Percolation model for simulation of coal combustion process

Proceedings of the Combustion Institute, Volume 29, 2002/pp. 459–466

PERCOLATION MODEL FOR SIMULATION OF COAL COMBUSTION PROCESS AKIRA SUZUKI,1 TSUYOSHI YAMAMOTO,2 HIDEYUKI AOKI2 and TAKATOSHI MIURA2 1

CD-adapco Japan Ltd. 16F Nisseki Yokohama Building, 1-1-8 Sakuragi-cho Naka-ku Yokohama-city 231-0062, Japan 2 Department of Chemical Engineering Tohoku University 07 Aza-Aoba Aramaki Aoba-ku Sendai-city 980-8579, Japan

A pulverized coal combustion simulation model applying a percolation theory based on a Monte Carlo method has been developed to predict swelling and fragmentation behaviors during a coal combustion process. The shape of pulverized coal particles before reaction was assumed as a three-dimensional cube arranged in large number of small lattices. These lattices were classified into char, volatile, ash, or macropore, depending on the coal’s industrial analysis value, and they were arranged randomly in the cubic. The coal combustion processes were classified as devolatilization and char combustion, and they were assumed to occur simultaneously. In the devolatilization process, the dual-competing reaction model determined the devolatilization time of a volatile lattice. With coal devolatilization, the coal particles swelled due to increase in internal pressure. With char combustion, O2 lattices were arranged around a coal particle and the random walk model was applied to represent the O2 diffusion behavior. Furthermore, the char reaction model was applied to determine the char reaction time. Thus, a char lattice was lost when its total reaction time was longer than the O2 diffusion time and the reaction time. With char combustion, ash agglomeration occurred. Char combustion finished when all of char lattices were burned out or the char lattices were completely surrounded by ash lattices, preventing oxygen lattices from coming into contact with the char lattices. It was shown that this model well represents the difficulty of char burnout caused by increase in diffusion resistance in the latter period of the reaction. A particle temperature profile was determined by a model calculation in an environment in which atmospheric temperature was 1500 K. Using only the industrial coal properties, this model predicts detailed variations of reaction rate, porosity, and maximum relative particle diameter with particle conversion in the pulverized coal combustion process.

Introduction It is very important to understand combustion behaviors of individual coal particles to achieve effective coal combustion control. Coal particles injected into a furnace are heated very rapidly at a heating rate between 104 and 105 K/s. The reaction processes in the coal combustion are roughly classified into a devolatilization process, caused by coal pyrolysis, and a char combustion process. In the coal heating process, coal softening and resolidifying behaviors are evident. It is well known that swelling occurs in the coal softening process. This occurs because the generated volatile causes the coal particle size to increase, due to the increase in the internal pressure. Furthermore, fragmentation occurs, causing the particle diameter to change suddenly in the latter period of the combustion process. However, it is very difficult to understand these coal combustion behaviors, because coal properties vary depending on the coal type, and the reaction occurs at high temperature and under complicated reaction fields. 459

In spite of these difficulties, various coal combustion models have been developed. However, according to Sahimi et al. [1], the former reaction models such as the volume reaction model, the grain model, the pore model, and the unreacted-core shrinking model cannot express the particle fragmentation behavior because they treat coal particles as continuum objects. Monte Carlo simulations based on percolation theory for char combustion processes (percolation model) have been under development since the 1980s [2,3]. A particular merit of percolation models is that they can take into account of the heterogeneous structure and the fragmentation behavior of char particle. They define a particle as an object arranged in a large number of interconnected lattices. Thus, particles fragment in a reaction process in which lattices are lost and the connection are burned out. Simulated and experimental results were compared among variations of pore structure, surface

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ENERGY PRODUCTION—Biomass, Coal, and Char Combustion

