ‡School of Mechanical Engineering, Pusan Clean Coal Center, Pusan National University, Busan 609-735, Republic of Korea ABSTRACT: Combustion of carbonaceous solid fuels was modeled using a number of methods, and the employed models were further improved by thoroughly studying the physical and chemical interactions between carbonaceous solid fuels and oxidizers. Simulation accuracy was improved by using special techniques to reduce the fitting errors of earlier models; e.g., errors in the isothermal coal char combustion rate model were reduced by modifying the well-established random pore model, with increased model flexibility generally considered vital for improvement. Thermogravimetric analyses were performed for four categories of carbonaceous fuels: semi-anthracite coals, bituminous coals, sub-bituminous coals, and biomass. Scanning electron microscopy imaging was employed to understand correlations between the fuel structure and model parameters. The obtained results were used to confirm the hypotheses of the used models, and a general model of carbonaceous solid fuel combustion, termed “flexibility-enhanced random pore model”, was established, improving correlation coefficients from 0.7 to 0.98 and decreasing deviations from 20 to 3%.

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INTRODUCTION Numerical simulations are widely used in many applications to predict the output trends of equipment or systems. The simplest models of processes are non-dimensional simulations (lump models) and one-dimensional simulations (distributed models). Lisandy et al. used lab-scale experiments to study the heterogeneous reaction kinetics of low-rank coal. Using the data that they obtained, they established a real-scale gasification process model (dry feed shell entrained-type gasifier) and a labscale combustion process model (drop-tube furnace).1,2 Kinetic research of gasification (heterogeneous char reaction with O2, CO2, and H2O in a low stoichiometric ratio/fuel-rich condition) and combustion (heterogeneous char reaction with O2 in a high stoichiometric ratio/fuel-lean condition) was performed using kinetic modeling techniques based on physical approaches, namely, the volumetric model (VM), grain model (GM), and random pore model (RPM). Among these models, the most useable model is the RPM.3 Despite lacking accuracy in terms of absolute values, RPM is well-suited for predicting the trends in unburned carbon (UBC) and NOx emission amounts in low-rank coal combustion simulations, as exemplified by a previous study.1 To improve the quality of simulation results, particularly the large disagreement observed in RPM fitting, a new RPM model should be proposed. The rate model for the heterogeneous reaction between porous solids and gases has been considered by many researchers. There are two approaches for modeling the chemical kinetics of heterogeneous reactions: the kinetic diffusion approach and the physical approach. In the kinetic diffusion approach, a calculation of the effective rate is achieved from the competition between the reaction rate and the mass transfer rate, and it is used in the intrinsic model, apparent rate diffusion model, and unreacted shrinking core model. The physical approach is a model based on the surface area development of a single particle, which is usually considered to be a sphere, e.g., VM, GM, and RPM (see Table 1). © XXXX American Chemical Society

Table 1. Reaction Rate Models with Equations model

rate equation

grain model (GM)

dx = k GM(1 − x)2/3 dt

volumetric model (VM)

dx = k VM(1 − x) dt

random pore model (RPM)

dx = kRPM(1 − x) 1 − ψRPM ln(1 − x) dt

(1) (2) (3)

The kinetic diffusion approach featured dividing the reaction regimes into three zones, controlled by chemical reaction kinetics (zone I) and mass transfer from surrounding gas to the external particle surface (zone III), with an in-between zone featuring intraparticle mass transfer inside the coal layer (zone II).2,4,5 An intrinsic model was developed to satisfy all reaction regimes, assuming that the apparent reaction rate is a product of the intrinsic reaction rate per surface area with internal (intraparticle) and external diffusion effectiveness. Internal effectiveness depends upon the pore diameter (being closely related to the Thiele modulus), whereas external effectiveness depends upon the concentration of reacting gas. An apparent rate diffusion model was developed to satisfy the regime of zone III, where the apparent reaction rate was determined by the competition between chemical reaction and mass diffusion rates. An unreacted shrinking core model considering intraparticle diffusion was developed to satisfy the regime of zone II, where the reaction rate was mainly limited by the layer of ash or solid fuel impurity leftovers.6,7 RPM was proposed by Gavalas8 by deriving the equation based on the random capillary model of a porous solid. Received: January 16, 2017 Revised: March 15, 2017 Published: March 15, 2017 A

