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Energy & Fuels 2000, 14, 994-1001
Measurement of the Sintering Kinetics of Coal Ash A. Y. Al-Otoom,* L. K. Elliott, T. F. Wall, and B. Moghtaderi Cooperative Research Centre for Black Coal Utilization, Department of Chemical Engineering, The University of Newcastle, Callaghan, NSW 2308, Australia Received February 3, 2000
A new technique has been developed to determine the sintering rate of coal ash based on the measurement of the pressure-drop across a pellet of ash. The technique monitors the changes in porosity as a function of time, which is an indication of the degree of strength development due to sintering. The technique developed in this study shows a good repeatability of the rate of sintering and confirms that viscous flow is the dominant mechanism for sintering of coal ash. The activation energies of the sintering process studied in this investigation were found to be in the range of 200-315 kJ/mol.
Introduction Sintering refers to the bonding or welding of adjacent particles in a powder medium under the influence of excess surface energy. This phenomenon is usually associated with the strength development of the compacted powders. In fluidized bed combustors, sintering is a major contributor to a number of operational problems such as bed agglomeration, deposition on gas circuits and heat exchanger tubes, as well as ash buildup and bridging on hot gas filtration systems. The viscous flow mechanism was shown to be the dominant mechanism of coal ash sintering.1 Frenkel2 was one of the first researchers to develop a model for the viscous flow mechanism by equating the change in the surface energy with the energy dissipated by the flow of material. The author suggested that, under the influence of surface tension, crystalline materials would behave like amorphous materials. Zagar3 used this model to obtain a relationship for the change in the porosity with time. This relationship is based on the reduction of the volume between a cluster of uniformly packed spherical particles of the same size as a result of sintering.
1-
()
9γ ) t 0 4ηr0
(1)
where η is the apparent viscosity, γ is the surface tension, and and 0 are the pore volume at time t ) t and at time t ) 0, respectively. Most experimental results suggest that the range of applicability of Frenkel’s equation is limited to a small time range of the initial stages of sintering. This led Lemaitre et al.4 to modify Frenkel’s equation based on the hypothesis that * Corresponding Author:
[email protected]. (1) Raask, E. Mineral Impurities in Coal Combustion; Behaviour, Problems and Remedial Measures; Hemisphere Publishing: Washington, DC, 1985. (2) Frenkel, J. Tech. Phys. Leningrad 1945, 9, 385. (3) Zagar, L. Sci. Sintering 1975, 7 (1), 35-43. (4) Lemaitre, J.; Bulens, M.; Delmon, B. Clay Miner. 1976, 11, pp 313-.
Figure 1. Mechanism of sintering of particles with wide size distribution showing the decrease of the size of the closed pores and increasing the size of the open pores.
the viscosity of the material changes linearly with time, at a constant temperature, during sintering by the equation,
η ) η0(1 + Rt)
(2)
where η0 is the initial viscosity, and R is a rate constant for the change of viscosity with time. The validity of this hypothesis was verified later in a number of experimental studies.5,6 These studies indicated that, during sintering, the material loses its excess surface energy by dissipating this energy into the deformation of this material, becoming less amorphous in behavior. Consequently, viscosity increases with time. The sintering kinetics is generally determined by measuring the changes in the physical dimensions of a pellet produced from the material of interest (dilatometry).6-8 Dilatometry is generally a very accurate technique; however, a new technique for measuring the sintering kinetics of coal ash has been developed in this study. This technique, which depends on the pressure-drop of a gas across an ash pellet, provides additional information about the internal changes within that pellet during sintering. In this technique, measurements of the pressure-drop of the airflow through a pellet of coal ash can be used to determine the sintering (5) Anseau, M. Deletter, M.; Cambier, F. Trans. J. Br. Ceram. Soc. 1981, 80, pp 142-. (6) Das, P.; Chowdhury, R. Mate. Sci. Technol. 1989, 5, 299-300. (7) Das, P.; Choudhury, R.; Behera, H. Ceram. Int. 1994, 20, 315318. (8) Rahaman, M. N. Ceramic Processing and Sintering; Marcel Dekker Inc., NY, 1995.
