Innovative Method Using Magnetic Particle Tracking to Measure

Sep 23, 2009 - Waynesburg UniVersity, 51 West College Street, Waynesburg, PennsylVania .... jack, which allowed the bed to be moved vertically to posi...
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Ind. Eng. Chem. Res. 2010, 49, 5037–5043

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Innovative Method Using Magnetic Particle Tracking to Measure Solids Circulation in a Spouted Fluidized Bed Emily E. Patterson and Jack Halow* Waynesburg UniVersity, 51 West College Street, Waynesburg, PennsylVania 15370

Stuart Daw Oak Ridge National Laboratory, KnoxVille, Tennessee 37932

We describe an innovative method for measuring particle motion inside spouted fluidized beds. The method uses a magnetic tracer particle, which follows the bulk particle flow and is continuously tracked by multiple magnetic field detectors located outside the bed. We analyze signals from the detectors to determine the tracer position at each instant in time. From statistical analysis of the tracer trajectory, characteristic measures of the bulk particle flow, such as the average recirculation frequency, can be determined as a function of operating conditions. For experiments with a range of particle sizes and densities in a 3.9-cm-diameter spouted bed, we find that average solids recirculation rates correlate with excess velocity (superficial minus minimum spouting velocity), particle density, and bed depth. Introduction Spouted fluidized beds are used extensively for processing solids in many applications.1-6 Spouted beds have also been studied extensively to determine the important parameters controlling the gas dynamics and gas-solids contacting.7-15 A recent thesis by Zhou details past studies of spouted beds and describes measurements for shallow beds of dense particles.16 Most past studies of spouted bed dynamics have relied on visual observation and pressure measurements to determine key hydrodynamic indicators such as minimum spouting velocity, spout height, and pulsation frequency. Studies of bulk solids circulation, however, have been very limited because of the difficulty of directly observing solids motion. In visual observations of three-dimensional beds, it is typically impossible to precisely track the motion of individual particles due to shielding by surrounding neighbors. For this reason, two-dimensional transparent beds and beds with semicircular cross sections (and a flat viewing window) have been used to enhance optical access. Mathur and Gishler,17 for example, studied half-round beds to observe solids flow in the spout. Unfortunately, twodimensional and half-round beds have hydrodynamic patterns and wall effects that do not match the three-dimensional bed geometries used in practical processes. In-bed sensors for observing particle motion have been developed to avoid the large-scale hydrodynamic distortions associated with two-dimensional and half-round beds. One such technique is that developed by Gorshtein and Soroko,18 who used piezoelectric probes inside the bed to measure directly the momentum of particle impacts, from which solid velocities can be deduced. Other sensor-based methods have relied on particle residence time distribution (RTD) measurements of the collective motion of groups of particles with distinctive characteristics such as chemical composition, ferromagnetism, phase change, color, high temperature, or phosphorescence. Harris20 provides an excellent recent summary of these methods in bubbling and entrained beds. Typically, RTDs are measured by injecting a collection of tracer particles into a fluidized system and * To whom correspondence should be addressed. E-mail: jhalow@ waynesburg.edu or [email protected].

measuring their local concentrations over space and time. RTDs can be interpreted in terms of diffusion or dispersion coefficients, but they do not directly yield information about individual particle trajectories. Nonintrusive imaging methods can eliminate potential flow field distortions by using external particle sensors. These methods include X-ray tomography, capacitance tomography, and magnetic resonance/nuclear magnetic resonance imaging (MRI/NMRI). X-ray19 and capacitance tomography19 both reconstruct the concentration of solids and voids over space and time but not the motion of individual particles. MRI/NMRI21 requires the presence of particles containing hydrogen or carbon, which can act like collective tracers to measure RTDs and in some cases particle motions. While very effective for spatiotemporal analysis, imaging methods require highly specialized, expensive equipment, large data set handling, and considerable operating expertise. Two other nonintrusive techniques have been developed to directly track the motion of individual particles. The first, usually referred to as computer aided radioactive particle tracking (CARPT), employs gamma emitting radioactive tracers embedded in single particles and external gamma detectors to follow the tracer motion.19 The second, positron emission tomography (PET) is similar to CARPT, except that it is based on a different type of radioactive isotope that emits correlated pairs of γ rays. Both of these methods allow direct measurement of tracer particle trajectories, but like the nonintrusive imaging approaches, they require expensive and specialized equipment and considerable operating expertise. They also require access to short-lived radioactive isotopes, and concomitant safety issues. The particle tracking method we describe here combines key features of the nonintrusive, single particle tracking ability of CARPT and PET with a much cheaper and safer magnetic tracer. The external sensing apparatus also uses inexpensive Hall-effect sensors instead of more expensive gamma detectors. As explained below, these advantages also involve certain limitations, including the complexity and limited range of the tracer’s bipolar magnetic field. Once implemented, however, the system is simple to operate and data collection routine. We expect that