DOI: 10.1021/acs.energyfuels.7b00159 Energy Fuels XXXX, XXX, XXX−XXX

Article

Energy & Fuels Table 2. Physical and Chemical Properties of Solid Fuels Obtained by Proximate and Ultimate Analyses semi-anthracite solid fuel type proximate (wt %, as received)

ultimate (wt %, daf basis)

moisture volatile FC ash total C H N O (calculated) S total

bituminous

sub-bituminous

biomass

carbo one

Macathur

Glencore

Moolarben

Suek

KPU

Adaro

WP

PKS

EFB

1.76 10.77 74.13 13.34 100 88.82 4.25 2.23 4.30 0.39 100

1.41 17.72 63.62 17.25 100 91.75 4.62 2.04 1.36 0.24 100

3.79 28.83 52.38 15.00 100 77.75 5.49 1.48 14.63 0.65 100

4.27 27.03 51.81 16.89 100 91.68 5.59 1.99 0.10 0.64 100

3.75 34.92 49.17 12.17 100 81.86 5.71 2.53 9.60 0.30 100

17.96 36.65 40.92 4.47 100 79.98 5.32 1.41 13.20 0.10 100

19.45 40.53 36.93 3.09 100 75.57 5.05 1.08 18.23 0.06 100

5.61 75.89 18.23 0.27 100 47.29 6.39 0.00 46.30 0.02 100

15.43 64.69 17.54 2.34 100 47.67 5.75 0.12 46.43 0.03 100

25.68 60.07 11.73 2.52 100 46.71 5.97 0.07 47.22 0.03 100

According to RPM, the reaction rate at a constant temperature is a function of the carbon conversion state. A maximum reaction rate is not established at the starting point of the reaction process, as described in VM or GM. Instead, RPM describes that a maximum value of the reaction rate is established in the middle of the reaction process, owing to the pore enlargement phenomenon, which broadens the specific surface area of the solid under investigation. Several studies were also performed by Bhatia and Perlmutter,9,10 and experimental results of solid fuel char reactions were compared to several models, e.g., the VM, GM, Petersen model, etc. RPM was also derived and proven to be the most suitable model. These two studies conclude that the reaction rates are functions of the carbon conversion state, which can be described using eq 3 in Table 1. x is the carbon conversion state; kRPM is the initial reaction rate as a function of the temperature; and ψ is the structural parameter that is theoretically independent of the temperature. Two important points from the described studies should be noted. First, the equation is only valid for kinetic-controlled regime reactions; i.e., it is only valid for low temperatures (below ∼900 °C, depending upon solid fuel type and reaction conditions) and small particles under 250 μm. Furthermore, the approximation of the kinetic-controlled criterion can be estimated using the Thiele modulus. Second, the theory is not fully correct in assuming that the structural parameters are independent of the temperature, which was also shown by Gavalas.8 The theoretical derivation of RPM was performed thoroughly in previous studies, informing the modeling of the reaction rate prediction over carbon conversion. Still, the theoretical calculation based on the pore size, surface area, and pore diameter data is more difficult to conduct compared to the fitting method based on experimental results. Therefore, many researchers determine the structural parameters based on experimental results. For most low-rank coal and biomass cases, the RPM cannot provide a good fit; however, some researchers have raised arguments about this assumption, such as Dassapa et al.11 and Fatehi and Bai.12 On the basis of these arguments, the theories originally developed for evolution of the pore structure of coal during the conversion may fail for biomass.13 Therefore, Wang et al.14 tried to improve the RPM (modified RPM) for biomass application by adding the power factor (a) into the equation, as shown below. dx = kMRPM(1 − x)a 1 − ψMRPM ln(1 − x) dt

