Powder Technology 318 (2017) 23–32
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Discrete element method simulations and experiments of dry catalyst impregnation for spherical and cylindrical particles in a double cone blender Yangyang Shen, William G. Borghard, Maria S. Tomassone ⁎ Department of Chemical and Biochemical Engineering, Rutgers, the State University of New Jersey, 98 Brett Rd., Piscataway, NJ 08854, United States
a r t i c l e
i n f o
Article history: Received 18 August 2016 Received in revised form 3 May 2017 Accepted 11 May 2017 Available online 15 May 2017 Keywords: Catalyst impregnation Discrete element method Granular mixing
a b s t r a c t The dry impregnation of catalyst supports is a widely used process in the preparation of heterogeneous catalysts, however there has not been a lot of work done computationally on this process. In this work, discrete element method (DEM) simulations coupled with an algorithm for the transfer of fluid to and between particles are used to study dry impregnation. We use a previously developed model, which has been further validated with geometrically equivalent experiments and the results show very good agreement. The effects of rotational speed, particle size and particle morphology are explored in order to achieve the best overall mixing and fluid content uniformity in the particle bed. We study spheres and cylinders of different sizes and aspect ratios. Axial mixing analysis and liquid distributions are used to investigate the propagation of the fluid throughout the particle bed with the goal of understanding the effect of operational and material parameters and ultimately to improve fluid content uniformity in systems with particles of different morphologies. The fluid content uniformity is characterized by the relative standard deviation (RSD) of the liquid content from all the particles in the system. Our results show that cylinders always take less time to mix than spheres of the same diameter and mixing times are also shorter for cylinders of higher aspect ratios when compared to cylinders of smaller aspect ratio. Likewise, the times to reach good fluid content uniformity are shorter for cylinders with higher aspect ratios as compared with cylinders with lower aspect ratios. We also observe that mixing time in the axial direction for both spheres and cylinders followed an exponential function of the surface area to volume ratio. We found a linear correlation between the times to achieve good axial mixing and the times to achieve good fluid content uniformity in the entire particle bed, which suggests that mixing in the axial direction controls fluid uniformity in the entire particle bed. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Impregnation is a crucial step in the manufacturing of heterogeneous catalysts [1–3]. Generally, the process of impregnation is performed in rotating vessels with one or more nozzles that distribute a solution of the metal precursor into the catalyst support particles. As the liquid penetrates into the dry particles, the particles absorb the fluid, and the density of the particles increases accordingly until they become saturated [4,5]. After saturation, the excess liquid forms liquid bridges between particles causing wet cohesive forces that disrupt particle flow and mixing and even form particle agglomerates [6]. All of these can adversely affect the homogeneous distribution of the metal precursor in the solid, resulting in unacceptable content variability in the final catalyst product. ⁎ Corresponding author. E-mail address:
[email protected] (M.S. Tomassone).
http://dx.doi.org/10.1016/j.powtec.2017.05.023 0032-5910/© 2017 Elsevier B.V. All rights reserved.
While dry impregnation is a widely used technique in catalysis manufacturing, the process is very seldom studied using computer simulations. Most research in this field has been done experimentally and mostly focused on aspects of the surface chemistry of the impregnation and the metal content inside individual support particles [7–9]. There have also been some transport models but those have covered a small window of the process [2]. In particular, discrete element method (DEM) has been increasingly used to study granular flow systems [10, 11]; however, most of this work is focused on the pharmaceutical area [12–14]. The catalyst manufacturing industry uses many similar processes. Heat and liquid transfer has been studied in a rotary kiln using DEM [15,16]. However the modeling of catalyst impregnation processes using DEM remains highly unexplored. To the best of our knowledge, the only reported DEM simulation study on dry impregnation of catalysis was done by our group [17]. In our previous study, we developed a fluid transfer algorithm and implemented it into a discrete element model to simulate the catalyst impregnation process. The simulations
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were validated by experiments utilizing a geometrically identical double cone blender with a single nozzle impregnator. The effects of two process parameters (i.e. flow rate and fill level) were explored. However, several effects were left unexplored, such as the effect of rotational speed and the effect of particle size and morphology. These are crucial parameters that may influence proper mixing in the particle bed for all the particles to receive similar amounts of liquid. Double cone blender is a standard industrial tumbling mixer and commonly used for catalyst impregnation. Mixing has been experimentally shown to not be a function of rotational speed in a double cone blender [18,19]. Using a multi-dimension double cone blender that rotates around two axes, it has been concluded that the rotation of the mixer at higher speeds around the horizontal axis resulted in a better mixing efficiency and lower mixing time [20,21]. These studies, however, were done in the absence of water in the particle bed. When liquid spraying is present, it creates moisture in the granular system leading to cohesion as a result of capillary forces, which can have a significant effect on the mixing and flow behavior of granular materials [22–24]. In all these previous studies, mixing under fluid spray as a function of rotation speed has not been previously quantified. In this paper, we investigate the overall mixing and fluid content uniformity in the liquid-impregnated particle bed at different rotation speeds and different particle sizes and morphologies. Particle size and distribution of particle sizes have a strong influence on the random diffusive particle motion in a granular bed. To the best of our knowledge this has never been reported in the literature. The remainder of this paper is organized as follows: simulation method and model validation are described in Section 2, experimental setup is given in Section 3, and results are presented in Section 4, followed by conclusions and recommendations, which are presented in Section 5. 2. Simulation method