area, and conversion with reaction time [4]. Furthermore, processes of ash transfer, ash agglomeration, and fly ash release were expressed by percolation models [5,6]. For particle fragmentation, the difference in degree of swelling and porosity in the devolatilization process is very important. Kang et al. also carried out a simulation that considered the difference in pore structure with heating rates in coal pyrolysis [7]. Because all of these models are based on the same percolation theory, it is possible to develop them into a total coal combustion model. Thus, a percolation model is developed in this study, involving both the devolatilization process with particle swelling and the char reaction process with ash agglomeration to express total coal particle combustion behaviors. In the devolatilization process, the dual-competing reaction model is applied to calculate the reaction time. The swelling behavior caused by increase in pressure within the coal particle is considered. In the char reaction process, diffusion of oxygen is considered by applying a random walk theory. A char reaction model is applied to calculate the char reaction time. Ash agglomeration is also taken into account. The difference in reactivity caused by variations in coal type is considered. Variations in reaction rate, porosity, and maximum relative particle diameter with particle conversion are discussed on the basis of simulated results which are calculated from the industrial coal properties. Model Description Coal Combustion Kinetics In this simulation model only one coal particle is considered because it assumes that the particles are far enough apart to behave independently. Also it is assumed that the initial coal particle is a simple three-dimensional cube in size L ⳯ L ⳯ L, arranged in smaller cubic lattices in size l ⳯ l ⳯ l. Thus, the total number of smaller cubic lattices is (L/l)3. The coal particle is arranged in Cartesian cubic coordinate of LM ⳯ LM ⳯ LM (LM ⬎ L) to represent coal particle swelling behaviors. The lattice components are distinguished between char, volatile, ash, and pore. Each lattice is arranged uniformly within the coal particle according to the weight fraction of each component as determined by the coal’s industrial analysis. Moisture is neglected because of its small quantity. Every solid lattice (except for pore) is defined to be connected with 26 neighbor lattices. The coal reaction process is classified into a homogeneous combustion process in the gas phase after devolatilization and a heterogeneous char combustion process. It is considered that the char combustion rate is generally faster than the devolatilization rate. However, it is reported that the devolatilization and char

surface reaction proceed simultaneously in the actual combustion process, because oxygen reaches the char surface caused by the slow release rate for volatile or the fact that devolatilization proceeds only on particular parts of the coal surface. According to Smoot et al. [8], the devolatilization and the char reaction proceed simultaneously at almost the same ratio for small particles. Thus, this study assumes that the devolatilization and the char reaction proceed simultaneously. Reaction Model Devolatilization Process Various pyrolysis models have been suggested to predict devolatilization behavior. However, prediction of the behavior is still very difficult because of the heterogeneity of coal properties. Here, the dualcompeting reaction model is employed to predict the devolatilization process, because this model is often used in commercial simulators for its convenience and accuracy at high temperatures. The equation of the dual-competing reaction model by Ubhayakar et al. [9] is dV ⳱ (␣1kV1 Ⳮ ␣2kV2)C dt

(1)

As a result of the transformation of equation 1, the time tV0 required to consume an arbitrary volatile lattice is tV0 ⳱

(␣1kV1

qV l 3 Ⳮ ␣2kV2)C

(2)

It is well known that coal particles swell under the devolatilization process. This occurs during the coal softening stage in the devolatilization process, resulting from the fact that volatile covers a particle’s pores (including micro-, meso-, and macropores) and that the internal pressure of the coal particle increases. The softening behavior of coal has been discussed from the viewpoint of coal viscosity [10,11]. Melta and Bowman characterized coal viscosity by three temperature-bounded zones: a rigid zone, a plastic zone, and a resolidifying zone based on a softening point and a resolidifying point (three-zone model). Coal swelling occurs in the plastic zone in this model. However, it is very difficult to define them in a large heating rate reaction field, such as that of pulverized coal combustion, because it is considered that the softening point and the resolidifying point varies with the heating rate. On the other hand, it is considered that the coal viscosity (softening degree) decreases with increase in the fraction of metaplast which is liquid tar in the coal particle. Thus, it is considered that, during the

PERCOLATION MODEL FOR COAL COMBUSTION

k⬘C ⳱ A exp(ⳮEa/RTp)

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at Tp ⬍ 1400 K and

k⬘C ⳱ (ⳮ0.49 ⳯ 103 Ⳮ 0.385Tp) at Tp ⱖ 1400 K Consequently, the chemical reaction time of one lattice tcr is tcr ⳱ qC l/k⬘CPO2

Fig. 1. Image of the swelling behavior of coal in the devolatilization process (V, volatile; C, char; A, ash; D, devolatilization; r, swelling direction).

devolatilization process, the coal particle swells because its internal pressure increases and its viscosity decreases due to the presence of metaplast in the coal particle. This study also adopts the concept that particles swell during the devolatilization process. An image illustrating the swelling behavior of coal in the devolatilization process is shown in Fig. 1. In the simulation model, if a volatile lattice is chosen arbitrarily as a reaction lattice, that lattice is lost. As the result, all six lattices surrounding the lost lattice are pushed out of the particle by some lattice length. In regard to the determination of the length, one lattice length is chosen because of the simplification, although it is necessary to take into account of the viscosity of metaplast, porosity, and porous structure of coal and the volume valance between released volatiles and displaced lattices. This increases the particle diameter and the porosity. The devolatilization process continues until all of volatile lattices are lost. Actually, some of pyrolytic gas and tar may deposit in the coal particles due to the low permeability of the coal particle. However, this study neglects this part, because it is considered to be included in the fixed carbon of the industrial analysis.