The improvements were significant and possibly reduced the error to under 7%; however, they did not result in a satisfactory model. The model could be improved by the addition of more correction parameters. In contrast, Fei et al. tried to modify the RPM using an internal function that also increased the complexity of the model (fractal RPM and two-stage RPM).15,16 They used the equation shown below. dx = kFRPM(1 − x) 1 − ψt′ ln(1 − x) dt ψt′ = ψ0 ; x < 0.7 ψt′ = ψ0 exp(λ(x − 0.7));

x ≥ 0.7

(5)

In addition, rather than modifying the RPM model, Fatehi and Bai12 used a model called the multipore model to match the simulations with experimental results. This work aims to provide higher accuracy predictions applicable to a broad range of fuel types, preferably by enhancing the flexibility of previously developed models12,14−16 and, thus, increasing their scope beyond char reactions, e.g., including devolatilization process modeling.17

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EXPERIMENTAL SECTION

To produce sufficient data for a new model, a broad range of carbonaceous solid fuel grades were used in this study. The samples consisted of 10 types of solid fuels that were divided into four categories, namely, (1) one semi-anthracite coal, Carbo one (carbo); (2) three bituminous coals, Macarthur (mac), Glencore (glen), and Moolarben (mool); (3) three sub-bituminous coals, Suek, KPU, and Adaro; and (4) three biomasses, wood pellet (WP), palm kernel shell (PKS), and empty fruit bunch (EFB). Typically, pulverized coal combustors require a specific particle size range. Therefore, the above samples were crushed into particles with 75−90 μm (coals) and 400−600 μm (biomasses) diameters. The pulverized samples were put in a closed glass vial containment to prevent any kind of sample alteration. Proximate and Ultimate Analyses. To determine the solid fuel grades and their chemical composition, proximate and ultimate analyses were conducted using the thermogravimetric analyzer (TGA) and the ultimate analyzer (UA). The results of these analyses were then arranged on the basis of the fixed carbon (FC) content and then categorized according to fuel grade (see Table 2). Thermogravimetric Analysis−Differential Scanning Calorimetry (TGA−DSC). To obtain the reaction rate of solid fuel char combustion with air (21% O2), TGA−DSC was used in this study. The char-making process was performed directly in the TGA−DSC unit by increasing the temperature up to 950 °C at 20 °C/min increments under 1 bar N2 atmosphere and holding isothermally for 10 min. After the char-making process, the temperature was then

(4) B


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Energy & Fuels decreased to 650 °C at 20 °C/min decrements under 1 bar N2 atmosphere. The flow rate of N2 was fixed at 300 mL/min. After the temperature reached 650 °C, the atmosphere changed into air with a 300 mL/min flow rate, which supported combustion. The samples were then held in this state for 20 min, and after this process, the char was believed to have completely burned. To analyze the results, especially the burnout rate data that are required in this case, the starting point and end point of the reaction are critical. Therefore, an estimation of the starting point was obtained by finding the intersection of the regression of the average constant char weight line and the average reducing char weight line (see Figure 1). The end point can be determined using the same method.

pore enlargement is not entirely applicable for a carbonaceous fuel with impurities (ash) and low sphericity. For high-accuracy modeling, the reaction rate development correlation was proposed in this study, as shown below dx = kFERPM[(1 − x)a 1 − ψFERPM ln(1 − x) dt tanh(cx) + (1 − x)b ]