where Eeff is the effective Young's modulus of two colliding entities (two particles or a particle and a wall). For entities with Poisson's ratios ν1 and ν2, Young's moduli E1 and E2, Eeff is given by: Eeff ¼
1−ν 1 2 1−ν 2 2 þ ; E1 E2
ð4Þ
where Reff is defined as the effective radius of the contacting particles. In case of a particle–wall collision, the effective radius is simply the particle radius. While in the case of particle–particle collision, with the two contacting particles having radii R1 and R2, the effective radius is obtained by: Reff ¼
R1 R2 : R1 þ R2
ð5Þ
With the knowledge of the normal stiffness coefficient and a chosen coefficient of restitution ε, the normal damping coefficient γn is calculated as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3ffi u 2 pffiffiffiffiffiffiffiffiffi u u5 6 ln ðεÞ mkn 7 γn ¼ 2u t3 4 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5; 2 ln ðεÞ þ π2
ð6Þ
where kn is the Hertzian normal stiffness coefficient. Following the work of Mindlin and Deresiewicz [28], the tangential force Ft is calculated in a similar method as its normal counterpart. The tangential contact force also consists of elastic and damping components. When a tangential overlap of δt is detected and there is a corresponding normal overlap of δn due to the same contact, then the tangential force is expressed by: 1 = F t ¼ −kt δt −γt δ_ t δn 4 ;
ð7Þ
Discrete element method (DEM) has been increasingly used to study granular materials and particle systems. In the DEM, the motion of individual particles is computed according to the Newton's second law of motion. The translational and rotational motions of a solid particle are expressed by:
where kt the tangential stiffness coefficient and γt is the tangential damping coefficient. In the above equation, kt is calculated by:
ma ¼ ∑F Contact þ ∑F Body ;
kt ¼ 8Geff
ð1Þ
where m and a are the mass and acceleration of a solid particle, respectively. The term ∑ FContact accounts for all the normal and tangential contact forces, which are due to particle-particle or particle-boundary collisions. ∑FBody denotes the sum of all body forces due to gravity. DEM simulations in this work were performed using the EDEM commercial software package, developed by DEM Solutions, Ltd., which is based on an original method proposed by Cundall and Strack [25]. The contact forces are calculated using Hertz-Mindlin no-slip contact model. It is based on a soft contact model or elastic approach, in which the magnitude of repulsive force is related of the amount of overlap. The normal force is calculated using a damped Hertzian normal contact model [26] with the damping term given by Tsuji et al. [27]. The magnitude Fn from a contact that resulted in a normal overlap δn is given by: 3 1 = = F n ¼ −kn δn 2 −γn δ_ n δn 4 ;
ð2Þ
where kn is the Hertzian normal stiffness coefficient, δn is the deformation (normal particle overlap), γn is the normal damping coefficient, and δ_ n is the rate of deformation. In the above equation, kn is obtained by: kn ¼
qffiffiffiffiffiffiffiffiffi 4 Reff ; E 3 eff
ð3Þ
qffiffiffiffiffiffiffiffipffiffiffiffiffi Reff δn ;
ð8Þ
where Geff is the effective shear modulus. For two entities with shear moduli G1 and G2, Geff is calculated as: 1 2−ν1 2−ν2 ¼ þ ; G1 G2 Geff
ð9Þ
where ν1 and ν2 are the Poisson's ratios. The tangential displacement (or overlap) δt is calculated by timeintegrating the relative velocity of tangential impact, vtrel between two colliding entities (either interparticle or particle–wall contact): ! ! δt ¼ ∫ vtrel dt:
ð10Þ
The capabilities of EDEM include user defined functions and various features for simulating impregnation process, which has been developed in our previous work [17]. The fluid spray components are modeled as discrete droplets, which are sprayed from above the rotating bed and are absorbed upon contact with the simulated catalyst particles. The corresponding contact causes the simulated fluid droplet to essentially disappear while simultaneously transferring the mass of the fluid droplet to the simulated catalyst support particle, leading to a net increase in the mass. The mass flow rate of the fluid is defined as: Q spr ¼ NV ¼ N
m ρ
ð11Þ
Y. Shen et al. / Powder Technology 318 (2017) 23–32
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where N is the number of fluid droplets, V is the volume, m is the mass and ρ is the density of each droplet. Analogous to the experimental conditions, the particles in this study are modeled to absorb fluid up to 35% of their weight. After saturation of the catalyst particle occurs, additional fluid allows the support particles to be considered supersaturated, and as a result, they transfer any excess of fluid to any non-saturated particle that they come into contact with. The amount of fluid transferred between two particles in every contact when one of them is supersaturated, is defined as: Q tr ¼ κ mi −m j :
ð12Þ
In the above equation, κ is a proportionality constant which reflects the rate of fluid transfer, and mi and mj are the respective mass of each of the particles; for this work, κ was defined as 0.01. So, the amount of fluid transferred per contact is a function of the difference in the wetness of the contacting particles. When the amount of fluid absorbed is more than the fluid contained in the pore volume, the fluid transfer algorithm allows the excess of fluid on a specific catalyst support particle to be transferred to another adjacent particle at a specific rate. In the simulations, a number of parameters were used to accurately represent the experimental system. The values of the material properties were obtained directly from the alumina catalytic support used in the experiments and are shown in Table 1. 3. Experimental setup Double cone blending experiments were conducted using PattersonKelly 10-quart rotating double cone blender as shown in Fig. 1A. Fig. 1B illustrates the schematic and dimensions of the double cone blender. Experiments were conducted with the vessel loaded at two fill levels of 30% and 45% by volume corresponding to 1.75 kg and 3 kg of alumina spheres, respectively. 