# Program of our Summer School 2019

“Particulate Systems: From Theory to Application”

.................................................................................................

## Monday, August 26, 2019

9:00 – 9:15

Opening of the Summer School**Andreas Seidel-Morgenstern** (Max Planck Institute for Dynamics of Complex Technical Systems)

9.15 – 10:45

"Introduction to population balance modeling of particulate processes"**Achim Kienle** (Otto-von-Guericke University Magdeburg)

11.15 – 12.45

"An introduction to Fluid Dynamics with a view towards particulate systems"

**Dominique Thévenin** (Otto-von-Guericke-University Magdeburg)

*12:45 - 14:00*

*Lunch*

14:00 - 15.00

"Population Balances and Computational Fluid Dynamics for Particulate systems"

**Daniele Marchisio **(Politechnico Torino)

15.00 – 17.30

"Quadrature-based Moments Methods: a Simple Tutorial"

**Antonio Buffo **(Politechnico Torino)

**18.00 Barbecue at the MPI Garden**

.................................................................................................

## Tuesday, August 27, 2019

8.30 – 12.30

"Brownian HydroDynamics of Colloidal Suspensions"

**Aleksandar Donev** (New York University)

*Optional for CORE students:*

*08.30 – 12.30 ** "Soft Skills in Scientific Teams" ** Dominik Frisch (FISCHERFRISCH*)

*12:30 - 14:00*

*Lunch*

14:00 - 15.30

"Numerical Techniques for Particle Aggregation"

**Sabine Le Borne **(Hamburg University of Technology)

*Optional for CORE students:*

*14.00 – 15.30*

*“Title TBC” *

* Martin Gerlach, Sabine Kirschtowski (OvGU)*

**19.30 – 21.30 Guided City Tour through Magdeburg**

.................................................................................................

## Wednesday, August 28, 2019

8.30 – 10.00

"Solid-liquid Phase Diagrams: Application and Impact on Material's Phase Behavior"

**Heike Lorenz** (Max Planck Institute for Dynamics of Complex Technical Systems)

10.30 – 12.00

"Mathematical Modeling, Real-time Sensing, and Parameter Estimation for Protein Crystallization in Droplet-based Systems"

**Richard Braatz** (Massachusetts Institute of Technology)

*12:00 – 13:00*

*Lunch*

13.00 – 14.30

"Modeling, Sensing, Design, and Control of the Continuous Manufacturing of Protein Crystals"

**Richard Braatz** (Massachusetts Institute of Technology)

**16.00 – 18.00 Canoe Excursion at the Elbe River **

**and **

**19.00 Summer School Dinner**

.................................................................................................

## Thursday, August 29, 2019

8.30 –10.00

"Overcoming Pharmaceutical Formulation Challenges with the Help of Colloidal Drug Delivery Systems"

**Heike Bunjes** (University of Technology Braunschweig)

10.30 – 12.00

"Spray Fluidized Bed Granulation and Coating"**Andreas Bück ** (Friedrich-Alexander-University of Erlangen-Nürnberg | FAU)

*12.00 – 13.00Lunch*

13.00 – 14.30

"Spray Fluidized Bed Agglomeration"

**Evangelos Tsotsas ** (Otto-von-Guericke University)

15.00 – 16.00

"From Process to Structure – Modeling in Polymer Reaction Engineering of Different Scales"

**Markus Busch ** (University of Technology Darmstadt)

16.30 – 18.00

"Modular Modeling, Parameter Estimation and Optimization in Polymer Reaction Engineering"

**Michael Wulkow ** (CiT GmbH Rastede)

.................................................................................................

## Friday, August 30, 2019

8.30 – 10.00

"Industrial Polymerization and Crystallization: How Theory helps Solving Practical Problems (and how not)"

**Christian Borchert **(BASF)

10.30 – 12.00

"Establishing API Physical Property Requirements and Developments of the Crystallization Processes to achieve them"** Chris Burcham **(Ely Lilly, Indianapolis)

*12.00 – 13.00*

*Lunch*

13.00 – 14.30

"Development of a Pharmaceutical Continuous Crystallization Processes"** Chris Burcham **(Ely Lilly, Indianapolis)

14.30

Final Remarks**Andreas Seidel-Morgenstern** (Max Planck Institute for Dynamics of Complex Technical Systems)

.................................................................................................

