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Experimental determination of transverse mixing kinetics in a rolling drum by image analysis
Powder Technology 106 Ž1999. 183–191 www.elsevier.comrlocaterpowtec
Experimental determination of transverse mixing kinetics in a rolling drum by image analysis D.R. Van Puyvelde a , B.R. Young a b
b,)
, M.A. Wilson a , S.J. Schmidt
c
Department of Chemistry, Materials and Forensic Science, UniÕersity of Technology, P.O. Box 123, Broadway, Sydney 2007, NSW, Australia Department of Chemical and Petroleum Engineering, UniÕersity of Calgary, 2500 UniÕersity DriÕe NW, Calgary, Alberta, Canada T2N 1N4 c Southern Pacific Petroleum (DeÕelopment), P.O. Box 7101, RiÕerside Centre, Brisbane 4001, QLD, Australia Received 1 October 1998; accepted 7 April 1999
Abstract Rotary kilns are commonly used for mixing of solids, such as grain, and heat transfer to solids, such as drying of fruit and calcination of cement. For a rotary kiln that has a wide range of solid feeds, it is desired to be able to know the kinetics of the mixing of solids inside the rotary kiln so that heat transfer between these solids can be predicted. Heat transfer between different solid feeds is particularly important in the rotating kiln being commissioned by Stuart Energy in Gladstone, Queensland for the processing of oil shale to produce oil. This paper describes a new way to determine the mixing rates of solids in a rotating drum using image analysis programming. Results of this analysis show that the mixing dynamics follow a constant rate until a completely mixed state is encountered. Upon closer analysis it was revealed that mixing occurred in steps, which has not been previously shown. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Rotary kiln; Transverse mixing; Dynamics; Image analysis
1. Introduction Granular materials are widely used in the chemical process industries. However, the behaviour of granular material is not as easily characterised as fluid behaviour by dimensionless parameters such as the Reynolds number. As a result, data obtained for one type of solid cannot easily be applied to a different type of solid. Therefore, there is a clear need to establish methods that can be used to determine mixing parameters for many types of solids. Mixing in a rotating drum is an important process in the particulate industries and is often accountable for the rate of heat transfer between the solids. This limiting rate directly affects the yield and efficiency of the process and is quite commonly a bottleneck. Mixing in a rotating drum occurs in two directions, namely, the transverse and the axial directions. However, mixing in the transverse direction is a few orders of magnitude faster compared to mixing in the axial direction
)
Corresponding author. Department of Chemical and Petroleum Engineering, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4. T el.: q 1-403-2208751; Fax: q 1-403-282-3945; E -m ail: [email protected]
w1x. Due to this, most of the mixing and segregation work in rotary drums has focussed on the transverse plane. The motion in the transverse plane was subdivided into six different regimes w2,3x. For the rolling regime, which is commonly used for mixing solids, the transverse plane was described as consisting of two distinct layers w4x, namely, the active layer and the stagnant layers. The active layer consists of the top section of the bed that is moving rapidly down the slope and is responsible for nearly all the mixing in the transverse direction w5x. Mixing occurs in this section due to the dilation of the material as it rolls down the plane. The gaps formed due to dilation result in other particles falling into them and hence mixing occurs. This mechanism is also responsible for segregation where the smaller particles migrate closer to the centre of rotation preferentially to the larger particles. The second layer observed in the transverse section is the stagnant or plug flow layer. This layer is highly compacted and no mixing is observed in this w4x. The transverse mixing has been modelled in various ways to either determine the residence time in a kiln w6x or to model the mixing kinetics of a binary system w7x. Early experimental determination of mixing dynamics involved measuring the bed temperature near the upper edge of the inclined slope after the addition of a batch of
0032-5910r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 9 . 0 0 0 7 4 - 1
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hot material to a cold rotating bed w4x. A rotational velocity of 2 rpm was used in a 310-mm diameter cylinder loaded with approximately 30% of 0.80 mm sand with a bulk density of 1480 kgrm3. A fully mixed bed was obtained after approximately 42 s. The mixing dynamics at the measurement point followed an oscillating exponential decay until the final bed temperature was reached. However, the mixing dynamics were not expressed for the complete transverse section, which makes it very difficult to extend the results of the work further. Subsequent experimental work w8x involved sampling from the upper surface of the bed of solids in a rotating drum and the bottom of the bed near the drum wall. The paired deviation between these two values was determined and used as a measure of the mixing extent. As the deviation approached zero, a fully mixed condition was assumed to take place, although an oscillation about the steady state was also observed. The experimental conditions were 3–15% drum loading of shell shaped particles of 1.27 mm with a bulk density of 380 kgrm3 rotated at 8.5 rpm. The mixing rate was found to be constant, although a rate value was not calculated. Mixing times were significantly different to the mixing times of previous experimental work w4x. For example, for the lowest loading the time required to reach the fully mixed state was 46 min. Even at the higher loading, the mixing times differed by at least a factor of 15. This discrepancy highlights the need for more work into characterising the mixing rate of solids in rotating drums. Although movement in the axial direction results in negligible mixing for a rolling bed w1x, axial mixing may be significant if the bed is operating in a cascading regime. Axial movement models have mostly been limited to determining the residence time of solids in a rotating drum w9x. A three dimensional model combining transverse and axial movement has not been found in the literature and would be a very useful tool for prediction of the behaviour of rotary kilns. Segregation or reverse mixing w10x is the focus of most current research. This is due to the importance of segregation in processes such as drying or calcining where the heat source is located above the rolling bed. Segregation most commonly arises due to large particle size differences in the granular material. Significant density differences between equal sized particles can also result in segregation w11x. A new development at Gladstone, Queensland uses an AOSTRA Taciuk rotary kiln w12x to extract oil vapours from oil shale. The oil shale needs to be heated at 773 K for complete pyrolysis w13x in the retort zone of the processor and hence the waste products contain large quantities of sensible heat. Small amounts of organic material are deposited on the shale surface due to the cracking of the pyrolysed kerogen on the hot solid surface. The remaining organic content is burned in the combustion zone of the AOSTRA Taciuk processor and raises the
temperature of the material to approximately 1000 K. This combusted material is then recycled into the retort zone and mixed with preheated incoming shale that is at approximately 500 K. In order for pyrolysis to occur heat must be transferred from the hot recycled material to the preheated material. It is vital to monitor the rate of heat transfer and this requires in depth knowledge of the mixing dynamics of the solids inside the rotary kiln. It was the aim of this work to use image analysis to develop an experimental method that can be used to determine the mixing dynamics of solid materials in a rotating drum. This novel approach enabled detailed observations of changes in important operating conditions such as the rotational velocity, the particle size and the drum loading by volume.
