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Gasification rate analysis of coal char with a pressurized drop tube furnace
Fuel 81 (2002) 539±546
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Gasi®cation rate analysis of coal char with a pressurized drop tube furnace q S. Kajitani*, S. Hara, H. Matsuda Yokosuka Research Laboratory, Central Research Institute of Electric Power Industry (CRIEPI), 2-6-1 Nagasaka, Yokosuka, Kanagawa 240-0196, Japan Received 20 November 2000; revised 12 February 2001; accepted 11 July 2001; available online 29 October 2001
Abstract Two coal chars were gasi®ed with carbon dioxide or steam using a Pressurized Drop Tube Furnace (PDTF) at high temperature and pressurized conditions to simulate the inside of an air-blown two-stage entrained ¯ow coal gasi®er. Chars were produced by rapid pyrolysis of pulverized coals using a DTF in a nitrogen gas ¯ow at 14008C. Gasi®cation temperatures were from 1100 to 15008C and pressures were from 0.2 to 2 MPa. As a result, the surface area of the gasi®ed char increased rapidly with the progress of gasi®cation up to about six times the size of initial surface area and peaked at about 40% of char gasi®cation. These changes of surface area and reaction rate could be described with a random pore model and a gasi®cation reaction rate equation was derived. Reaction order was 0.73 for gasi®cation of the coal char with carbon dioxide and 0.86 for that with steam. Activation energy was 163 kJ/mol for gasi®cation with carbon dioxide and 214 kJ/mol for that with steam. At high temperature as the reaction rate with carbon dioxide is about 0.03 s 21, the reaction rate of the coal char was controlled by pore diffusion, while that of another coal char was controlled by surface reaction where reaction order was 0.49 and activation energy was 261 kJ/mol. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Coal char; Gasi®cation reaction rate equation; Random pore model
1. Introduction Power plants such as the Integrated Coal Gasi®cation Combined Cycle (IGCC) are being developed worldwide to use coal more ef®ciently and cleanly. In Japan, electric power companies decided to construct a 250 MW IGCC demonstration plant. Air-blown two-stage entrained ¯ow gasi®cation technology is employed in the demonstration plant. This type of gasi®er was initially developed by CRIEPI and Mitsubishi Heavy Industries, Ltd using the 2 T/D bench scale gasi®er [1] located in our laboratory, and was scaled up to the 200 T/D pilot plant in the national project [2]. Because these plants are operated at high temperature and high pressure, a pressurized drop tube furnace facility (PDTF) was developed to investigate coal reactivity under the same conditions as inside a gasi®er [3]. Coal reactions in a gasi®er are typically examined by using two processes: coal pyrolysis and char gasi®cation. In the coal pyrolysis process, char is produced by rapid pyrolysis and the volatile matter is decomposed simultaneously. In the char gasi®cation process, char reacts with gasifying agents to produce a combustible gas. It is a gas±
solid reaction. The rate of pyrolysis is so rapid that the gas± solid reaction of char is regarded as the rate-determining process. The gasi®cation reaction rate of char has been discussed by several groups [4±6]. Thermogravimetric analysis (TGA), a common method of measuring a reaction rate, generally requires experiments at a low temperature (below 10008C) because of its inability to measure a true reaction rate at high temperatures where diffusion of a gasifying agent has a greater effect on an apparent reaction rate. However, an entrained ¯ow reactor is suitable for measurement of a reaction at a temperature and pressure as high as in a gasi®er. For this reason, in this study a PDTF was used for gasi®cation tests of char exposed to high temperature, high pressure and carbon dioxide or steam, simulating an airblown two-stage entrained ¯ow coal gasi®er, and the gasi®cation reaction rate based on gas±solid reaction models was analyzed.
2. Experimental 2.1. Char preparation
* Corresponding author. Tel.: 181-468-56-2121, fax: 181-468-57-5829. E-mail address: [email protected] (S. Kajitani). q Published ®rst on the web via Fuel®rst.com-http://www.fuel®rst.com
Test chars were prepared prior to the gasi®cation test. Two coals were used; one is Australian NL bituminous
0016-2361/02/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0016-236 1(01)00149-1
540
S. Kajitani et al. / Fuel 81 (2002) 539±546
Table 1 Properties of coal and the prepared char. (The test chars were prepared by rapid pyrolysis in nitrogen using an atmospheric DTF at 14008C) NL coal Proximate analysis (wt% dry basis) Ash Volatile matter Fixed carbon HHV (kJ/kg) Average diameter (mm)
13.8 28.7 57.5 2.99 £ 10 4 26.3
Ultimate analysis (wt% dry ash-free basis) C 82.5 H 5.1 N 1.4 S 0.5 O 10.5
NL test char 21.2 0.4 78.4 44.1 98.3 0.1 1.4 , 0.2
Maceral analysis (% mineral-free basis) Vitrinite 32.9 Exinite 8.4 Inertinite 58.7 Ash fusibility (8C, ASTM method in reducing atmosphere) IDT .1500 ST .1500 HT .1500 FT .1500 Ash composition (wt%) SiO2 Al2O3 FeO2 CaO TiO2 MgO SO3 P2O5
9.9 37.6 4.4 1.8 1.7 0.7 0.8 1.1
coal having a high fuel ratio and high ash melting point, and the other is Chinese S bituminous coal having a low fuel ratio and low ash melting point. The properties of these coals and the prepared chars are shown in Table 1. During char preparation, the pyrolysis conditions have to be carefully controlled since they have an effect on the reactivity of the char produced [7,8]. Regarding NL coal, a study was made of the correlation between pyrolysis conditions and the gasi®cation reactivity of the produced char with the conclusion that pyrolysis temperature and heating rate have an in¯uence on the char gasi®cation reactivity more than does pyrolysis pressure [9]. Therefore, the test chars were prepared by rapid pyrolysis in nitrogen using an atmospheric DTF at 14008C, assumedly equal to the temperature in the vicinity of reductor coal burner of an air-blown two-stage entrained ¯ow coal gasi®er. Residence time was set at about 3 s. 2.2. Char gasi®cation test The PDTF facility shown in Fig. 1 was used for the char gasi®cation test. This facility enables the simulation of an actual plant, because rapid heating is possible and the
S coal
S test char
4.9 36.9 58.2 2.93 £ 10 4 39.0
7.7 1.4 90.9
78.4 5.6 1.0 0.1 14.9
96.7 0.2 1.1
43.9
, 2.0
33.4 1.6 65.0 1360 1390 1400 1410 21.1 9.5 7.8 33.7 0.5 1.6 4.5 0.0
furnace condition sure set for predetermined temperature, pressure and gas ¯ow. Since the ¯ow in the furnace can be assumed to be a plug ¯ow, analysis of the results is simple. Gasi®cation conditions were established so as to simulate a reductor of an air-blown two-stage entrained-¯ow coal gasi®er (temperature: 1200±14008C; pressure: 2±3 MPa; carbon dioxide concentration: 10±15 vol%; steam concentration: 2±5 vol%). Carbon dioxide and/or steam were used as gasifying agents for NL test char, and only carbon dioxide was used for S test char. Test conditions are as follows: furnace temperature: 1100±15008C; furnace pressure: 0.2± 2 MPa; carbon dioxide partial pressure: 0.05±0.3 MPa or steam partial pressure: 0.02±0.1 MPa. Residence time was controlled by vertically traversing a water-cooled sampling probe inserted upward from the bottom of furnace. A ¯at temperature pro®le was observed in the reaction zone, meaning that the water-cooled probe does not affect the furnace temperature pro®le in the reaction zone. Judging from the fact that the terminal velocity of char particles in free fall is far lower than the gas ¯ow velocity, particle residence time was assumed to be equal to gas residence time. In order to investigate the in¯uence of the concentration
S. Kajitani et al. / Fuel 81 (2002) 539±546
541
Fig. 1. Schematic of the PDTF facility.