4.76 mm γ-alumina spheres (3/16 in.) were kindly donated from Saint-Gobain Norpro (Stow, OH, USA). The granular spheres contained a surface area of 200 m2/g and a pore volume of 0.389 cm3/g. An impregnator was retrofitted into the system using Swagelok ¼ in. fittings and a ¼ inch NPT nozzle adapter. In our experiments we used three different spray nozzles: MW-105, MW-145, and MW-275 Microwhirl™ nozzles purchased from BETE Fog Nozzle, Inc. (USA). The nozzles correspond to three flow rates: 1.5, 2.5, and 5 L/h and the flow was controlled using a Cole-Parmer Masterflex™ peristaltic pump retrofitted to the Swagelok fittings. Fluid was sprayed in an 8 cm diameter circle at the center of the vessel, corresponding to 1/3 of the rotational axis under spray (~11% of the surface area). During the impregnation process, samples were retrieved every 1 min. The 4.7 mm spheres were removed for analysis at 7 points across the axis of rotation at the top of the bed, as shown in Fig. 1C. Each sample contained approximately 20–25 particles. All samples were stored in air-tight glass vials prior to analysis for moisture. Moisture was analyzed by heating the samples to 300 °C for 6 h and measuring the associated mass change. Moisture content was normalized by the weight of the sample. The fluid content uniformity was characterized by using the relative standard deviation (RSD), which was calculated from the ratio of the standard deviation (σ) and the average value of the fluid content
Table 1 Initial parameters and material properties used in the simulations. Parameter
Value
Density of particle Diameter of particle Shear modulus Poisson ratio Coefficient of restitution Coefficient of static friction Coefficient of rolling friction
1500 kg/m2 4.7 mm 2 × 106 N/m2 0.25 0.1 0.5 0.1
Fig. 1. (A) Patterson-Kelly 10-quart double cone apparatus retrofitted with a single centerlocated spray nozzle used in the experiments. (B) Schematic and dimensions of the double cone blender. (C) Schematic of the cylindrical part of the double cone viewed from the top. Seven sampling positions along the axis of rotation are shown in red circles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
(C) in the samples of catalytic particles after impregnation. RSD was calculated by the two equations shown below: RSD ¼
σ C
ð13Þ
and
σ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 n∑C i 2 −ð∑C i Þ ; nðn−1Þ
ð14Þ
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where Ci is the fluid concentration at each sampling position and n is the number of samples. Lower RSD values indicate less variability between samples, which implies better mixing and fluid content uniformity. There is not a general consensus regarding a fixed value for the relative standard deviation (RSD) uncertainty to indicate uniformity; rather, the value of the RSD used as a threshold depends on the application and the sample size [29]. In some cases, the observed variability is combined with the observed bias in the sample average to provide a combined criterion [30], so that the limit in RSD actually depends on the observed level of deviation in the sample mean. The size of our samples is about 20 to 25 particles per sample, and in each experiment, we tested 7 samples taken at two different times, with 3 repetitions with 20–25 particles in each sample, therefore a total of approximately 1050 units per experiment were tested which provides enough measurements to yield a normal or near to normal distribution. It is standard and widely accepted [29,30] to consider a 95% or higher confidence interval in normal distributions to have assurance of batch acceptability. Our data show a 95% confidence interval (i.e. two standard deviations from the mean value taken at 100% pore volume filling) and our measurements of the RSD on those samples show RSD values that range from 0.09 to 0.109. Hence, we take RSD b 0.1 as our criterion for a reasonably good degree of uniformity since RSD values smaller than 0.1 correspond to a 95% confidence interval. In addition, in general, in the catalysis industry it is widely accepted that a 10% variation in the catalyst quality is a reasonable variability, since other quality factors (surface area, activity, metals dispersion, crush strength, etc.) are often specified to this level of variation. 4. Results To validate our model, DEM simulations and experiments were performed in a double cone blender of 24 cm in diameter and 30 cm in height, which was operated at a constant rotation speed of 25 rpm. The dimensions and setup are identical in both simulations and experiments. Sampling in the simulations was performed by taking 9 cm3 boxes located in the positions indicated in Fig. 1C. These positions are located at the top part of the particle bed and the number of particles in each of these sampling boxes varies between 20 and 25 particles per box. The variation in the number of particles per sampling box is due to the fact that at the top part of bed the particles are not densely packed. The particles in each box were analyzed for water content and subsequently compared to the experimental results. The uniformity of fluid content in these boxes was analyzed in the same manner that was done in experiments (i.e. by computing the relative standard deviation). The total water content in the particle system was compared between experiments and simulations for 3 different flow rates (1.5 L/h, 2.5 L/h and 5 L/h), as shown in Fig. 2. Fig. 2 also includes the total amount of water that has been sprayed (solid curves) for comparison. It is important to note that the 5 L/h flow rate results in the catalyst support reaching the pore volume shortly after 8 min; therefore, only the first 8 min are shown. There clearly exists good quantitative agreement for the overall fluid content within the granular catalyst bed for all three flow rates. The content uniformity is compared by calculating the relative standard deviation (RSD) of the water content at the seven sampling positions along the horizontal axis as shown in Fig. 1C for both experiments and simulations. The RSD curves calculated from both simulation and experimental data are shown in Fig. 3 for two different fill levels (30% and 45%) for a flow rate of 1.5 L/h. It is clear from this figure that in both experiments and simulations the 30% fill level reaches a wellmixed system, with an RSD value b0.1, at a slightly faster rate than the 45% fill level. The 30% fill level case mixes slightly better despite the larger ratio of spray-rate to mass of catalyst support. It is well known that the flow of particles in the double cone blender has two regions [19]: the cascading region and the rotating region. On the surface
Fig. 2. Comparison of overall fluid content within the granular bed at 30% fill level; dotted lines are simulation data, symbols are experimental data, error bars represent one standard deviation from the experimental mean, and the solid lines correspond to the total amount of water sprayed, also included for comparison.