Char Combustion Process The char combustion rate is determined by both the chemical kinetic reaction rate and the diffusion rate to the particle surface and internal pore for the reactive gas. This study considers the surface reaction which is given in equation 3 as a dominant reaction of char combustion: C Ⳮ O2 r CO/CO2

(3)

The surface reaction rate by Field [12] is shown in equation 4 as dC ⳱ k⬘CPO2 l 2 dt where

(4)

(5)

When the surrounding gas and the particles are at a high temperature, the chemical kinetic reaction ratio increases exponentially. This means that the reaction rate is subjected to the diffusion rate for the reactive gas to the particle surface and the internal pore. Hence, the diffusion behavior of the reactive gas (especially oxygen) to the surface and inner pore is very important to the char combustion process. Previous char reaction models applied to percolation theory are classified as uniform reaction models and diffusion limited reaction models. Uniform reaction models express the char reaction by losing a surface char lattice randomly. Thus, the reactivity of all the surface char lattices is the same, even if the locations of the surface lattices of the internal pore and the surface shell are different. The diffusionlimited reaction model expresses the reaction by losing a surface char lattice that has reacted with oxygen [13]. Thus, the difference in reactivity caused by the difference in the location can be taken into account. Therefore, the study also applies to the diffusionlimited reaction model. A diffusion process is expressed by taking a broad view of the random walk motion for molecules [14]. The diffusion coefficient for oxygen based on threedimensional random walk theory is 1 2 ␣C (6) 6 The jumping distance of an oxygen molecule ␣ is much smaller than the lateral size of the lattice l for this percolation model. However, it is necessary to define an oxygen lattice that includes oxygen molecules with the volume fraction of oxygen and to consider oxygen diffusion by a unit of the lattice’s length in this simulation model. Thus, it is necessary to consider the time required for an oxygen molecule to pass through one lattice length to relate the microscopic motion of oxygen to the macroscopic one. The RMS translated distance for an oxygen molecule after n time’s jump is (7) 冪R¯ 2a ⳱ 冪n␣ ⳱ 冪6DO t DO2 ⳱

2

The transformation of equation 7 gives the average time tN to pass N lattices for an oxygen lattice shown as (Nl)2 (8) 6DO2 Thus, when an oxygen lattice passing (N ⳮ 1)’s lattices moves to N’s lattice, the average time required to move the oxygen lattice is tN ⳱

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ENERGY PRODUCTION—Biomass, Coal, and Char Combustion 1.75

冢T 冣

P0 (10) P The diffusion process for pulverized coal combustion is subjected to diffusion of oxygen in the internal pore of the coal particle. Thus, the effective diffusion coefficient DeffO2 is DO2 ⳱ D0O2

T

0

DeffO2 ⳱ c0DO2 (11) A char lattice reaction time tr is shown as equation 12, because the chemical reaction rate and the diffusion rate for oxygen determine the char reaction rate. Fig. 2. Image of random walk of oxygen lattices around a coal particle (V, volatile; C, char; A, ash; O2, oxygen; r, direction of movement of oxygen lattice).

