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GENERAL RESEARCH Minimum and Terminal Velocities in Fluidization of Particulate Ceramsite at Ambient and Elevated Temperature Miloslav Hartman,* Otakar Trnka, and Michael Pohorˇ ely´ Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, 165 02 Prague 6-Suchdol, Czech Republic
Ceramsite is an inert, heat-resistant, porous material that is made via the calcination of carbonaceous claystone in an oxidizing environment. Its basic mineral constituents are mullite, hematite, quartz, and kaolinite. Ceramsite particles have been proven to be a very practical and convenient bed material for performing various chemical reactions in high-temperature fluidized beds. Experimental measurements were performed to determine minimum fluidization velocities and the terminal (entrainment) velocities of beds of ceramsite at ambient and superambient temperature. Using air, experiments were conducted in a column with an inner diameter (ID) of 9.4 cm, with very narrow fractions of ceramsite particles spanning a wide range of 0.13-2.25 mm. The minimum fluidizing velocity was determined to decrease as the operating temperature increased for the beds of all the particles, except for the largest ones (2.25 mm). The bed of these particles exhibited an extremal (nonmonotonic) dependence of the minimum fluidizing velocity on temperature. Novel explicit equations have been developed that enable the direct estimation of the particle size corresponding to chosen minimum fluidizing and/or terminal velocities. Those formulas can be applied in engineering considerations and design calculations of fluidizing ceramsite and similar materials. Introduction Fluidization is now firmly established as a major unit operation in the processing industries1 (e.g., catalytic oxidation, combustion, gasification, and polymerization). A theoretical framework of the subject is quite solidly based on observations and data amassed under ambient conditions. However, it is not immediately obvious how theoretical predictions of fluidizedbed behavior would extrapolate to high temperatures (and pressures).2-4 The fluidized-bed flow regime or mode of contacting gas and particulate solids varies widely. The flow regime is dependent on the particle size, particle density and particle geometry, gas density and gas viscosity, and gas velocity and column architecture. In practical situations, effects of particle-size distribution and/or particle-density distribution also must be considered.5,6 The operation regimes, in which the solid particles are fluidized but not yet entrained from a vertical vessel, are bounded by the minimum (incipient, critical) and terminal (freefall) velocities.7-12 Both the minimum fluidization velocity and the terminal velocity are fundamental characteristics of a fluidized bed. Their accurate predictions are of primary importance for the successful design and operation of fluidized-bed units. Experimental measurements of the minimum fluidization velocities at high temperature are scant in the literature.13-16 To the best knowledge of the authors,17,18 no experimental data on the terminal velocities of particles at elevated temperatures are available in the literature. * To whom correpondence should be addressed. Tel.: +420 220390254. Fax: +420 220920661. E-mail address: hartman@ icpf.cas.cz.
Sand is usually used as an inert bed material in experimental, high-temperature studies on fluidization. Unfortunately, in practice, quartz (silicon dioxide) is strongly susceptible to combining with alkalis at elevated temperature and forming unwanted low-melting-point eutectics. To avoid undesirable softening of the surface of particles, we have been using chemically and thermally stable ceramsite for several years in our combustion19,20 and gasification studies. It also resists softening because of its lower content of alkaline components. This commercial, inexpensive material is originally claystone that has been calcined to constant mass at 950 °C in an oxidizing atmosphere. Because of its lower density, ceramsite fluidizes more smoothly than sand does. In the present study, the investigation has been undertaken to explore the minimum fluidization velocity and entrainment velocities for ceramsite particles at ambient and superambient temperature. The experimental results have led to the development of explicit formulas that permit estimation of the sizes of nonspherical ceramsite particles that occur at the point of minimum fluidization and also those sizes that are just entrained from the reactor under different conditions of operation. Experimental Section Procedure. The point of minimum fluidization was determined by the standard procedure of measuring the dependence of bed pressure drop on air flow with the air velocity gradually reduced from a well-fluidized state to a packed (static) bed. Measurement was made at a bed aspect ratio (height-to-diameter ratio) close to unity. Entrainment velocity was determined from the plot of pressure drop across the fluidized bed versus the velocity of air. Ueb is the superficial gas velocity at which the first noticeable decrease