of the granular bed is the cascading region, and below the surface is the rotating region. In the cascading region, particles are driven by gravity and flow down the slope; mixing of particles largely occurs in the cascading region. While in the rotating region, particles are more packed and the material is compacted; no axial mixing is essentially observed. Thus, as the fill level decreases, a larger fraction of the bed is in the cascading region, resulting in a better mixed system and consequently smaller values of RSD. In addition, it should be noted that no fluid was sprayed in the 45% fill level case after 10 min, yet approximately 6 min or 150 additional rotations were required to reach the same level of RSD exhibited by the 30% fill level case. Fig. 4 shows a comparison between experiments and simulations for the water content distribution in the axial direction for the 30% fill level case (for both experiments and simulations data points were also taken at the 7 sampling positions indicated in Fig. 1C). A more uniformed fluid distribution was found for lower spray rates at the end of spraying. We observed symmetric profiles and good quantitative agreement in the axial water distribution in both experiments and simulations for all flow rates. In summary, our DEM model with a fluid transfer algorithm was further validated and it accurately represents the dry catalyst impregnation for a double cone blender. Using the model, we demonstrated
Fig. 3. Relative standard deviation of the fluid concentration in the axial direction for both simulation and experimental dry impregnation at the 30% and 45% fill levels. Spraying was stopped at t = 10 min for both fill levels. For the 45% fill level, additional rotations were performed after spraying was stopped. It was not necessary to include additional rotations to the 30% fill level since the RSD had already reached values smaller than 0.1.
Y. Shen et al. / Powder Technology 318 (2017) 23–32
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Our method for the computational evaluation of mixing within the dry impregnation system was to color-tag the particles in two halves (particles separated by a mid-plane perpendicular to the axis of rotation) and subsequently evaluate the relative standard deviation of the color-tagged particles, a significant advantage resulting from the development of a DEM model system [17]. Results are depicted in Figs. 5A and B. Fig. 5A displays the relative standard deviation (RSD) of axial mixing of impregnated particles as a function of time for different rotational speeds. Notice that this value of RSD is obtained without considering the water content, using just the particle positions to evaluate whether the impregnated particles are well mixed. From Fig. 5A it can be clearly observed that the axial mixing was faster for higher rotational speeds. However, when the same data were plotted against the number of rotations, (see Fig. 5B), the three curves almost overlap indicating the mixing rate per revolution of the vessel was independent of the rotational speed. These results for a dry impregnated system coincide with previous studies for double cone blenders of non-impregnated particles [18,19]. In other words, mixing in impregnated systems occurs in the same manner as in nonimpregnated systems. It does not matter how much time the system is mixed; rather, it depends on the number of rotations. One of the most important goals in the impregnation process is to obtain a homogeneous distribution of water in the entire particle bed. So we wanted to obtain the effect of rotational speed on the uniformity of the fluid not only in the axial direction but also in the entire particle bed of impregnated particles. Fig. 6A and B shows the RSD curves of the water content uniformity in the axial direction plotted against time and the number of revolutions respectively for different rotation
Fig. 4. Final water content as a function of filled pore volume percentage along the axis of rotation for both DEM simulations (solid lines) and experiments (symbols with dashed lines) at different flow rates: (A) 1.5 L/h, (B) 2.5 L/h, and (C) 5 L/h.
qualitative and significant quantitative agreement in the total water distribution for all fill levels and flow rates and in the axial direction. The value of the relative standard deviation (RSD) has also shown good agreement between experiments and simulations. This systematic validation has paved the way for using our DEM model and corresponding algorithm to study a variety of operating parameters and different support morphologies.
4.1. Effect of rotational speed on mixing and fluid content uniformity In this section we explored the effect of rotational speed on mixing and water content uniformity in the particle bed. The goal was to achieve high fluid content uniformity and a thus, a well-mixed system, which is generally exhibited by a relative standard deviation (RSD) of b0.1. DEM simulations were performed in a double cone blender filled to 30%, and the spray rate was kept constant at 1.5 L/h. Three rotational speeds were compared: 5 rpm, 15 rpm, and 25 rpm. It is important to elucidate to what extent the mixing of particles in the axial direction controls the water uniformity in the particle bed. So, we first focused on the mixing of the dry impregnated particles and then on the distribution of water in the particle bed. It has been shown that mixing is not a function of rotation speed in the absence of fluid in a double cone blender [18,19]. Therefore, even though we used fluid in our studies, it was expected that rotation speed was not a significant factor affecting the mixing results.
Fig. 5. (A) Relative standard deviation for mixing in the axial direction as a function of time for different rotational speeds. (B) The calculated RSD for mixing in the axial direction as a function of the number of revolutions for different rotational speeds.