2. Experimental 2.1. Materials used A bulk volume of oil shale was sieved into the size fractions as shown in Table 1. This material was then washed to remove the surface dust and coloured using a water based ink to obtain visually different materials. The colours chosen were black, due to its high hiding power, and orange, since it complemented the natural light brown base colour of the shale. A water based dye was used to colour the shale in order to have a minimal effect on the surface properties of the shale. The physical properties of the coloured material were measured and compared to the original shale properties, as shown in Table 1. As can be seen, the angle of repose did not change, indicating that the water-based ink did not significantly affect the surface properties of the particles. However, the bulk density of the coloured material was less than that measured for the raw shale, but not significantly so, and thus the materials would not segregate due to density differences as previously described w11x. A dependence on particle size was Table 1 Physical properties of raw and coloured shale particles Ža. Particle size range and bulk density Size range Žmm.
Mean size Žmm.
Raw shale Žgrl.
Black coloured shale Žgrl.
Orange coloured shale Žgrl.
q3.86–6.30 q3.02–3.86 q2.00–3.02 q1.40–2.00 q0.60–1.04
5.08 3.44 2.51 1.70 0.82
720 698 700 695 693
671 656 634 622 610
706 658 651 653
Raw shale Ž8.
Coloured shale Ž8.
Žb. Static angle of repose Size range Žmm.
Mean size Žmm.
q2.00–3.02
2.51
33
33
D.R. Van PuyÕelde et al.r Powder Technology 106 (1999) 183–191
observed, being most significant for the black coloured shale. 2.2. Equipment used 2.2.1. TransÕerse drum section A 50-mm thick cross-section of a 570-mm inner diameter steel drum was used to represent the transverse plane of a rotary kiln. The rear of this section was welded to a steel plate and attached to a shaft powered by a variable DC power supply. Power was supplied to the motor using a variable AC–DC converter. This power supply allowed velocities of 3–20 rpm with 35% drum loading. Lower rotational velocities were not allowed due to a minimum power requirement to drive the motor. The front surface of the drum section was constructed of two removable semi-circular 10-mm thick plate glass sections. These were attached to the frame using a hook and catcher arrangement. A thin silicone seal was placed between the glass sections and the frame and the glass to contain any small particles inside the drum. 2.2.2. Image capture Mixing dynamics were captured by using a Nikon F3 camera with a Nikon MD-60 motor drive and Nikon MF-240 data back. This allowed a maximum of 240 consecutive images to be captured for a single experiment. Image capture rates were fixed at 3.8 framesrs. The negative film was developed and mounted. These mounts were scanned into a personal computer using a Nikon Coolscan LS-1000 film scanner that was fitted with a bulk loader to automate the download process. The images were scanned at the maximum equipment resolution of 2700 dpi. These images were cropped and filtered to remove background and noise using Adobe PhotoShop V4. Colour enhancement was carried out on these images to increase the contrast between the orange and black material using the red channel of the images and various filters. The images were saved as sequential files and analysed to calculate the extent of mixing using the 256-colour bitmap format with the standard Windows colour palette. The standard Windows colour palette was used since it is a standard available to all Windows applications.
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The images were analysed pixel by pixel, the colour of which indicated the type of particle occupied by each pixel. Three different colours types were considered in this work, these being black for the black material, orange for the orange material and white for the background of the drum. The contact of each pixel was then analysed with respect to the surrounding pixels. Contact between the two materials occurred if different colour types occupied pixels adjacent to one another. The total contact was calculated for the orange material and was expressed as a numerical value by calibrating the physical size represented by a pixel. This image analysis methodology may be best illustrated by means of an example. Fig. 1 shows an enlarged extract from a well-mixed bed on which is superimposed a grid to represent the different pixels of a bitmap. As can be seen, any pixel in the array either represents the black, orange or background type. P w i, j x represents the pixel in the ith row and the jth column. Contact between the orange and the black material was calculated for the orange material. Only contact between adjacent edges was considered. Edge to edge contact increased the contact by 1. For example, looking at P w1,1x, an orange pixel, the contact between P w1,1x and the surrounding pixels is 1 since the only contact with black material is due to P w1,2x. The contact from P w1,2x was not calculated since this was not of the orange type. Contact with the background material was not considered since this was not representative of the mixing kinetics between the orange and black materials. Calculating the total contact between the orange and the black material for the array as shown in Fig. 1 indicated a total contact value of 61. To convert this to a measurement in m or mm, the resolution of the image was calibrated. In most cases each pixel represented was approximately 0.18 mm of the drum, but this was different for each experiment due to slightly
2.3. Image analysis Each of the images downloaded were analysed using custom image analysis software written in Borland C q q. In order to achieve this, the format of the bitmap file must be known. The bitmap file is divided into four sections, each of which and its’ functions are described in the literature w14,15x. The materials used were firstly standardised by capturing their colours. It was found that the materials used had completely different colour characteristics. This was as expected since the colours were selected for this purpose.
Fig. 1. Extract from a well-mixed bed showing a sample calculation of contact measurement.
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Fig. 2. Sample photos of the experimental bed: Ža. initial bed configuration used to calibrate the material colours; Žb. initial point taken for the mixing dynamics after the rolling regime was developed; Žc. one complete bed revolution after the initial mixing point showing the widening of the ‘‘orange’’ Žlight grey. material; and Žd. steady state bed configuration.
different camera positions and therefore this parameter was calculated for each experiment. Using a resolution of 0.18
mmrpixel, Fig. 1 represents a total of 10.98 mm of contact between the orange and the black material. The
Table 2 Experimental conditions and results Experiment Rotational Particle Kiln Loading Mixing Rate Mixing Rate Mixing Rate Mixing Rate Average Average Steady State Velocity Size corrected to Ratio Error Steady State Steady State Standard 10 rpm Contact Contact Ratio Deviation rpm
mm
Rotational velocity experiments 1 5.17 2.51 2 9.05 2.51 3 11.74 2.51 4 15.10 2.51 Drum loading experiments 5 7.97 2.51 6 8.45 2.51 2 9.05 2.51 7 8.03 2.51 Particle size experiments 8 10.10 0.89 9 9.96 1.70 2 9.05 2.51 10 9.81 3.44 11 8.83 5.08
% volume
mmrsec
wrt EXP2
mm
wrt EXP2
30 30 30 30
1236 1602 1984 2957
1880 1740 1706 1899
0.77 1.00 1.24 1.85
1442 1305 1637 1841
41088 39948 43483 43638
1.03 1.00 1.09 1.09
1433 746 2145 1323
10 20 30 40
987 1321 1602 1774
1177 1511 1740 2105
0.62 0.82 1.00 1.11
1131 1017 1305 2264
12411 24029 39948 55701
0.31 0.60 1.00 1.39
296 871 746 2205
30 30 30 30 30
3107 2377 1602 1559 815
3080 2385 1740 1585 902
1.94 1.48 1.00 0.97 0.51
4095 2332 1305 2192 2727
60100 50211 39948 38713 30090
1.50 1.28 1.00 0.97 0.75
3461 2060 746 1699 2326
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Fig. 3. Mixing dynamics as a function of rotational velocity.
