(666d) The Development of a Multivariate Model for Predicting the Performance of Powder Feeders on a Comprehensive Range of Particulate Materials

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The accurate and consistent feeding of powder materials into reaction systems, mixers and other processing equipment is necessary to maintain optimal conditions and generate products of the required quality at the required rate. 

Predicting feed rates has historically used engineering estimation based on experience/extrapolation and pre-existing measured performance information – either from pilot scale trials of from data collected at earlier installations.  This has typically led to equipment that does not meet the target design requirements and/or resulted in sub-specification operation or in extremis, complete process failure [1,2].

The complexity of powders systems means that design using first principles and particle properties is currently not tenable due to the inability to accurately predict and scale shear rates and stresses and translate those features into an understanding of how the powder will behave in the equipment.  However, the goal of comprehensive process models is still worthwhile as it will dramatically reduce the costs associated with extensive pilot trials, unachievable production rates, variable product quality and process interruption. 

Modelling of powder processes is not new, but invariably the defining experiments are based on a limited range of real powders or a more unrealistic simulant, such as glass beads [3-5].  Many are focused on the influence of particle properties that are difficult/expensive to measure for industrial equipment manufacturers.  Even the most widely accepted model in powder systems engineering – the hopper design method developed by Jenike [6] – has measurement and application limitations that frequently require an expert to assist with the analysis and implementation of the test results.  Equally, designing an experiment that can isolate individual bulk powder/particle variables to study the influence of a specific parameter on a given process is generally unfeasible due to the interdependence of many powder/particle properties – for example size/shape/texture – combined with the difficulty of actually creating test aliquots that differ only in variable under investigation. 

One approach is to use statistical, multivariate models to evaluate the relationships between powder behaviour and process performance, but many studies are hampered by being restricted in using overly simplistic characteristics of the bulk powder, such as angle of repose; flow through an orifice etc., which are unrepresentative of the forces that the powder is subjected to in the process environment.  However, modern, computer controlled instrumental techniques have enabled direct measurements of a powders response to process relevant conditions, such as dynamic flow, aeration, consolidation and changes in flow rate as well as quantifying shear and bulk properties (such as density, compressibility and permeability).  These improved characterisation techniques allow researchers to develop improved, process relevant statistical models.

This study is designed to demonstrate how it is possible to generate a design and operating model based around the measurement of robust rheological properties of powders and a standard multiple linear regression (MLR) technique.  The results show the potential of rapidly generating simple and robust performance models for two types of auger powder feeders based on the accurate determination of powder properties from a diverse range of materials (cement to maltodextrin) and that these models can be used to accurately predict the feed rate performance of unrelated powders in the those feeders based on their measured flow behaviour.

Methods and Means

Two different commercially available feeders (GLD – full flight; single screw and GZD – flat base; twin screw) (Gericke, CH) were employed in this study.

A selection of powders were tested in both types of screw feeder to measure volumetric feed rate in L/hr at 80Hz.

The rheological characteristics of the powders were measured using an FT4 Powder Rheometer (Freeman Technology, UK) including Dynamic Flow behaviour, Aeration, Permeability, Compressibility and Shear properties [7].

The materials tested were calcium hydroxide, maltodextrin, milk protein, cellulose, calcium citrate.  These samples were selected to give a range of flowability.  Two additional powders, cement and lactose, were also tested and the results from these samples were used to validate the model that was developed.

Results & Discussion

The MLR analysis was undertaken to relate the powder characteristics to the feed rates generated in both types of feeder.

The relationship between GZD feedrates and measured powder characteristics is shown in Equation 1 with an R2 value of 0.84.

Feed Rate of GZD = -0.1114 AE40 + 34.82                  (1)

Where the AE40 is the aeration energy of the powder subjected to a superficial gas velocity of 40mm/s [7].  This result suggests that the aeratability of the powder – which is an indicator of the absolute level of cohesion at low stress – is the key characteristic in this twin screw feeder.

By contrast, the relationship between GLD feedrates and measured powder characteristics is shown in Equation 2 with an R2 value of 0.95.

Feed Rate GLD = 49.54 FRI – 13.81 SE + 163.8           (2)

Where the FRI is the flow rate index and SE is the specific energy generated in a dynamic evaluation of the powders [7].  This indicates how the dynamic behaviour of the powder is the key characteristic for a single screw configuration.

The additional two powders were tested and the feed rate and flowability results were compared to the feed rates predicted by the model for each feeder

The predictions of flow rate for the two validation samples show good agreement with the measured values – the resultant R2 values are 0.78 and 0.91 for the GZD and GLD feeders respectively.

 

Conclusions

  • Different screw feeders subject powders to a range of different flow and stress regimes.
  • Powders have many characteristics, so single number characterisation, or even a single technique cannot thoroughly describe powder behaviour in every type of feeder – a multivariate analysis is required.
  • Multiple Linear Regression (MLR) can be used to quickly generate relationships between GLD/GZD performance and powder properties.
  • The validation sets for the MLR model generates R2 values > 0.8, indicating a good representation of the data in each case.
  • The model has been tested by predicting behaviour of two new powders, and has successfully predicted process behaviour with R2 > 0.75 in each case.

It is therefore clear that this type of evaluation, when using suitable range of powders, can quickly produce a simple and robust model.

The testing of additional materials can be used to further improve the reliability of the model and will allow the equipment manufacturers to accurately predict feed rates for new materials based on a small number of measured powder characteristics.

References

[1] E. W. Merrow. A Quantitative Assessment of R&D Requirements for Solids Processing Technology, The Rand Corporation, (1986) R-3216-DOE/PSSP.

[2] T. Taylor. The Global Status of Bulk Solids Handling (2013), BMHB.

[3] B. Wu et al. Multiresolution analysis of pressure fluctuations in a gas–solids fluidized bed: Application to glass beads and polyethylene powder systems. Chemical Engineering Journal (2007), 131(1–3) 23-33.

[4] J.-G Rosenboom et al. Characterisation of lactose powder and granules for multivariate wet granulation modelling. Chemical Engineering Science (2015), 123(0) 395-405.

[5] Q.T., Zhou et al. Characterization of the surface properties of a model pharmaceutical fine powder modified with a pharmaceutical lubricant to improve flow via a mechanical dry coating approach. J Pharm Sci (2011), 100(8) 3421-30.

[6] A. W. Jenike. Storage and Flow of Solids (1964), University of Utah, Bulletin 123.

[7] R. Freeman. Powder Technology (2007), 174 25-33.

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