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4.2. Effect of particle size and morphology for fluid impregnated systems Since catalyst support particles come in a wide variety of shapes and sizes, it is with great interest that we investigate the behavior of different catalyst supports during the impregnation process. Both spherical and cylindrical particles were considered to determine the effect of particle morphology and particle size on an impregnated particle bed. Spheres were tested at various diameters; Table 2 lists all the cases of spheres and cylinders studied. Cylinders were selected to examine various particle sizes and aspect ratios. Simulations were performed at a fixed speed of 25 rpm and a fixed flow rate of 1.5 L/h for a 30% filled double cone blender. Simulation snapshots of dry impregnation using spherical particles of different sizes are shown in Fig. 7. Cylindrical particles were formed with a multi-sphere approach [31,32], where a number of spheres are bonded together and shaped into a cylinder. These spheres have the same size and are allowed to superimpose to form the required cylindrical shape. For example, a cylinder of 3 mm in diameter and 6 mm in length (i.e. 3 mm × 6 mm) is composed of 5 interlinking spheres, which have the same diameter of 3 mm. These spheres are located in a row and the separation between 2 spheres is fixed at half of their diameter (1.5 mm). Simulation snapshots of dry impregnation using cylindrical particles of 3 mm in diameter and different aspect ratios are shown in Fig. 8. The construction of cylinders by multiple spheres is shown in a schematic next to the corresponding snapshot in Fig. 8. In all the simulation snapshots, the particle bed surface shows a similar curvature, forming a nearly continuous and steady flow for the entire process [33].
Fig. 6. (A) Relative standard deviation for water content uniformity in the axial direction as a function of time for different rotational speeds. (B) Relative standard deviation for water content uniformity in the axial direction as a function of the number of revolutions for different rotational speeds. The inset figure shows the calculated relative standard deviation for water content uniformity in the entire particle bed as a function of the number of revolutions for different rotational speeds.
speeds. Fig. 6B inset shows the time to achieve water content uniformity in the entire particle bed as a function of number of revolutions. A very interesting observation is that in Fig. 6A, the relative standard deviation for the axial fluid content uniformity as a function of time is higher for higher rotational speeds whereas, when compared with Fig. 5A we see that the RSD for axial mixing is smaller for higher rotational speeds. We believe that one possible reason why this happens is that for higher speeds the curvature of the particle surface in the cascading zone is more curved so more particles spend time in the mixing zone [18,19]; conversely for higher speeds, when particles are faster, the particles spend less time under the water spraying zone (the projected area of the fluid cone onto the particle bed whose area is 11% the area of the cascading zone) and that causes the particles to not get the same amount of fluid that they would get at slower speeds. For this reason, the RSD for water uniformity in the axial direction is poorer for higher speeds and the RSD for axial mixing it is better for higher speeds. There is an intrinsic difference in the way that water spreads and impregnates the particles in the particle bed compared to the way in which dry impregnated particles mix and move. By comparing the results of Fig. 6B (i.e. RSD of water content uniformity in the axial direction) with Fig. 6B (inset) (i.e. RSD of water content uniformity in the entire particle bed) we do not find overlap of the curves as a function of the number of revolutions. This indicates that the water content uniformity does depend on the rotational speed of the vessel.
4.2.1. Effect of size and morphology on axial mixing In this section we present DEM simulations focused on the effect of size and morphology on mixing. The axial mixing time is defined as the time necessary to reach a well mixed system with RSD b 0.1 in the axial direction for a system of fluid impregnated particles. Five sizes of spheres were considered, ranging from 2 to 10 mm. Table 2 lists the diameter and the labels used in Fig. 9 for all the spheres studied. It is clear that the mixing time of the impregnated particles decreases with increasing size and decreasing surface area to volume ratio (S/V). Cylinder-shaped catalyst support particles of various sizes and aspect ratios were also simulated. It is interesting to notice that as the surface area to volume ratio (S/V) decreases with increasing cylinder length, the mixing time decreases. Fig. 9A shows the results for the mixing time in the axial direction versus the surface area to volume ratio (S/V) for both spheres and cylinders for a rotational speed of 25 rpm. It can be clearly observed that the mixing time for cylinders is shorter than that for spheres. We also performed these simulations for a rotational speed of 5 rpm and found
Table 2 Dimensions for spheres and cylinders and symbols used in Fig. 9A, A inset and B. Spheres, diameter
Cylinders, diameter × length
Sphere 2 mm (S1) Sphere 2.5 mm (S2) Sphere 3 mm (S3) Sphere 4.7 mm (S4) Sphere 6 mm (S5) Sphere 10 mm (S6)
Cylinder 2 mm × 3 mm (C1) Cylinder 2 mm × 4 mm (C2) Cylinder 2 mm × 6 mm (C3) Cylinder 3 mm × 4.5 mm (C4) Cylinder 3 mm × 6 mm (C5) Cylinder 3 mm × 7.5 mm (C6) Cylinder 3 mm × 9 mm (C7) Cylinder 3 mm × 12 mm (C8) Cylinder 3 mm × 15 mm (C9) Cylinder 6 mm × 7 mm (C10) Cylinder 6 mm × 9 mm (C11) Cylinder 6 mm × 12 mm (C12) Cylinder 6 mm × 15 mm (C13) Cylinder 6 mm × 18 mm (C14) Cylinder 6 mm × 24 mm (C15)
Y. Shen et al. / Powder Technology 318 (2017) 23–32
Fig. 7. Simulation snapshots of dry impregnation using spherical particles of different sizes: (A) 3 mm, (B) 6 mm, and (C) 10 mm.
