Crystal size, shape, and conformational changes drive both the disappearance and reappearance of ritonavir polymorphs in the mill.

Organic compounds can crystallize in different forms known as polymorphs. Discovery and control of polymorphism is crucial to the pharmaceutical industry since different polymorphs can have significantly different physical properties which impacts their utilization in drug delivery. Certain polymorphs have been reported to 'disappear' from the physical world, irreversibly converting to new ones. These unwanted polymorph conversions, initially prevented by slow nucleation kinetics, are eventually observed driven by significant gains in thermodynamic stabilities. The most infamous of these cases is that of the HIV drug ritonavir (RVR): Once its reluctant form was unwillingly nucleated for the first time, its desired form could no longer be produced with the same manufacturing process. Here we show that RVR's extraordinary disappearing polymorph as well as its reluctant form can be consistently produced by ball-milling under different environmental conditions. We demonstrate that the significant difference in stability between its polymorphs can be changed and reversed in the mill-a process we show is driven by crystal size as well as crystal shape and conformational effects. We also show that those effects can be controlled through careful design of milling conditions since they dictate the kinetics of crystal breakage, dissolution, and growth processes that eventually lead to steady-state crystal sizes and shapes in the mill. This work highlights the huge potential of mechanochemistry in polymorph discovery of forms initially difficult to nucleate, recovery of disappearing polymorphs, and polymorph control of complex flexible drug compounds such as RVR

Graphical processing unit (GPU) acceleration for numerical solution of population balance models using high resolution finite volume algorithm

© 2016 Elsevier LtdPopulation balance modeling is a widely used approach to describe crystallization processes. It can be extended to multivariate cases where more internal coordinates i.e., particle properties such as multiple characteristic sizes, composition, purity, etc. can be used. The current study presents highly efficient fully discretized parallel implementation of the high resolution finite volume technique implemented on graphical processing units (GPUs) for the solution of single- and multi-dimensional population balance models (PBMs). The proposed GPU-PBM is implemented using CUDA C++ code for GPU calculations and provides a generic Matlab interface for easy application for scientific computing. The case studies demonstrate that the code running on the GPU is between 2–40 times faster than the compiled C++ code and 50–250 times faster than the standard MatLab implementation. This significant improvement in computational time enables the application of model-based control approaches in real time even in case of multidimensional population balance models

Nonlinear Model Predictive Control for Gas Antisolvent Recrystallization Process

학위논문(석사)--서울대학교 대학원 :공과대학 화학생물공학부,2013. 2. 이종민.Crystallization techniques have been played an important role for several decades in producing various chemical products such as polymers, dyes, pharmaceuticals, and explosives. It is also essentially used in separation and purification stages of petrochemical and fine-chemical industries. Conventional crystallization processes, however, have practical problems in that toxic waste solvent streams are inevitably produced in the process and some substances are contaminated with the solvent, deteriorating the purity. In this reason, novel crystallization processes using supercritical fluids have recently attracted much attention. They are environmentally acceptable due to the use of benign solution such as CO2, applicable to various solutes, and operated at mild conditions, 25℃ and 5-100 bar. These include rapid expansion of supercritical solution (RESS), gas antisolvent (GAS) process, and particles from gas-saturated solutions (PGSS). It is well known that GAS crystallization process attains a very rapid, essentially uniform and very high supersaturation upon reduction of the solid solubility in its solution with dissolution of antisolvent CO2. This owes to the two way mass transfer of CO2 and solvent, for dissolution of CO2 and evaporation of solvent, respectively. This facilitates uniform nucleation and almost instantaneous crystallization, which make the antisolvent crystallization a unique process resulting in the formation of ultra-fine particles with a narrow particle size distribution and controlled morphology. In this work, a dynamic model for GAS process is presented and control approach to obtain a desired particle size distribution (PSD) is proposed. At first, a mathematical model from a population balance model (PBM) is developed to describe PSD of GAS process. The developed GAS model consists of a partial differential equation (PDE), a set of ordinary differential equations (ODE), and algebraic equations associated with it. Thus, it requires a numerical discretization method to solve the PDE. A high resolution (HR) scheme is presented since it is rather simple to implement and more accurate than other discretization methods. Simulation results show the effect of CO2 addition rate on the final particle size distribution in the process. Control issues in GAS processes are quite challenging since the system is highly nonlinear and includes complex crystallization kinetics, nucleation and growth. Researchers have investigated the control of liquid antisolvent crystallization process to find optimal input profile, but the control for gas antisolvnet process has not been much tried yet. It is generally more difficult to control GAS process than liquid antisolvent process since the liquid-vapor phase equilibrium should be considered in the system model. A nonlinear model predictive control (MPC) strategy is proposed to control the particle size distribution of GAS process. Linear MPC, successive linearized MPC are applied to the system and the control results are compared.Abstract i 1. Introduction 1 1.1 Crystallization process in industry 1 1.2 Crystallization mechanism 2 1.3 Crystallization techniques using supercritical fluids 5 1.3.1 Rapid expansion of supercritical solutions (RESS) 5 1.3.2 Gas antisolvent process (GAS) 7 1.3.3 Particles from gas-saturated solutions (PGSS) 9 1.4 Control issues for crystallization process 10 1.5 Outline of the thesis 13 2. Experiment 14 2.1 Materials and equipments 15 2.2 Experimental results 18 3. Modeling and Simulation for GAS process 24 3.1 Population balance model 24 3.2 Mathematical model for GAS process 27 3.3 High resolution method for solving PDE 32 3.4 Simulation results 37 4. Nonlinear Model Predictive Control for GAS Process 42 4.1 Model predictive control algorithm 44 4.2 MPC results of GAS process 49 5. Concluding Remarks 54 Bibliography 56Maste

