(428f) A Surrogate-Based Topological Compartment Model for Counter-Current Spray Dryers.

Surrogate-based topological compartment models have been widely used to predict the internal distribution of properties in a unit, providing comparable accuracy to CFD models but with less computational cost. In the area of particle technology, the approach has gained attention for aggregating detailed physics into process models in units such as blenders, coaters, and fluidized beds [1]. However, the use of compartment models in spray drying has been limited. To date, only hybrid data-driven and first principles-based models have been proposed for counter-current spray dryers. The two most relevant models have been developed by Process System Enterprise (PSE) [2] and Ali et al. [3]. In both cases, the fluxes were extracted from a CFD-DPM model and used as boundary conditions to a first-principles model incorporating mass and energy balances for the compartment. The main difference between the two approaches lies in the generation of the compartments and the drying model used. PSE uses homogeneous zones with different diffusion-based models available. Meanwhile Ali et al. [3] prosed a fixed compartmentalization with a combined diffusion and boiling model. The results of both showed low error against the CFD-DPM model that was used for the construction. However, a change in the operating conditions modifies the structure and fluxes, making it necessary to rerun the CFD model every time and thus limiting the reapplication of the model. To overcome these drawbacks, in this work a surrogate-based compartment model is proposed as an alternative.

The surrogate-based compartment model has been generated following a step-by-step validation procedure with a decoupling of the momentum, heat, and mass transfer mechanisms as presented in [4]. In the first stage, the distribution and size of each of the zones have been identified based on the volume fraction of the particles. These zones presented in Figure 1 have been made flexible using surrogate models. In the second stage, the fluxes of particles and air between the compartments and the residence time of the particles have been modeled. Unlike previous works, a new numerical procedure has been developed for surrogates based on dimensionless groups. The methodology is based on a three-step algorithm that first selects the necessary dimensionless groups based on minimizing the Bayesian Information Criteria. The second step models the mass fluxes based on these dimensionless groups in the form of Eq. (1) and evaluates the quality of the model; an alternative statistical model is proposed if the model is not good enough. In the same way, the third step of the process generates the surrogate models for the energy fluxes, which have been evaluated under different operating conditions including the heat and mass transfer model defined as in [5]. These surrogate models have been implemented into the final model where the discrete phase is defined by means of a multi-dimensional population balance. The single droplet drying model for the particles includes diffusion and boiling mechanisms as in [5] and it is implemented employing finite differences. The model is finally solved by defining a two-way iterative scheme in Python.

F=Ar^a·Re^b·...·St^c (1)

The model has been validated by decoupling the physics and evaluating it step-by-step. The validation against the momentum of the particles is carried out with the mean residence time of monodispersed injections. The prediction of the mean residence time shows a relative root mean square error of 7%. The validation including the heat and mass transfer is carried out with the temperature at the entrance and exit of every compartment showing an average error of 5 K and a maximum of 11 K in all the compartments evaluated. Even though the differences in predicting the mean residence time and the temperature are low, the errors are still too high to implement the agglomeration and breakage kernels as characterized in the CFD-DPM model. The relative time at which the discrete phase has a wet surface only represents around 1.6% of the total mean residence time. This high level of accuracy required results in too small feasible region for maintaining the surrogate models of the kernels. Thus, the implementation of these kernels into process or compartment models requires at least the use of a data-driven model as an intermediate step and may not yield a significant improvement in the reduction of computational cost.

References

[1] Rogers, A. Ierapetritou, M. (2015) Challenges and opportunities in modeling pharmaceutical manufacturing processes. Computers & Chemical Engineering, 81, 32-39.

[2] Process System Enterprise (2020) Mulizonal tool and Counter-current spray drying model. gProms® Formulated Products.

[3] Ali, M. Mahmud, T. Heggs, P.J. Ghadiri, M. (2020) Zonal modelling of a counter-current spray drying tower. Chemical Engineering Research and Design, 155, 180-199.

[4] Hernández, B. Fraser, B. Martin de Juan, L. Martin, M. (2018) Computational fluid dynamics (CFD) modeling of swirling flows in industrial counter-current spray-drying towers under fouling conditions. Industrial & Engineering Chemistry Research, 57 (35), 11988-12002.

[5] Hernandez, B. Mondragon, R. Pinto, M.A. Hernandez, L. Julia, J.E. Jarque, J.C. Chiva, S. Martin, M. (2021) Single droplet drying of detergents: Experimentation and modelling. Particuology, 58, 35-47.