## Abstracts of the lectures (current status)

**Dominique Thévenin**

*„An introduction to Fluid Dynamics with a view towards particulate systems“*

Most particulate systems in process engineering involve a continuous phase - either gas or liquid - that will control to a large extent the physicochemical behaviour of the resulting multiphase flow.

The purpose of this introductory lecture is:

- to recall the most important properties of flows considered as a continuum;

- to introduce relevant variables, parameters and non-dimensional quantities;

- to discuss the intrinsic multi-scale nature of multiphase flows;

- to present open scientific challenges associated to this configuration;

- to briefly discuss tools allowing detailed investigations of such flows.

**Daniele Marchisio**

**"Population balances and computational fluid dynamics for particulate systems"**

With this lecture the derivation of the two-fluid (and multi-fluid) model governing equations from the population balance equation is explained. The derivation requires the use of the method of moments and of quadrature approximations to overcome the closure problem.

** Antonio Buffo**

** "Quadrature-based Moments Methods: a Simple Tutorial” **

*In this session a few significant examples regarding the application of the Quadrature-Based Moments Methods for the description of simplified multiphase systems are considered.*

The description of multiphase is often carried out with the implicit assumption that the evolution of the disperse phase is completely separated from the fluid dynamics and phase-coupling issues, considering a non-physical population of elements (e.g., bubbles, drops and particles) with a monodisperse distribution of size, velocity and composition. Otherwise, in realistic systems, the disperse phase is polydispersed, namely it is constituted by elements characterized by distributions of properties; the momentum, mass and energy phase coupling can be successfully described only if the existence of these distributions is accounted for, by considering a Generalized Population Balance Equation (GPBE), a multidimensional integro-differential equation that properly descibes the interactions between the continuous phase and the disperse elements.

A suitable approach for solving the GPBE is represented by the Quadrature-Based Moments Methods (QBMM), where the evolution of the relevant properties are recovered by considering some lower order moments of the distribution. All the methods belonging to this family assume a particular shape of the element distribution: a

*N*-node quadrature formula, namely a summation of

*N*weighted kernel density functions, each centered on an abscissa. The most commonly employed kernel density function is the Dirac delta function: Quadrature Method of Moments (QMOM) and Direct Quadrature Method of Moments (DQMOM) are based on this assumption, leading to the solution of moment transport equations (in the case of QMOM) or the solution of the transport equation for the quadrature itself (in the case of DQMOM). Moreover, the extension of the QMOM to multivariate problems is known under the name of Conditional Quadrature Method of Moments (CQMOM). Lastly, the Extended Quadrature Method of Moments (EQMOM) is instead useful when the physical problem under investigation requires the assumption of a continuous distribution, namely when evaporation or dissolution of elements occurs.

In this tutorial, we will see the application of some of these methods to a few practical problems. These examples will show the importance of preserving some mathematical properties of the moments of the distribution, such as moment realizability and boundedness, using proper numerical schemes.

**Sabine Le Borne **

** "Numerical techniques for Particle Aggregation"**

A variety of production processes in chemistry and biotechnology are concerned with particles dispersed in an environmental phase. The particle distribution is mathematically described by the solution of population balance equations of integro-differential type. These equations include terms to model processes like nucleation, growth, aggregation and breakage of particles. In this presentation, we will focus on the aggregation term which models the collision of two particles, resulting in the formation of a single new particle in exchange for the original two particles. Mathematically, it is described in terms of a convolution integral that is numerically expensive to evaluate and often dominates the total simulation cost.

We begin with the univariate case, i.e. only a single particle property, often its mass, is considered. Starting with the popular fixed pivot method, we describe various discretization schemes and their subsequent numerical evaluation. We will discuss aspects such as grid refinement (e.g., uniform, locally refined, structured or unstructured grids), order of discretization, and fast Fourier transformation (FFT) based fast evaluation methods which, if the aggregation kernel can be represented or approximated in separable form, allow to reduce the computational complexity from quadratic O(n^{2}) to almost linear O(n log n) order where n denotes the number of unknowns (i.e., the number of considered particle size classes).