Numerical Study of Crystallization Process Using CFD Tools

Crystallization is the formation of solid particles within a homogenous phase. Crystallization is considered a last stage purification step in pharmaceutical, chemical, agrochemical and food industries. Crystallization is mostly used for separation of a pure product from an impure solution and the product formed is suitable for packing and marketing. Good yield and purity are important for crystallization; apart from it crystal size distribution also plays a vital role in the design of crystallization. The energy required for crystallization is less than distillation. The study is made on crystallization process of sucrose in a continuous rectangular flow chamber. The present work is aimed to compare the simulation results with experimental results and to study the parametric sensitivity on mean crystal diameter of sucrose and total crystal production with variation in inlet velocity of solution, inlet mass fraction of sucrose and wall temperature of crystallizer. The transient simulations are carried out to study the crystallization process. The simulation results when validated against experimental results are found to be consistent.The simulation results show that as the inlet mass fraction of sucrose is increased, then the mean crystal size and total crystal production are observed to be increased. The mean crystal size is increased and total crystal production is decreased with decrease in inlet velocity of solution. The mean crystal size is observed to be invariant with change in wall temperature of the crystallizer but the total crystal production is increased with increase in wall temperature

Modeling, optimization, and sensitivity analysis of a continuous multi-segment crystallizer for production of active pharmaceutical ingredients

We have investigated the simulation-based, steady-state optimization of a new type of crystallizer for the production of pharmaceuticals. The multi-segment, multi-addition plug-flow crystallizer (MSMA-PFC) offers better control over supersaturation in one dimension compared to a batch or stirred-tank crystallizer. Through use of a population balance framework, we have written the governing model equations of population balance and mass balance on the crystallizer segments. The solution of these equations was accomplished through either the method of moments or the finite volume method. The goal was to optimize the performance of the crystallizer with respect to certain quantities, such as maximizing the mean crystal size, minimizing the coefficient of variation, or minimizing the sum of the squared errors when attempting to hit a target distribution. Such optimizations are all highly nonconvex, necessitating the use of the genetic algorithm. Our results for the optimization of a process for crystallizing flufenamic acid showed improvement in crystal size over prior literature results. Through the use of a novel simultaneous design and control (SDC) methodology, we have further optimized the flowrates and crystallizer geometry in tandem.^ We have further investigated the robustness of this process and observe significant sensitivity to error in antisolvent flowrate, as well as the kinetic parameters of crystallization. We have lastly performed a parametric study on the use of the MSMA-PFC for in-situ dissolution of fine crystals back into solution. Fine crystals are a known processing difficulty in drug manufacture, thus motivating the development of a process that can eliminate them efficiently. Prior results for cooling crystallization indicated this to be possible. However, our results show little to no dissolution is used after optimizing the crystallizer, indicating the negative impact of adding pure solvent to the process (reduced concentration via dilution, and decreased residence time) outweighs the positive benefits of dissolving fines. The prior results for cooling crystallization did not possess this coupling between flowrate, residence time, and concentration, thus making fines dissolution significantly more beneficial for that process. We conclude that the success observed in hitting the target distribution has more to do with using multiple segments and having finer control over supersaturation than with the ability to go below solubility. Our results showed that excessive nucleation still overwhelms the MSMA-PFC for in-situ fines dissolution when nucleation is too high