29
Fig. 8. Simulation snapshots of dry impregnation using cylindrical particles of 3 mm in diameter and different aspect ratios: (A) 3 mm × 4.5 mm, (B) 3 mm × 6 mm, (C) 3 mm × 7.5 mm, and (D) 3 mm × 9 mm. A schematic of the cylinder formed with a multi-sphere approach is shown next to the snapshots. The spraying droplets are not shown for clarity.
where τ is the mixing time, and τ0 and α are fitting parameters. The correlations and the corresponding coefficients of determination R2 are as follows: similar trends, although the results are not shown. This is consistent with work by Guo et al. [34] where they found that cylinders have smaller fluctuating velocities and larger particle collision frequency, so they take less time to mix. We fit the data to exponential functions in search of a mathematical correlation between the mixing time and the surface area to volume ratio (S/V). We found: S τ ¼ τ0 eα ½V
ð15Þ
For spheres : τ ¼ 44:496e0:90754ðS=VÞ ; with a correlation coefficient R2 ¼ 0:9961
ð16Þ
For cylinders we found some interesting behavior. In Fig. 9A it is possible to observe that depending on the diameter (d) of the cylinder we obtained different exponential fitting curves that converge to the value of the mixing time for a sphere with the same diameter (which
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Y. Shen et al. / Powder Technology 318 (2017) 23–32
cylinders with smaller diameters take more time to mix. Also, for a cylinder of a fixed diameter, the higher the aspect ratio, the smaller the mixing time, which is also consistent with Guo et al. [34]. We can also observe that for the same value of the aspect ratio, cylinders with smaller diameters tend to have longer mixing times. (i.e. C2 and C5 have the same aspect ratio but C2 has a smaller diameter and longer mixing times). In general we also observe that as the S/V ratio increases which corresponds to the case of smaller particles, the mixing time is longer. To understand the reason why cylinders mix and spread the fluid faster than spheres, we hypothesize that the moment of inertia (MI) of spheres is always smaller than the moment of inertia of cylinders regardless of their axes of rotation [35]. The MI of the particles measures an object's resistance to any change in its state of rotation. Spheres have a smaller MI, thus, they can rotate more easily, and their rotational velocity is faster than the cylinders' rotational velocities when rolling down the slope in the cascading zone of particle bed. In addition, they are faster because they collide less. In fact, previous work [34] showed that the probability of collision is lower for spheres. Smaller chance to collide leads to poorer mixing. Previous work has also shown that as the particle aspect ratio increases the probability of particle collision also increases [34], which implies that cylinders, which have higher aspect ratios than spheres, experience more collisions than spheres. As a result, mixing is enhanced for cylinders and they take less time to mix.
Fig. 9. (A) Time to achieve good axial mixing (for values of RSD b 0.1) for various particle morphologies as a function of surface area to volume ratio (S/V). Spherical particles of different diameters are labeled S1–S6 according to the cases listed in Table 2. Cylindrical particles of different diameters and aspect ratios are labeled C1–C15 according to the cases listed in Table 2. Notice that some labels are omitted for clarity. The data points were fitted with exponential functions. (Inset) Time to achieve good fluid content uniformity in the entire particle bed vs. surface area to volume ratio. (B) Linear correlations for spheres and cylinders were found between the time needed to achieve fluid content uniformity in the entire particle bed and the time needed to achieve good axial mixing (both times area calculated when RSD b 0.1) for spheres and cylinders of different diameters and aspect ratios.
corresponds to cylinders with aspect ratio equal to 1 with that diameter). For example, the data points corresponding to the mixing time for cylinders with diameters d = 3 mm and high aspect ratios, (i.e. C4–C9) fall in a curve that converges to the mixing time for spheres of diameter 3 mm at the point S3 (which is also essentially the limit for a cylinder with aspect ratio equal to 1). The fittings for these curves are: For cylinders with d ¼ 2 mm : τ ¼ 16:063e1:2363ðS=VÞ ; with a correlation coefficient R2 ¼ 0:9994 ð17Þ For cylinders with d ¼ 3 mm : τ ¼ 6:7095e1:8499ðS=VÞ ; with a correlation coefficient R2 ¼ 0:9934 ð18Þ For cylinders with d ¼ 6 mm : τ ¼ 3:8574e3:3736ðS=VÞ ; with a correlation coefficient R2 ¼ 0:9913: ð19Þ These correlations represent the mixing time for each set of impregnated cylinders of a given diameter for different aspect ratios. Clearly
4.2.2. Effect of size and morphology on fluid content uniformity The fluid content uniformity in the entire particle bed has also been analyzed in systems that have different particle sizes and shapes (spheres and cylinders) as a function of surface to volume ratio for a fixed rotation rate. The results are shown in Fig. 9A inset. As we can observe in the inset the curves for fluid content uniformity have very similar trends than Fig. 9A. These results suggested that there was a strong correlation between axial mixing and fluid content uniformity in the entire particle bed. We indeed found a strong linear correlation between the times needed to achieve good axial mixing and the times needed to achieve good fluid content uniformity in the entire particle bed for both spheres and cylinders of different aspect ratios and the results are shown in Fig. 9B. These results suggest that axial mixing controls the fluid uniformity in the entire particle bed. In Fig. 9B we can observe that the impregnation