Role of Coke Characteristics in the Regeneration of a Catalyst for the

Jan 6, 1997 - Departamento de Ingeniería Química, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain .... In a previous paper (Benito et...
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Ind. Eng. Chem. Res. 1997, 36, 60-66

Role of Coke Characteristics in the Regeneration of a Catalyst for the MTG Process Jose´ M. Ortega,* Ana G. Gayubo, Andre´ s T. Aguayo, Pedro L. Benito, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain

The effect on combustion in air of the nature of the coke deposited in HZSM5 zeolites used in the MTG process has been studied. This coke is highly hydrogenated and unstable, and its H/C ratio decreases during combustion or when a previous thermal treatment is carried out. Coke H/C ratio greatly affects its reactivity during combustion; consequently, a severe thermal equilibration treatment is recommended for reproducibility of results. Combustion kinetics of equilibrated coke, when it is released from the catalyst, has been proven to be similar to that of the coke deposited on other catalysts for several processes. Lower coke reactivity for aging and combustion, on being deposited within the HZSM5 zeolite, must be attributed to air-coke contact restrictions due to the location of the coke, which partially impedes the flow of air into the crystals. 1. Introduction The MTG process (transformation of methanol into hydrocarbons of boiling point range within that of gasoline) is subjected to the deactivation of the HZSM5 zeolite-based catalyst. The cause of deactivation is coke deposition within the zeolite crystals (Guisnet and Magnoux, 1994). As a consequence of deactivation, MTG process economy requires catalyst regeneration by coke combustion. In industry, the reaction is carried out in an adiabatic fixed bed by reaction-regeneration cycles (Schipper and Krambeck, 1986; Allum and Williams, 1988; Avidan, 1988; Yurcha´k, 1988; Tabak and Yurcha´k, 1990; McDougall, 1991), and it can also be carried out in a fluidized bed with catalyst circulation, which is regenerated in another unit (Avidan and Edwards, 1986; Edwards and Avidan, 1986; Chang and Silvestri, 1987; Socha et al., 1987). Despite the strategic importance of this subject, studies in the literature about regeneration of catalysts used for this process are very scarce. In all of them, it has been pointed out that coke combustion on air or on diluted oxygen is slower than for other catalysts (Bibby et al., 1992). This result is attributed, in the literature, to the effect of the porous structure, to the distance between HZSM5 zeolite acid sites, and to the nature of the sites (Guisnet and Magnoux, 1994). Nevertheless, slow coke combustion is in contradiction to its highly hydrogenated nature. This paper seeks to improve the knowledge about catalyst regeneration kinetics for the MTG process, for which it is necessary to ascertain whether slow coke combustion is due to the coke nature or to the porous structure of the catalyst. This subject has not been studied in the literature, which can be explained on the basis of the difficulty in reproducing the combustion of the coke deposited within the HZSM5 zeolite. This difficulty is due to two peculiar characteristics of the coke (Benito et al., 1996): (1) it is a slightly developed coke, whose structure, and consequently whose combustion, are very sensitive to thermal treatment prior to combustion and (2) the coke is deposited within the crystals of the zeolite and is heterogeneously distributed within the channels and their intersections. To measure the importance of each one of these characteristics, their effect on coke combustion must be studied in isolation. With this aim, this paper has been centered on the study of the effect of coke nature on its combusS0888-5885(95)00733-0 CCC: $14.00