of the gasifying agent on reactivity, it is important to prevent the concentration of the gasifying agent from decreasing in the furnace. The gasifying agent was conditioned to be far richer by feeding no more char than 25% of the theoretical amount. Furnace products were collected by isokinetic sampling using the above probe and ®ltered through a thimble for collection. (This char is hereinafter called `sampled char', and prepared char for gasi®cation test is called `test char'.) The gas which was produced was subjected to on-line quantitative analysis with analytical equipment such as MS, FT±IR and gas chromatograph. Sampled char was characterized by means of ultimate analysis and various parameters. A DTF is effective in measuring a fast reaction rate at a high temperature, but is not suited for use in taking measurements in the slow reaction rate zone where reaction barely progresses within several seconds. For this reason, the gasifying test with carbon dioxide or oxygen was also carried out at low temperatures using thermogravimetry (TG). Char was heated in ¯owing argon to the prescribed temperature, at which point this gas was replaced by a gasifying agent and measurement of the reaction rate by the isothermal method was performed.
Fig. 2. Speci®c surface area of NL sampled char. (a) Surface area by BET method (absorbate: N2). (b) Surface area including micro pore by D-A method (absorbate: CO2).
3. Results and discussion 3.1. Study of reaction models Fig. 2 shows that speci®c surface areas of NL coal char increased rapidly with the progress of reaction and peaked with a conversion ratio of about 0.4. Speci®c surface areas shown in Fig. 2(a) are the result of the analysis of nitrogen gas adsorption isotherms at 77 K by the BET method, though this measurement is dif®cult to apply microporosity of below about 0.5 nm because of restrictive activated diffusion effect [10]. Fig. 2(b) shows measurements taken of
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S. Kajitani et al. / Fuel 81 (2002) 539±546
pore structure. It is calculated as follows using pore length (L0) and porosity (e 0) per unit volume of solid: C 4pL 0 1 2 e0 =S20 3
Fig. 3. Time series of the gasi®cation reaction rate of NL test char measured with the TG.
carbon dioxide gas adsorption isotherms at 273 K to minimize this effect and to evaluate micro pores more exactly. The adsorption isotherms were analyzed by the Dubinin± Astakhov method (D-A method), and the respective speci®c surface areas calculated using the method developed by Marsh and co-workers [10,11]. The test char is considered to be dominated by micro pores because its speci®c surface area is nearly 10 times the size of the speci®c surface area resulting from nitrogen gas adsorption. Therefore, the preferred way to estimate the speci®c surface area of char at the early stage of reaction is to measure the adsorption isotherm of carbon dioxide. Pores in the surfaces of char particles are considered to widen rapidly from micro pores into meso pores with the progress of the reaction. In respect of such changes in speci®c surface area, a comparison was made between a grain model and a random pore model, both being typical models of gas and solid reaction. The grain model [12] assumes that a char particle is an aggregation of smaller grains, each of which follows the unburned core model. Assuming that grains are spheres of uniform size, the equation to calculate speci®c surface area S is expressed as follows: S S0 1 2 x2=3
1
where S0 means the initial speci®c surface area and x indicates a conversion ratio of char. In a random pore model, it is assumed that the char particle is porous and the internal surfaces of such pores serve as reaction interfaces. The random pore model we employed is the one developed by Bhatia and Perlmutter [13] where cylindrical pores of uneven diameter are assumed to enlarge as their internal surfaces are eroded with the progress of the reaction and eventually merge together. According to this model, speci®c surface area is denoted as follows: p S S0 1 2 x 1 2 Cln 1 2 x 2 where C is a dimensionless parameter indicating the initial
As is shown in Fig. 2(b), the peak of speci®c surface area observed in experiments could not be con®rmed by the grain model represented by a broken line in this ®gure, but could be con®rmed by the random pore model represented by the solid line, and the desirable value of C was about 14. We also compared test results with model-based calculation results in respect of changes over time in conversion ratio and in reaction rate. Fig. 3 shows the results of gasi®cation of NL test char in the TG balance where it is easier to make detailed observations of reaction rate compare with the PDTF. In these experiments, measurements were taken in the low-temperature zone where the reaction rate was very low, with the aim of minimizing the effect possibly exerted by the mass transfer of gasifying agent and instrumental errors. The gasi®cation reaction rate with carbon dioxide showed a moderate peak in the early stages of reaction. In the grain model, the reaction rate is expressed as follows: dx k g 1 2 x2=3 dt
4
In the random pore mode, it is denoted as follows: p dx kp 1 2 x 1 2 Cln 1 2 x dt
5
Where t is time and kg and kp are reaction rate constants. Here also, the grain model cannot demonstrate the reaction rate peak. The Random Pore model, on the other hand, showed that the larger the value of C , the more acute is the peak. However, the Random Pore model-based analysis of plotted experimental values convinced us that the ideal value of C should be 3 for NL test char, which was different to the result obtained from the observation of speci®c surface area. The value of C varied depending on the gasifying agent. For gasi®cation of NL test char with oxygen, the ideal value of C was 14. As such, the random pore model seems superior in precision to the grain model. For this reason, we analyzed reaction rate based on the random pore model using the above values of C . Nevertheless, the current version of the random pore model was still unable to simultaneously substantiate both reaction rates and speci®c surface areas obtained from experiments. The reason for the inability is the assumed existence of major structural changes that are unaccountable if C is assumed to remain stable during the reaction. This suggests the need for a further improvement in the random pore model developed by Bhatia and Perlmutter [13]. 3.2. Kinetic analysis of char gasi®cation As is evident from Eq. (5), kp is equal to the initial gasi®cation reaction rate dx/dtux0, but the initial reaction
S. Kajitani et al. / Fuel 81 (2002) 539±546
Fig. 4. Initial gasi®cation reaction rate of NL test char measured with the PDTF. (a) In¯uence of partial pressure. (b) In¯uence of total pressure.