times to achieve good fluid content uniformity are on the order of minutes, not seconds. This can be understood in the following manner: in our case study, the particle bed receives the liquid at the center of the blender where the nozzle is placed. It is not until the particles are saturated with water that they can start transferring the excess liquid. For that reason, we see that it takes much longer times for the water to be transferred to areas outside the wetting zone cone determined by the nozzle location than what it takes to achieve good mixing in those areas. In Fig. 9A we see that the axial mixing time for spherical impregnated 3 mm particles is 280 s. However, in Fig. 9B we see that time that it takes for the same spheres to achieve good fluid content uniformity is approximately 1800 s (30 min). Fig. 10A and B shows the RSD curves plotted as a function of time for spheres and 3 mm cylinders, respectively. In Fig. 10A it is observed that the smaller values of the RSD for the water content uniformity inside the particle bed correspond to the larger size spheres. This is not surprising, because it is consistent with the mixing time for the larger spheres. Larger spheres mix faster and also achieve water content uniformity faster in time, conversely small spheres take a longer time to mix and achieve the target relative standard deviation (0.1). This performance is also directly related to the longer mixing times of the smaller spheres. Fig. 10B shows the RSD value of the water content for 3 mm cylinders of different lengths (aspect ratios). It is observed that the smaller RSD for water content inside the bed corresponds to the larger aspect ratios of the selected sets of cylinders. For the cylinders of different aspect ratios, much longer spraying times are necessary for smaller
Y. Shen et al. / Powder Technology 318 (2017) 23–32
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aspect ratios. This is due to the increased fluctuating velocities and particle collision frequency in cylinders as the aspect ratio increases, which facilitates mixing and in this case, it also facilitates transfer of liquid between particles. It was found that the mixing time in the axial direction for both spheres and cylinders followed an exponential function of the surface area to volume ratio. We found different correlation functions for cylinders depending on their value of the diameter. These correlations reveal that as the aspect ratio decreases for cylinders with the same diameter the mixing time of cylinders converge to the value of the mixing time of a sphere with the same diameter (i.e. the sphere of the same diameter represents the limit of aspect ratio equal to 1). Likewise the fluid content uniformity as a function of S/V in the entire particle bed has the same trends than for the axial mixing times as a function of S/V. We found a strong linear correlation between axial mixing time and water content uniformity in the entire particle bed implying that in a double cone blender axial mixing controls fluid content uniformity. In our case study the particles receive the liquid at the center of the blender, where the nozzle is placed. It is not until the particles are saturated with water they start transferring the excess liquid. For that reason, we observe that it takes much longer times for the water to be transferred to areas outside of the wetting zone cone determined by the nozzle location than what it takes to achieve good mixing in those areas. A crucial step in the impregnation of catalysts is the distribution of a metal solution in the particle bed. Metals can be fast absorbing or weakly absorbing to the porous surfaces of the particles. Metal solutions will not necessarily have the same response as water and need to be investigated separately. This topic will be treated in future publications. Fig. 10. Relative standard deviation for fluid content uniformity as a function of time for (A) different sizes of spheres and (B) different aspect ratios of cylinders with the same diameter of 3 mm.
Acknowledgments
cylinders to reach wetness uniformity. Cylinders with larger aspect ratios yield the target RSD value in a shorter time.
The authors gratefully acknowledge funding of the Catalyst Manufacturing Science and Engineering Consortium at Rutgers University.
5. Conclusions
References
We used and further validated a discrete element method model with an algorithm of fluid transfer between particles that we had previously developed [17] to investigate the catalysis impregnation process. Good agreement was observed between simulations and experimental results. We used our validated DEM fluid transfer model to predict the mixing and fluid content uniformity of particles of different sizes and morphologies as a function of process parameters. The mixing performance for fluid impregnated particles in the axial direction is found to be a function of the number of revolutions and is independent on the rotational speed of the vessel. However the total fluid content uniformity depends strongly on the rotational speed, the larger the rotational speed of the vessel, the less uniform the distribution of water in the particle bed is, indicated by a larger value of the relative standard deviation. We analyzed the effect of morphology in both mixing and fluid content uniformity of the impregnated systems. Specifically, we considered spheres and cylinders. We analyzed the mixing time in the axial direction versus the surface area to volume ratio (S/V). It was observed that the mixing time for cylinders was shorter than that for spheres. This is consistent with work by Guo et al. [34] where they found that cylinders have smaller fluctuating velocities and larger particle collision frequency, so they take less time to mix. In general we also observed that as the S/V ratio increases (i.e. for smaller particles), the mixing time also increases. We also observe that the smallest values of RSD for fluid content uniformity correspond to cylinders with the largest aspect ratios. The spraying times to reach fluid content uniformity are shorter for cylinders with higher aspect ratios as compared with cylinders with lower