tion. Subsequently, the aging and combustion of the released coke have been compared with the aging and combustion of the coke deposited within the catalyst. By means of this comparison, the restrictions of coke combustion kinetics when it is within the catalyst can be quantified. The coke deposited on HZSM5 zeolites is more hydrogenated than that deposited on other catalysts, and its H/C ratio is dependant on reaction conditions (Dejaifve et al., 1981; Schulz et al., 1987; Sexton et al., 1988; Meinhold and Bibby, 1990). It is slightly developed coke, with low molecular weight components (in the 200-300 mass unit range), which consists of alkylated biaromatics as heavier hydrocarbons (Aguayo et al., 1994). The coke is unstable, and its structure can be altered by aging, which is due to the low molecular weight of its components. Instability of the coke deposited on HZSM5 zeolites has previously been indicated by Nova´kova´ and Dolejsek (1990), who noticed the H/C ratio decrease when the coke was subjected to treatment by pyrolysis. H/C ratio decrease during combustion has been indicated by Carlton et al. (1986). Removal of 34 wt % of coke deposited at 350 °C by a severe degasifying treatment under vacuum (10-4 mmHg at 300 °C) has been reported by Benito et al. (1996). Schulz et al. (1995) have carried out a study on the reactivation of the HZSM5 zeolite by sweeping with an inert gas and on the effect of the reaction conditions on the structure of the coke and its elimination. Coke instability affects combustion kinetics reproducibility, which is a serious problem for obtaining valid kinetic parameters, and, even more serious, it makes combustion control in the reactor difficult. Royo et al. (1994, 1996) have studied the effect of the H/C ratio of the coke on the regeneration of a Cr2O3/Al2O3 catalyst in an adiabatic fixed bed. By virtue of this effect, coke aging prior to combustion is needed. To clarify this aspect, coke aging during the thermal treatment prior to combustion and its effect on coke combustion kinetics have been studied in this paper. The thermal treatment must be, at least, the temperature increase from that of reaction to that of regeneration, which must last the time required for this step and for sample stabilization at the regeneration temperature (in the kinetic study of the regeneration) or for stabilization of the catalyst bed (in the regeneration in the industrial process). Moreover, a sweeping treatment © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 61 Table 1. Denomination and H/C Ratios of the Coke Samples samples of coke released from the catalyst reaction temperature, °C sweeping time at 550 °C, min H/C ratio

samples of coke deposited on the catalyst

1

2

3

4

5

6

1′

2′

3′

4′

5′

6′

350 0 2.35

350 20 1.11

350 60 0.51

400 0 1.75

400 20 0.72

400 60 0.48

350 0 2.35

350 20 1.4

350 60 1.1

400 0 1.75

400 20 1.2

400 60 1.0

with an inert gas at the regeneration temperature is generally needed in order to remove the volatile coke components, whose combustion during regeneration will be uncontrollable. 2. Experimental Section The catalyst has been prepared from a HZSM5 zeolite synthesized according to the methods proposed by Mobil (Argauer and Landolt, 1972). The zeolite has been subjected to an agglomeration process with bentonite (Exaloid), using fused alumina (Martinswerk) as inert charge. The properties of the HZSM5 zeolite are Si/Al, 24; Brønsted/Lewis ratio, 2.9; pore volume, 0.65 cm3 g-1; micropore volume, 0.17 cm3 g-1 (99% of diameter < 0.7 nm); apparent density, 0.94 g cm-3; BET area (ASAP 2000 from Micromeritics), 420 m2 g-1; crystallinity, 93%; crystal size, 6.3 µm. The catalyst properties are particle size, between 0.3 and 0.5 mm; pore volume, 0.43 cm3 g-1; apparent density, 1.21 g cm-3; BET area, 124 m2 g-1. The reaction has been carried out in an automated isothermal fixed-bed integral reactor (Gayubo et al., 1993a) under the following conditions: temperature, within the 350-400 °C range; contact time, 0.03 (g of catalyst) h (g of methanol)-1; time on stream, 6 h; partial pressure of methanol in the feed, 88 kPa, corresponding to 0.32 (g of methanol) min-1, and 37 (cm3 of He) min-1. After the reaction, the catalyst bed was subjected to sweeping the He (100 cm3 min-1) for 30 min. To study coke aging and combustion without any catalyst interference, the catalyst structure has been destroyed by a treatment with hydrofluoric acid, as was proposed by Magnoux et al. (1987). This technique does not affect coke structure (Guisnet and Magnoux, 1989; Magnoux and Guisnet, 1989; Pieck et al., 1992). The entire mass of deactivated catalyst in each run has been previously homogenized, as it has been proven that the amount, and presumably the structure, of coke deposited differ along the longitudinal position in the reactor (Benito et al., 1996). Coke combustion has been studied by thermogravimetry (Setaram TAG 24) and by differential scanning calorimetry (Setaram DSC 111). A temperature-time ramp has been used in both combustion techniques. This method allows for the calculation of the frequency factor and the activation energy with only one run (Gayubo et al., 1994). When the differential scanning calorimetry was used, the FTIR analysis of the combustion products (CO, CO2, and H2) was carried out on-line in a Nicolet 740 FTIR spectrophotometer. The limitation to the internal air diffusion in coke particles is negligible due to the fact that coke released from the catalyst is a powder with particle diameter smaller than 60 µm. In the same way, the conversion from CO to CO2 is presumably negligible. It has been experimentally proven that CO conversion on the catalyst is lower than 5% (maximum value for the fresh catalyst) at 550 °C and decreases as the catalyst deactivates, which concurs with the studies of Moljord et al. (1995) for a SiO2 and a Y zeolite without Na.