(6)

where kFERPM is the initial reaction rate as a function of the temperature and a, b, and c are the extra parameters for improving the accuracy of the prediction. The idea behind developing an enhanced flexibility model is to combine several models into a general model. Similar to the kinetic diffusion model, which features contributions of reaction- and diffusioncontrolled models, the reaction actually occurs via both pathways, with proper weighing factors required for different conditions. The internal−external intrinsic reaction rate mechanism also relies on the same concept, using internal and external effectiveness factors for weighing. Equation 6 in this work was developed in the same way, putting more emphasis on the empirical results derived from experimental data, owing to the aim of this work. The tangent hyperbolic function is derived from the tendency of low-carbon content fuels to produce an increment in ASA at the late stage of the reaction. Addition of the term (1 − x)b increases the flexibility of the model, allowing it to overcome the tendency of volumetric or grain model reactions when the ASA decreases. High values of c and b will return the model to its basic state. Setting c to 0 and giving b a value that ranges from 0.3 to 1 will produce a nth-order reaction model. This equation can sophisticatedly cover a broad range of solid fuel kinetic models. The basics for combining this new model were also studied by Lopez et al.,24 who considered a homogeneous model, shrinking core model, nth-order model, and RPM. Except for the a value, the model cannot be explained by any physical attributes of the fuels; however, the model has been proven to improve the accuracy of the carbonaceous solid fuel combustion rate prediction, as demonstrated in Figure 6 and Table 3. Many researchers have derived models from physical attributes and/or chemical properties of test substances. However, owing to the random shapes and pore structures of a broad range of carbonaceous solid fuels, a model that is a derivation result of empirical data was used by perforce to obtain a high-accuracy prediction.

Figure 1. Determining the starting point of the reaction by linear regression intersection. However, a simpler method can be used, whereby the end point is defined as a point after the burnout rate falls below 1%/min. This method can be applied to all coals and biomasses. Scanning Electron Microscopy (SEM). The char morphologies are important for this study, because the model proposed is based on the physical approach. Therefore, SEM was used to quantitatively determine the physical characteristics of the raw coal and char. The images of raw fuels and chars were taken using SEM at 1800× and 3000×. For the biomasses, the images were taken at 150× and 200×, owing to their larger particle size, and for the biomass surface analyses, the images were taken at 2000×.

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FLEXIBILITY-ENHANCED RANDOM PORE MODEL (FERPM) There is a phenomenon in pore structure development of lowrank coal and biomasses, in which the reaction rate does not decrease after the carbon conversion state is more than 0.4, as predicted by the currently used RPM. Dassapa et al.11 examined this phenomenon by measuring the specific surface area of different biomass chars at conversions of up to 80% using the Brunauer−Emmett−Teller (BET) technique, revealing only weak variations, whereas Lussier et al.18 reported a continuous increase of the surface area for beech wood char. However, most results show a major surface area change at the initial reaction stage, followed by a smaller change at later stages, as summarized by Gil et al.17 Brown coal shows a similar surface area development pattern, as highlighted by Agarwal and Sears.19 There is a lack of consensus among researchers regarding the importance of the concentration of active sites on the char surface in determining char conversion kinetics.20−23 The reactivity of char is not solely affected by its specific surface area; it is also affected more or less by its active site area (ASA). Therefore, pure modeling of the surface area development by

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RESULTS AND DISCUSSION Chemical and Physical Analyses. The physical and chemical properties determined by proximate and ultimate analyses are listed in Table 2. Lower FC and ash contents were generally observed for low-grade fuel, especially for biomass, with moisture and volatile contents increasing with a decreasing fuel grade. On a dry and ash-free (daf) basis, coals and biomasses exhibited extremely different C and O contents, whereas the H contents were relatively stable in the range of 4− 6%. The N and S contents of biomass were close to zero, being far lower than those of coals. SEM imaging revealed the qualitative differences between raw fuel and char structures (see Table 3), revealing that FC content (fuel grade) is positively correlated with particle sphericity and negatively correlated with porosity, particularly for biomass fuels, which exhibit more fibrous and elongated C