rate can barely be measured directly either in a PDTF or in a TG. Accordingly, an analysis was performed by the following method: Firstly, concerning test results obtained from the PDTF, kp was calculated by applying Eq. (5) to plots of residence time versus conversion ratio measured under the same test conditions with least square approximation. The value of C for gasi®cation of NL test char with steam was assumed to be 3, as for gasi®cation with carbon dioxide, because it was found that gasi®cation with steam showed a reaction rate of virtually the same order as one with carbon dioxide. Next, concerning test results obtained from the TG,
543
kp was calculated by applying Eq. (5) to reaction rate dx/ dtux0.5 which is the differential of TG curve at a conversion ratio of 0.5. These results enabled the analysis of the in¯uence of temperature, total pressure and partial pressure on the reaction rate of gasi®cation of NL test char with major gasifying agents at a high temperature under highly pressurized conditions. The reaction rate when partial pressure of the steam or carbon dioxide was changed with temperature and total pressure being set at 13008C and 0.5 MPa, respectively is shown in Fig. 4(a). An experiment using the PDTF revealed a reaction rate of NL test char proportional to the 0.73 power of carbon dioxide partial pressure and to the 0.86 power of steam partial pressure. At low temperatures, on the other hand, the reaction rate measured using the TG was proportional to the 0.54 power of carbon dioxide partial pressure and to the 0.68 power of oxygen partial pressure. Fig. 4(b) shows the reaction rate that occurred when total pressure was varied and temperature (13008C) and carbon dioxide partial pressure (about 0.2 MPa) or steam partial pressure (about 0.05 MPa) was ®xed. The minor in¯uence of total pressure was observed in that reaction rates at 0.2 and 2.0 MPa differed from that measured at 0.5 MPa by no more than ^20%. In light of the fact that an IGCC gasi®er uses a pressure of 2±3 MPa, which is very unlikely to have a signi®cant in¯uence on reaction rate, it was decided not to include a term for total pressure in the rate equation. Arrhenius plots of the initial reaction rate are shown in Fig. 5. Gasi®cation reaction rates of NL test char with steam measured at 1150±13008C showed a linear correlation, and activation energy in this temperature range reached 214 kJ/mol. However, at 14008C or above where dx/dtux0 was more than about 0.2 s 21, the reaction rate remained below the straight line. We felt that the reason was that the effect of bulk surface diffusion might also occur in an entrained ¯ow reactor such as a PDTF at such high temperatures. In contrast, in a gasi®er involving a ®eld of stronger turbulence, the temperature at which bulk surface diffusion controls the apparent reaction rate is considered slightly higher than that in a PDTF. Activation energies of gasi®cation of NL test char with carbon dioxide showed a downturn upon reaching a temperature of about 12008C where dx/dtux0 was more than about 0.03 s 21, and amounted to 283 kJ/mol at lower temperatures and 163 kJ/mol at higher temperatures. It means that the apparent reaction rate seems to be the same as the chemical surface reaction rate at temperatures below about 12008C, while it is presumed that pore diffusion acts as a ratecontrolling factor at 12008C or higher. On the other hand, the reaction rate of S test char with carbon dioxide is controlled by surface reaction even if it is at higher temperature, because the reaction rate was on the straight line from lower temperature to higher temperature where dx/dtux0 was from 0.009 to 0.34 s 21. Activation energy amounted to 261 kJ/mol, and from the above method the values of C and reaction order for gasi®cation of S test char with
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S. Kajitani et al. / Fuel 81 (2002) 539±546
Fig. 5. Arrhenius plots of the gasi®cation reaction rate of test chars.
carbon dioxide were assumed to be 0.1 and 0.49, respectively. These factors show that the reaction rate constant kp is proportional to the power of partial pressure of gasifying agent and follows the equation of Arrhenius. Therefore, Eq. (5) was evolved to the following reaction equation and the kinetic parameters shown in Table 2 was obtained to explain the gasi®cation reaction rate of test char with major gasifying agents at a high temperature under pressurized conditions. p dx A 0 ´PnA ´e2E=RT ´ 1 2 x´ 1 2 Cln 1 2 x dt
6
where A0 is frequency factor, E is activation energy, n is reaction order, PA is partial pressure of gasifying agent, R is gas constant and T is temperature. Though an in¯uence of catalytic activity of mineral matter such as calcium or sodium on gasi®cation [4,14] is not considered in this
study, that will be included in the value of kinetic parameters in the gasi®cation reaction rate equation. 3.3. Morphological study of gasi®ed char In order to improve particle reaction models and clear the deference between coal species, it is important to gain a grasp of the morphological changes of char during gasi®cation under the conditions of high temperature and high pressure. Because speci®c surface area has already been discussed in above paragraph, the following is other observations of NL coal char. SEM Photographs of char surfaces are shown in Fig. 6. Test char is mostly composed of shell-like particles. This indicates that pulverized coal swells from inside due to the release of volatile matter during pyrolysis. Despite their relative smoothness, the surfaces of test char proved to have irregularities of the order of 10 nm when observed at
Table 2 Gasi®cation reaction rate equation and kinetic parameters for coal char Test char
NL test char
Gasifying agent
CO2
Applicability a
High temp. (.12008C) (pore diffusion)
Pore structure: C Reaction order: n Activation energy: E (kJ/mol) Frequency factor: A0
3 0.73 163 6.78 £ 10 4
S test char H2O
O2
CO2
Low temp. (,12008C) (reaction control)
High temp.