10.1021/ie0615685 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/03/2007
Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 7261 Table 1. Major Components Contained in Ceramsitea constituent Al2O3 CaO Fe2O3 K2O MgO Mn3O4 Na2O P2O5 TiO2 SiO2 SO3 sum base-acid (B/A)
onset of
temperature (oC)
27.59 2.38 12.58 3.13 2.48 0.12 1.35 0.69 3.34 44.76 0.05
sintering softening melting flowing (fluid)
1160 1315 1375 1395
98.47 ratiob
Table 2. Heat-Resistant Characteristics (Fusibility) of Ceramsite
amount (wt %)
0.290
Carbonaceous claystone rock calcined to constant mass at 950 °C in an oxidizing atmosphere. b Used as an indication of propensity toward melting and slagging, defined as B/A ) [(CaO + Fe2O3 + K2O + MgO + Na2O)/(Al2O3 + SiO2 + TiO2)].22 a
in ∆P was observed and particles began to be elutriated from the top of the column. The value of the air flow rate (Uef) at which just the last particles were entrained out of the vessel and the pressure drop across the bed was close to zero, was also measured. The mean value (Uem ) (Ueb + Uef)/2) then was taken as the entrainment velocity of a given narrow fraction of the solids.21 It is apparent that the entrainment velocity determined in this way is a property of the entire bed of many different particles, rather than the free-fall velocity of an isolated particle. We believe that Uem better represents the entire bed than does the terminal velocity of a single particle in an infinite medium. The span of the difference Uef - Ueb usually varied over a range of 0.20-0.30 m/s. Only those experimental data that were reproducible within (3%-5% were used. Materials Used. Experiments were conducted with inert, porous particles of ceramsite. This term denotes an inexpensive, inert particulate material that is made via the high-temperature calcination of carbonaceous claystone rock dropping from the opencast mining of Czech lignites (brown coals). The raw claystone rock occurs as the roof of many lignite seams. The specific material used in this study was provided by Lias Vintı´ˇrov, under the tradename Liapor. The chemical specifications of the calcined material are listed in Table 1. As can be seen, the main constituents of ceramsite are silicon dioxide (45 wt %), aluminum oxide (28 wt %), and iron oxide (13 wt %). Significant amounts of titanium dioxide, alkali-earth metals, and alkali metals are also present. The main minerals found in ceramsite, using X-ray diffraction (XRD) analysis, were mullite (Al6Si2O13, ∼58 wt %), hematite (Fe2O3, ∼20 wt %), quartz (SiO2, ∼20 wt %), and kaolinite (Al2(OH)4Si2O5) and/or cristobalite (SiO2) (∼2 wt %). Ceramsite is an inert and stable material. For example, it dissolves only slightly in hot aqua regia. The base-acid (B/A) ratio, which is defined and given in Table 1, can be used as an indication of the propensity of the ceramsite toward melting. The lower value of B/A found in this work (0.29) has a tendency to decrease the melting propensity of ceramsite. Standard fusion tests were also performed to measure the softening and melting behavior of the ceramsite. The results presented in Table 2 indicate a very good resistance of the ceramsite to elevated temperatures (up to 1160 °C), which may be viewed as a limit for the use of ceramsite in common high-temperature, fluidized-bed processes. Commercial pellets of ceramsite were crushed, sieved, and calcined again for 2 h at 950 °C in an electric muffle furnace.
Table 3. Physical Characteristics of Ceramsite Particlesa sieve size fraction
mean particle size, dp (mm)
0.10-0.16 mm 0.20-0.25 mm 0.25-0.315 mm 0.40-0.50 mm 0.50-0.63 mm 0.63-0.80 mm 0.80-1.00 mm 1.00-1.25 mm 2.00-2.500 mm
0.130 0.225 0.282 0.450 0.565 0.715 0.900 1.125 2.25
a Physical properties: particle density (determined by mercury displacement), Fp ) 1470 kg/m3; true solid density (determined by helium displacement), FHe ) 2248 kg/m3; fractional particle porosity, ) 0.3461; and pore volume, Vp ) 0.2354 cm3/g.