tr ⳱ dmax1[tcr, tm] (12) Here, the function dmax1 means the largest one between brackets. According to equation 3, there must be at least the same number of oxygen lattices m as the half-mole number of carbons organized in a char lattice to burn out a char lattice. Thus, m is shown as 1 qC l 3 PfO2 l 3 (13) 2 mC RT Figure 2 shows an image of a random walk of oxygen lattices. In the simulation model, the oxygen lattices are arranged outside the surface lattice for the coal particle because of the assumption that oxygen is distributed uniformly around the coal particle. The oxygen lattices that satisfy equation 9 are moved randomly to one of the six neighbors unless there is another oxygen, volatile, or ash lattice. It is assumed that if an oxygen lattice reaches a char lattice, the oxygen included in the oxygen lattice reacts with char and then CO/CO2 generated by the reaction is quickly removed. When a char lattice takes the first oxygen lattice, the reaction starts and chemical kinetic reaction time tcr is calculated by equation 5. According to equation 12, when the passage time of a char lattice becomes longer than the time of both the oxygen diffusion and the chemical kinetic reaction, the char lattice is lost. This study also considers ash agglomeration. Fig. 3 shows an image of ash transfer. If the ash lattice is located where the neighbor is the lost char lattice and all of the five neighbor lattices except for the lost char lattice are pore lattices, the ash lattice transfers to the lost char lattice position caused by ash’s surface tension. This is because the ash melts in the high-temperature region. Actually, the char reaction proceeds simultaneously in the plural char lattices. The char reaction continues until all char lattices are lost or only char lattices surrounded by ash lattice remain, because no oxygen can reach the char surface. m⳱

Fig. 3. Image of ash transfer (V, volatile; C, char; A, ash; B, burnout char).

TABLE 1 Coal properties for simulation Coal type

Newlands

Volatile weight fraction in solid phase Carbon weight fraction in solid phase Ash weight fraction in solid phase Volatile density in solid phase Fixed carbon density in solid phase Ash density in solid phase Porosity Particle diameter

t(Nⳮ1)rN ⳱

Taiheiyo

0.299

0.502

0.554

0.369

0.147

0.129

1200 [kg/m3]

1200 [kg/m3]

1200 [kg/m3] 2500 [kg/m3] 0.20 50 [lm]

1200 [kg/m3] 2500 [kg/m3] 0.20 50 [lm]

l2 [N2 ⳮ (N ⳮ 1)2] 6DO2

(9)

The diffusion coefficient varies with temperature, pressure, and the structure of the object to diffuse. The experimental equation for diffusion coefficient is [15]

冫

Calculation Conditions Coal properties and calculation conditions are shown in Tables 1 and 2, respectively. To clarify the

PERCOLATION MODEL FOR COAL COMBUSTION TABLE 2 Calculation condition Maximum lattice number: LM ⳯ LM ⳯ LM Initial lattice number: L ⳯ L ⳯ L Initial temperature Atmospheric temperature Volume fraction of oxygen Gas pressure

100 ⳯ 100 ⳯ 100 40 ⳯ 40 ⳯ 40 623.15 K 1500 K 0.1 1.013 ⳯ 105 Pa

difference of the swelling behavior resulting from the volatile quantity of coal, two types of coal are considered: Newlands coal (a semibituminous coal) and Taiheiyo coal (lignite). Temperature History Variations of temperature during the pulverized coal combustion process greatly influence the reaction. However, it is very difficult to predict the particle temperature distribution because the temperature in a coal particle varies during very short time.

463

To determine the particle temperature, it is assumed that the temperature distribution in a coal particle is uniform and the particle shape is spherical with the diameter resulting from the percolation simulation. The temperature history of a coal particle combustion process was calculated assuming 1500 K for surrounding temperature. The energy equation of a coal particle injected into a combustion furnace is Cpmp

dTp ⳱ Qpc Ⳮ Qpr Ⳮ Qpb Ⳮ Qpl dt

(14)

Results and Discussion Figure 4 shows variations in the morphology for Newlands and Taiheiyo coal particle. As the reaction proceeds, both coal particles swell with devolatilization. Then reduction and fragmentation occur with char combustion. Furthermore, the char lattices retreat inside the particles as the reaction proceeds, since oxygen penetrates through the particle surface. For the Newlands coal particle, volatile and char lattices are lost almost uniformly. For the Taiheiyo coal particle, the volatile lattices remain until

Fig. 4. Simulated results of coal combustion behaviors: (a) Newlands coal; (b) Taiheiyo coal (䊏, volatile; 䊏, char; 䊐, ash).

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ENERGY PRODUCTION—Biomass, Coal, and Char Combustion

Fig. 5. Variations of non-dimensional reaction rate and particle temperature with conversion.