maximum resolution was used in all cases as this would allow the interface between the particles to be more detailed and thus more accurate. By analysing all the images using the above procedure and obtaining a contact measurement for each image, the mixing rate was calculated. 2.4. Experimental technique The bed was loaded using a specified geometry as shown in Fig. 2a and experimental conditions as shown in
Table 2. The fraction of the material in each experiment was 50% of each of the black and orange materials. The black material was added to the drum first, then an orange layer was placed on top of this. An initial photo was taken of the stationary bed and was used to calibrate the colours for each experiment. After the drum section was closed, the camera was set to automatic and the rotation was started, with an image being captured every 1r3.8 s until the end of the film. This film was then processed and scanned into a personal computer using the equipment and method described above. These results were then plotted
Fig. 4. Mixing dynamics as a function of particle size.
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against time and analysed. As can be seen from the results, complete mixing was achieved within 1 min in all cases.
3. Results The mixing dynamics with respect to the rotational velocity, percentage drum loading and particle size were studied in this experimental work. The rotational velocity range was from 5 to 15 rpm, which covered the rolling regime. Drum loading from 10 to 40% of the total drum volume was tested. The particle size range tested was from 0.89 to 5.08 mm. The initial point of mixing was taken as the point where the bed was fully developed as being in the rolling regime. This occurred a short time after the rotation was started since the material was initially stationary and the upper surface of the bed was initially horizontal. This initial point is shown in Fig. 2b, which clearly shows the wavelike structure of the bed. By using this configuration of the bed as the initial mixing condition, the errors were reduced. Figs. 3–5 show the results of the mixing dynamics experiments. Fig. 3 shows the dynamic response for the different rotational velocities, Fig. 4 shows the dynamic response for the different particle sizes and Fig. 5 shows the effect on the dynamics of mixing of changing the loading of the drum. Both a steady state Žfinal. contact and the mixing rate were calculated for each experiment. As can be seen from the results, a straight line can approximate the mixing rate. This was followed by a fluctuating
contact about a steady state point. These fluctuations were assumed to occur due to the stochastic nature of the mixing process and also included experimental errors. Errors were determined for the steady state contact and it was assumed that the same errors were applicable to mixing dynamics, as the dynamics were obtained in identical experimental conditions. This error was checked against the variance from the constant rate. Table 2 shows the mixing experiments carried out, the resulting rate of mixing and final contact value, as well as the error and deviations.
4. Discussion 4.1. Mixing mechanism As described previously, the transverse section consists of both an active and a stagnant layer. The active layer is responsible for all the mixing in a rotary drum. However, the mixing rate is determined from the rotation of the complete transverse bed section at different times. By enlarging any of the mixing figures a step function was observed. This is shown in Fig. 6 for experiment 2. The circulation time, or the time spent in the stagnant layer for this experiment was approximately 2 s. As can be seen from Fig. 6, the steps are approximately 2 s in length. The increase in contact occurred when the two different materials entered the active layer together and were subsequently mixed. The time spent in the active layer was much shorter
Fig. 5. Mixing dynamics as a function of drum loading.
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Fig. 6. Enlarged section of experiment 2 showing the stepwise mixing behaviour.
compared to the time spent in the stagnant layer. The magnitudes of the step changes were approximately constant. By neglecting the time spent in the stagnant layer, the mixing rate can be said to be of a constant rate. As time progresses, the two materials become more mixed and thus the distinction of the steps is reduced until at the steady state limit where the stepwise behaviour is not observed at all. This observation of stepwise mixing confirms the nature of the original lumped parameter modelling work of the authors w7x. Comparison of these results with the work of Lehmberg et al. w4x is difficult, as their mixing dynamics were not expressed for the complete transverse section. However, the qualitative experimental results of their work agree with the current work. Woodle and Munro w8x also found the mixing rate to be of constant value but failed to note the stepwise nature of the mixing rate observed in this work. They also did not express the mixing rate as a workable number. They did however observe a deviation about the steady state value, which was also observed in the current work. For Woodle and Munro’s lowest loading experiment w8x, the time required to reach the fully mixed state was 46 min. This is significantly different to the mixing times of the current work and of the work by Lehmberg et al. w4x. Furthermore, Woodle and Munro w8x found that the mixing times decreased as the loading increased. Whereas, it was shown in the current work that whilst the mixing rate increases with drum loading, so does the total time required to reach the fully mixed state. These discrepancies again show the need for more work into characterising the mixing rate of solids in rotating drums. 4.2. Mixing rates The mixing rate was observed to be of a constant nature for all the experiments. This rate was subsequently calcu-
lated and compared between the different experiments. For the velocity experiments it was observed that the mixing rate increased exponentially with increasing rotational velocity at constant drum loading. The relationship was found to be: R Ž v . s 757.22e 0.0868 v mmrs
Ž 1.
where RŽ v . is the mixing rate with respect to rotational velocity and v is the rotational velocity in rpm. This correlation would only apply to bed configurations where the loading is 30% of the drum volume. The increase in mixing rate with rotational velocity is as expected since the material moves faster through the active layer and does so more times within a certain time limit. Also as the velocity increases, the active layer proportion also increases and thus would allow more mixing to occur. Correcting the particle size mixing rates to a common velocity of 10 rpm allowed the mixing rates between these experiments to be compared. It was assumed that this correction did not introduce any great errors since the drum loading was the same for both the velocity and particle size experiments. This correction had a small effect on the mixing rate with respect to particle diameter but reduced the correlation deviation, enforcing that the true mixing rate is linear with respect to particle size. The mixing rate with respect to particle size, at a constant loading, was found to be: R Ž Dp . s y494.58 Dp q 3285.7 mmrs
Ž 2.