10.1021/ef0000126 CCC: $19.00 © 2000 American Chemical Society Published on Web 08/16/2000
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Energy & Fuels, Vol. 14, No. 5, 2000 995
Figure 2. Experimental setup showing the sample arrangement and typical results from Ash-1. Table 1. Chemical Composition of the Laboratory Coal Ashes (Calculated as wt % Oxide) Used in the Experimental Program and the Mean Particle Size sample
SiO2
Al2O3
CaO
Fe2O3
MgO
Na2O
K2O
TiO2
SO3
Dpm (µm)
Ts (°C)a
ash-1 ash-2 ash-3 ash-4 ash-5 ash-6
37.7 40.9 25.51 44.4 46.25 36.8
20.3 28.5 17.8 29.3 35.2 22.8
2.65 14.47 27.32 4.7 3.93 16.4
31.5 6.6 6.76 12.9 4.7 17.4
1.45 0.32 5.92 2.03 0.97 3.4
0.29 0.15 2.24 0.24 0.28 0.22
3.05 0.1 0.35 0.51 0.28 0.40
0.65 2.06 1.2 1.75 3.78 0.8
1.92 6.23 8.64 2.76 3.15 0.8
29 21 9.7 15 21 30
815 880 730 920 860 800
a
The sintering temperatures obtained from the pressure-drop experiments.
temperature of the pellet, as well as the rate of change of its porosity with time. The kinetic parameters of the sintering process can be extracted from these data using a combination of eqs 1 and 2 and conventional kinetic analysis. The capabilities of the new technique are demonstrated here by extracting the kinetic parameters of six Australian coal ashes.
surface energy. This reduction can occur by shrinkage or growth of the pores.9 Most materials exhibit pore growth under sintering conditions,9-11 A possible mechanism for pore growth is illustrated in Figure 1. As fine particles densify, large voids develop through the interstices of the large particles, resulting in an increase in the average pore size with little change in the total
Pressure-Drop Sintering Technique (PDS)
(9) Whittermore, O.; Varela, J. Pore Distributions and Pore Growth During The Initial Stages of Sintering. In Sintering Processes; Kuczynski, G. C., Ed.; Plenum Press, New York, 1980; pp 51-60. (10) Whittermore, O.; Sipe, Powder Technol. 1974, 9, 159-164. (11) Whittermore, O. J. Mater. Sci. Res. 1978, 11, 125-133.
Theoretical Basis of the PDS Technique. The driving force behind sintering is the reduction of free
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Energy & Fuels, Vol. 14, No. 5, 2000
Al-Otoom et al.
Figure 4. Isothermal changes of the pore size during sintering of ash-3 at 830 °C.
Combining eqs 3 and 4 results in 2
∆P 1.115uη ((1- o) + 0.018) ) L d2 (1 - ) 1.5 m
Figure 3. Particle size distribution of the samples used in the experiment determined by Malvern instrument.
porosity.10 The large particles are believed to maintain the original frame of the compacted material, so the total porosity remains, relatively, constant. From Figure 1, there are two distinct types of porosity, the open porosity and the closed porosity. The open pores are referred to as the accessible pores for a gas flow (capillaries) which formed between the interstices of large particles, while the closed pores are those formed as a result of closed packing between the small particles. Since the volume of the open pores or the accessible pores increases, the pressure-drop of a gas across the pellet decreases, because the pressure-drop across porous media is inversely proportional to the diameters of the capillaries. Therefore, measurements of the pressure-drop of the airflow across the ash pellet under sintering conditions should provide the necessary information about the sintering temperature and its kinetic parameters. Kozeny12 presented a correlation between the pressure-drop of a gas across a fixed bed and the porosity,
u)
( )( ) ( ) 1 C
o3d2m 36η
×
∆P L
(3)
where u is the velocity, C is a constant, which depends on the open porosity ο, dm is the average particle diameter, η is the gas viscosity, and ∆P is the pressuredrop of the gas across a bed of a length L. The constant C can be related to the open porosity using the following expression proposed by Rose,13
C)
(
1000 × o3
36(1 - o)
)
2
((1 - )2 + 0.018)
( )
1- 1.115 1.5
(4)
o
(5)
o
From eq 5, the open porosity (capillary volume) of a consolidated media can be calculated if measurements of the pressure-drop across that material are available. Such measurements can be obtained using the experimental setup developed in this investigation. Thermomechanical analyses of these coal ash pellets indicate that the maximum shrinkage at the temperatures used in this study is around 5%. From that, the length of the sample can be assumed to be constant with a maximum error of 5%. Since there is little change in the total porosity during the initial stages of sintering, as indicated earlier, it can be assumed to be constant. Also, the size of large voids or accessible pores between large particles increases during initial stages of sintering, therefore, the size of closed pores or inaccessible voids is reduced accordingly. From a simple mass balance, the closed porosity can be calculated from the total and the open porosity:
t ) c + o
(6)
where t is the total porosity, c is the closed porosity, and o is the open porosity. Since gas flows only through the open pores, the pressure-drop reading reflects the magnitude of the open porosity. The initial total porosity can be calculated using the density-porosity relationship, which comes from a simple mass balance as indicated in eq 7.