Low temp. (reaction control)
High and low temp. (reaction control)
3 0.54 283 1.09 £ 10 9
3 0.86 214 2.45 £ 10 7
14 0.68 130 1.36 £ 10 6
0.1 0.49 261 1.23 £ 10 9
a
The reaction rate equation based on the Random Pore Model is the following: p dx A 0 ´PnA ´e2E=RT ´ 1 2 x´ 1 2 C´ln 1 2 x dt x: conversion ratio [±], t: time [s], PA: partial pressure of gasifying agent [MPa], T: temperature [K], gas constant: R 8.314 £ 10 23 kJ/mol K.
S. Kajitani et al. / Fuel 81 (2002) 539±546
545
Fig. 6. SEM photographs of NL sampled char gasi®ed with steam. (a) The test char (conversion 0). (b) The test char (conversion 0). (c) The sampled char (conversion 0.61). (d) The sampled char (conversion 0.35).
a high magni®cation. Because the crystallite size of carbon atoms described later is of the order of 1 nm, such irregularities may be aggregations of crystallites. The surfaces of test char have micro pores invisible to SEM, judging from the speci®c surface area. Observations showed that once the gasi®cation reaction began, char surfaces became rough, consuming active site to form particles of the order of 10 nm and causing the thin skin of shell-like char to become thinner and for holes to appear. An example of particle size distribution is shown in Fig. 7(a). The vertical axis shows a volume-based frequency obtained by the laser diffraction method on the assumption that such a particle is of spherical shape. Fig. 7(b) shows average particle diameters corresponding to a cumulative frequency of 50%. Particle size distributions showed no changes until the conversion ratio reached about 0.5. It is reasonable to infer that the average particle diameter decreases with a conversion ratio exceeding 0.5, notwithstanding a scarcity of data. The crystal structure of carbon contained in char [15] was also measured by XRD. Analysis results of (002) diffraction pattern are shown in Fig. 8. As the reaction progresses, the peak integrated intensity declines due to decreased carbon
content, but graphitic interlayer spacing d002 and crystallite size Lc002 remained unchanged. Speculation drawn from these ®ndings is that the gasifying agent reacts on carbon at the edge of a hexagonal lattice layer. Though it means that La decreases, it was impossible to analyze the value of La from (110) diffraction pattern showing a minor peak. From the above ®ndings, we inferred that morphological changes of char particles would occur as follows. When rapidly heated, pulverized coal swells due to the release of volatile matter, producing profuse shell-like char of large particle size along with the progress of graphitization due to thermal metamorphism. The next process to occur is diffusion of the gasifying agent over the char surfaces and into micro pores where it makes contact with active sites at the edges of carbon crystallites, thereby giving rise to the gasi®cation reaction. With the progress of the reaction entailing the gradual erosion of pores, the surface roughness of char rapidly increases. By the time the conversion ratio reaches about 0.4, char surfaces become rough enough to suppress the expansion of speci®c surface area. The char shell slowly grows thinner, eventually causing cavities to form and becomes more friable. As long as the conversion ratio is below about 0.5, the particle size remains unchanged
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S. Kajitani et al. / Fuel 81 (2002) 539±546
Fig. 8. Crystal structure of carbon in NL sampled char from XRD.
Fig. 7. Particle size distribution of NL sampled char. (a) Cumulative frequency distribution. (b) Average particle diameter (50%, average).
because its shell-like form is maintained intact, but its bulk speci®c gravity decreases with the progress of the reaction. With a conversion ratio reaching 0.5±0.6, however, the breakup of large shell-like char changes the particle size distribution and lowers the average particle diameter. 4. Conclusions Coal chars were gasi®ed with carbon dioxide and steam using the PDTF at high temperature and pressurized conditions to simulate the inside of an air-blown two-stage entrained-¯ow coal gasi®er. As a result, it was proved that the combination of experiment using a PTDF and that using a TG is effective to reach the gasi®cation reaction rate equation. This equation reached in this study is based on a random pore model and is able to be applied to gasi®ers where high temperature and pressure prevail. The difference in a rate-controlling factor at the same reaction rate between coal species was clear. At high temperature, as the reaction rate dx/dt with carbon dioxide is about 0.03 s 21, the reaction rate of NL test char was
controlled by pore diffusion, while that of S test char was controlled by surface reaction. It is necessary hereafter to include an in¯uence of coal species on kinetics. Gasi®ed char of NL coal was characterized and morphological changes in the char became clear. The surface area of gasi®ed char increased rapidly with the progress of gasi®cation up to about six times the size of initial surface area and peaked at about 40% of char gasi®cation, while the particle size distribution of char did not change until about 50% of char gasi®cation had occurred, and the value of d002 or Lc002 of carbon crystallites remained unchanged during gasi®cation.
References [1] Inumaru J, Hara S, Hamamatsu T, Ishikawa H. In: Proceedings of International Conference on Coal Science. IEA, Japan, 1989. p. 297. [2] Araki S. In: Proceedings of Third Clean Coal Technology Technical Seminar. APEC, Korea, 1995. p. 97. [3] Kajitani S, Matsuda H, Hara S, Ashizawa M, Takahashi T. In: Proceedings of 13th Annual International Pittsburgh Coal Conference. University of Pittsburgh, USA, 1996. p. 976. [4] Takarada T, Tamai Y, Tomita A. Fuel 1985;64:1438. [5] Miura K, Hashimoto K, Silveston PL. Fuel 1989;68:1461. [6] Roberts DG, Harris DJ. Energy and Fuels 2000;14:483. [7] van Heek KH, Muhlen HJ. Fuel Processing Technology 1987;15:113. [8] Kasaoka S, Sakata Y, Shimada M. Fuel 1986;66:697. [9] Kajitani S, Matsuda H. In: Proceedings of 8th Australian Coal Science Conference. University of New South Wales, Australia, 1998. p. 295± 300. [10] Marsh H, Siemieniewska T. Fuel 1965;44:355. [11] Marsh H. Carbon 1987;25:49. [12] Sohn HY, Szekely. J Chem Eng Sci 1972;27:763. [13] Bhatia SK, Perlmutter DS. AIChE J 1980;26:379. [14] Radovic LR, Walker Jr PL, Jenkins RG. Fuel 1984;63:1028. [15] Ergun S. US Bureau of Mines Bulletin 1968:648.