where RŽ Dp . is the mixing rate with respect to particle size and Dp is the particle size in mm. It is with caution that this equation should be applied since it indicates that particles larger than 6.64 mm would have a negative mixing rate which is physically impossible. These particle size experiments were carried out at 30% loading. For the loading experiments, the speed correction resulted in an offset Žan increase in rate for all points. and
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also reduced the deviation between the individual points and the line of best fit. This increase in mixing rate was due to the fact that all the velocities for the drum loading experiments were below 10 rpm. Correcting these mixing rates to 10 rpm would thus increase the mixing rate. It is with caution that the rates of the loading experiments were corrected since the speed correction relation was established for experiments with a constant bed loading. As has previously been shown w5x, the bed loading has an effect on the active layer size and thus could effect the mixing rate since mixing only occurs in the active layer. Our experiments indicated however that this active layer size effect was not significant for the small velocity changes required. The corrected mixing rate with respect to drum loading was found to be: R Ž %V . s 30.114%V q 3285.7
mmrs
ences in the final contact value are due to the small differences in the initial configurations. This was unavoidable due to the nature of the experimental work. A higher steady state contact was obtained for smaller particles. This arose since the smaller particles, on a unit volume basis, have more surface area compared to larger particles, thus it is possible to have a higher extent of mixing. This has been shown to occur in the particle size experiments. A direct dependence was observed between the steady state contact and the drum loading in the loading experiments. This is also as expected since the presence of more material enables a greater amount of contact. 4.4. Errors
Ž 3.
where RŽ%V . is the rate with respect to loading and %V is the percentage volume loading of the drum. These experiments were carried out using 2.51 mm particles. As the drum loading was increased, the mixing rate increased linearly. This may be due to the larger active layer with respect to drum loading. As the active layer proportion increases, more material would be in the active layer and thus more mixing would be able to occur. Also, since there is more material in the drum at the higher loading, the final contact increased proportionally. Using the experimental results, a correlation can be constructed to predict the mixing rate that is dependent upon the rotational velocity, particle size and drum loading. This algorithm would first calculate the rate for the loading by assuming 2.51 mm particles and a speed of 10 rpm. This value would then be corrected for the particle diameter and the rotational speed. 4.3. Steady state The steady state, although not strictly steady, was taken to be the point where the contact between the two materials fluctuated about a constant value. This constant value was calculated and assumed to be the steady state or maximum contact value. This value was compared with the theoretical maximum contact, which was calculated from the bed loading, the particle size and the actual ratio of the material. In all cases the actual steady state was slightly less than the theoretical maximum contact and this is as expected as the material is also in contact with the walls, but this does not form part of the contact between the orange and black material as described in the methodology. The fluctuations about this final contact value are considered in Section 4.4. For the speed experiments, all the experiments obtained a similar final contact value. This is as expected since the same initial bed configuration and proportions were used for each of the rotational velocity experiments. The differ-
The standard deviation about the final contact value was used as a measure of the experimental error of the experiments. The standard error was calculated for the rate values and this was used as an estimate of the error in the mixing rate determination. In most cases the rate error was larger than the steady state error. The white seal between the two semi-circular panes of the glass surface may be responsible for causing some errors. This is especially true for the mixing rate values since this seal could have hid a well-mixed part of the bed and thus reduce the overall contact for this image. Incorrect film exposure was another source of error but was eliminated by checking each exposure and eliminating the exposure from the data set if it was not exposed correctly. Under- or over-exposed images resulted in misrepresentation of colours and thus gave a false measure of the black and orange pixels. This could be checked for in each image. The black and orange pixel counts were similar in all correctly exposed images since equal fractions of material were used. A large fluctuation in the black to orange ratio was a clear indication of incorrectly exposed images. The movement into or away from the surface could also contribute to the experimental error. It was assumed that this movement resulted in an equilibrium of material moving into or away from the surface. This equilibrium should have maintained the composition at the surface constant. However, due to the stochastic nature of the mixing process some fluctuation can be expected, as shown by the fluctuations at the steady state. The experimental error of the steady state value is in most cases less than 5%. The absolute mixing rate error is in most cases higher than its steady state complement, but not significantly so. This indicates that the experimental errors described are also applicable to the rate data. One further aspect of the rate data to be considered is due to the step nature of mixing. This behaviour forces data away from the constant rate line as shown by the circled data points in Fig. 6. This indicates that the rate
D.R. Van PuyÕelde et al.r Powder Technology 106 (1999) 183–191
measurements obtained using this method are quite accurate.
5. Conclusions A new technique was developed to measure the mixing rate of solids in a rotating drum using image analysis using a Nikon F3 camera. These images were converted to Windows bitmap files and were analysed to determine the contact between the black and orange materials using custom C q q software. The experiments carried out tested the variation in mixing dynamics due to changes in rotational velocity from 5 to 15 rpm, the particle size from 0.89 to 5.08 mm and the drum loading from 10 to 40% by volume. It was observed that the mixing rates for all experiments were constant and that a steady state was achieved in less than 30 s. The mixing rate increased exponentially with rotational velocity, decreased linearly with increasing particle size and increased linearly with drum loading. The steady state contact did not vary with rotational speed, but increased with decreasing particle size and increased with drum loading. The experimental errors observed, while not insignificant, were as expected. The observations were sufficiently accurate to enable resolution of stepwise mixing. Overall a new technique has been developed which will allow the mixing rates of materials in a rotary drum to be easily measured, modelled and predicted.
6. Nomenclature RŽ v . RŽ Dp . RŽ%V . %V Dp v
Mixing rate as a function of rotational velocity Žmmrs. Mixing rate as a function of particle diameter Žmmrs. Mixing rate as a function of drum loading by volume Žmmrs. Drum loading by volume Mean particle diameter Žmm. Rotational velocity Žrpm.
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Acknowledgements The authors wish to thank the Australian Research Council, the University of Technology, Sydney and Southern Pacific Petroleum ŽDevelopment. for funding this work.
