(T1530-11-65) Developing a Spray Flux Equation for a Semi-Continuous Fluid Bed Granulation System

Purpose: Wet granulation (WG) is commonly used to improve physical characteristics of challenging powder formulations (flowability, compressibility, and content uniformity). Recognizing the well-established benefits of batch and continuous, a state-of-the-art commercial scale fluid bed granulation (FBG) system (SL2) was recently implemented, as part of a semi-continuous WG platform (Figure 1). To enable early formulation and process development with limited material availability, a lab-scale FBG unit (SL1) was also implemented, thus requiring an appropriate scale-up approach. Litster (2003) proposed the use of regime maps for scale up of wet granulation processes by first quantifying the three rate processes of granulation: wetting and nucleation, growth and consolidation, and breakage and attrition [1]. Dimensionless spray flux (ψ_a in Equation 1) is a simple scaling term for high shear wet granulation (HSWG) processes which is defined by the ratio of wetted area covered by the nozzle to the spray area in the nucleation zone (Hapgood et al., 2003), describing a 2-dimensional phenomenon.

ψ_a = 3V / 2Ad_d               (Equation 1)

In Equation 1, V is the volumetric spray rate, A is the powder flux through the spray zone, and d_d is the diameter of the spray droplet [2]. The purpose of this work is to adapt the concept of spray flux for a FBG process to enable the manipulation of granule characteristics and guide a regime map-based scale up.

Methods: In this study, 17 granulations were performed at lab scale and 15 granulations at commercial scale with varied process and design inputs. Micronized APAP was selected as a model API in a challenging MCC-based high drug load formulation (DL ≥ 40%). In a separate study, the spray droplet size and spray area were measured at varying spray distances, polymers, binder concentrations, spray air cap diameters, spray rates, and atomizing air pressures at both granulation scales. Statistical models were built to predict spray droplet size and spray area. The workflow for calculating spray flux is described in Figure 2.

Results: The proposed spray flux for FBG is an empirically derived equation that considers influential process and design parameters. Specifically, when considering the original spray flux equation proposed by Hapgood, the spray rate, binder droplet volume, spray area, and jet velocity in the spray zone were found to be significant. Spray flux for a FBG process should be proportional with spray rate and droplet size, and inversely proportional to spray area and jet velocity. The equation for spray flux, ψ_FB, is proposed below:

ψ_FB = V x V_d / A x U_e              (Equation 2)

where V is the volumetric spray rate, V_d is the average droplet volume, A is the spray area, and U_e is the effective velocity. The average droplet volume and spray area terms are generated from the statistical model stated above and the effective velocity is calculated from the combination of atomization pressure and the inlet air flow rate. First, the jet velocity of the inlet air flow through the disk jet is calculated by Equation 3:

U_jet = Q/A                  (Equation 3)

where U_jet is the jet velocity, Q is the volumetric flow rate, and A is the open area of the disk jet. Next, the jet velocity contributions from the atomization air within the spray zone is considered. In lieu of computationally intensive fluid dynamics-based modeling of air velocity, the velocity contribution from the spray air is modeled as a compressible fluid flowing through a frictionless nozzle [3]. A decay factor is applied to the combined jet velocity contributions from the spray air and the inlet air resulting in the effective velocity, U_e [4]. The resulting spray flux ψ_FB was calculated for each batch (Equation 2) and was plotted against particle size in Figure 3, along with a logarithmic regression trendline. The regressions show agreement with the actual particle size (R2 = 0.57-0.76) indicating that ψFB may be used as a tool for enabling process development. Importantly, the proposed spray flux is not dimensionless, thus, a notable gap is observed across scales.

Conclusion: In this work, an equation is proposed for spray flux which combines several key variables in FBG. The correlation of ψ_FB with granule particle sizes across lab and commercial scales indicates its potential for manipulating granule characteristics and enabling process development.

References: 1. Litster, J.D. “Scaleup of wet granulation processes: Science not art.” Powder Technology, vol. 130, no. 1–3, pp. 35–40, 2003.
2. Hapgood, Karen P., et al. “Nucleation regime map for liquid bound granules.” AIChE Journal, vol. 49, no. 2, pp. 350–361, 2003.
3. Green, Don W., and Robert H. Perry. Perry’s Chemical Engineers’ Handbook (8th Edition). McGraw-Hill Professional Publishing, 2007.
4. Koleilat, L., et al. “Flow field analysis of a toroidal flow fluidized bed granulator,” Chemical Engineering Research and Design, 208 (2024) 359-368.

Figure 1.

Figure 2.

Figure 3.