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Energy & Fuels

Table 3. SEM Results, TGA Experimental Results, and RPM and FERPM Fitting Comparisons for (a) Semi-anthracite and Bituminous Coals, (b) Sub-bituminous Coals, and (c) Biomasses

D


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Energy & Fuels Table 3. continued

E


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Energy & Fuels Table 3. continued

solid fuels with spherical particles. The image of swelled Moolarben coal char showed a smooth surface, owing to the molten contents covering its pores. As a result, the reaction rate

structures. These structures can significantly affect the combustion process and the RPM, which failed to predict the behavior of biomasses when first developed for microporous F


Article

Energy & Fuels of this char was reduced far more than it would have been in the case of non-swelled coal. The results of TGA analyses are presented in Table 3; the raw data were normalized from weight loss into carbon conversion, in which the result points are shown by the symbols. Fuel reaction rates increased with a decreasing carbon content, reaching maxima of 15, 20, 25, and 45%/min for semianthracite coals, bituminous coals, sub-bituminous coals, and biomasses, respectively. This behavior was mainly attributed to the effects of lower carbon content and higher porosity discussed above. Comparison of RPM to FERPM. The results of the TGA− DSC experiment were then analyzed and fitted onto RPM and FERPM. The results are shown in Table 3. The results of the experiment with semi-anthracite char showed good agreement with RPM; therefore, significant improvements were not obtained when FERPM was used. The results of the bituminous char experiment had little disagreement with RPM; therefore, slight improvements were observed when FERPM was applied. The Moolarben char was a special case; owing to its swelling characteristics during the char-making process, the pores that it developed were coated by the sintering effect of its melted carbonaceous substrance, increasing its sphericity and lowering its porosity. This change gave it characteristics that were similar to those of the semi-anthracite char. Therefore, a good agreement between the results of the experiment with Moolarben char and RPM was achieved for the combustion process. The results of the experiment with sub-bituminous chars had a large disagreement with RPM; therefore, significant improvements were achieved when FERPM was applied. On the basis of the results, particle sphericity, ash content, and number of macropores were assumed to affect the ASA development pattern. The experiment using biomass chars furnished results that significantly disagree with the RPM prediction, implying that a significant improvement was achieved in the case of FERPM. The fibrous shape, lower ash content, and large number of macropores of WP and EFB, which are easily found in other types of biomasses, were assumed to significantly affect ASA development, resulting in a constant reaction rate up to late conversion stages. The fitting results, correlation factor, and percent deviation are shown in Figure 2. The deviation was calculated using the following equation:

⎛ dx ⎞ DEV⎜ ⎟ (%) = 100 ⎝ dt ⎠

Figure 2. Fitting correlation factors and residues for different kinds of carbonaceous solid char.

porosity ( 50%), the RPM was a better model, especially for the late stage of combustion (see Figure 6a for the period of 6−11 min and H


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Energy & Fuels

Figure 6. (a) Semi-anthracite, (b) bituminous, (c) sub-bituminous, and (d) biomass carbon conversion states over time, with a comparison between experimental data, the RPM prediction, and the FERPM prediction.

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ACKNOWLEDGMENTS This work was supported by grants from the Human Recources Development Program (20144010200780) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) funded by the Korean government’s Ministry of Trade, Industry and Energy.

carbonaceous solid fuels, the larger disagreements between experimental results and RPM were observed in this study, especially in calculating late-stage combustion, in which case the RPM underpredicted the carbon conversion result. (2) With decreases in the FC content, the ath order in the FERPM decreased according to the logistic function and ranged from 1 to 0.4. The prediction function was successfully established for non-swelling coals. (3) The FERPM was successfully established and very useful for high-accuracy modeling of the combustion of a broad range of carbonaceous solid fuels, and the fitting errors were suppressed to under 3%, with a 0.99 correlation factor. (4) The qualitative assessment of SEM images showed that, as the FC content decreased, more porosity and macropores were observed. Furthermore, subbituminous coals became non-spherical, and biomasses became more fibrous. (5) The correlation of additional FERPM parameters b and c to physical and/or chemical properties is a challenge for future research.