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Gasi®cation rate analysis of coal char with a pressurized drop tube furnace q S. Kajitani*, S. Hara, H. Matsuda Yokosuka Research Laboratory, Central Research Institute of Electric Power Industry (CRIEPI), 2-6-1 Nagasaka, Yokosuka, Kanagawa 240-0196, Japan Received 20 November 2000; revised 12 February 2001; accepted 11 July 2001; available online 29 October 2001
Abstract Two coal chars were gasi®ed with carbon dioxide or steam using a Pressurized Drop Tube Furnace (PDTF) at high temperature and pressurized conditions to simulate the inside of an air-blown two-stage entrained ¯ow coal gasi®er. Chars were produced by rapid pyrolysis of pulverized coals using a DTF in a nitrogen gas ¯ow at 14008C. Gasi®cation temperatures were from 1100 to 15008C and pressures were from 0.2 to 2 MPa. As a result, the surface area of the gasi®ed char increased rapidly with the progress of gasi®cation up to about six times the size of initial surface area and peaked at about 40% of char gasi®cation. These changes of surface area and reaction rate could be described with a random pore model and a gasi®cation reaction rate equation was derived. Reaction order was 0.73 for gasi®cation of the coal char with carbon dioxide and 0.86 for that with steam. Activation energy was 163 kJ/mol for gasi®cation with carbon dioxide and 214 kJ/mol for that with steam. At high temperature as the reaction rate with carbon dioxide is about 0.03 s 21, the reaction rate of the coal char was controlled by pore diffusion, while that of another coal char was controlled by surface reaction where reaction order was 0.49 and activation energy was 261 kJ/mol. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Coal char; Gasi®cation reaction rate equation; Random pore model
1. Introduction Power plants such as the Integrated Coal Gasi®cation Combined Cycle (IGCC) are being developed worldwide to use coal more ef®ciently and cleanly. In Japan, electric power companies decided to construct a 250 MW IGCC demonstration plant. Air-blown two-stage entrained ¯ow gasi®cation technology is employed in the demonstration plant. This type of gasi®er was initially developed by CRIEPI and Mitsubishi Heavy Industries, Ltd using the 2 T/D bench scale gasi®er [1] located in our laboratory, and was scaled up to the 200 T/D pilot plant in the national project [2]. Because these plants are operated at high temperature and high pressure, a pressurized drop tube furnace facility (PDTF) was developed to investigate coal reactivity under the same conditions as inside a gasi®er [3]. Coal reactions in a gasi®er are typically examined by using two processes: coal pyrolysis and char gasi®cation. In the coal pyrolysis process, char is produced by rapid pyrolysis and the volatile matter is decomposed simultaneously. In the char gasi®cation process, char reacts with gasifying agents to produce a combustible gas. It is a gas±
solid reaction. The rate of pyrolysis is so rapid that the gas± solid reaction of char is regarded as the rate-determining process. The gasi®cation reaction rate of char has been discussed by several groups [4±6]. Thermogravimetric analysis (TGA), a common method of measuring a reaction rate, generally requires experiments at a low temperature (below 10008C) because of its inability to measure a true reaction rate at high temperatures where diffusion of a gasifying agent has a greater effect on an apparent reaction rate. However, an entrained ¯ow reactor is suitable for measurement of a reaction at a temperature and pressure as high as in a gasi®er. For this reason, in this study a PDTF was used for gasi®cation tests of char exposed to high temperature, high pressure and carbon dioxide or steam, simulating an airblown two-stage entrained ¯ow coal gasi®er, and the gasi®cation reaction rate based on gas±solid reaction models was analyzed.
2. Experimental 2.1. Char preparation
* Corresponding author. Tel.: 181-468-56-2121, fax: 181-468-57-5829. E-mail address: [email protected] (S. Kajitani). q Published ®rst on the web via Fuel®rst.com-http://www.fuel®rst.com
Test chars were prepared prior to the gasi®cation test. Two coals were used; one is Australian NL bituminous
0016-2361/02/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0016-236 1(01)00149-1
540
S. Kajitani et al. / Fuel 81 (2002) 539±546
Table 1 Properties of coal and the prepared char. (The test chars were prepared by rapid pyrolysis in nitrogen using an atmospheric DTF at 14008C) NL coal Proximate analysis (wt% dry basis) Ash Volatile matter Fixed carbon HHV (kJ/kg) Average diameter (mm)
13.8 28.7 57.5 2.99 £ 10 4 26.3
Ultimate analysis (wt% dry ash-free basis) C 82.5 H 5.1 N 1.4 S 0.5 O 10.5
NL test char 21.2 0.4 78.4 44.1 98.3 0.1 1.4 , 0.2
Maceral analysis (% mineral-free basis) Vitrinite 32.9 Exinite 8.4 Inertinite 58.7 Ash fusibility (8C, ASTM method in reducing atmosphere) IDT .1500 ST .1500 HT .1500 FT .1500 Ash composition (wt%) SiO2 Al2O3 FeO2 CaO TiO2 MgO SO3 P2O5
9.9 37.6 4.4 1.8 1.7 0.7 0.8 1.1
coal having a high fuel ratio and high ash melting point, and the other is Chinese S bituminous coal having a low fuel ratio and low ash melting point. The properties of these coals and the prepared chars are shown in Table 1. During char preparation, the pyrolysis conditions have to be carefully controlled since they have an effect on the reactivity of the char produced [7,8]. Regarding NL coal, a study was made of the correlation between pyrolysis conditions and the gasi®cation reactivity of the produced char with the conclusion that pyrolysis temperature and heating rate have an in¯uence on the char gasi®cation reactivity more than does pyrolysis pressure [9]. Therefore, the test chars were prepared by rapid pyrolysis in nitrogen using an atmospheric DTF at 14008C, assumedly equal to the temperature in the vicinity of reductor coal burner of an air-blown two-stage entrained ¯ow coal gasi®er. Residence time was set at about 3 s. 2.2. Char gasi®cation test The PDTF facility shown in Fig. 1 was used for the char gasi®cation test. This facility enables the simulation of an actual plant, because rapid heating is possible and the
S coal
S test char
4.9 36.9 58.2 2.93 £ 10 4 39.0
7.7 1.4 90.9
78.4 5.6 1.0 0.1 14.9
96.7 0.2 1.1
43.9
, 2.0
33.4 1.6 65.0 1360 1390 1400 1410 21.1 9.5 7.8 33.7 0.5 1.6 4.5 0.0
furnace condition sure set for predetermined temperature, pressure and gas ¯ow. Since the ¯ow in the furnace can be assumed to be a plug ¯ow, analysis of the results is simple. Gasi®cation conditions were established so as to simulate a reductor of an air-blown two-stage entrained-¯ow coal gasi®er (temperature: 1200±14008C; pressure: 2±3 MPa; carbon dioxide concentration: 10±15 vol%; steam concentration: 2±5 vol%). Carbon dioxide and/or steam were used as gasifying agents for NL test char, and only carbon dioxide was used for S test char. Test conditions are as follows: furnace temperature: 1100±15008C; furnace pressure: 0.2± 2 MPa; carbon dioxide partial pressure: 0.05±0.3 MPa or steam partial pressure: 0.02±0.1 MPa. Residence time was controlled by vertically traversing a water-cooled sampling probe inserted upward from the bottom of furnace. A ¯at temperature pro®le was observed in the reaction zone, meaning that the water-cooled probe does not affect the furnace temperature pro®le in the reaction zone. Judging from the fact that the terminal velocity of char particles in free fall is far lower than the gas ¯ow velocity, particle residence time was assumed to be equal to gas residence time. In order to investigate the in¯uence of the concentration
S. Kajitani et al. / Fuel 81 (2002) 539±546
541
Fig. 1. Schematic of the PDTF facility.