To smooth the sharp edges of the recalcined particles, they were intensively fluidized for 3 h at ambient temperature. The smoothed particles then were carefully sieved by hand again with the use of the Czech Standard series of screens arranged in multiples of ∼1.25. The fractions investigated in this work were comprised of very narrow fractions in the range of 0.132.25 mm; this information is given along with other important physical properties in Table 3. As can be seen, these fractions belong to Geldart group A, B, and D fluidizable materials.23 Examinations via optical microscopy revealed that the particles had irregular and varied shapes. They were mostly isometric (aspect ratio of ∼1), with an uneven and rough surface. These particles were appreciably porous (their fractional porosity was 0.346). Filtered air with a relative humidity of φ ) 0.75, containing ∼1.9 vol % of water vapor, was used as a fluidizing gas. The effect of temperature and pressure on the density of air was approximated by the equation of state of an ideal gas:
Fair )
352.8 T
(at P ) 101.32 kPa)
(1)
The viscosity of air is only weakly dependent on pressure, but it increases markedly with temperature:24
µair ) (4.261 × 10-7)T0.66
(2a)
In view of its definition, the Archimedes group for given particles fluidized with air decreases quickly as the operating temperature increases; this relationship can be approximated by the expression
Ar ≈ T-2.3
(2b)
where Ar is the Archimedes number. One should note that the Archimedes criterion is influenced by the temperature dependency of fluid density and viscosity. Apparatus. Minimum fluidization velocities and terminal velocities of ceramsite particles at ambient and superambient temperatures were investigated in a high-temperature reactor (9.4 cm inner diameter (ID)) used in our recent combustion studies.20,25 The length of the reactor tube above the perforatedplate gas distributor was 98 cm. The bed was heated electrically by two heaters. The reactor was thoroughly insulated to avoid heat losses. There was also a provision for independent
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preheating the air entering the reactor, the flow rate of which was controlled by mass flow controllers. Thermocouples were inserted into the bed from the top to monitor the bed temperature. Pressure taps were provided at appropriate points, to measure the pressure drops. Carefully replicated measurements of the minimum (incipient) fluidization velocity showed good reproducibility in the range of 2%-5% also at high temperature. Results and Discussion Incipient Fluidized State at Ambient Temperature. Measurements of the minimum fluidization velocity were conducted at 20 ( 0.5 °C with six narrow fractions of ceramsite, the average particle size of which increased from 0.282 mm to 2.25 mm. The correponding incipient fluidization velocities determined by experimentation with these particles ranged from 3.5 cm/s to 79.2 cm/s. Ergun26 and others researchers27 assumed that the total energy loss (total pressure drop) in static (fixed) beds can be treated as the sum of viscous and kinetic energy losses. The Ergun capillary flow model treats the flow resistance as the sum of a viscous resistance corresponding to the linear term in the minimum fluidization velocity (Umf) (i.e., Remf) and an inertial (kinetic) resistance corresponding to the quadratic term in Umf (Remf). Ergun also showed that the total pressure drop across a fixed (and an incipiently fluidized) bed is dependent on the flow rate and the physical properties of fluid, bed voidage, particle shape, and particle size. As can be shown,9 in the viscous flow regime (i.e., for low Reynolds numbers (Re < 1)), the viscous loss is dominant, compared to the kinetic loss. In the kinetic flow regime (i.e., for high Reynolds numbers (Re > 1000)), the kinetic loss dominates and the total pressure drop across the bed can be approximated solely by the kinetic loss. To avoid the problems and uncertainties with the estimation of bed voidage and particle shape accompanying the use of the original Ergun model, we fitted our minimum fluidization velocities Umf, which were measured at ambient temperature, to the following empirical expression, which has a structure similar to the Ergun equation:
Remf ) (29.382 + 0.03467Ar)0.5 - 29.38
(3)
The numerical constants in eq 3 were determined by the simplex method, which minimizes the sum of the squares of the residuals.28 The differences between the experimental and predicted Umf are very similar to the experimental reproducibility (approximately (6%). The numerical coefficients in eq 3 agree with those found by Lucas et al.29,30 for round particles (29.5 and 0.0357), using the results from more than a hundred experimental data points, taken from different sources. The form of eq 3 exhibits another useful feature that, thus far, has not been exploited. This relationship makes it possible to estimate the size of particles that have a given (chosen) Umf without resorting to trial-and-error calculations. When introducing the dimensionless group (ymf), which is defined by the equation
ymf )
Remf3 Umf3F2f ) Ar g(Fp - Ff)µf
(4)
eq 3 can be rewritten as
[
(
Remf ) ymf 14.42 + 207.94 +
)]
1694.8 ymf
0.5
(5)
Figure 1. Measured and predicted minimum fluidization velocity (Umf) of ceramsite at different temperatures. Symbols represent experimental data obtained under the following conditions: mean particle size, 0.565 mm; Archimedes number (Ar) ) 9500-468; and Reynolds number under minimum fluidization (Remf) ) 5.1-0.28. Solid line shows the predictions of eq 3 (maximum relative deviation, 9%).
Figure 2. Measured and predicted Umf of ceramsite at different temperatures. Symbols represent experimental data obtained under the following conditions: mean particle size, 0.715 mm; Ar ) 19250-948; and Remf ) 9.7-0.56. Solid line shows the predictions of eq 3 (maximum relative deviation, 9%).