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NOMENCLATURE a = FERPM parameter b = FERPM parameter c = FERPM parameter i = data sample number k = initial reaction rate (s−1) N = number of total data population t = time (s) x = carbon conversion

Greek Letters

λ = structural parameter increment factor (FRPM) τ = time step (s) ψ = structural parameter

AUTHOR INFORMATION

Corresponding Author

Subscripts

*E-mail: [email protected].

calc = calculation result exp = experimental result FERPM = flexibility-enhanced random pore model FRPM = fractal random pore model GM = grain model

ORCID

Kevin Yohanes Lisandy: 0000-0002-0876-1280 Notes

The authors declare no competing financial interest. I


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Energy & Fuels

(21) Radovic, L. R.; Walker, P. L.; Jenkins, R. G. Importance of Carbon Active-Sites in the Gasification of Coal Chars. Fuel 1983, 62 (7), 849−856. (22) Van de Steene, L.; Tagutchou, J. P.; Escudero Sanz, F. J.; Salvador, S. Gasification of wood chip particles: Experimental and numerical study of char−H2O, char−CO2, and char−O2 reactions. Chem. Eng. Sci. 2011, 66 (20), 4499−4509. (23) Radovic, L. R. Importance of Carbon Active Sites in Coal Char Gasification8 Years Later. Carbon 1991, 29 (6), 809−811. (24) Lopez, G.; Alvarez, J.; Amutio, M.; Arregi, A.; Bilbao, J.; Olazar, M. Assessment of steam gasification kinetics of the char from lignocellulosic biomass in a conical spouted bed reactor. Energy 2016, 107, 493−501. (25) Xie, K.-C. Structure and Reactivity of Coal: A Survey of Selected Chinese Coals; Springer: Berlin, Germany, 2015; DOI: 10.1007/978-3662-47337-5. (26) Hill, S. C.; Smoot, L. D. Modeling of nitrogen oxides formation and destruction in combustion systems. Prog. Energy Combust. Sci. 2000, 26 (4−6), 417−458. (27) Zhou, H.; Liu, Z. H.; Cheng, M.; Zhou, M. X.; Liu, R. P. Influence of Coke Combustion on NOx Emission during Iron Ore Sintering. Energy Fuels 2015, 29 (2), 974−984. (28) Zhou, H.; Zhou, M. X.; Liu, Z. H.; Cheng, M.; Chen, J. Z. Modeling NOx emission of coke combustion in iron ore sintering process and its experimental validation. Fuel 2016, 179, 322−331. (29) Bugge, M.; Skreiberg, O.; Haugen, N. E. L.; Carlsson, P.; Houshfar, E.; Lovas, T. Numerical simulations of staged biomass grate fired combustion with an emphasis on NOx emissions. Energy Procedia 2015, 75, 156−161.

