(597c) Characterization and Modeling of Continuous Convective Powder Mixing Processes

Powder mixing efficiency is crucial for many processing stages within the pharmaceutical, catalysis, food, construction, and mineral industries, to name but a few. A significant problem hindering process design is the paucity of information about the effects of changing process parameters on mixing efficiency (Laurent and Bridgwater [1]). The main target of our research is to investigate continuous mixing as an efficient alternative method for powder mixing that allows for on-line control and optimization of mixing performance. Interestingly, continuous processing has been utilized by petrochemical and chemical manufacturing but has yet to reach the pharmaceutical industry to a meaningful extent. Pharmaceuticals are most commonly made by powder mixtures that are difficult to characterize (Jaeger and Nagel [2]). Recent research efforts indicate that a well-controlled continuous mixing process can improve productivity. Toward this objective, we have identified the following specific aims in this work.

The first specific aim demonstrates the effectiveness of continuous mixing for powders using a set of experiments. A number of operating parameters, including fill level, residence time, rotation rate, feed variability, and processing angle, are investigated to determine their effects on mixing performance. Two types of continuous mixers are considered. The first is a horizontal mixer with a series of blades. The horizontal mixer is 736 mm long and has an internal diameter of 152 mm. Each blade is 52 mm long with 28 mm width. The convective motion arising from the blades drives the powder flow. An adjustable number of long-flat blades are placed within the horizontal mixer, which affects the distance between blades. Blade location is shown to be important, as discussed by Laurent and Bridgwater [1], because the number of blades within the mixer affects the axial dispersion coefficient independent of rotational speed and fill level. An additional parameter that affects granular flow is the angle that the horizontal mixer forms with the ground. The second continuous mixer studied is a conical mill fed in a controlled manner. It has a 127 mm diameter screen with a capacity of to 220 kg/hr-360 kg/hr, equipped with an adjustable rotation rate for the conical blade.

Model blends have been formulated using the following materials: Iron Oxide (FeO) tracer particles (particle diameter=.9µm), Avicel (90µm), Fast-Flo Lactose (75-250µm), and Acetaminophen (510µm). The homogeneity of samples retrieved from the outflow is measured using Near Infrared Spectroscopy (NIR). The variation between particle size distributions is potentially important, since it is known to affect both the flow properties and the segregation tendencies of blends. Our studies show that for both continuous mixers, formulations with large particle size ratios exhibit higher sample-to-sample variances than mono-dispersed blends. For ?poorly-mixed? outcomes, we examine re-circulation of the outflow of the mixer. This step takes advantage of continuous processing and our studies show that for both mixing processes, this step decreases the sample-to-sample variability. Interestingly, a limitation exists; as the granular material is re-processed, the sample variability reaches a limit and the standard deviation no longer decreases as time increases. In order to minimize the chances of forming agglomerates both mixers discharge the powder through a perforated screen. The smaller the pores within the screen, the greater the material remains within the mixer, increasing the residence time. In addition to screen pore size, our studies show that changing the process angle alters the residence time, and disparity in material outflow homogeneity occurs when the material remains in the process for an insufficient amount of time, thus suggesting that the residence time distribution might be an essential variable.

Our second aim is to develop an efficient modeling approach that will enable the simulation, optimization, and control of mixing processes. Notably, powder mixing models are restricted due to computational limitations and obstacles associated with correlating simulation-time to real-time. Thus, we are proposing the use of a hybrid methodology that utilizes compartment modeling to simulate the areas within the mixing system that do not require detailed description and Discrete Element Method for the areas where a more comprehensive description is needed, for example areas around the impeller. The effectiveness of the methodology is demonstrated by modeling powders under the influence of a succession of impellers that exist within the continuous blender. This is computationally very expensive or even infeasible with existing modeling methods.

In order to reduce the computational complexity of powder mixing simulations we propose partitioning the mixing system into regions of higher complexity to be modeled by DEM and regions of lower complexity to be simulated using compartment modeling. We focus on using compartment models because of the modeling flexibility and effectiveness as shown in our recent work (Portillo et. al [4]). The basic idea behind compartment modeling is to spatially discretize a mixer into a finite number of compartments. A stipulated number of particles are initially loaded within the compartment where each particle is tagged with its chemical and physical identity. Time is also discretized so that at each time step a number of particles are exchanged between compartments. The particles selected to leave and enter the system are randomly chosen following the ideas of Fan et al. [5], who described solid mixing as a random process. The main idea behind the proposed approach is to identify areas that can be solved using a statistical model and the areas that require a detailed particle dynamic model. This methodology has been applied to model a horizontal mixer with one impeller, and as a result the computational time is reduced while capturing the mixing characteristics of the system. In the case of modeling the horizontal mixer with a succession of blades, we propose simulating the system as a plug-flow process. A plug-flow process can be modeled as a series of continuous stirred mixers. As a result, each compartment represents a continuous stirred mixer, and the entire structure of compartments captures the mixing process, while some of the mixing process is modeled with a statistical approach and the remaining is simulated with a particle dynamic methodology.

References:

[1] Laurent B.F.C., Bridgwater J., ?Performance of single and six-bladed powder mixers?, Chemical Engineering Science, 2002, 57, 1695-1709.

[2] Jaeger H.M, Nagel S., ?Physics of the Granular State?, Science, 1992, 256, 20,1523-1531.

[3] Weinekötter R., Reh L., ?Continuous Mixing of Fine Particles?, Particle and Particle Systems Characterization, 1995, 12, 1, 46-53.

[4] Fan L.T., Chen S.J., Watson C.A., ?Solids Mixing?, Industrial and Engineering Chemistry, 1970, 62, 7, 53-69.

[5] Portillo P.M., Muzzio F.J., Ierapetritou, M.G. ?Characterizing powder mixing processes utilizing compartment models?, International Journal of Pharmaceutics, Accepted March 2006.