Fig. 6. Variations of non-dimensional maximum relative particle diameter and porosity with conversion.

the latter period of the reaction because it has a higher volatile fraction. Figure 5 shows the simulated result of variations of non-dimensional reaction rate and particle temperature with conversion for Newlands and Taiheiyo coal. The reaction rate increases in the early period of the reaction and then decreases. The reaction rate is greatly influenced by the temperature profile. However, in the latter period of the reaction, the oxygen penetration resistance is also one of the major factors of the decreased reaction rate. Actually, Fig. 5 shows the simulated results up to 99% conversion, because the reaction almost stops after that due to the greatly increased resistance to oxygen diffusion. This simulated result shows the difficulty of controlling coal burnout. Therefore, the diffusionlimited reaction model is very important in simulating coal combustion behaviors. Figure 6 shows the simulated variations of nondimensional maximum relative particle diameter and porosity with conversion for Newlands and Taiheiyo coal. Here, the value of the maximum relative particle diameter is the cubic root of the number of all lattices organized a maximum fragment (including

pore lattice) in the fragments of a simulated coal particle. The particle diameter increases in the early period of the reaction and decreases in the latter period of the reaction. The particle diameter of Taiheiyo coal is slightly larger than that of Newlands coal. This is because Taiheiyo coal swells more than Newlands coal since Taiheiyo coal releases more volatile. However, because the porosity also increases, the particle fragmentation is stimulated as the reaction proceeds, and the particle diameter decreases suddenly. This model assumes that ash melts and translates easily forced by the surface tension in the high-temperature atmosphere. However, ash may not melt in the real condition owing to the ash component and temperature distribution in the coal particle. Thus, to predict ash aggregation, it is desirable to predict ash viscosity (melting degree) by a numerical model such as the Urbain model [16], which can predict the viscosity of ash arranged a large number of inorganic components. Although it is very difficult to adopt a swelling model which assumes that particle shape is spherical [10] to the percolation model, it is desirable to develop a swelling model involving behaviors that coal viscosity (softening degree) decreases with increase in the metaplast fraction and the internal pressure increases. Furthermore, it is desired to predict the variations of volatile and fixed carbon fraction which actually varies with heating rate, temperature, and pressure surrounding a coal particle. This simulation model can predict various parameters for a single coal particle in the coal combustion process. These simulated results and experimental results need to be compared. Conclusions A pulverized coal combustion simulation model that applied a percolation theory based on a Monte Carlo method was developed to predict swelling and fragmentation behaviors in a coal combustion process. The simulation was carried out for Newlands coal and Taiheiyo coal, which have different volatile fractions. This simulation model can predict swelling, reduction, and fragmentation behaviors in a coal combustion process for different kinds of coal. Furthermore, an oxygen diffusion-limited model can predict the difficulty of coal burnout in the latter period of the reaction. From the results of variations of reaction rate, porosity, and maximum relative particle diameter with conversion, we can get detailed data that cannot be obtained by previous global treatments of coal combustion such as a those assuming that coal particles are spherical. To develop a quantitative model, it is desirable to compare simulated and experimental results. The

PERCOLATION MODEL FOR COAL COMBUSTION

simulated results are useful for predicting detailed particle behaviors in total coal combustion simulations. Nomenclature A C C0 Cp c0 DO2 D0O2 DeffO2 Ea fO2 k⬘C kV1, kV2 L LM l m mC mp N n P P0 PO2 Qpb Qpc Qpl Qpr R Rn T T0 Tp t t tcr tm tN

pseudo frequency factor (⳱ 85.98) [kg C/(m2 s Pa O2)] mass of char lattice [kg] row coal mass [kg] specific heat of a coal particle [J/(kg K)] morphological coefficient (⳱ 0.2) diffusion coefficient for oxygen [m2/s] diffusion coefficient for oxygen at 273.15 K and 1.013 ⳯ 105 Pa (⳱ 1.78 ⳯ 10ⳮ5) [m2/s] effective diffusion coefficient for oxygen [m2/s] pseudo activation energy (⳱ 1.49 ⳯ 105) [J/mol] volume fraction for oxygen in the air pseudo rate constant [kg C/(m2 s Pa O2)] pseudo rate constant [1/s] lateral length of particle [m] maximum length of coordinate [m] lateral length of lattice [m] number of oxygen lattices to burn out a char lattice molecular weight for carbon [kg/mol] mass of a coal particle [kg] number of passage lattice for oxygen lattice jumping number pressure [Pa] normal pressure (⳱ 1.013 ⳯ 105) [Pa] partial pressure of oxygen [Pa] heat of combustion [J] heat of convection [J] heat of devolatilization [J] heat of radiation [J] gas constant [J/(mol K)] RMS translated distance for an oxygen lattice after n⬘ time’s jump [m] gas temperature [K] gas normal temperature (⳱ 273.15) [K] particle temperature [K] time [s] passage time for n time’s jump for an oxygen molecule [s] chemical kinetic reaction time of char lattice [s] oxygen diffusion time to take m oxygen lattices for a char lattice [s] oxygen diffusion time to pass N lattices [s]