10.1021/ie9008698 CCC: $40.75  2010 American Chemical Society Published on Web 09/23/2009

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Figure 1. Tracer particle with embedded cubic neodymium magnet.

Figure 2. Overall spouted bed experimental setup.

the method described here will be able to fill an important niche in particle measurement technology. Experimental Method Our particle tracking method utilizes neodymium magnets and Hall-effect magnetic field detectors to continuously locate the position of a single tracer particle over time. Neodymium magnets are currently the strongest permanent magnetic material available and can be purchased in various geometries and sizes down to approximately 1 mm. We create spherical tracer particles by embedding either cubic or disk shaped magnets in plastic. These tracers are composite materials. The neodymium magnets have a particle density of approximately 7.4, and the plastics, a density of slightly more than 1.0. As composites, the tracer particles have densities between these limits and depend on the relative volumes of the magnetic material and the plastic coating. We determine the precise diameter of each tracer by accurately measuring the diameter in several directions and averaging. Then, we precisely weigh the particle on an analytical balance and compute a density from the weight and diameter assuming the particle is spherical. We have prepared tracer particles with a range of diameters and densities using different size magnets, coating materials, and coating thicknesses. This gives us a selection of tracer particles from which we can pick the appropriate size and density to use with different bed materials. Figure 1 shows a tracer made from a cubic magnet. This tracer is about 3 mm in diameter. Spouted Fluidized Bed Apparatus. Our experimental spouted bed system configuration is illustrated in Figure 2. A standard oil-less 200-psig shop air compressor with a 15 gal air tank and two additional air tanks [11 gal each] for added capacitance

Figure 3. Magnetic sensors positioned around a spouting bed.

supplied the air. After passing through a filter and pressure regulator, the air was metered with a rotameter and bubbled through a tank containing distilled water to humidify the air. Flexible clear plastic tubing was used upstream of the humidifying tank to the pressure regulator. Rigid polyethylene tubing was used downstream of the humidifying tank to the inlet of the bed to avoid any possible effect of tubing flexing with the pressure pulsations that can occur in fluidized beds. The spouted bed consisted of a 39-mm-diameter by 390-mmlong glass tube attached to a plastic 45° funnel. A 4.09-mmdiameter inlet tube was attached to the funnel at its apex. The bed assembly was clamped to a ring stand mounted onto a lab jack, which allowed the bed to be moved vertically to position the stationary probes at different bed heights. The magnetic sensor stand consisted of a flat wooden and plastic probe holder set on a PVC pipe stand. Four magnetic sensor probes [model no. MG-BTA from the Vernier Software and Equipment Company] were secured to the holder around and perpendicular to the fluidized bed with their axis oriented north, south, east, and west. Figure 3 is a photograph of the magnetic sensors positioned around a spouting bed. The probe ends where placed against the outside wall of the bed. Procedure. Solids circulation measurements were made with a range of particle sizes and densities as summarized in Table 1. Test materials included glass, zirconium silicate (ZrSiO4), and zirconium oxide (ZrO2). Particle density was measured by water displacement in a pycnometer. The minimum fluidization velocity was determined from plots of pressure drop versus velocity in a 39 mm bed with a perforated plate distributor. The minimum spouting velocity was determined in the spouted bed by first increasing the gas velocity well above minimum spouting, then decreasing velocity to a value that would just maintain the spout for at least 5 min. Experiments were conducted at several bed heights with a range of velocities studied at each bed height. Before each set of experiments, the bed was vertically aligned and the orientation of the probes was adjusted to ensure that they were aligned north, south, east, and west. The particles (except the tracer) were then poured into the bed and the bed was fluidized to fluff the bed. The bed elevation was then adjusted so that the loose-packed settled bed surface was at the elevation of the probes. The bed was then thoroughly fluidized, and the minimum-spouting velocity was determined. For each airflow, the magnetic field probes were initially zeroed, data acquisition was initiated, and a single tracer particle was dropped