RPM = random pore model VM = volumetric model

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REFERENCES

(1) Lisandy, K. Y.; Kim, J. W.; Lim, H.; Kim, S. M.; Jeon, C. H. Prediction of unburned carbon and NO formation from low-rank coal during pulverized coal combustion: Experiments and numerical simulation. Fuel 2016, 185, 478−490. (2) Lisandy, K. Y.; Kim, R. G.; Hwang, C. W.; Jeon, C. H. Sensitivity test of low rank Indonesian coal utilization using steady state and dynamic simulations of entrained-type gasifier. Appl. Therm. Eng. 2016, 102, 1433−1450. (3) Bahrami, R.; Ebrahim, H. A.; Halladj, R. Comparison of random pore model, modified grain model, and volume reaction model predictions with experimental results of SO2 removal reaction by CuO. J. Ind. Eng. Chem. 2015, 30, 372−378. (4) Everson, R. C.; Neomagus, H. W. J. P.; Kaitano, R. The random pore model with intraparticle diffusion for the description of combustion of char particles derived from mineral- and inertiniterich coal. Fuel 2011, 90 (7), 2347−2352. (5) Walker, P. L.; Rusinko, J. F.; Austin, L. G. Gas reactions of carbon. Adv. Catal. 1959, 11, 133−221. (6) Safari, V.; Arzpeyma, G.; Rashchi, F.; Mostoufi, N. A shrinking particle-shrinking core model for leaching of a zinc ore containing silica. Int. J. Miner. Process. 2009, 93 (1), 79−83. (7) Wu, Y. Q.; Wu, S. Y.; Gao, J. S. A Study on the Applicability of Kinetic Models for Shenfu Coal Char Gasification with CO2 at Elevated Temperatures. Energies 2009, 2 (3), 545−555. (8) Gavalas, G. R. A Random Capillary Model with Application to Char Gasification at Chemically Controlled Rates. AIChE J. 1980, 26 (4), 577−585. (9) Bhatia, S. K.; Perlmutter, D. D. A Random Pore Model for FluidSolid Reactions. 1. Isothermal, Kinetic Control. AIChE J. 1980, 26 (3), 379−386. (10) Bhatia, S. K.; Perlmutter, D. D. A Random Pore Model for Fluid-Solid Reactions. 2. Diffusion and Transport Effects. AIChE J. 1981, 27 (2), 247−254. (11) Dasappa, S.; Paul, P. J.; Mukunda, H. S.; Shrinivasa, U. The Gasification of Wood−Char Spheres in CO2−N2 MixturesAnalysis and Experiments. Chem. Eng. Sci. 1994, 49 (2), 223−232. (12) Fatehi, H.; Bai, X. S. Effect of pore size on the gasification of biomass char. Energy Procedia 2015, 75, 779−785. (13) Mermoud, F.; Golfier, F.; Salvador, S.; Van de Steene, L.; Dirion, J. L. Experimental and numerical study of steam gasification of a single charcoal particle. Combust. Flame 2006, 145 (1−2), 59−79. (14) Wang, G. W.; Zhang, J. L.; Shao, J. G.; Liu, Z. J.; Wang, H. Y.; Li, X. Y.; Zhang, P. C.; Geng, W. W.; Zhang, G. H. Experimental and modeling studies on CO2 gasification of biomass chars. Energy 2016, 114, 143−154. (15) Fei, H.; Hu, S.; Xiang, J.; Sun, L. S.; Fu, P.; Chen, G. Study on coal chars combustion under O2/CO2 atm with fractal random pore model. Fuel 2011, 90 (2), 441−448. (16) Fei, H.; Sun, L. S.; Hu, S.; Xiang, J.; Song, Y.; Wang, B.; Chen, G. The combustion reactivity of coal chars in oxyfuel atmosphere: Comparison of different random pore models. J. Anal. Appl. Pyrolysis 2011, 91 (1), 251−256. (17) Gil, S.; Mocek, P.; Bialik, W. Changes in Total Active Centres on Particle Surfaces during Coal Pyrolysis, Gasification and Combustion. Chem. Process Eng. 2011, 32 (2), 155−169. (18) Lussier, M. G.; Zhang, Z.; Miller, D. J. Characterizing rate inhibition in steam/hydrogen gasification via analysis of adsorbed hydrogen. Carbon 1998, 36 (9), 1361−1369. (19) Agarwal, A. K.; Sears, J. T. The coal char reactions with CO2− CO gas mixtures. Ind. Eng. Chem. Process Des. Dev. 1980, 19 (3), 364− 371. (20) Laurendeau, N. M. Heterogeneous Kinetics of Coal Char Gasification and Combustion. Prog. Energy Combust. Sci. 1978, 4 (4), 221−270. J


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