The H/C ratio for the initial coke and the ratio during combustion have been calculated from the measurement of combustion products. Total carbon content measured as CO2 and CO concurs with the quantity measured using oxidation of the sample at 1050 °C in the presence of excess oxygen, treatment in copper oxide of the gas liberated in order to obtain complete oxidation, and determination of the CO2. Area calibration in FTIR analysis for CO2 (2400-2200 cm-1), CO (2200-2006 cm-1), and H2O (2006-1250 cm-1) has been carried out following the decomposition in inert atmosphere of a given amount of calcium oxalate monohydrate, according to the stoichiometry

CaC2O4H2O f CaC2O4 + H2O CaC2O4 f CaCO3 + CO CaCO3 f CaO + CO2 The results of FTIR analysis are of greater reliability than those of conventional techniques based on the trapping and weighing of the oxidation products (Moljord et al., 1995), on gas chromatography (Pieck et al., 1992), on mass spectrometry (McLellan et al., 1988), and on the combination of mass spectrometry with water retention in a hygrometer (Nova´kova´ and Dolejsek, 1990). 3. Results 3.1. Effect of Coke Aging. In a previous paper (Benito et al., 1996), coke deposition and the characteristics of the coke deposited on the same catalyst used in this paper were studied in an isothermal fixed-bed reactor and under a wide range of operating conditions. It is important to point out the hydrogenated character of the coke, which at reaction temperatures below 400 °C deposits mainly in the internal zeolite channels until activity for hydrocarbon production falls close to zero. This coke is unstable; hence, it can be partially removed from the internal channels by a vacuum of 10-4 mmHg at 300 °C. Table 1 shows the coke samples studied, which have been numbered from 1 to 6. They have been obtained by aging of the coke released from the catalyst deactivated at 350 and 400 °C, under the reaction conditions previously mentioned. Aging treatment has consisted of sweeeping with a He stream of 100 cm3 min-1, at 550 °C, for 20 min and 1 h. Results for zero treatment time correspond to samples subjected to sweeping with a He stream of 100 cm3 min-1 at reaction temperature for 30 min. This treatment is needed for eliminating the reaction products retained in the internal channels of the zeolite and which are not part of the deactivating coke. Figure 1 shows product distribution in coke combustion of samples 4-6, defined in Table 1. Results correspond to a combustion temperature ramp of 5 °C min-1 from 200 to 550 °C. Under these conditions, total combustion of all the cokes studied is achieved.

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Figure 1. Gaseous product distribution in combustion of coke samples subjected to different aging conditions.

Figure 1 shows a noticeable difference in coke combustion when it is subjected to different previous aging conditions. For sample 4 (Figure 1a), water formation can be observed from the beginning of combustion. CO and CO2 appear in measurable quantities after the first 10 min of combustion. The formation of H2O occurs at longer times and, therefore, at higher temperatures for aged samples 5 (Figure 1b) and 6 (Figure 1c). Samples 5 and 6 also present a delay in the beginning of the curves corresponding to evolution of CO and CO2, and for these samples, the first shoulder that is evident in the curves of CO2 and CO of sample 4 is not observed. The difference in the combustion of samples in Figure 1 must be attributed to the difference in the nature of the corresponding coke. Due to the previously mentioned coke instability, it has been proven that the coke suffers a noticeable alteration to its structure during the usual conditioning treatment prior to the kinetic combustion experiments. Methane presence, as a coke pyrolysis product, has been recorded by FTIR analysis of the gas stream in all aging experiments. Values of initial H/C ratio of coke samples, Table 1, have been calculated from the results of Figure 1 and from those corresponding to samples 1-3. Table 1 shows that the H/C ratio corresponding to coke deposited at different reaction temperatures decreases, with aging treatment, toward a stable value, which is approximately 0.5 for the studied aging treatment. This result concurs with that of Schulz et al. (1996). In the same way, the ratio H/C ) 0.5 is peculiar to the coke deposited on nonmetallic catalysts and on the support of the metallic catalysts (Parera et al., 1983; Pieck et al., 1992; Barbier et al., 1980, 1985a,b). In must be pointed out that the temperature for the aging study of the catalyst was 550 °C, as this is the catalyst calcination temperature; therefore, a higher temperature damages the acid structure. Nevertheless, this temperature does not correspond to the catalyst maximum activity, but it has been established in order for the catalyst to recover its activity and selectivity during reaction-regeneration cycles (Benito, 1995). The decrease in coke H/C ratio with the aging treatment was previously observed for hydrogenated cokes deposited on Ni-Mo/Al2O3 (Nalitham et al., 1985), on amorphous silica/alumina (Gayubo et al., 1993b), on Cr2O3/Al2O3 (Royo et al., 1994), and on HZSM5 zeolites (Nova´kova´ and Dolejsek, 1990). The highly hydrogenated character of the coke studied in this paper explains the pronounced aging effect. 3.2. Effect of the H/C Ratio on Coke Combustion. Kinetic study of coke combustion has been carried