References w1x N. Nityanand, B. Manley, H. Henein, An analysis of radial segregation for different sized spherical solids in rotary cylinders, Metallurgical Transactions B 17B Ž1986. 247–257. w2x H. Henein, J.K. Brimacombe, A.P. Watkinson, The modelling of transverse solids motion in rotary kilns, Metallurgical Transactions B 14B Ž1983. 207–220. w3x H. Henein, J.K. Brimacombe, A.P. Watkinson, Experimental study of transverse bed motion in rotary kilns, Metallurgical Transactions B 14B Ž1983. 191–205. w4x J. Lehmberg, M. Hehl, K. Schugerl, Transverse mixing and heat transfer in horizontal rotary drum reactors, Powder Technology 18 Ž1977. 149–163. w5x A.A. Boateng, Rotary kiln transport phenomena, PhD Dissertation, University of British Columbia, British Columbia, Canada, 1993. w6x F. Kelbert, C. Royere, Lateral mixing and heat transfer in a rolling bed, International Chemical Engineering 31 Ž1991. 441–449. w7x D.R. Van Puyvelde, B.R. Young, M.A. Wilson, S.J. Schmidt, Dynamic modelling of transverse mixing in a rotary kiln, Proceedings of the 25th Australian and New Zealand Chemical Engineers Conference and Exhibition, Particle Technology Workshop, 271– 282, Rotorua, New Zealand, 1997. w8x G. Woodle, J. Munro, Particle motion and mixing in a rotary kiln, Powder Technology 76 Ž1993. 241–245. w9x R.W. Pickering, F. Feakes, M. Fitzgerald, Time for passage of material through rotary kilns, Journal of Applied Chemistry 1 Ž1951. 13–19. w10x A.A. Boateng, P. Barr, A thermal model for the rotary kiln including heat transfer within the bed, International Journal of Heat and Mass Transfer 39 Ž1996. 2131–2147. w11x M. Alonso, M. Satoh, K. Miyanami, Optimum combination of size ratio, density ratio and concentration to minimize free surface segregation, Powder Technology 68 Ž1991. 145–152. w12x W. Taciuk, L.R. Turner, Development status of Australian oil shale processing utilising the taciuk processor, Fuel 67 Ž1988. 1405. w13x A.J. Berkovich, B.R. Young, A. Ray, S.J. Schmidt, The effects of minerals on retorting enthalpies of some Australian tertiary oil shales, Fuel 77 Ž9r10. Ž1998. 987–993. w14x D. Charlip, The BMP file format: Part 1, Dr. Dobb’s Journal 20 Ž3. Ž1995. 44–49. w15x D. Charlip, The BMP file format: Part 2, Dr. Dobb’s Journal 20 Ž4. Ž1995. 34–42.
Experimental determination of transverse mixing kinetics in a rolling drum by image analysis D.R. Van Puyvelde a , B.R. Young a b
b,)
, M.A. Wilson a , S.J. Schmidt
c
Department of Chemistry, Materials and Forensic Science, UniÕersity of Technology, P.O. Box 123, Broadway, Sydney 2007, NSW, Australia Department of Chemical and Petroleum Engineering, UniÕersity of Calgary, 2500 UniÕersity DriÕe NW, Calgary, Alberta, Canada T2N 1N4 c Southern Pacific Petroleum (DeÕelopment), P.O. Box 7101, RiÕerside Centre, Brisbane 4001, QLD, Australia Received 1 October 1998; accepted 7 April 1999
Abstract Rotary kilns are commonly used for mixing of solids, such as grain, and heat transfer to solids, such as drying of fruit and calcination of cement. For a rotary kiln that has a wide range of solid feeds, it is desired to be able to know the kinetics of the mixing of solids inside the rotary kiln so that heat transfer between these solids can be predicted. Heat transfer between different solid feeds is particularly important in the rotating kiln being commissioned by Stuart Energy in Gladstone, Queensland for the processing of oil shale to produce oil. This paper describes a new way to determine the mixing rates of solids in a rotating drum using image analysis programming. Results of this analysis show that the mixing dynamics follow a constant rate until a completely mixed state is encountered. Upon closer analysis it was revealed that mixing occurred in steps, which has not been previously shown. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Rotary kiln; Transverse mixing; Dynamics; Image analysis
1. Introduction Granular materials are widely used in the chemical process industries. However, the behaviour of granular material is not as easily characterised as fluid behaviour by dimensionless parameters such as the Reynolds number. As a result, data obtained for one type of solid cannot easily be applied to a different type of solid. Therefore, there is a clear need to establish methods that can be used to determine mixing parameters for many types of solids. Mixing in a rotating drum is an important process in the particulate industries and is often accountable for the rate of heat transfer between the solids. This limiting rate directly affects the yield and efficiency of the process and is quite commonly a bottleneck. Mixing in a rotating drum occurs in two directions, namely, the transverse and the axial directions. However, mixing in the transverse direction is a few orders of magnitude faster compared to mixing in the axial direction
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Corresponding author. Department of Chemical and Petroleum Engineering, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4. T el.: q 1-403-2208751; Fax: q 1-403-282-3945; E -m ail: [email protected]
w1x. Due to this, most of the mixing and segregation work in rotary drums has focussed on the transverse plane. The motion in the transverse plane was subdivided into six different regimes w2,3x. For the rolling regime, which is commonly used for mixing solids, the transverse plane was described as consisting of two distinct layers w4x, namely, the active layer and the stagnant layers. The active layer consists of the top section of the bed that is moving rapidly down the slope and is responsible for nearly all the mixing in the transverse direction w5x. Mixing occurs in this section due to the dilation of the material as it rolls down the plane. The gaps formed due to dilation result in other particles falling into them and hence mixing occurs. This mechanism is also responsible for segregation where the smaller particles migrate closer to the centre of rotation preferentially to the larger particles. The second layer observed in the transverse section is the stagnant or plug flow layer. This layer is highly compacted and no mixing is observed in this w4x. The transverse mixing has been modelled in various ways to either determine the residence time in a kiln w6x or to model the mixing kinetics of a binary system w7x. Early experimental determination of mixing dynamics involved measuring the bed temperature near the upper edge of the inclined slope after the addition of a batch of
0032-5910r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 9 9 . 0 0 0 7 4 - 1
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hot material to a cold rotating bed w4x. A rotational velocity of 2 rpm was used in a 310-mm diameter cylinder loaded with approximately 30% of 0.80 mm sand with a bulk density of 1480 kgrm3. A fully mixed bed was obtained after approximately 42 s. The mixing dynamics at the measurement point followed an oscillating exponential decay until the final bed temperature was reached. However, the mixing dynamics were not expressed for the complete transverse section, which makes it very difficult to extend the results of the work further. Subsequent experimental work w8x involved sampling from the upper surface of the bed of solids in a rotating drum and the bottom of the bed near the drum wall. The paired deviation between these two values was determined and used as a measure of the mixing extent. As the deviation approached zero, a fully mixed condition was assumed to take place, although an oscillation about the steady state was also observed. The experimental conditions were 3–15% drum loading of shell shaped particles of 1.27 mm with a bulk density of 380 kgrm3 rotated at 8.5 rpm. The mixing rate was found to be constant, although a rate value was not calculated. Mixing times were significantly different to the mixing times of previous experimental work w4x. For example, for the lowest loading the time required to reach the fully mixed state was 46 min. Even at the higher loading, the mixing times differed by at least a factor of 15. This discrepancy highlights the need for more work into characterising the mixing rate of solids in rotating drums. Although movement in the axial direction results in negligible mixing for a rolling bed w1x, axial mixing may be significant if the bed is operating in a cascading regime. Axial movement models have mostly been limited to determining the residence time of solids in a rotating drum w9x. A three dimensional model combining transverse and axial movement has not been found in the literature and would be a very useful tool for prediction of the behaviour of rotary kilns. Segregation or reverse mixing w10x is the focus of most current research. This is due to the importance of segregation in processes such as drying or calcining where the heat source is located above the rolling bed. Segregation most commonly arises due to large particle size differences in the granular material. Significant density differences between equal sized particles can also result in segregation w11x. A new development at Gladstone, Queensland uses an AOSTRA Taciuk rotary kiln w12x to extract oil vapours from oil shale. The oil shale needs to be heated at 773 K for complete pyrolysis w13x in the retort zone of the processor and hence the waste products contain large quantities of sensible heat. Small amounts of organic material are deposited on the shale surface due to the cracking of the pyrolysed kerogen on the hot solid surface. The remaining organic content is burned in the combustion zone of the AOSTRA Taciuk processor and raises the
temperature of the material to approximately 1000 K. This combusted material is then recycled into the retort zone and mixed with preheated incoming shale that is at approximately 500 K. In order for pyrolysis to occur heat must be transferred from the hot recycled material to the preheated material. It is vital to monitor the rate of heat transfer and this requires in depth knowledge of the mixing dynamics of the solids inside the rotary kiln. It was the aim of this work to use image analysis to develop an experimental method that can be used to determine the mixing dynamics of solid materials in a rotating drum. This novel approach enabled detailed observations of changes in important operating conditions such as the rotational velocity, the particle size and the drum loading by volume.