of the gasifying agent on reactivity, it is important to prevent the concentration of the gasifying agent from decreasing in the furnace. The gasifying agent was conditioned to be far richer by feeding no more char than 25% of the theoretical amount. Furnace products were collected by isokinetic sampling using the above probe and ®ltered through a thimble for collection. (This char is hereinafter called `sampled char', and prepared char for gasi®cation test is called `test char'.) The gas which was produced was subjected to on-line quantitative analysis with analytical equipment such as MS, FT±IR and gas chromatograph. Sampled char was characterized by means of ultimate analysis and various parameters. A DTF is effective in measuring a fast reaction rate at a high temperature, but is not suited for use in taking measurements in the slow reaction rate zone where reaction barely progresses within several seconds. For this reason, the gasifying test with carbon dioxide or oxygen was also carried out at low temperatures using thermogravimetry (TG). Char was heated in ¯owing argon to the prescribed temperature, at which point this gas was replaced by a gasifying agent and measurement of the reaction rate by the isothermal method was performed.
Fig. 2. Speci®c surface area of NL sampled char. (a) Surface area by BET method (absorbate: N2). (b) Surface area including micro pore by D-A method (absorbate: CO2).
3. Results and discussion 3.1. Study of reaction models Fig. 2 shows that speci®c surface areas of NL coal char increased rapidly with the progress of reaction and peaked with a conversion ratio of about 0.4. Speci®c surface areas shown in Fig. 2(a) are the result of the analysis of nitrogen gas adsorption isotherms at 77 K by the BET method, though this measurement is dif®cult to apply microporosity of below about 0.5 nm because of restrictive activated diffusion effect [10]. Fig. 2(b) shows measurements taken of
542
S. Kajitani et al. / Fuel 81 (2002) 539±546
pore structure. It is calculated as follows using pore length (L0) and porosity (e 0) per unit volume of solid: C 4pL 0 1 2 e0 =S20 3
Fig. 3. Time series of the gasi®cation reaction rate of NL test char measured with the TG.
carbon dioxide gas adsorption isotherms at 273 K to minimize this effect and to evaluate micro pores more exactly. The adsorption isotherms were analyzed by the Dubinin± Astakhov method (D-A method), and the respective speci®c surface areas calculated using the method developed by Marsh and co-workers [10,11]. The test char is considered to be dominated by micro pores because its speci®c surface area is nearly 10 times the size of the speci®c surface area resulting from nitrogen gas adsorption. Therefore, the preferred way to estimate the speci®c surface area of char at the early stage of reaction is to measure the adsorption isotherm of carbon dioxide. Pores in the surfaces of char particles are considered to widen rapidly from micro pores into meso pores with the progress of the reaction. In respect of such changes in speci®c surface area, a comparison was made between a grain model and a random pore model, both being typical models of gas and solid reaction. The grain model [12] assumes that a char particle is an aggregation of smaller grains, each of which follows the unburned core model. Assuming that grains are spheres of uniform size, the equation to calculate speci®c surface area S is expressed as follows: S S0 1 2 x2=3
1
where S0 means the initial speci®c surface area and x indicates a conversion ratio of char. In a random pore model, it is assumed that the char particle is porous and the internal surfaces of such pores serve as reaction interfaces. The random pore model we employed is the one developed by Bhatia and Perlmutter [13] where cylindrical pores of uneven diameter are assumed to enlarge as their internal surfaces are eroded with the progress of the reaction and eventually merge together. According to this model, speci®c surface area is denoted as follows: p S S0 1 2 x 1 2 Cln 1 2 x 2 where C is a dimensionless parameter indicating the initial
As is shown in Fig. 2(b), the peak of speci®c surface area observed in experiments could not be con®rmed by the grain model represented by a broken line in this ®gure, but could be con®rmed by the random pore model represented by the solid line, and the desirable value of C was about 14. We also compared test results with model-based calculation results in respect of changes over time in conversion ratio and in reaction rate. Fig. 3 shows the results of gasi®cation of NL test char in the TG balance where it is easier to make detailed observations of reaction rate compare with the PDTF. In these experiments, measurements were taken in the low-temperature zone where the reaction rate was very low, with the aim of minimizing the effect possibly exerted by the mass transfer of gasifying agent and instrumental errors. The gasi®cation reaction rate with carbon dioxide showed a moderate peak in the early stages of reaction. In the grain model, the reaction rate is expressed as follows: dx k g 1 2 x2=3 dt
4
In the random pore mode, it is denoted as follows: p dx kp 1 2 x 1 2 Cln 1 2 x dt
5
Where t is time and kg and kp are reaction rate constants. Here also, the grain model cannot demonstrate the reaction rate peak. The Random Pore model, on the other hand, showed that the larger the value of C , the more acute is the peak. However, the Random Pore model-based analysis of plotted experimental values convinced us that the ideal value of C should be 3 for NL test char, which was different to the result obtained from the observation of speci®c surface area. The value of C varied depending on the gasifying agent. For gasi®cation of NL test char with oxygen, the ideal value of C was 14. As such, the random pore model seems superior in precision to the grain model. For this reason, we analyzed reaction rate based on the random pore model using the above values of C . Nevertheless, the current version of the random pore model was still unable to simultaneously substantiate both reaction rates and speci®c surface areas obtained from experiments. The reason for the inability is the assumed existence of major structural changes that are unaccountable if C is assumed to remain stable during the reaction. This suggests the need for a further improvement in the random pore model developed by Bhatia and Perlmutter [13]. 3.2. Kinetic analysis of char gasi®cation As is evident from Eq. (5), kp is equal to the initial gasi®cation reaction rate dx/dtux0, but the initial reaction
S. Kajitani et al. / Fuel 81 (2002) 539±546
Fig. 4. Initial gasi®cation reaction rate of NL test char measured with the PDTF. (a) In¯uence of partial pressure. (b) In¯uence of total pressure.