Next, we proceed to the multivariate case in which a particle may be characterized by multiple properties, e.g. mass, porosity, concentration of some substance, etc. In our model, we assume all considered properties to be additive, i.e., all properties can be measured by some positive real number, and aggregation of two particles leads to the addition of their respective values for the resulting particle. Many of the methods for the univariate case can be (and have been) generalized to the multivariate case where they suffer from the so-called curse of dimensionality - their numerical complexity grows exponentially and quickly reaches the limits of modern machines both with respect to the required storage and computational time. We introduce some modern approaches that address and even may resolve these difficulties, including the application of multidimensional FFT methods (again requiring a separable aggregation kernel), parallelization, and modern tensor formats for the multivariate density functions.

We will provide numerical illustrations for many of the introduced methods with our focus on their numerical performance.

**Heike Lorenz**

* "Solid-Liquid Phase Diagrams: Application and Impact on Material’s Phase Behavior"* Solid-liquid equilibria (SLE) form the thermodynamic basis of crystallization processes and consequently are of fundamental importance for crystallization process design in the related pharmaceutical, fine and bulk chemical industries. Phase diagrams as graphical representation of SLE data provide essential information on feasibility of a certain crystallization task, on the maximum theoretical yield and purity achievable, on number and identity of solid phases occurring in the system and moreover, facilitate identification of suitable approaches to solve a particular crystallization problem [1]. Often, in addition, liquid-liquid and solid-solid equilibria (LLE and SSE) interfere with SLE and thus complicate the phase behaviour in a system.

In the lecture, first, the fundamentals of solubility equilibria are introduced and the main types of phase diagrams representing SLE are depicted. The major part of the talk is concerned with equilibria between solid(s) and a classical solvent since crystallization in presence of a solvent (or solvent mixture) is most frequently applied in industrial crystallization and, with water as solvent also of particular significance in natural processes and their understanding. The lecture thus addresses solubility curves with their typical features, binary compound/solvent phase diagrams and outlines solubility phase diagrams in ternary and quaternary systems with respect to representation and usage for separation purposes.

In the tutorial part, the understanding of such phase diagrams together with the consequences on phase behaviour and application-related properties of a certain material will be deepened. One example will be a salt/water system of interest as latent heat storage material.

References

[1] Lorenz, H.

*Solubility and Solution Equilibria in Crystallization*, In W. Beckmann (Ed.),

*Crystallization: Basic Concepts and Industrial Applications*, Wiley-VCH: Weinheim, 2013, pp. 35–74.

**Andreas Bück**

** "Coating of particulate solids"**

Granulation, coating and layering are important particle formation processes used in many industries, for example in the food and feed, pharmaceutical and chemical industry. Coating of a core particle with a second solid can be used to design different product properties, for instance release rates of ingredients (APIs in a tablet), to provide required experiences in taste, or to design optical responses of a material.

In this lecture, three different approaches to coating of particulate solids are presented in a unified way: dry coating, chemical vapour deposition and spray coating, with the focus on the latter process. Main principles and major process technologies are presented. Additionally, ways to design particle and product properties by choice of process parameters will be presented and explained. Process models based on population balance equations will be introduced and it will be shown how these can be used to establish regime maps.

Interspersed in the lecture are small examples and excercises that further deepen the understanding of the presented material.

