Abstract

Dimensionless analytical models for cylindrical pans under fixed bed conditions were developed that provided mechanistic relationships between material, equipment, and process parameters; and coating uniformity for development- and production-scale processes in batch and continuous operation. The batch coating model was verified with the exact analytical solution derived using the binomial distribution and was found to agree well with literature data. The models were then used to provide insights into formulation changes that resulted in higher coating uniformity for batch and continuous coating processes. A stochastic model was used to check the validity of the non-cylindrical pans and dynamic bed conditions. Both analytical and practical solutions for bridging coating performances between batch and continuous processes, and different formulations are presented.

Extended Abstract

The main goal of a tablet coating process is to arrive at processing conditions that result in high-quality, evenly coated tablets. It follows that the control strategy for coating processes should be the coating uniformity endpoint but, apart from the drug-layering process, this is rarely done in the industry largely due to a lack of knowledge and/or the high cost of coating uniformity characterization. This work was undertaken to provide an analytical comparison for easier visualization of performance differences between batch and continuous coating processes, as well as between development-scale and production-scale processes for seamless technology transfers. This is achieved through derivations of dimensionless mechanistic models by applying simplification to a few process/equipment parameters provided in a coating uniformity simulation patent (Choi, 2009).

Model Derivation

Statistical and analytical coating uniformity models were derived based on the coating schematics shown in Figures 1 and 2 for the batch and continuous mode of operation, respectively. The models assume the same quantity of coating is received per pass through the coating zone and the probability of entering the coating zone per cycle is x_c. This assumption proved to be a good approximation regardless of the shape of the coating distribution since all approach normal distribution with an increasing number of cycles according to the central limit theorem.

The exact analytical models were derived by summing all probabilities of tablets passing through the coating zone. The resulting binomial distribution models for the batch and continuous (see Choi and Meisen, 1997) coating processes, respectively, were:

Equation (see attachment) (1)

And Equation (see attachment) (2)

The statistical model for the batch coating schematic shown in Figure 1 was derived using the central limit theorem as follows:

Equation (see attachment) (3)

Substituting the geometric relationship for a cylindrical pan shown in Figure 3; assuming a static bed; and using the tablet wall velocity relationship given by Chen et al. (2010); Equation 3 could be expressed as

Equation (see attachment) (4)

where Equation (see attachment) (5)

and Equation (see attachment) (6)

Results

The exact analytical model (Equation 1) results were indistinguishable from those of the statistical model (Equation 3); therefore, Equations 1 and 3 are considered the same. The statistical model (Equation 4) agreed well with the Chen et al. data: the bed loading had the index of 0.58 compared with 0.5 in both Pandey et al. (2006) and Chen et al. (2010). The model predicted 3.85% compared to the experimental result of 3.8%ⁱⁱ when the pan speed was changed. The effect of tablet diameter could be matched exactly to the experimental data (Chen et al., 2010). The statistical model, by using a formulation coefficient for x_c, also predicted the higher coating uniformity results seen in a high-solids-load coating formulation (Karan et al., 2019) for batch and continuous coating processes.

To test the validity of the assumptions using static bed and cylindrical pan, stochastic simulations for a non-cylindrical pan and dynamic bed were conducted. Stochastic simulations of a 60” pan with 6” cone extensions on either side pan showed no discernable difference in coating uniformity from that of a cylindrical pan with the same diameter. The stochastic simulations showed 5% increase in coating uniformity for a 22% weight gain while the statistical model gave a 4% difference between the initial and the final bed size with 22% weight gain.

Despite the simplicity of assumptions used, the models derived in this work agreed well with the literature data and stochastic simulations.

Implications

The implications of this work is that the analytical models can be used to select and monitor coating uniformity, typically expressed in relative standard deviation or Acceptance Value, as the critical quality attribute to ensure the desired performance in a manufacturing control strategy for both functional and non-functional tablet coating processes.

For process bridging, the models can be used to calculate the relationship between different scales of equipment as well as between batch and continuous coating processes. Figure 5 shows an example of how the coating time needs to be adjusted with increasing pan diameter for the same relative bed loading and spray coverage. Figure 6 shows the characteristics of continuous coating design that is needed to match the coating uniformity of batch coating process.

Symbols

d_p tablet diameter, Sauter or surface-volume diameter used

D pan diameter

F_B coating distribution for the batch process

F_C coating distribution for the continuous process

h bed height

i denotes the position in the number of cycles or the number of passes through the spray zone

k coefficient

n number of cycles

P_i probability of i

RSD relative standard deviation

x_c probability of tablet going through the spray zone

x_e exit probability of tablets in continuous processes

Δ depth of the spray zone

_φ pan rotational speed

σ population standard deviation

θ angle shown in Figure 1

_θΔ angle accounting for the thickness of the coating zone depth

Ï„ total coating time

References

Chen, W., Chang, S-Y, Kiang, S., Marchut, A., Lyngberg, O., Wang, J., Rao, V., Desai, D., Stamato, H., and Early, W., “Modeling of Pan Coating Processes: Prediction of Tablet Content Uniformity and Determination of Critical Process Parameters”, J Pharm. Sci., 99 (7), July, 2010.

Choi, M., “Pan Coating Simulation for Determining Tablet Coating Uniformity”, US Patent #10/981,812, December, 2009.

Choi, M. and Meisen, A., “Sulfur Coating of Urea in Shallow Spouted Beds”, Chemical Engineering Science, v52, p1073 (1997).

Karan, K., Hach, R., Lenick, L., During, T., Marjeram, J., Stevenson, G., Kuczynski, C., and Botnick, M. “Evaluation of Tablets Coated in a High Throughput Continuous Coater Using an Ultra-high Solids Film Coating System”, Poster T1330-08-56, presented at the Annual AAPS Meeting & Convention in San Antonio (2019).

Pandey, P., Katakdaunde, M., and Turton, R., “Modeling Weight Variability in a Pan Coating Process Using Monte Carlo Simulations”, AAPS PharmSciTech, 7 (4), 2006.