rate can barely be measured directly either in a PDTF or in a TG. Accordingly, an analysis was performed by the following method: Firstly, concerning test results obtained from the PDTF, kp was calculated by applying Eq. (5) to plots of residence time versus conversion ratio measured under the same test conditions with least square approximation. The value of C for gasi®cation of NL test char with steam was assumed to be 3, as for gasi®cation with carbon dioxide, because it was found that gasi®cation with steam showed a reaction rate of virtually the same order as one with carbon dioxide. Next, concerning test results obtained from the TG,
543
kp was calculated by applying Eq. (5) to reaction rate dx/ dtux0.5 which is the differential of TG curve at a conversion ratio of 0.5. These results enabled the analysis of the in¯uence of temperature, total pressure and partial pressure on the reaction rate of gasi®cation of NL test char with major gasifying agents at a high temperature under highly pressurized conditions. The reaction rate when partial pressure of the steam or carbon dioxide was changed with temperature and total pressure being set at 13008C and 0.5 MPa, respectively is shown in Fig. 4(a). An experiment using the PDTF revealed a reaction rate of NL test char proportional to the 0.73 power of carbon dioxide partial pressure and to the 0.86 power of steam partial pressure. At low temperatures, on the other hand, the reaction rate measured using the TG was proportional to the 0.54 power of carbon dioxide partial pressure and to the 0.68 power of oxygen partial pressure. Fig. 4(b) shows the reaction rate that occurred when total pressure was varied and temperature (13008C) and carbon dioxide partial pressure (about 0.2 MPa) or steam partial pressure (about 0.05 MPa) was ®xed. The minor in¯uence of total pressure was observed in that reaction rates at 0.2 and 2.0 MPa differed from that measured at 0.5 MPa by no more than ^20%. In light of the fact that an IGCC gasi®er uses a pressure of 2±3 MPa, which is very unlikely to have a signi®cant in¯uence on reaction rate, it was decided not to include a term for total pressure in the rate equation. Arrhenius plots of the initial reaction rate are shown in Fig. 5. Gasi®cation reaction rates of NL test char with steam measured at 1150±13008C showed a linear correlation, and activation energy in this temperature range reached 214 kJ/mol. However, at 14008C or above where dx/dtux0 was more than about 0.2 s 21, the reaction rate remained below the straight line. We felt that the reason was that the effect of bulk surface diffusion might also occur in an entrained ¯ow reactor such as a PDTF at such high temperatures. In contrast, in a gasi®er involving a ®eld of stronger turbulence, the temperature at which bulk surface diffusion controls the apparent reaction rate is considered slightly higher than that in a PDTF. Activation energies of gasi®cation of NL test char with carbon dioxide showed a downturn upon reaching a temperature of about 12008C where dx/dtux0 was more than about 0.03 s 21, and amounted to 283 kJ/mol at lower temperatures and 163 kJ/mol at higher temperatures. It means that the apparent reaction rate seems to be the same as the chemical surface reaction rate at temperatures below about 12008C, while it is presumed that pore diffusion acts as a ratecontrolling factor at 12008C or higher. On the other hand, the reaction rate of S test char with carbon dioxide is controlled by surface reaction even if it is at higher temperature, because the reaction rate was on the straight line from lower temperature to higher temperature where dx/dtux0 was from 0.009 to 0.34 s 21. Activation energy amounted to 261 kJ/mol, and from the above method the values of C and reaction order for gasi®cation of S test char with
544
S. Kajitani et al. / Fuel 81 (2002) 539±546
Fig. 5. Arrhenius plots of the gasi®cation reaction rate of test chars.
carbon dioxide were assumed to be 0.1 and 0.49, respectively. These factors show that the reaction rate constant kp is proportional to the power of partial pressure of gasifying agent and follows the equation of Arrhenius. Therefore, Eq. (5) was evolved to the following reaction equation and the kinetic parameters shown in Table 2 was obtained to explain the gasi®cation reaction rate of test char with major gasifying agents at a high temperature under pressurized conditions. p dx A 0 ´PnA ´e2E=RT ´ 1 2 x´ 1 2 Cln 1 2 x dt
6
where A0 is frequency factor, E is activation energy, n is reaction order, PA is partial pressure of gasifying agent, R is gas constant and T is temperature. Though an in¯uence of catalytic activity of mineral matter such as calcium or sodium on gasi®cation [4,14] is not considered in this
study, that will be included in the value of kinetic parameters in the gasi®cation reaction rate equation. 3.3. Morphological study of gasi®ed char In order to improve particle reaction models and clear the deference between coal species, it is important to gain a grasp of the morphological changes of char during gasi®cation under the conditions of high temperature and high pressure. Because speci®c surface area has already been discussed in above paragraph, the following is other observations of NL coal char. SEM Photographs of char surfaces are shown in Fig. 6. Test char is mostly composed of shell-like particles. This indicates that pulverized coal swells from inside due to the release of volatile matter during pyrolysis. Despite their relative smoothness, the surfaces of test char proved to have irregularities of the order of 10 nm when observed at
Table 2 Gasi®cation reaction rate equation and kinetic parameters for coal char Test char
NL test char
Gasifying agent
CO2
Applicability a
High temp. (.12008C) (pore diffusion)
Pore structure: C Reaction order: n Activation energy: E (kJ/mol) Frequency factor: A0
3 0.73 163 6.78 £ 10 4
S test char H2O
O2
CO2
Low temp. (,12008C) (reaction control)
High temp.
