(498c) Predicting Filtration Performance By Studying the Pore Network of the Filter Cake: The Case of Needle-like Crystals

Filtration is extensively used in pharmaceutical manufacturing to recover the crystals of active ingredients and intermediates. This operation is often a slow processing step, accounting for a substantial quota of the process time. Furthermore, its design requires extensive experimental investigations at different scales as the impact of most driving factors is not sufficiently well understood to allow quantitative modeling of the process [1]. The structure of the filter cake is a result of the packing of its building blocks, i.e., the crystals and the way they arrange within the structure. The resulting network of pores ultimately affects the filtrate flow, hence the processing time. Here, we propose a combined modelling and experimental strategy to quantitatively understand the packing of powders based on their particle size and shape distributions. Needle-like crystals are here chosen as case study due to their extensive presence in pharmaceutical manufacturing [2,3]. Our results show how the structure of the cake can be linked to the performance of the filtration unit and therefore used to predict filtration times.

Methods

In this work we present a computational methodology to simulate the cake formation of needle-like crystals and to determine the filtration performance of the cake. Monte Carlo sampling is used to simulate the pressure driven packing of crystals. The spherocylinder, i.e. a cylinder capped by hemispheres at each end, is used as model shape [4]. Systems with statistically relevant number of particles and with polydispersities that resemble experimental distributions are used [5]. A graphical example of a filter cake produced with such methodology is presented in Fig.1(a).

We also provide an experimental counterpart to analyze filter cake properties and to validate the simulation protocol. For this purpose, X-ray tomography is used in this work to determine the structure of the pore space and how this develops along the cake [6]. Furthermore, an in-house segmentation algorithm is used to identify the shape, positions and orientation of individual needle-like crystals forming the experimental cake structure. Fig. 1 b. presents a small section of a real filter cake and shows the segmented single particles with different colors.

The structure of the pore space that forms inside filter cakes, both experimental and simulated, is then represented through a pore-network model [7,8]. Within pore network modeling, the connectivity of the pores is approximated via cylindrical channels, namely the throats, whose flow properties can be easily estimated using the Hagen-Poiseuille equation. An example of how the pores are distributed and interconnected inside the filter cake is presented in Fig. 2. This approach allows us to determine the permeability of the structure and therefore the filtration time.

Results

The modeling and experimental methodology described above has been used to evaluate the filtration dependency on particle morphology for a series of compounds, some of which taken from current development projects of AstraZeneca. The results collected confirm the strong dependency of filtration performance on particle morphology. The ability of these simulation routines to account for diverse particle size and shape distributions enables us to explore the effect of polydispersity on cake structure. Polydispersity appears to have a substantial effect on cake porosity, comparable to the one of the particle aspect ratio. This highlights that size control strategies employed during crystallization can have a tremendous impact on filtration time and that crystallization control is paramount.

The simulation strategy proposed in this work has been applied to investigate the packing of crystals of β L-Glutamic Acid with known particle size and shape distributions (determined in a previous experimental work [1]). The outcome of this investigation is reported in Fig. 3 [5]. The porosity of the simulated cake structures is compared to the one of the experimental cakes. It can be observed in Fig. 3(a) how both datasets follow the same trend, but that there is a constant offset between the two. The linear relation between the two (R²=0.93) is further highlighted by the parity plot in Fig. 3(b). This confirms that the model is able to accurately predict the porosity trend using exclusively information about the particle size and shape distributions. The constant shift between the datasets is likely caused by the fact that we are simulating smooth spherocylinders that have a significantly different morphology and surface roughness compared to real faceted crystals. Furthermore, our simulations do not cover substance and system-specific properties (particle-particle and particle-solvent interactions).

Comparisons between simulation and experimental results also highlight that the porosity and permeability of the filter cakes are not directly related to each other. Our efforts using pore network modeling show that the properties of the filter cake structure (i.e., the throats sizes, their distribution and interconnectivity) play a vital role in determining the permeability as well. Using our combined approach of simulating packings and then processing them with the help of a pore network model, however, allows us to predict the permeability trend in dependence of the particle size and shape distributions of the underlying powders.

Conclusions and outlook

The modeling protocol presented here sheds light on the crucial importance of the polydispersity of crystal populations on filtration performance. It also shows its ability to successfully predict the porosity of real cakes of crystals. Quantitatively knowing a priori the filterability of a population of crystals will ultimately allow pinpointing the optimal distribution of particle size and shape to minimize filtration time. This could then be used as a decision criterion in the process development phase where the gain in filtration time should be counter-weighed with the effort required in the crystallization process to obtain a tailored particle size distribution. Our contribution therefore opens up new avenues to integrate different unit operations (crystallization and filtration) into an overall optimized process with high productivity.

References

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