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Table 1. Particle Properties particles/ bed depth 0.8 5.5 7.0 1.2 3.5 5.5 6.5 1.5 3.5 5.3 6.5 2.0 3.5 5.5 7.0 1.0 3.5 5.5 6.5 1.0 3.5 5.5 6.5 7.3

mm glass cm bed cm bed mm glass cm bed cm bed cm bed mm glass cm bed cm bed cm bed mm glass cm bed cm bed cm bed mm ZrSiO4 cm bed cm bed cm bed mm ZrO cm bed cm bed cm bed cm bed

density g/cm3

min fluid. vel. cm/s

2.5

56

min, spouting vel. cm/s 48.7 51.6

2.5

102 63.0 84.4 100.7

2.5

104

Figure 4. Magnetic field strength versus distance.

80.6 101.0 107.8 2.5

135 102.2 114.7 115.9

4.11

126 83.9 97.5 106

5.72

118 82.8 100.5 102.2 106.6

into the bed. The height of the spout was also visually estimated for each condition. The recorded magnetic field signals from each probe were used to calculate two horizontal (X, Y) coordinates and one vertical (Z) coordinate of the tracer over time as described below. The first 20 s of recorded data were not used for analysis to remove any initial transients. Fifteen tests were typically run for each particle type. Algorithm for Calculating the Position of the Tracer. The basic principle behind our tracer method is that the measured field strength at each probe is a function of the distance between the tracer and the probe tip and simultaneous measurements by multiple probes will allow the position of the tracer to be calculated. An immediate difficulty in interpreting the probe signals using the approach is the vector nature of the tracer’s magnetic field. If the tracer were randomly reoriented by bed turbulence, accurately determining tracer position from a few probe signals would be extremely difficult. However, contrary to this intuition, we found that the tracer particle tends to align its magnetic axis with the earth’s magnetic field (like a compass needle). It does so along the earth’s magnetic field including the declination, which in our location is about 68° from the horizontal toward magnetic south or 112° from magnetic north. Observations of tracers show that if they are repeatedly dropped onto a smooth surface, they quickly reorient into the north-south direction. A further confirmation of the tracer’s tendency to maintain its orientation is the experimental magnetic field measurements themselves. If tracers were susceptible to random changes in orientation when in the fluid bed, we would expect to see corresponding random fluctuations in the magnetic readings. To the contrary, the magnetic field measurements exhibited no such fluctuations as the tracers circulated through the bed (see for example Figure 7). Rather they exhibit periodic peaks corresponding to the times when the tracer is at the bed surface and nearest the probes confirmed by observations of the times when the tracer appears on the bed surface. In general, the magnetic field strength around a dipole will be inversely proportional to a power of the distance and proportional to a function of the angle between the dipole’s magnetic axis and the direction to the sensor. We experimentally determined the relationships between field strength, distance and orientation for our probes and tracers using a template on which a sensor and tracer magnet could be accurately positioned and

Figure 5. Probe orientation and coordinate definition.

aligned. Figure 4 shows the results for field strength versus distance relationships for two tracer magnets. The red line (upper) is for 1/16 in. diameter by 1/32 in. thick disk magnets and the blue (lower) line for 1/16 in. cube magnets. The relationships in Figure 4 can be closely approximated by d)R