Fapparent ) Fparticles (1 - t)
(7)
where Fapparent is the apparent density, which can be calculated from the mass and dimensions of the pellet, and is the individual particle density. An average of 2.4 g/cm3 value was used in this study1 which generally represents the density of ash particles (Fparticles). The typical values for the total porosity from this study are 50%-65%, using 0.35 MPa of initial pellet compression, while the range of the open porosity obtained by the pressure-drop readings was 10-30%. (12) Carman, P. C. Flow of Gases Through Porous Media; Academic Press, Inc.: New York, 1956; pp 11-22. (13) Rose, H. E. Proc. Inst. Mech. Eng. London 1945, 153, 141-148.
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Figure 6. Scanning electron microscope images showing the changes of open and closed pores during sintering for ash-3. Samples treated at 850 °C for various times.
Figure 5. Comparison of the open porosity obtained using N2 surface adsorption and that obtained from the pressuredrop technique. (A) Ash-3 at 830 °C, (B) ash-4 at 960 °C.
Method of Extracting Kinetic Parameters of Sintering Process from PDS Technique. The kinetics of sintering in this study will focus on the changes of closed porosity, since the reduction of closed porosity is responsible for increasing the effective particle size when considering agglomeration and strength development of deposits in fluidized bed combustion systems. Using Zagar’s model, eq 1, and the assumption that the viscosity changes linearly with time, eq 2. The rate of porosity changes with time can be shown by the following expression:
( ) 1-
c t 9γ ) c0 4r0η0 (1 + Rt)
(8)
Assuming K ) 9γ/4r0η0, eq 8 can be written as
tc0 ∆c
)
1 R + t, K K
(9)
where ∆c represents (c0 - c). In a plot of tc0 /∆c against time t, the constants K and R can be calculated from the intercept and the slope of the line, respectively. Pressure-drop readings acquired in PDS experiments are used to provide values for c and c0 via eqs 5 and 6. Once K, which is a rate constant, is known, the other kinetic parameters, such as preexponential factor A and activation energy E, can be extracted from the data using conventional kinetic analysis. For this purpose, one needs to plot (-ln(K)) versus (1/T) where T is the temperature. The slope of the resulting line will be E/R, where R is the gas constant, and its intercept with the abscissa will be -ln(A).
The Experimental Setup. This experimental setup was originally designed to determine the sintering temperature of coal ash.14 The experimental apparatus used in this investigation comprises of a tube furnace fitted with a temperature controller, a sample holder, a data acquisition system, a mass flow controller, and a pressure transmitter. A schematic diagram of the experimental setup is presented in Figure 2. Air, from a compressor, passes through a mass flow controller and into an alumina tube, 12.7 mm-ID, in which a mass of ash (0.5-1 g) is compressed to 0.35 MPa. The range of airflow achievable in this setup is between 15 and 30 cm3/min. The alumina tube is heated from ambient at a rate of 10 °C/min in the tube furnace to the desired temperature and held there for a period of time. The variation of pressure-drop with time is continuously recorded by the data acquisition device. The amount of ash used is such that the length of the ash pellet is smaller than the radius. This forces air to pass through the center of the pellet through a hole in the alumina sheath as indicated in the Figure 2. Method and Materials. A range of subbituminous and bituminous coal ashes was used in this study. These ashes were prepared by initially crushing the coal to