2. Experimental 2.1. Materials used A bulk volume of oil shale was sieved into the size fractions as shown in Table 1. This material was then washed to remove the surface dust and coloured using a water based ink to obtain visually different materials. The colours chosen were black, due to its high hiding power, and orange, since it complemented the natural light brown base colour of the shale. A water based dye was used to colour the shale in order to have a minimal effect on the surface properties of the shale. The physical properties of the coloured material were measured and compared to the original shale properties, as shown in Table 1. As can be seen, the angle of repose did not change, indicating that the water-based ink did not significantly affect the surface properties of the particles. However, the bulk density of the coloured material was less than that measured for the raw shale, but not significantly so, and thus the materials would not segregate due to density differences as previously described w11x. A dependence on particle size was Table 1 Physical properties of raw and coloured shale particles Ža. Particle size range and bulk density Size range Žmm.
Mean size Žmm.
Raw shale Žgrl.
Black coloured shale Žgrl.
Orange coloured shale Žgrl.
q3.86–6.30 q3.02–3.86 q2.00–3.02 q1.40–2.00 q0.60–1.04
5.08 3.44 2.51 1.70 0.82
720 698 700 695 693
671 656 634 622 610
706 658 651 653
Raw shale Ž8.
Coloured shale Ž8.
Žb. Static angle of repose Size range Žmm.
Mean size Žmm.
q2.00–3.02
2.51
33
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observed, being most significant for the black coloured shale. 2.2. Equipment used 2.2.1. TransÕerse drum section A 50-mm thick cross-section of a 570-mm inner diameter steel drum was used to represent the transverse plane of a rotary kiln. The rear of this section was welded to a steel plate and attached to a shaft powered by a variable DC power supply. Power was supplied to the motor using a variable AC–DC converter. This power supply allowed velocities of 3–20 rpm with 35% drum loading. Lower rotational velocities were not allowed due to a minimum power requirement to drive the motor. The front surface of the drum section was constructed of two removable semi-circular 10-mm thick plate glass sections. These were attached to the frame using a hook and catcher arrangement. A thin silicone seal was placed between the glass sections and the frame and the glass to contain any small particles inside the drum. 2.2.2. Image capture Mixing dynamics were captured by using a Nikon F3 camera with a Nikon MD-60 motor drive and Nikon MF-240 data back. This allowed a maximum of 240 consecutive images to be captured for a single experiment. Image capture rates were fixed at 3.8 framesrs. The negative film was developed and mounted. These mounts were scanned into a personal computer using a Nikon Coolscan LS-1000 film scanner that was fitted with a bulk loader to automate the download process. The images were scanned at the maximum equipment resolution of 2700 dpi. These images were cropped and filtered to remove background and noise using Adobe PhotoShop V4. Colour enhancement was carried out on these images to increase the contrast between the orange and black material using the red channel of the images and various filters. The images were saved as sequential files and analysed to calculate the extent of mixing using the 256-colour bitmap format with the standard Windows colour palette. The standard Windows colour palette was used since it is a standard available to all Windows applications.
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The images were analysed pixel by pixel, the colour of which indicated the type of particle occupied by each pixel. Three different colours types were considered in this work, these being black for the black material, orange for the orange material and white for the background of the drum. The contact of each pixel was then analysed with respect to the surrounding pixels. Contact between the two materials occurred if different colour types occupied pixels adjacent to one another. The total contact was calculated for the orange material and was expressed as a numerical value by calibrating the physical size represented by a pixel. This image analysis methodology may be best illustrated by means of an example. Fig. 1 shows an enlarged extract from a well-mixed bed on which is superimposed a grid to represent the different pixels of a bitmap. As can be seen, any pixel in the array either represents the black, orange or background type. P w i, j x represents the pixel in the ith row and the jth column. Contact between the orange and the black material was calculated for the orange material. Only contact between adjacent edges was considered. Edge to edge contact increased the contact by 1. For example, looking at P w1,1x, an orange pixel, the contact between P w1,1x and the surrounding pixels is 1 since the only contact with black material is due to P w1,2x. The contact from P w1,2x was not calculated since this was not of the orange type. Contact with the background material was not considered since this was not representative of the mixing kinetics between the orange and black materials. Calculating the total contact between the orange and the black material for the array as shown in Fig. 1 indicated a total contact value of 61. To convert this to a measurement in m or mm, the resolution of the image was calibrated. In most cases each pixel represented was approximately 0.18 mm of the drum, but this was different for each experiment due to slightly
2.3. Image analysis Each of the images downloaded were analysed using custom image analysis software written in Borland C q q. In order to achieve this, the format of the bitmap file must be known. The bitmap file is divided into four sections, each of which and its’ functions are described in the literature w14,15x. The materials used were firstly standardised by capturing their colours. It was found that the materials used had completely different colour characteristics. This was as expected since the colours were selected for this purpose.
Fig. 1. Extract from a well-mixed bed showing a sample calculation of contact measurement.