**Evangelos Tsotsas**

**"Spray Fluidized Bed Agglomeration"**

Spray fluidized bed agglomeration is a key process for the industrial production of foods, pharmaceuticals and chemicals with superior instant and dosing properties. In the classical view, it is described mathematically by aggregation population balance equations (PBE). Significant research is still going on to improve the accuracy and speed of numerical solutions of such equations as well as to advance our ability of solving the inverse problem, i.e. of identifying the aggregation kernel or rate on the basis of experimental results. Despite of recent progresses with advanced identifications methods, this inverse problem remains difficult. Conventionally, a size-dependent part of the kernel is set by trial-and-error to one out of several proposed forms, whereas the pre-factor is fitted to typically time-dependent expressions (instead of constant factors). Since this is not satisfactory, completely different approaches have also been developed in the last decade. One of them uses (instead of the continuous PBE model) stochastic micro-scale models, often denoted by Monte-Carlo models. In this way experimental data can be described with minimal need for fitting. Moreover, the discrete models have been used to develop new population dynamics approaches, which turned out to be of superior predictive capacity because of their multivariate nature (the internal coordinate of particle size is fully resolved, whereas many other internal coordinates that refer to, among others, wetting and drying are captured by average values). Additionally, agglomerate morphology has been studied by 3D-imaging and descriptor analysis, and interrelations of morphology to operating conditions (especially to drying conditions) have been revealed. Further progresses that will be reviewed refer to the implementation of morphology into the process model, the implementation of agglomerate breakage, and the investigation of both, agglomeration with and without binder.

**Chris Burcham**

*"Establishing API Physical Property Requirements and Development of the Crystallization Processes to Achieve Them"*

The manufacture of small molecule pharmaceuticals commences with the multi-step synthesis of the active pharmaceutical ingredient (API) from commercially available starting materials through to the isolated drug substance that is then incorporated into the final dosage form. Crystallization is a key unit operation as it provides the following:

- The ability to isolate both the drug substance as well as intermediates throughout the synthesis.
- Separation of the desired product from process or other related impurities, offering a product typically in excess of 99% purity.
- Engineered physical properties designed to meet the processing or performance attributes needed for downstream processing or patient performance, respectively.

In recent years the third point has been an area of great focus within the manufacture of active pharmaceutical ingredients utilizing particle engineering to tailor the physical properties of the isolated product. This has resulted in powders that offer improvements to downstream unit operations, such as filtration or drying of the crystalline material as part of the drug substance manufacturing process. Particle engineering has also provided for improvements to the drug product manufacturing process, by providing for drug substance with improved powder flow properties or increased bulk density, both of which aid powder mixing and tableting operations while ensuring product performance is not compromised.

This session will focus on the development process and workflow necessary to deliver on these objectives, starting with salt and form selection through to technology transfer and scale-up of the final commercial crystallization process. Considerations to ensure bioavailability of the drug substance and the content uniformity of the drug substance in the final dosage while will be presented. The impact of physical properties of the drug substance on filtration and tablet manufacture will also be illustrated. Case studies have been selected to highlight the development process and application of the workflow.

**Chris Burcham**

*"Development of a Pharmaceutical Continuous Crystallization Processes"*

Active pharmaceutical ingredients have historically been produced using batch manufacturing processes. Over the last decade, initiatives by regulatory agencies as well as efficiency drivers have focused the pharmaceutical industry to consider continuous processing in the development of manufacturing processes for innovative compounds in clinical development. Utilization of flow chemistry has afforded opportunities to implement continuous crystallization in drug substance manufacturing. The small lot sizes, purity, and control of physical properties create unique challenges in development of a continuous crystallization process. However, with these challenges comes opportunity. Both the challenges and advantages of continuous crystallization will be presented in this talk.

Due to material and time constraints, experimentation alone often cannot provide a means to design and optimize a continuous crystallization process. In the crystallization of active pharmaceutical ingredients, specific particle size distributions (PSD) requirements are often a crucial to the manufacturability and bioavailability of the final drug (solid dosage form). The combination of batch experimentation, modeling and optimization are utilized to decrease material consumption during develop while also reducing the develop cycle time to ensure the desired PSD is achieved.

In this session, examples of the experimental workflow needed to provide the data necessary to regress kinetic parameters associated with crystallization; nucleation, growth and agglomeration, are provided. The examples will highlight both the experimental and computation aspects of the work and subsequent refinements as continuous crystallization results are collected later in development.

Once a population balance model is formulated, it is utilized as a means for process optimization of continuous crystallization process. Process optimization is subject to constraints on the processing conditions (e.g. fouling, or minimum filtration rates) and on product performance constraints (e.g. bioavailability and content uniformity) to provide the optimal processing conditions. This session concludes with insights regarding the implementation of process optimization as a part of a proposed “universal” work flow for the design of continuous crystallizations.