tV0 V ␣

␣1, ␣2 C qC qV

465

devolatilization time for a volatile lattice [s] volatile yield [kg] jumping distance of an oxygen molecule [m] mass stoichiometric coefficient number of oxygen molecule’s jump per unit time (C ⬅ n/t) [1/s] density of char [kg/m3] density of volatile [kg/m3] Acknowledgments

The financial support of the New Energy and Industrial Technology Development Organization (Japan) is gratefully acknowledged.

REFERENCES 1. Sahimi, M., Gavalas, G. R., and Tsotsis, T. T., Chem. Eng. Sci. 45:1443 (1990). 2. Kerstein, A. R., and Niksa, S., Proc. Combust. Inst. 20:941 (1984). 3. Kerstein, A. R., and Edwards, B. F., Chem. Eng. Sci. 42:1629 (1987). 4. Sandmann Jr., C. W., and Zygourakis, K., Chem. Eng. Sci. 41:733 (1986). 5. Kang, S.-G., Helble, J. J., Sarofim, A. F., and Beer, J. M., Proc. Combust. Inst. 22:231 (1988). 6. Miccio, F., Salatino, P., and Tina, W., Proc. Combust. Inst. 28:2163 (2000). 7. Kang, S.-G., Sarofim, A. F., and Beer, J. M., Proc. Combust. Inst. 24:1153 (1992). 8. Smoot, L. D., and Horton, M. D., Prog. Energy Combust. Sci. 3:235 (1977). 9. Ubhayakar, S. K., Stickler, D. B., Von Rosenberg Jr., C. W., and Gannon, R. E., Proc. Combust. Inst. 16:427 (1976). 10. Oh, M. S., Peters, W. A., and Howard, J. B., AIChE J. 35:775 (1989). 11. Melta, P. F., and Bowman, C. T., Combust. Sci. Technol. 31:195 (1983). 12. Field, M. A., Combust. Flame 13:237 (1969). 13. Miccio, F., and Salatino, P., Proc. Combust. Inst. 24:1145 (1992). 14. Shewmon, P. G., Diffusion in Solids, 2nd ed., Minerals, Metals & Materials Society, Warrendale, PA, 1989. 15. Washburn, E. W., et al., International Critical Tables of Numerical Data, Physics, Chemistry and Technology, 1st ed., Vol. 5, prepared under the Auspices of the International Research Council and the National Academy of Sciences, McGraw-Hill, New York, 1929, p. 62. 16. Urbain, G., Cambier, F., Deletter, M., and Anseau, M. R., Trans. J. Br. Ceram. Soc. 80:139 (1981).

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COMMENTS Akira Tomita, Tohoku University, Japan. Prediction of swelling behavior of a particular coal as a function of density would be rather easy. However, a more difficult task would be the prediction of swelling of a variety of coals, since we really don’t know which parameters control the swelling phenomenon. Among many parameters, which ones are the most important ones? Author’s Reply. As you mentioned, there are various parameters. Among those, coal viscosity and internal pressure (difference from external pressure) of coal are very important, since the swelling phenomenon is dominated by a balance between the conservation force of the present shape (viscosity) and the deformation force of the shape (internal pressure). In our opinion, all the other parameters (temperature, porosity, oxygen concentration, ash contents, etc.) could be taken into account as variables of these two parameters.

● Todd Lang, Brown University, USA. Your model computes reaction time by considering when either there remains no more char or the remaining char is surrounded by ash lattice. Have you observed an approximate ash content (%) at which your model tends to go to completion because of surrounding ash rather than because of no remaining char? Author’s Reply. Though char lattices are surrounded by ash lattices theoretically, almost all char lattices are not surrounded by ash lattices in the case of simulation of L ⳯ L ⳯ L ⳱ 40 ⳯ 40 ⳯ 40 lattices. However, conversion from 99% to 100% is very difficult because of the presence of many ash lattices around char lattices. Therefore, char reaction appears to have stopped.