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Fig. 2. Sample photos of the experimental bed: Ža. initial bed configuration used to calibrate the material colours; Žb. initial point taken for the mixing dynamics after the rolling regime was developed; Žc. one complete bed revolution after the initial mixing point showing the widening of the ‘‘orange’’ Žlight grey. material; and Žd. steady state bed configuration.
different camera positions and therefore this parameter was calculated for each experiment. Using a resolution of 0.18
mmrpixel, Fig. 1 represents a total of 10.98 mm of contact between the orange and the black material. The
Table 2 Experimental conditions and results Experiment Rotational Particle Kiln Loading Mixing Rate Mixing Rate Mixing Rate Mixing Rate Average Average Steady State Velocity Size corrected to Ratio Error Steady State Steady State Standard 10 rpm Contact Contact Ratio Deviation rpm
mm
Rotational velocity experiments 1 5.17 2.51 2 9.05 2.51 3 11.74 2.51 4 15.10 2.51 Drum loading experiments 5 7.97 2.51 6 8.45 2.51 2 9.05 2.51 7 8.03 2.51 Particle size experiments 8 10.10 0.89 9 9.96 1.70 2 9.05 2.51 10 9.81 3.44 11 8.83 5.08
% volume
mmrsec
wrt EXP2
mm
wrt EXP2
30 30 30 30
1236 1602 1984 2957
1880 1740 1706 1899
0.77 1.00 1.24 1.85
1442 1305 1637 1841
41088 39948 43483 43638
1.03 1.00 1.09 1.09
1433 746 2145 1323
10 20 30 40
987 1321 1602 1774
1177 1511 1740 2105
0.62 0.82 1.00 1.11
1131 1017 1305 2264
12411 24029 39948 55701
0.31 0.60 1.00 1.39
296 871 746 2205
30 30 30 30 30
3107 2377 1602 1559 815
3080 2385 1740 1585 902
1.94 1.48 1.00 0.97 0.51
4095 2332 1305 2192 2727
60100 50211 39948 38713 30090
1.50 1.28 1.00 0.97 0.75
3461 2060 746 1699 2326
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Fig. 3. Mixing dynamics as a function of rotational velocity.
maximum resolution was used in all cases as this would allow the interface between the particles to be more detailed and thus more accurate. By analysing all the images using the above procedure and obtaining a contact measurement for each image, the mixing rate was calculated. 2.4. Experimental technique The bed was loaded using a specified geometry as shown in Fig. 2a and experimental conditions as shown in
Table 2. The fraction of the material in each experiment was 50% of each of the black and orange materials. The black material was added to the drum first, then an orange layer was placed on top of this. An initial photo was taken of the stationary bed and was used to calibrate the colours for each experiment. After the drum section was closed, the camera was set to automatic and the rotation was started, with an image being captured every 1r3.8 s until the end of the film. This film was then processed and scanned into a personal computer using the equipment and method described above. These results were then plotted
Fig. 4. Mixing dynamics as a function of particle size.
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against time and analysed. As can be seen from the results, complete mixing was achieved within 1 min in all cases.
3. Results The mixing dynamics with respect to the rotational velocity, percentage drum loading and particle size were studied in this experimental work. The rotational velocity range was from 5 to 15 rpm, which covered the rolling regime. Drum loading from 10 to 40% of the total drum volume was tested. The particle size range tested was from 0.89 to 5.08 mm. The initial point of mixing was taken as the point where the bed was fully developed as being in the rolling regime. This occurred a short time after the rotation was started since the material was initially stationary and the upper surface of the bed was initially horizontal. This initial point is shown in Fig. 2b, which clearly shows the wavelike structure of the bed. By using this configuration of the bed as the initial mixing condition, the errors were reduced. Figs. 3–5 show the results of the mixing dynamics experiments. Fig. 3 shows the dynamic response for the different rotational velocities, Fig. 4 shows the dynamic response for the different particle sizes and Fig. 5 shows the effect on the dynamics of mixing of changing the loading of the drum. Both a steady state Žfinal. contact and the mixing rate were calculated for each experiment. As can be seen from the results, a straight line can approximate the mixing rate. This was followed by a fluctuating
contact about a steady state point. These fluctuations were assumed to occur due to the stochastic nature of the mixing process and also included experimental errors. Errors were determined for the steady state contact and it was assumed that the same errors were applicable to mixing dynamics, as the dynamics were obtained in identical experimental conditions. This error was checked against the variance from the constant rate. Table 2 shows the mixing experiments carried out, the resulting rate of mixing and final contact value, as well as the error and deviations.
4. Discussion 4.1. Mixing mechanism As described previously, the transverse section consists of both an active and a stagnant layer. The active layer is responsible for all the mixing in a rotary drum. However, the mixing rate is determined from the rotation of the complete transverse bed section at different times. By enlarging any of the mixing figures a step function was observed. This is shown in Fig. 6 for experiment 2. The circulation time, or the time spent in the stagnant layer for this experiment was approximately 2 s. As can be seen from Fig. 6, the steps are approximately 2 s in length. The increase in contact occurred when the two different materials entered the active layer together and were subsequently mixed. The time spent in the active layer was much shorter
Fig. 5. Mixing dynamics as a function of drum loading.
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Fig. 6. Enlarged section of experiment 2 showing the stepwise mixing behaviour.
compared to the time spent in the stagnant layer. The magnitudes of the step changes were approximately constant. By neglecting the time spent in the stagnant layer, the mixing rate can be said to be of a constant rate. As time progresses, the two materials become more mixed and thus the distinction of the steps is reduced until at the steady state limit where the stepwise behaviour is not observed at all. This observation of stepwise mixing confirms the nature of the original lumped parameter modelling work of the authors w7x. Comparison of these results with the work of Lehmberg et al. w4x is difficult, as their mixing dynamics were not expressed for the complete transverse section. However, the qualitative experimental results of their work agree with the current work. Woodle and Munro w8x also found the mixing rate to be of constant value but failed to note the stepwise nature of the mixing rate observed in this work. They also did not express the mixing rate as a workable number. They did however observe a deviation about the steady state value, which was also observed in the current work. For Woodle and Munro’s lowest loading experiment w8x, the time required to reach the fully mixed state was 46 min. This is significantly different to the mixing times of the current work and of the work by Lehmberg et al. w4x. Furthermore, Woodle and Munro w8x found that the mixing times decreased as the loading increased. Whereas, it was shown in the current work that whilst the mixing rate increases with drum loading, so does the total time required to reach the fully mixed state. These discrepancies again show the need for more work into characterising the mixing rate of solids in rotating drums. 4.2. Mixing rates The mixing rate was observed to be of a constant nature for all the experiments. This rate was subsequently calcu-
lated and compared between the different experiments. For the velocity experiments it was observed that the mixing rate increased exponentially with increasing rotational velocity at constant drum loading. The relationship was found to be: R Ž v . s 757.22e 0.0868 v mmrs
Ž 1.