Figure 2. Thermogravimetric results of combustion of coke samples subjected to different aging conditions.

out by thermogravimetry (Setaram TAG 24) with a rate of 5 °C min-1 from 200 to 550 °C. Figure 2 shows the results for samples 4-6. Results of coke content remaining in the catalyst, Cc, have been fitted to a first-order kinetics for each of the reactants, that is, the solid (coke) and the gas (O2):

-

dCc ) krCcPO2 dt

(1)

or, in the integrated form,

ln(1 - X) ) -krPO2t

(2)

where X is coke conversion,

X ) 1 - Cc/Cc0

(3)

kr ) Ar exp(-Er/RT)

(4)

and

Equation 1, with order one with respect to coke, has been adopted for the kinetic study, as it is the commonly used kinetic model for a coke of homogeneous nature and for catalysts without metallic function for catalyzing combustion. Querini and Fung (1994) discuss the validity of this model under different experimental circumstances. The kinetic study method has been described in a previous paper (Gayubo et al., 1994) and consists of fitting experimental data obtained in the thermogravi-

Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 63 Table 2. Kinetic Parameters and Combustion Heats of Coke Samples Released from the Catalyst sample number Ar, atm-1 min-1 Er, kcal mol-1 ∆H, kcal (g of coke)-1

1

2

3

4

5

6

2.86 × 104 16.3 9.1

9.65 × 109 34.9 8.3

1.57 × 1011 39.5 7.13

1.76 × 107 25.6 8.8

2.75 × 1011 30.5 7.7

5.91 × 1011 40.6 7.1

Figure 3. Results of combustion kinetic study of coke samples subjected to different aging conditions. Points, experimental results. Lines, values calculated using eq 5.

metric equipment following a programmed temperature-time sequence (T ) T0 + βt), to integrated eq 1, expressed as a temperature function:

ln

-ln(1 - X) T

2

[

) ln

)]

(

ArPO2 R 2RT 1β Er Er

-

Er RT

(5)

Values of frequency factor, Ar, and activation energy, Er, corresponding to the best fit are calculated by a Complex optimizing algorithm which minimizes the error function: n

∑ i)1 ARE )

(

)

|Xi - Xi*| Xi n

2

(6)

Values of the kinetic parameters obtained during coke combustion corresponding to different reaction conditions and different conditioning treatments prior to combustion are set out in Table 2. As an example of the adequacy of the kinetic parameter fitting, Figure 3 shows the results of the kinetic study for the combustion of samples 4 (without aging treatment) and 6 (subjected to aging). The points correspond to experimental results and the lines to values calculated with eq 5 by using the values for frequency factor, Ar, and activation energy, Er, from Table 2. In Table 2, it can be observed that combustion kinetic parameters are very sensitive to coke aging and, consequently, to the H/C ratio value of the coke. Activation energy lies between 16.3 kcal mol-1 for the most hydrogenated coke sample, sample 1 (H/C ) 2.35), and 40.6 kcal mol-1 for sample 6 (H/C ) 0.48). These activation energies correspond to extreme values within the range previously obtained in the literature for the combustion of cokes of relatively hydrogenated nature (Nalitham et al., 1985; Gayubo et al., 1994). It is clear that, for a coke with a higher H/C ratio, combustion reactivity is higher and activation energy value is lower.