 M1

(1)

where d is distance in centimeters and M is field strength in milliteslas. For the cubic magnetic tracers, R is 0.315, and for the disk magnetic tracers, R is 0.1683. We set the probe tips against the external bed wall and align them as illustrated in Figure 5. The probes lie in a plane perpendicular to the bed and point in opposing north-south and east-west directions. The probe design is such that they measure the magnetic field component parallel to their axis, so the measured signal changes with the angle (φ) between the magnet axis and each probe axis by a factor cos2(φ). Thus, in general, eq 1 becomes d)R

 cos(φ) M

(2)

When the tracer is in the plane of the probes, the magnetic axis of the tracer forms an angle (φn) with the axis of the north probe that is the same as the angle (φs) formed with the axis of the south probe. Likewise, the angles formed between the magnet axis and the axes of the east and west probes are the same (φe ) φw). If we set the central axis of the bed as the origin, we can define X and Y coordinates for any point in the plane of the probes relative to the origin. We compute ratios involving the N-S and E-W probe signals such that the angular component cancels. Geometric identities were found which satisfies this condition and also have linear dependencies on x and y:

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Y ) y/R )

(

dn - d s dn + ds

)

(3)

X ) x/R )

(

de - dw de + dw

)

(4)

and

where R is the bed radius and ds, dn, de, and dw are distances of the tracer from each of the probe tips. From the distance versus probe signal strength relationship in eq 1, we can convert eqs 3 and 4 to

Y)

X)

( (

   

1 |Mn | 1 + |Mn |

1 |Me | 1 + |Me |

  | |

1 |Ms | 1 |Ms |

) )

1 |Mw |

(5)

((

))

(6)

(7)

The Knoise factor is one when the sum of both field strengths is above a noise threshold Pnoise, and it decreases proportionately as the strengths approach zero below the noise threshold. We found that a reasonable value for Pnoise is 0.0015 based on the probe signal noise we observed at the start of runs before the tracer was placed in the bed. An analogous factor based on Me and Mw is used for the X coordinate. The X and Y coordinates determined from eqs 5 and 6 are multiplied by Knoise to give the final coordinates. The final step in the tracer-tracking algorithm is to determine the vertical or Z coordinate. This is done using the estimates for the X and Y and the separation distance, d, from the probe closest to the tracer. By the Pythagorean theorem for each probe: Z ) √d2 - x2 - y2)

Z) South probe Z) East probe

West probe

1 |Mw |

|Mn | + |Ms | ,1 Pnoise

North probe

Z)

where Mn, Ms, Me, and Mw are the magnetic field strengths for the north, south, east, and west probes, respectively. Note that in eqs 5 and 6, the effect of the tracer-probe alignment angles cancel, leaving us with a way to explicitly determine the horizontal coordinates without knowing the direction of the tracer’s magnetic axis. When the magnetic field signals approach the level of measurement noise, the calculated coordinates exhibit a great deal of scatter. In a spouted fluidized bed with its conical bottom and with the probes located at the bed level in the cylindrical part of the bed, we know that the tracer must be confined inside the bed. We apply a correction factor that constrains the X and Y estimates to this limit when the field strength signals approach the noise levels. For the computed Y coordinate, this constraint requires that Knoise ) min

dimensionless coordinates with the origin at the axis of the bed in the plane of the probes. We use the probe measurement with the highest absolute value to determine Z to give the most accurate estimate of Z. The explicit relationships for the four probes used to determine Z are

(8)

where Z is measured downward from the plane of the probes, d is the distance from the probe to the tracer, and x and y are determined from the position of the probe. Using eq 2, we can substitute for d in this equation and express Z as a function of one of the magnetic field measurements. We must also express x and y in terms of the X and Y

Z)

(

cos(φn) - R2(X2 + (1 - Y)2) |Mn |

(

cos(φs) - R2(X2 + (1 + Y)2) |Ms |

(

cos(φe) - R2((1 - X)2 + Y2) |Me |

R2

R2

R2

( R2

)

(9a)

)

(9b)

)

(9c)

)