where RŽ v . is the mixing rate with respect to rotational velocity and v is the rotational velocity in rpm. This correlation would only apply to bed configurations where the loading is 30% of the drum volume. The increase in mixing rate with rotational velocity is as expected since the material moves faster through the active layer and does so more times within a certain time limit. Also as the velocity increases, the active layer proportion also increases and thus would allow more mixing to occur. Correcting the particle size mixing rates to a common velocity of 10 rpm allowed the mixing rates between these experiments to be compared. It was assumed that this correction did not introduce any great errors since the drum loading was the same for both the velocity and particle size experiments. This correction had a small effect on the mixing rate with respect to particle diameter but reduced the correlation deviation, enforcing that the true mixing rate is linear with respect to particle size. The mixing rate with respect to particle size, at a constant loading, was found to be: R Ž Dp . s y494.58 Dp q 3285.7 mmrs
Ž 2.
where RŽ Dp . is the mixing rate with respect to particle size and Dp is the particle size in mm. It is with caution that this equation should be applied since it indicates that particles larger than 6.64 mm would have a negative mixing rate which is physically impossible. These particle size experiments were carried out at 30% loading. For the loading experiments, the speed correction resulted in an offset Žan increase in rate for all points. and
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also reduced the deviation between the individual points and the line of best fit. This increase in mixing rate was due to the fact that all the velocities for the drum loading experiments were below 10 rpm. Correcting these mixing rates to 10 rpm would thus increase the mixing rate. It is with caution that the rates of the loading experiments were corrected since the speed correction relation was established for experiments with a constant bed loading. As has previously been shown w5x, the bed loading has an effect on the active layer size and thus could effect the mixing rate since mixing only occurs in the active layer. Our experiments indicated however that this active layer size effect was not significant for the small velocity changes required. The corrected mixing rate with respect to drum loading was found to be: R Ž %V . s 30.114%V q 3285.7
mmrs
ences in the final contact value are due to the small differences in the initial configurations. This was unavoidable due to the nature of the experimental work. A higher steady state contact was obtained for smaller particles. This arose since the smaller particles, on a unit volume basis, have more surface area compared to larger particles, thus it is possible to have a higher extent of mixing. This has been shown to occur in the particle size experiments. A direct dependence was observed between the steady state contact and the drum loading in the loading experiments. This is also as expected since the presence of more material enables a greater amount of contact. 4.4. Errors
Ž 3.
where RŽ%V . is the rate with respect to loading and %V is the percentage volume loading of the drum. These experiments were carried out using 2.51 mm particles. As the drum loading was increased, the mixing rate increased linearly. This may be due to the larger active layer with respect to drum loading. As the active layer proportion increases, more material would be in the active layer and thus more mixing would be able to occur. Also, since there is more material in the drum at the higher loading, the final contact increased proportionally. Using the experimental results, a correlation can be constructed to predict the mixing rate that is dependent upon the rotational velocity, particle size and drum loading. This algorithm would first calculate the rate for the loading by assuming 2.51 mm particles and a speed of 10 rpm. This value would then be corrected for the particle diameter and the rotational speed. 4.3. Steady state The steady state, although not strictly steady, was taken to be the point where the contact between the two materials fluctuated about a constant value. This constant value was calculated and assumed to be the steady state or maximum contact value. This value was compared with the theoretical maximum contact, which was calculated from the bed loading, the particle size and the actual ratio of the material. In all cases the actual steady state was slightly less than the theoretical maximum contact and this is as expected as the material is also in contact with the walls, but this does not form part of the contact between the orange and black material as described in the methodology. The fluctuations about this final contact value are considered in Section 4.4. For the speed experiments, all the experiments obtained a similar final contact value. This is as expected since the same initial bed configuration and proportions were used for each of the rotational velocity experiments. The differ-
The standard deviation about the final contact value was used as a measure of the experimental error of the experiments. The standard error was calculated for the rate values and this was used as an estimate of the error in the mixing rate determination. In most cases the rate error was larger than the steady state error. The white seal between the two semi-circular panes of the glass surface may be responsible for causing some errors. This is especially true for the mixing rate values since this seal could have hid a well-mixed part of the bed and thus reduce the overall contact for this image. Incorrect film exposure was another source of error but was eliminated by checking each exposure and eliminating the exposure from the data set if it was not exposed correctly. Under- or over-exposed images resulted in misrepresentation of colours and thus gave a false measure of the black and orange pixels. This could be checked for in each image. The black and orange pixel counts were similar in all correctly exposed images since equal fractions of material were used. A large fluctuation in the black to orange ratio was a clear indication of incorrectly exposed images. The movement into or away from the surface could also contribute to the experimental error. It was assumed that this movement resulted in an equilibrium of material moving into or away from the surface. This equilibrium should have maintained the composition at the surface constant. However, due to the stochastic nature of the mixing process some fluctuation can be expected, as shown by the fluctuations at the steady state. The experimental error of the steady state value is in most cases less than 5%. The absolute mixing rate error is in most cases higher than its steady state complement, but not significantly so. This indicates that the experimental errors described are also applicable to the rate data. One further aspect of the rate data to be considered is due to the step nature of mixing. This behaviour forces data away from the constant rate line as shown by the circled data points in Fig. 6. This indicates that the rate
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measurements obtained using this method are quite accurate.
5. Conclusions A new technique was developed to measure the mixing rate of solids in a rotating drum using image analysis using a Nikon F3 camera. These images were converted to Windows bitmap files and were analysed to determine the contact between the black and orange materials using custom C q q software. The experiments carried out tested the variation in mixing dynamics due to changes in rotational velocity from 5 to 15 rpm, the particle size from 0.89 to 5.08 mm and the drum loading from 10 to 40% by volume. It was observed that the mixing rates for all experiments were constant and that a steady state was achieved in less than 30 s. The mixing rate increased exponentially with rotational velocity, decreased linearly with increasing particle size and increased linearly with drum loading. The steady state contact did not vary with rotational speed, but increased with decreasing particle size and increased with drum loading. The experimental errors observed, while not insignificant, were as expected. The observations were sufficiently accurate to enable resolution of stepwise mixing. Overall a new technique has been developed which will allow the mixing rates of materials in a rotary drum to be easily measured, modelled and predicted.
6. Nomenclature RŽ v . RŽ Dp . RŽ%V . %V Dp v
Mixing rate as a function of rotational velocity Žmmrs. Mixing rate as a function of particle diameter Žmmrs. Mixing rate as a function of drum loading by volume Žmmrs. Drum loading by volume Mean particle diameter Žmm. Rotational velocity Žrpm.
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Acknowledgements The authors wish to thank the Australian Research Council, the University of Technology, Sydney and Southern Pacific Petroleum ŽDevelopment. for funding this work.
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