3.3. Coke Combustion Heat. The interpretation given to results in Table 1 is supported by combustion studies carried out in a differential scanning calorimeter. Figure 4 shows the results of heat released throughout the combustion of samples 4-6, for a ramp of 5 °C min-1. A higher reactivity is observed for young coke in sample 4, whose peak of released heat starts, and reaches its maximum, at lower temperatures. The extent and deformity of the heat flow curve corresponding to sample 4 is noteworthy, which can be explained by the heterogeneity of this coke. The similarity between these released heat curves in Figure 4 and those in Figure 1, corresponding to the evolution of combustion products, can be observed. The results of coke combustion heat set out in Table 2 have been obtained by integration of released heat curves corresponding to Figure 4 and to the other coke samples; consequently, they are mean values corresponding to the experimental temperature range studied. It can be observed that combustion heat decreases, as does the initial H/C ratio of the coke sample. The results of Table 2 differ by less than 2% from the combustion heat values calculated from the H/C ratio using literature data for the combustion of H2 and C (Lee et al., 1989; Acharya et al., 1992). The heterogeneity observed in young coke combustion is somewhat similar to the combustion of coke deposited on supported metallic catalysts (Pieck et al., 1992; Querini and Fung, 1994). For these catalysts, combustion of the coke deposited on metallic sites (catalyzed combustion) is first identified; subsequently, at higher temperatures, combustion of the coke deposited on the support (noncatalyzed combustion) takes place. Nevertheless, for combustion of the coke deposited on the internal channels of HZSM5 zeolites, we are not dealing with two different specific cokes but rather with one with a wide distribution of structures and molecular weights, which explains the amplitude in the heat flow band in Figure 4. 3.4. Evolution of the H/C Ratio throughout Coke Combustion. Another factor that alters uniformity throughout combustion of highly hydrogenated coke is the evolution of its structure, which was previously observed for the coke deposited on supported metallic catalysts (Pieck et al., 1992). The results of the H/C ratio decrease with combustion time (Figure 5) have been obtained from the results of CO, CO2, and H2O production, measured by FTIR (Figure 1). It can be observed that the H/C ratio decreases throughout combustion, the decrease being more pronounced as the initial coke is more hydrogenated. The evolution observed in the H/C ratio during coke oxidation is interpreted in the literature as a consequence of a series of transformation reactions of the coke, with formation of ether and carbonyl groups, which decompose to CO and CO2. Hydrogenated coke is more reactive in these intermediate combustion reactions (Furimsky et al., 1988; Pieck et al., 1992). Given its highly hydrogenated nature, in combustion of sample 4, selective combustion of coke hydrogenated components may take place together with aging of the

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Figure 5. Evolution of coke H/C ratio throughout combustion time for coke samples subjected to different aging conditions.

Figure 4. Results of heat released throughout the combustion of coke samples subjected to different aging conditions.

remaining coke. For combustion of previously aged sample 6, decrease of the H/C ratio during combustion is attributed to selective combustion of the most hydrogenated coke components. 3.5. Restrictions to Aging and Combustion of the Coke within the Catalyst. The same aging treatment previously carried out on the coke released from the catalyst has been carried out on the samples of catalyst containing coke, in order to analyze separately the effect of the presence of catalyst on the aging of coke. Values of the H/C ratio for the samples resulting from these treatments, number from 1′ to 6′, have been set out in Table 1. The results of Table 1 have been obtained following the evolution of gaseous combustion products by FTIR. It can be observed that, when coke aging is carried out, an equilibrium value near 1.0 is obtained for the H/C ratio. Aging of the coke released from the catalyst is more pronounced under the same treatment conditions (Table 1), and the H/C ratio stabilizes in a value near 0.5. The difference in the results can be attributed to (1) deficient contact of He stream with deposited coke, which blocks internal channels of zeolite crystals (Benito et al., 1996), and (2) the fact that the coke chemisorbed in zeolite acid sites is less reactive for pyrolysis than released coke. As is observed in Table 1, the same H/C ratio is obtained for the coke released from the catalyst (samples 1 and 4) as for the coke within the catalyst (samples 1′ and 4′). This result shows that zeolite destruction by treatment with hydrofluoric acid does not affect the coke. The combustion reactivity of the deposited coke is lower than that of the coke released from the catalyst. An activation energy of Er ) 27.3 kcal mol-1 has been calculated by fitting the experimental results of coke combustion of sample 6′ to eq 5. This value is noticeably lower than the one for released coke (Er ) 40.6 kcal mol-1). Taking into account the frequency factor values (Ar ) 5.52 × 106 atm-1 min-1 for sample 6′ and Ar ) 5.91 × 1011 atm-1 min-1 for sample 6), the combustion kinetic constant at 550 °C (temperature recommended for activity recovering; Benito, 1995) is kr ) 0.31 atm-1 min-1 for sample 6′, which is a value rather lower than the value kr ) 9.75 atm-1 min-1 for sample 6 of released coke. These results confirm the restriction to coke combus-

Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 65

tion observed in previous studies on the regeneration of HZSM5 zeolites used for the MTG process (Bibby et al., 1992) and for other reactions (Guisnet and Magnoux, 1994). 4. Conclusions The coke deposited on an HZSM5 zeolite-based catalyst, which is used for the MTG process in the range from 300 to 400 °C, is unstable and undergoes severe aging (with the H/C ratio decrease) during the thermal treatment at regeneration temperature. Coke combustion kinetics is conditioned by the coke H/C ratio; as a consequence, it depends on reaction conditions (temperature, contact time, time on stream) and on aging treatment, due to the fact that these factors noticeably affect coke H/C ratio. Coke instability will have a strong incidence on regeneration kinetic studies and on catalyst regeneration in the reactor. On the basis of the results obtained in this paper, an aging treatment by sweeping with inert gas is needed in both cases, in order to obtain reproducible and well-controlled results under conditions in which coke is equilibrated. This situation of equilibration of the coke released from the catalyst corresponds to an H/C ratio of approximately 0.5, and under these conditions, coke presents a reproducible combustion with the kinetic parameters obtained in this paper. This coke equilibrating treatment is essential for regeneration in an industrial adiabatic fixed-bed process, in order to avoid catalyst sintering, which would take place as a result of inadequate control of the temperature profile in the reactor during combustion. Restrictions to coke reactivity during aging treatment and combustion have been quantified. The H/C ratio of coke retained inside the catalyst reaches an equilibrium value near 1.0. The value of the kinetic constant for the coke combustion on air during catalyst regeneration at 550 °C is 1/30th of the value of the kinetic constant corresponding to the coke released from the catalyst. As has been proven in this paper, restriction to combustion cannot be attributed to coke structure, but to catalyst structure, whose effect will be studied in later papers in order to advance toward the proposal of a realistic model which takes into account the peculiar coke deposition in these microporous zeolites. The establishment of this model requires distinguishing between several possible causes of coke combustion limitation: diffusional restrictions of combustion gas; heterogeneous deposition of the coke within the porous structure (either in different spatial positions within the internal channels or constituting nuclei of different structure or of different H/C ratio and molecular weight); or the incidence of catalyst acidic sites on the evolution of labile oxygenate components in the combustion mechamism. Acknowledgment This work was carried out with financial support from the University of the Basque Country/Euskal Herriko Unibertsitatea (Project UPV 069.310-EB004/92) and from DGICYT (Project PB93-0505). Nomenclature ARE ) average relative error Ar ) frequency factor of the regeneration kinetic constant, atm-1 min-1

Cc, Cc0 ) coke content in the catalyst and initial content Er ) regeneration activation energy, kcal mol-1 ∆H ) coke combustion heat, kcal g-1 kr ) regeneration kinetic constant, atm-1 min-1 n ) number of experimental points PO2 ) oxygen partial pressure, atm R ) gas constant, kcal mol-1 K-1 T ) temperature, °C T0 ) initial temperature of the ramp, °C t ) time, min X ) coke conversion throughout combustion Xi, Xi* ) experimental and calculated conversion values during combustion Greek Letter β ) temperature ramp, °C min-1

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Received for review December 4, 1995 Revised manuscript received October 17, 1996 Accepted October 22, 1996X IE9507336

X Abstract published in Advance ACS Abstracts, December 15, 1996.