Low temp. (reaction control)
High and low temp. (reaction control)
3 0.54 283 1.09 £ 10 9
3 0.86 214 2.45 £ 10 7
14 0.68 130 1.36 £ 10 6
0.1 0.49 261 1.23 £ 10 9
a
The reaction rate equation based on the Random Pore Model is the following: p dx A 0 ´PnA ´e2E=RT ´ 1 2 x´ 1 2 C´ln 1 2 x dt x: conversion ratio [±], t: time [s], PA: partial pressure of gasifying agent [MPa], T: temperature [K], gas constant: R 8.314 £ 10 23 kJ/mol K.
S. Kajitani et al. / Fuel 81 (2002) 539±546
545
Fig. 6. SEM photographs of NL sampled char gasi®ed with steam. (a) The test char (conversion 0). (b) The test char (conversion 0). (c) The sampled char (conversion 0.61). (d) The sampled char (conversion 0.35).
a high magni®cation. Because the crystallite size of carbon atoms described later is of the order of 1 nm, such irregularities may be aggregations of crystallites. The surfaces of test char have micro pores invisible to SEM, judging from the speci®c surface area. Observations showed that once the gasi®cation reaction began, char surfaces became rough, consuming active site to form particles of the order of 10 nm and causing the thin skin of shell-like char to become thinner and for holes to appear. An example of particle size distribution is shown in Fig. 7(a). The vertical axis shows a volume-based frequency obtained by the laser diffraction method on the assumption that such a particle is of spherical shape. Fig. 7(b) shows average particle diameters corresponding to a cumulative frequency of 50%. Particle size distributions showed no changes until the conversion ratio reached about 0.5. It is reasonable to infer that the average particle diameter decreases with a conversion ratio exceeding 0.5, notwithstanding a scarcity of data. The crystal structure of carbon contained in char [15] was also measured by XRD. Analysis results of (002) diffraction pattern are shown in Fig. 8. As the reaction progresses, the peak integrated intensity declines due to decreased carbon
content, but graphitic interlayer spacing d002 and crystallite size Lc002 remained unchanged. Speculation drawn from these ®ndings is that the gasifying agent reacts on carbon at the edge of a hexagonal lattice layer. Though it means that La decreases, it was impossible to analyze the value of La from (110) diffraction pattern showing a minor peak. From the above ®ndings, we inferred that morphological changes of char particles would occur as follows. When rapidly heated, pulverized coal swells due to the release of volatile matter, producing profuse shell-like char of large particle size along with the progress of graphitization due to thermal metamorphism. The next process to occur is diffusion of the gasifying agent over the char surfaces and into micro pores where it makes contact with active sites at the edges of carbon crystallites, thereby giving rise to the gasi®cation reaction. With the progress of the reaction entailing the gradual erosion of pores, the surface roughness of char rapidly increases. By the time the conversion ratio reaches about 0.4, char surfaces become rough enough to suppress the expansion of speci®c surface area. The char shell slowly grows thinner, eventually causing cavities to form and becomes more friable. As long as the conversion ratio is below about 0.5, the particle size remains unchanged
546
S. Kajitani et al. / Fuel 81 (2002) 539±546
Fig. 8. Crystal structure of carbon in NL sampled char from XRD.
Fig. 7. Particle size distribution of NL sampled char. (a) Cumulative frequency distribution. (b) Average particle diameter (50%, average).
because its shell-like form is maintained intact, but its bulk speci®c gravity decreases with the progress of the reaction. With a conversion ratio reaching 0.5±0.6, however, the breakup of large shell-like char changes the particle size distribution and lowers the average particle diameter. 4. Conclusions Coal chars were gasi®ed with carbon dioxide and steam using the PDTF at high temperature and pressurized conditions to simulate the inside of an air-blown two-stage entrained-¯ow coal gasi®er. As a result, it was proved that the combination of experiment using a PTDF and that using a TG is effective to reach the gasi®cation reaction rate equation. This equation reached in this study is based on a random pore model and is able to be applied to gasi®ers where high temperature and pressure prevail. The difference in a rate-controlling factor at the same reaction rate between coal species was clear. At high temperature, as the reaction rate dx/dt with carbon dioxide is about 0.03 s 21, the reaction rate of NL test char was
controlled by pore diffusion, while that of S test char was controlled by surface reaction. It is necessary hereafter to include an in¯uence of coal species on kinetics. Gasi®ed char of NL coal was characterized and morphological changes in the char became clear. The surface area of gasi®ed char increased rapidly with the progress of gasi®cation up to about six times the size of initial surface area and peaked at about 40% of char gasi®cation, while the particle size distribution of char did not change until about 50% of char gasi®cation had occurred, and the value of d002 or Lc002 of carbon crystallites remained unchanged during gasi®cation.
References [1] Inumaru J, Hara S, Hamamatsu T, Ishikawa H. In: Proceedings of International Conference on Coal Science. IEA, Japan, 1989. p. 297. [2] Araki S. In: Proceedings of Third Clean Coal Technology Technical Seminar. APEC, Korea, 1995. p. 97. [3] Kajitani S, Matsuda H, Hara S, Ashizawa M, Takahashi T. In: Proceedings of 13th Annual International Pittsburgh Coal Conference. University of Pittsburgh, USA, 1996. p. 976. [4] Takarada T, Tamai Y, Tomita A. Fuel 1985;64:1438. [5] Miura K, Hashimoto K, Silveston PL. Fuel 1989;68:1461. [6] Roberts DG, Harris DJ. Energy and Fuels 2000;14:483. [7] van Heek KH, Muhlen HJ. Fuel Processing Technology 1987;15:113. [8] Kasaoka S, Sakata Y, Shimada M. Fuel 1986;66:697. [9] Kajitani S, Matsuda H. In: Proceedings of 8th Australian Coal Science Conference. University of New South Wales, Australia, 1998. p. 295± 300. [10] Marsh H, Siemieniewska T. Fuel 1965;44:355. [11] Marsh H. Carbon 1987;25:49. [12] Sohn HY, Szekely. J Chem Eng Sci 1972;27:763. [13] Bhatia SK, Perlmutter DS. AIChE J 1980;26:379. [14] Radovic LR, Walker Jr PL, Jenkins RG. Fuel 1984;63:1028. [15] Ergun S. US Bureau of Mines Bulletin 1968:648.