(9d)

cos(φw) - R2((1 + X)2 + Y2) |Mw |

The constant R comes from the field strength-distance relationship given in eqs 1. The angles are the angles between the magnetic axis and the line from the tracer to the respective probe. These angles can be determined by iteration of the calculation of Z. In the results reported here, we have used an approximate value of 60°. Comparison of Magnetic Tracer Results with Visual Observations. As with any new measurement technique, it would be desirable to directly compare the magnetic tracer measurements described above with results from other established techniques. Unfortunately, we have not been able to find comparable measurements in the literature. Measurements with other nonintrusive methods such as NMR and PET appear to have only been made for bubbling beds, where the solids motion is known to be rather different from spouted beds. Spouted bed particle motion has so far been primarily studied visually in half-round columns with transparent fronts, where of course the flow behavior is likely to be distorted. The bed size, bed geometry, particle properties, and operating conditions reported in the literature differ considerably from our experiments. Because of the lack of independent, comparable measurements in the literature, we evaluated the validity of our magnetic tracer method by making a small number of independent measurements in our experimental setup using a magnetic particle tracer that was easily distinguished by color from other bed particles. The independent measurements were made with a video camera that monitored the bed surface for successive reappearances of the colored tracer. Video recordings were made at 30 frames per second for 30-50 s with a standard Olympus digital camera equipped with a macro lens and movie function. Frame by frame analysis of the video allowed us to determine the times at which the tracer first appeared on the surface on each of its recirculation loops. A sequence of such times was obtained and the difference in these times of adjacent appearances was equal to the period of that particular loop. The solids motion in this bed can best be thought of as a torroidal vortex rotating at a nearly constant angular velocity. If the tracer is on the outside of the torus, it is brought to the surface on each revolution. However, sometimes it is below the surface and so is not seen at the bed surface on recirculation loops. These missed observations were easily recognized and discounted when processing the cycle statistics because they

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confidence error bars shown for the video results. At the lowest velocity, the video observations included only five tracer circulation loops, so our estimate for the error here may be low. The average absolute difference between the recirculation frequencies determined by the two methods in this example is 0.025 Hz. Because the magnetic tracer method generates statistics from 5 min of continuous observations, it includes many more particle cycles than the 30-50 s video analysis. Therefore, statistically, we expect the magnetic method is more reliable than the visual method. Figure 6. Comparison of recirculation frequencies from visual tracer reappearances and magnetic tracer observations. Table 2. Experimental Conditions and Results for Zirconium Oxide Spouted Bed Tests superficial recirculation recirculation bed bed velocity spout frequency rate depth (cm) weight (g) (cm/s) height (cm) (1/s) (g/s) 3.5 3.5 3.5 3.5 3.5 5.5 5.5 5.5 5.5 5.5 6.5 6.5 6.5 6.5 6.5 7.3 7.3 7.3 7.3 7.3 7.3

142.5 142.5 142.5 142.5 142.5 212.5 212.5 212.5 212.5 212.5 250.2 250.2 250.2 250.2 250.2 280.7 280.7 280.7 280.7 280.7 280.7

84.2 90.0 98.9 106.3 113.8 102.0 106.5 114.0 121.7 129.3 106.5 113.9 121.5 129.1 137.1 108.0 114.0 121.6 129.5 137.2 145.4

5.5 6.6 8.0 9.3 10.0 7.0 7.5 8.3 9.5 10.0 7.5 8.0 8.8 9.8 10.9 8.0 8.4 9.0 10.0 10.9 12.0

0.28 0.35 0.34 0.41 0.44 0.24 0.31 0.33 0.36 0.38 0.2 0.27 0.31 0.33 0.36 0.18 0.23 0.27 0.34 0.34 0.36

39.9 49.9 48.5 58.4 62.7 51.0 65.9 70.1 76.5 80.8 50.0 67.6 77.6 82.6 90.1 50.5 64.6 75.8 95.4 95.4 101.1

lead to periods that were approximately multiples of the shortest loop periods. After discounting the multiple loops, we computed the average cycle time for the particle circulation. An autocorrelation analysis of the magnetic probes measurements directly yields the lowest order frequency of recirculation regardless of whether the tracer reaches the surface or not. We then compared the average video cycle times expressed as frequencies with those computed from the magnetic probe measurements. Figure 6 shows a comparison between the visual and magnetic tracer results for 1.5 mm glass beads in a 6.5 cm deep bed. This specific material was chosen because we had observed that, with this material, magnetic tracers appeared frequently at the bed surface, i.e. the recirculation loops with these glass beads generally bring all the particles to the surface. As can be seen in Figure 6, the magnetic and visual tracer recirculation frequencies agreed quite well over a wide range of velocities. To assist the comparison, a smooth curve has been drawn through the magnetic tracer results and an estimate for the 95%