One can note that the particle size does not occur on the righthand sides of eqs 4 and 5. As eq 4 indicates, the cube root of ymf (ymf1/3) may be viewed as a dimensionless minimum fluidization velocity. Ergun’s model, on which eqs 3 and 5 are based, is wellsupported by experimental evidence and has some solid foundation in theory. Therefore, we believe that the predictive relationships given in eqs 3 and 5 deserve to be examined and considered to describe the fluidization of ceramsite at elevated temperature. Incipient Fluidized State at Elevated Temperature. The experimental measurements were conducted with five narrow fractions of ceramsite, as listed in Table 3 (0.565, 0.715, 0.900, 1.125, and 2.25 mm) at temperatures in the range of 20-800 °C. In this temperature interval, the air density changes by a factor of 0.273, whereas its viscosity changes by a factor of 2.36. Presumably, the particle shape does not change with temperature. Particle dilatation (thermal expansion) with temperature was neglected in enumerating the Archimedes and Reynolds numbers (Ar and Re, respectively). The data amassed from the relationship between the minimum fluidization velocity (Umf) and temperature (t) are plotted in Figures 1-5. In this work, the Ar values are between 400 and 6 × 105, and there is an ∼20-fold decrease in Ar as the operating
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increases. The combined effect of changes in gas density and gas viscosity results in Ar and Re decreasing steadily with increasing temperature. It is not immediately obvious from eq 3 how this will affect Umf. Nevertheless, it follows from eq 3 that, for small Reynolds numbers,
Umf ≈
1 µf
(for Remf < 1)
(6)
and for air, Umf decreases with temperature:
Umf ≈ T -0.66
(for Remf < 1)
(7)
(for Remf > 1000)
(8)
For large Reynolds numbers, Figure 3. Measured and predicted Umf of ceramsite at different temperatures. Symbols represent experimental data obtained under the following conditions: mean particle size, 0.900 mm; Ar ) 38400-1890; and Remf ) 17.5-1.1. Solid line shows the predictions of eq 3 (maximum relative deviation, 7%).
Umf ≈
() 1 Ff
1/2
and Umf increases with temperature:
Umf ≈ T1/2
(for Remf > 1000)
(9)
In the transition regime of flow conditions (1 < Remf < 1000, in air), Umf is proportional to the thermodynamic temperature, T, raised to a power in the range between -0.66 and +0.5:
Umf ≈ T -0.66 to T +0.5
Figure 4. Measured and predicted Umf of ceramsite at different temperatures. Symbols represent experimental data obtained under the following conditions: mean particle size, 1.125 mm; Ar ) 75000-3694; and Remf ) 29.5-2.1. Solid line shows the predictions of eq 3 (maximum relative deviation, 6%).
Figure 5. Measured and predicted Umf of ceramsite at different temperatures. Symbols represent experimental data obtained under the following conditions: mean particle size, 2.25 mm; Ar ) 6 × 105-2.95 × 104; and Remf ) 118-10. Solid line shows the predictions of eq 3 (maximum relative deviation, 5%).
temperature increases from 20 °C to 800 °C with our airfluidized system. The upper horizontal axes in Figures 1-5 indicate how the Ar values decrease as the operating temperature increases for different particles. The density of an ideal gas is inversely proportional to its thermodynamic (absolute) temperature; the viscosity of gases, on the other hand, increases markedly as the temperature
(for 1 < Re < 1000) (10)
Generally, Umf is a nonlinear function of temperature which can exhibit a maximum. The sets of experimental data points shown in Figures 1-4 demonstrate that the Umf value appreciably decreases with increasing operating temperature within the range of particle size of 0.565-1.125 mm. These results indicate that, over the range of the amassed data (Remf ) 0.3-30), the viscous energy losses are dominant. The monotonic decrease of Umf with increasing operating temperature presented in Figures 1-4 for the beds of smaller particles [(dUmf/dT) < 0] manifests that the increasing viscosity of the fluidizing gas is the controlling factor under the more-or-less laminar flow conditions that have been used. The experimental results measured with the largest ceramsite particles under turbulent/transitional flow conditions (dp ) 2.25 mm; Remf ) 120-10) and plotted in Figure 5 show a picture that is remarkably different from that for the beds of smaller particles (presented in Figures 1-4). In contrast to the monotonic behavior displayed in Figures 1-4, the curve in Figure 5 exhibits extremal (nonmonotonic) behavior. As can be seen, the results suggest the existence of a flat maximum [(dUmf/dT) ) 0] in the dependence Umf ) Umf(T) in Figure 5. The maximum seems to occur somewhere near 350-400 °C (Remf ) 40-30), which suggests conditions under which changes in the viscous and kinetic energy losses with temperature are equal or very similar to each other. Alternatively, it is entirely reasonable to accept that a decrease in the gas density with increasing temperature is just compensated by an increase in the gas viscosity at Remf ) 30-40. The rising branch of the curve in Figure 5 [(dUmf/dT) > 0] outlines a region of flow behavior where the decreasing gas density is a dominant factor and Umf increases as the temperature increases. At temperatures above 350-400 °C, the descending branch of the curve [(dUmf/dT) < 0] in Figure 5 again indicates the governing effect of the gas viscosity increasing with increasing temperature. It can be shown from the definition of Umf that its temperature dependence is an intricate, nonlinear
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Equations 12 and 13 make it possible to circumvent iterative solutions of eq 11 to evaluate Ret. As shown in Figure 6, the relative departures of the predicted and experimental velocities are