[1] James A. Schwarz, Methods for preparation of catalytic materials, Chem. Rev. 95 (1995) 477–510. [2] A.J. van Dillen, R.J.A.M. Terörde, D.J. Lensveld, J.W. Geus, K.P. de Jong, Synthesis of supported catalysts by impregnation and drying using aqueous chelated metal complexes, J. Catal. 216 (2003) 257–264. [3] L. Barthe, S. Desportes, M. Hemati, K. Philippot, B. Chaudret, Synthesis of supported catalysts by dry impregnation in fluidized bed, Chem. Eng. Res. Des. 85 (2007) 767–777. [4] T. Gluba, B. Kochaski, Water penetration into the bed of fine-grained materials, Physicochem. Prob. Miner. Process. 39 (2005) 67–76. [5] K.D. Danov, B. Pouligny, P.A. Kralchevsky, Capillary forces between colloidal particles confined in a liquid film: the finite-meniscus problem, Langmuir 17 (2001) 6599–6609. [6] A. Lekhal, S.L. Conway, B.J. Glasser, J.G. Khinast, Characterization of granular flow of wet solids in a bladed mixer, AICHE J. 52 (2006) 2757–2766. [7] Peter Munnik, Petra E. de Jongh, Krijn P. de Jong, Recent developments in the synthesis of supported catalysts, Chem. Rev. 115 (2015) 6687–6718. [8] A. Lekhal, B.J. Glasser, J.G. Khinast, Influence of pH and ionic strength on the metal profile of impregnation catalysts, Chem. Eng. Sci. 59 (2004) 1063–1077. [9] X. Liu, J.G. Khinast, B.J. Glasser, A parametric investigation of impregnation and drying of supported catalysts, Chem. Eng. Sci. 63 (2008) 4517–4530. [10] M.W. Weber, D.K. Hoffman, C.M. Hrenya, Discrete-particle simulations of cohesive granular flow using a square-well potential, Granul. Matter 6 (2004) 239–254. [11] C.Q. LaMarche, P. Liu, K.M. Kellogg, A.W. Weimer, C.M. Hrenya, A system-size independent validation of CFD-DEM for noncohesive particles, AICHE J. 61 (12) (2015) 4051–4058. [12] B. Chaudhuri, A. Mehrotra, F.J. Muzzio, M.S. Tomassone, Cohesive effects in powder mixing in a tumbling blender, Powder Technol. 165 (2) (2006) 105–114. [13] A. Faqih, B. Chaudhuri, A.W. Alexander, C. Davies, F.J. Muzzio, M. Silvina Tomassone, An experimental/computational approach for examining unconfined cohesive powder flow, Int. J. Pharm. 324 (2) (2006) 116–127. [14] E. Sahni, R. Yau, B. Chaudhuri, Understanding granular mixing to enhance coating performance in a pan coater: experiments and simulations, Powder Technol. 205 (1–3) (2011) 231–241. [15] D. Shi, W.L. Vargas, J.J. Mccarthy, Heat transfer in rotary kilns with interstitial gases, Chem. Eng. Sci. 63 (2008) 4506–4516.
32
Y. Shen et al. / Powder Technology 318 (2017) 23–32
[16] D. Shi, J.J. McCarthy, Numerical simulation of liquid transfer between particles, Powder Technol. 184 (2008) 64–75. [17] F.S. Romanski, A. Dubey, A.W. Chester, M.S. Tomassone, Dry catalyst impregnation in a double cone blender: a computational and experimental analysis, Powder Technol. 221 (2012) 57–69. [18] A. Chester, J. Kowalski, M. Coles, E. Muegge, F. Muzzio, D. Brone, Mixing dynamics in catalyst impregnation in double cone blenders, Powder Technol. 102 (1999) 85–94. [19] D. Brone, F.J. Muzzio, Enhanced mixing in double-cone blenders, Powder Technol. 110 (2000) 179–189. [20] S.S. Manickam, R. Shah, J. Tomei, T.L. Bergman, B. Chaudhuri, Investigating mixing in a multi-dimensional rotary mixer: experiments and simulations, Powder Technol. 201 (2010) 83–92. [21] J. Cho, Y.F. Zhu, K. Lewkowicz, S. Lee, T. Bergman, B. Chaudhuri, Solving granular segregation problems using a biaxial rotary mixer, Chem. Eng. Process. 57-58 (2012) 42–50. [22] R. Mendez, F.S. Romanski, M.S. Tomassone, Density behavior of cohesive granular materials, Powder Technol. 211 (2011) 189–198. [23] C.D. Willett, M.J. Adams, S.A. Johnson, J.P.K. Seville, Capillary bridges between two spherical bodies, Langmuir 16 (2000) 9396–9405. [24] S. Herminghaus, Dynamics of wet granular matter, Adv. Phys. 54 (2005) 221–226. [25] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 517. [26] H. Hertz, On the contact of elastic solids, J. Reine Angew. Math. 92 (1882) 156–171.
[27] Y. Tsuji, T. Tanaka, T. Ishida, Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe, Powder Technol. 71 (1992) 239–250. [28] R.D. Mindlin, H. Deresiewicz, Elastic spheres in contact under varying oblique forces, J. Appl. Mech. 20 (1953) 327. [29] Guidance for industry: powder blends and finished dosage units — stratified inprocess dosage unit sampling and assessmentsee internet source: https://www. fda.gov/OHRMS/DOCKETS/98fr/03d-0493-gdl0001.pdf. [30] 〈905〉 Uniformity of Dosage Units, The United States Pharmacopeial Convention, 2011, see internet source: http://www.usp.org/sites/default/files/usp_pdf/EN/ USPNF/2011-02-25905UNIFORMITYOFDOSAGEUNITS.pdf. [31] J.F. Favier, M.H. Abbaspour-Fard, M. Kremmer, Modeling nonspherical particles using multisphere discrete elements, J. Eng. Mech. 127 (2001) 971–977. [32] M. Kodam, R. Bharadwaj, J. Curtis, B. Hancock, C. Wassgren, Force model considerations for glued-sphere discrete element method simulations, Chem. Eng. Sci. 64 (2009) 3466–3475. [33] J. Mellmann, The transverse motion of solids in rotating cylinders - forms of motion and transition behavior, Powder Technol. 118 (2001) 251–270. [34] Y. Guo, C. Wassgren, W. Ketterhagen, B. Hancock, B. James, J. Curtis, A numerical study of granular shear flows of rod-like particles using the discrete element method, J. Fluid Mech. 713 (2012) 1–26. [35] Parviz Ghavami, Mechanics of Materials, an Introduction to Engineering TechnologyISBN: 978-3-319-07571-6 2015.