Experimental Limitations The magnetic tracer technique has several constraints that need to be considered for any given application. One obvious limitation is the sensitivity of the Hall effect probes to the magnetic fields generated by the tracers. The probes need to detect the tracer magnet’s field regardless of where the tracer is in the bed. Field strength is approximately inversely proportional to the square of the distance between the probe and the tracer, so larger beds will require larger magnets or probes that are more sensitive. The probes and magnets we used in our experiments work quite well over distances of about 5 cm, but these would probably not be practical for beds much larger than ours. With our experimental setup, the smaller tracers with an embedded disk magnet could be used with particles as small as 1 mm. The slightly larger tracers with an embedded cube were useful for particles 1.2 mm and larger. Brief surveys of commercially available magnetic field sensors indicate that much more sensitive probes (several orders of magnitude more sensitive) are available. We expect larger beds could be studied with these sensors with our current tracers. Depending on the process of interest, it is also important to consider differences between the tracer particles and the other bed particles. For studies where the objective is to study beds of uniform particles, one would typically want the tracers to be as close in size and density as possible to the bed particles. On the other hand, some processes utilize beds having differing particle properties, so in this case, the tracer would need to be matched to the size and density of the particles of most interest. In these experiments, we did not attempt to exactly match the size and density of our tracer particles and the rest of the bed. We note that it is not necessary to exactly match these parameters because uniform or nonsegregating fluidization can be carried out with distributions of particle sizes and with some variation in density, especially under spouting conditions. We did try, however, to identify tracer particle properties that obviously caused it to segregate from the bulk. In the circulation rate trends described below, we eliminated any cases where the tracer stopped circulating and we also repeated experiments with different tracer sizes and densities to identify when there was a noticeable effect on the results. Overall, we found that for our particular spouted bed there was little tendency for tracer segregation once the gas velocity was even slightly above the minimum spouting condition. Bubbling and slugging beds may require a closer match of tracer properties to bed particle properties Results

Figure 7. Smoothed magnetic probe signals.

Illustration of Results for a Single Bed Material. In the following example results, we illustrate how our tracer method can be used to measure recirculation rate in a spouted bed. For this set of experiments, the bed particles were 1.0 mm ZrO2 beads with static bed depths of 3.5, 5.5, 6.5, and 7.3 cm. The

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Figure 8. Vertical position of the tracer.

Figure 9. FFT of the tracer vertical position.

Figure 10. Recirculation rate versus excess gas velocity.

superficial velocities for these tests along with other experimental conditions and results are summarized in Table 2. Over most of the experimental conditions, this material exhibits a central well-defined particle spout, which grew higher with increasing velocity. The tracer could often be periodically seen in the spout as it rose through the central core, came out the top of the spout, and falling onto the bed surface. Figure 7 illustrates an example set of magnetic field measurements made at a bed height of 6.5 cm and at a bed superficial velocity of 106 cm/s. The original probe signals have been smoothed with a moving average window to reduce high frequency noise. Traces from each of the four sensors, north (NS), south (SS), east (SE), and west (SW) are shown in the figure. The peaks correspond to times when the tracer is expelled from the spout and lands close to the sensors. On different cycles, the tracer ends up on different positions on the bed surface leading to maximum peaks from different sensors on subsequent cycles.

Figure 11. Correlation of particle recirculation rate and excess gas velocity.

The south probe has positive peaks, and the north probe has negative peaks consistently. This agrees with the idea that the tracer is aligning with the earth’s magnetic field. The earth’s north magnetic field is actually a positive or south magnetic pole. The earth’s magnetic field would cause the freely suspended tracer to align itself with its south or positive pole declined to the south and its north or negative pole declined to the north. The peaks in the east and west probes vary in sign depending on the north-south location of the tracer on the bed surface. Figure 8 gives the vertical position of the tracer as a function time. We see a periodic motion with a steep rise corresponding to the tracer rising in the central jet and a gradual fall corresponding to the tracer in the downflowing annular zone. Figure 9 shows the fast Fourier transform (FFT) amplitude versus frequency for this vertical tracer position, Z. The most prominent peak occurs at 0.2 Hz, which is the average frequency at which the tracer cycles through the bed. If we assume that the tracer indeed is like every other particle in the bed, then this frequency corresponds to the rate at which the entire bed passes through the cycle. The recirculation rate is then this frequency times the weight of the bed material or 50 g/s. We determined the recirculation rate in this way at various superficial velocities for several bed heights. The trend in

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recirculation rate with gas velocity is depicted in Figure 10. Generally, we see an initial rise in circulation rate with increasing gas flow, followed by a gradual leveling off at higher flows. With some materials, the recirculation rate appears to plateau for a range of gas velocities, while for others there can be abrupt increase in recirculation above a critical gas flow. Correlation of Circulation Rates for Various Bed Particles. From experiments such as those described above, we found that the recirculation rates varied with all of the parameters evaluated, including particle size and density, bed height, and superficial velocity. Measurements at various bed heights indicate that higher velocities were needed to achieve a given circulation rate as the bed height was increased. The minimum spouting velocity increases with bed depth, which suggested that perhaps an excess velocity, or superficial minus minimum spouting velocity would better correlate the data from various bed depths. One method of correlating our observations that looks promising involves the recirculation rate (g/s) times the square root of the bed height (cm) as a function of the difference between superficial velocity (cm/s) and minimum spouting velocity (cm/s) times particle density (g/cm3). Note that the latter term is a type of momentum per unit volume based on the excess gas velocity. Momentum as a correlating factor is consistent with that reported in the work of Shadle et al.23 Figure 11 illustrates the correlation using these groups of parameters. Conclusions These results demonstrate that magnetic particle tracing is capable of providing accurate measurements of solids circulation rates in spouted fluidized beds and promises to be a useful tool for expanding the fundamental understanding of spouted bed dynamics. For the bed configuration, particle properties, and operating conditions studied, our results demonstrate that the bulk solids circulation rate depends on gas superficial velocity, minimum spouting velocity, density, and bed height. Our experience with the technique suggests that the magnetic tracer approach should be capable of extension to other fluid-solids systems. Magnetic field detectors, with much higher sensitivity than the Vernier probes, could be used to enhance sensitivity. Such probes should make it possible to study finer bed materials and larger beds. We expect this approach is also not limited to spouted beds. It should be useful in studying solids mixing in bubbling or slugging beds or in any multiphase system where the detailed particle motion is important. Acknowledgment We thank Waynesburg University’s Center for Research and Economic Development and it is director, Ms. Barbara Kirby, for their encouragement and financial support of this project. Literature Cited (1) Mathur, K. B.; Epstein, N. Spouted Beds; Academic Press: New York, 1974.

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(2) Jono, K.; Ichikawa, H.; Miyamoto, M.; Fukumori, Y. A review of Particulate Design for Pharmaceutical Powders and Their Production by Spouted Bed Coating. Powder Technol. 2000, 113, 269. (3) Khoshnoodi, M.; Weinberg, F. J. Combustion in Spouted Beds. Combust. Flame 1978, 33, 11. (4) Passos, M. L.; Massarani, G.; Freire, J. T.; Mujumdar, A. S. Drying of Pastes in Spouted Beds of Inert Particles: Design Criteria and Modeling. Drying Technol. 1997, 15, 605. (5) Salam, P. A.; Bhattacharya, S. C. A comparative Study of Charcoal Gasification in Two Types of Spouted Bed Reactors. Energy 2006, 31, 228. (6) Scott, C. D.; Hancher, C. W. Use of a tapered Fluidized Bed as a Continuous Bioreactor. Biotechnol. Bioeng. 1976, 18, 1393. (7) Lefroy, G. A.; Davidson, J. F. The mechanics of spouted beds. Trans. Inst. Chem. Eng. 1969, 47, T120. (8) He, Y. L.; Lim, C. J.; Grace, J. R. Scale-up Studies of Spouted Beds. Chem. Eng. Sci. 1997, 52, 329. (9) Jing, S.; Hu, Q.; Jin, Y. Fluidization of Coarse Particles in GasSolid Conical Beds. Chem. Eng. Prog. 2000, 39, 379. (10) Kmiec, A. Hydrodynamics of Flow and Heat Transfer in Spouted Beds. Chem. Eng. J. 1980, 51, 189. (11) Peng, Y.; Fan, L. T. Hydrodynamic Characteristics of Fluidization in Liquid-Solid Tapered Beds. Chem. Eng. Sci. 1997, 52, 2277. (12) Sau, D. C.; Moharty, S.; Biswal, K. C. Minimum Fluidization Velocities and Maximum Bed Pressure Drops for Gas-Solid Tapered Fluidized Beds. Chem. Eng. J. 2006, 118, 151. (13) Shirvanian, P. A.; Calo, J. M. Hydrodynamic Scaling of Rectangular Spouted Bed Vessel with a Draft Tube. Chem. Eng. J. 2004, 103, 29. (14) Wang, Z.; Bi, X.; Lim, C. J.; Su, P. Determination of Minimum Spouting Velocities in Conical Spouting Beds. Can. J. Chem. Eng. 2004, 82, 11. (15) Mikhailik, V. D. The pattern of change of spout diameter in a spouting bed. Collected works on Research on Heat and Mass Transfer in Technological Processes; Nauka I Tekhnika BSSR: Minsk, 1966. (16) Zhou, J. Characterizing and Modeling the Hydrodynamics of Shallow Spouted Beds; The University of Tennessee: Knoxville, TN, 2008. (17) Mathur, K. B.; Gishler, P. E. A Technique for Contacting Gases with Coarse Solid Particles. AIChE. J. 1955, 1, 157. (18) Gorshtein, A. E.; Soroko, V. E. Piezoelectric method of studying a suspended layer. IzV. Vyssh. Ucheb. ZaVed. Khim. Khim. Tekhnol. 1964, 4, 137. (19) Larachi, F.; Chaouki, J.; Kennedy, J. G.; Dudukovic, M. F. Radioactive particle tracking in multiphase reactors: principles and application. Non-inVasiVe Monitoring of Multiphase Flows; Elsevier: New York, 1997. (20) Harris, A. T.; Davidson, J. F.; Thorpe, R. B. A Novel method for measuring the residence time distribution in short time scale particulate systems. Chem. Eng. J. 2002, 89, 127. (21) Holland, D. J.; Fennell, P. S.; Muller, C. R.; Dennis, J. S.; Gladden, L. F.; Sederman, A. J. In Situ Measurement of Dynamic Mixing in GasSolid Fluidized Beds Using Magnetic Resonance. Proceedings of the 2007 ECI Conference on the 12th International Conference on Fluidization New Horizons in Fluidization Engineering, Berruti, F., Bi, X., Pugseley, T., Eds.; Vancouver, Canada, May 13–17, 2007; paper 61. (22) Ingram, A.; Yang, Z.; Bakalis, S.; Parker, D. J.; Fan, X.; Fryer, P. J.; Seville, J. P. K. Multiple particle tracking in a fluidized bed. Proceedings of the 2007 ECI Conference on the 12th International Conference on Fluidization - New Horizons in Fluidization Engineering, Berruti, F., Bi, X., Pugseley, T., Eds.; Vancouver, Canada, May 13–17, 2007; paper 54. (23) Shadle, L.; Shamsi, A.; Zhang, G.; Archer, D. Solids mixing in a spouted fluidized bed, cold model. Proceedings of the 15th International Conference on Fluidized Bed Comb, Savannah, Georgia, May 16–19,1999; paper no. FBC99-0112.

ReceiVed for reView May 26, 2009 ReVised manuscript receiVed August 24, 2009 Accepted August 28, 2009 IE9008698