Modeling of polythermal preferential crystallization

Die Bevorzugte Kristallisation ist ein kostengünstiges Verfahren zur Trennung von Enantiomerengemischen. Insbesondere in der Pharmazie wächst die Bedeutung der Trennung dieser speziellen Klasse von Isomeren. Trotz des relativ geringen apparativen Aufwandes wird das Verfahren in der industriellen Praxis selten angewendet. Eine Ursache könnte in der vermeintlichen Störungsanfälligkeit des kinetisch kontrollierten Trennprozesses liegen. Die vorliegende Arbeit leistet einen Beitrag zum Verständnis des Prozesses und bietet einen Leitfaden zur modellgestützten Prozessauslegung. Damit soll dazu beigetragen werden, dass die Bevorzugte Kristallisation stärker als bisher als alternatives Trennverfahren den Weg in die industrielle Praxis findet. Daneben können die verwendeten und entwickelten Methoden teilweise auch auf andere Prozess übertragen werden. Zunächst wird ein Konzept für die a priori Prozessevaluierung vorgestellt, dass auf Löslichkeitsdaten und metastabilen Breiten der betrachteten Stoffsysteme beruht. Die Anwendung dieses einfachen Konzeptes ermöglicht es, für zwei untersuchte Beispielstoffsysteme Prozessbedingungen zu identifizieren, bei denen ein Trennprozess Erfolg versprechend ist und eine maximale Ausbeute und/oder Produktivität erzielt werden kann. Die Prozessevaluierung wird dabei am Beispiel der Stoffsysteme DL-Threonin/Wasser (Konglomerat) und R,S-Mandelsäure/Wasser (verbindungsbildend) vorgenommen. Weiterhin wird am Beispiel des Stoffsystems DL-Threonin/Wasser, basieren auf dem Konzept der Populationsbilanzen, eine ausführlichere dynamische Modellierung vorgenommen. Unter Verwendung der gemessenen Daten von Trennprozessverläufen werden freie kinetische Parameter für die verwendeten Modelle abgeschätzt. Die Bewertung der Abschätzungsgüte erfolgt mit gängigen statistischen Methoden unter Verwendung der Fisher-Informationsmatrix sowie einen Bootstrap-Verfahrens. Zusätzliche Versuche werden mit Hilfe der entwickelten Modelle so geplant, dass sie ein Maximum an Information für die Identifizierung der kinetischen Parameter bieten (dynamisches experimentelles Design). Neben der Prozessmodellierung wird eine Online- und Inlineanalytik etabliert, die nach entsprechender Kalibrierung in der Lage ist, die untersuchten Prozesse sowohl hinsichtlich der Flüssigphasenzusammensetzung, als auch bezüglich der festen Phase zu verfolgen. Je nachdem, ob aus den Messungen Informationen bezüglich der Parikelgrößenverteilung vorhanden sind, können ein voll diskretisiertes oder ein auf die Momente der Verteilung reduziertes Modell gelöst werden. Das reduzierte Modell bietet den Vorteil geringerer Rechenzeit. Das entwickelte kinetische Modell wird einerseits in Matlab® implementiert, andererseits mit Hilfe eines kommerziellen Siumlationstools, Parsival®, gelöst. Der Vergleich der verschiedenen Simulationsansätze ermöglicht es für eine spezifische Anwendung die geeignete Simulationsstrategie auszuwählen. Abschließend wird ein in Parsival® implementiertes, parametrisiertes und validiertes Modell verwendet, um eine Prozessoptimierung hinsichtlich der Produktivität vorzunehmen

A comparative study of high resolution schemes for solving population balances in crystallization

This article demonstrates the applicability and usefulness of high resolution finite volume schemes for the solution of population balance equations (PBEs) in crystallization processes. The population balance equation is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models, the one independent variable represents the time, the other(s) are “property coordinate(s)”, e.g. the particle size in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes. These include crystallization, polymerization, emulsion and cell dynamics. The high resolution schemes were originally developed for compressible fluid dynamics. The schemes resolve sharp peaks and shock discontinuities on coarse girds, as well as avoid numerical diffusion and numerical dispersion. The schemes are derived for general purposes and can be applied to any hyperbolic model. Here, we test the schemes on the one-dimensional population balance models with nucleation and growth. The article mainly concentrates on the re-derivation of a high resolution scheme of Koren (Koren, B. (1993). A robust upwind discretization method for advection, diffusion and source terms. In C. B. Vreugdenhill, & B. Koren (Eds.), Numerical methods for advection–diffusion problems, Braunschweig: Vieweg Verlag, pp. 117–138 [vol. 45 of notes on numerical fluid mechanics, chapter 5]) which is then compared with other high resolution finite volume schemes. The numerical test cases reported in this paper show clear advantages of high resolutions schemes for the solution of population balances. ©2006 Elsevier Ltd. All rights reserved [accessed 2013 November 27th

Sensitivitätsanalyse und robustes Prozessdesign pharmazeutischer Herstellungsprozesse

The existence of parameter uncertainties(PU) limits model-based process design techniques. It also hinders the modernization of pharmaceutical manufacturing processes, which is necessitated for intensified market competition and Quality by Design (QbD) principles. Thus, in this thesis, proper approaches are proposed for efficient and effective sensitivity analysis and robust design of pharmaceutical processes. Moreover, the point estimate method (PEM) and polynomial chaos expansion (PCE) are further implemented for uncertainty propagation and quantification (UQ) in the proposed approaches. Global sensitivity analysis (GSA) provides quantitative measures on the influence of PU on process outputs over the entire parameter domain. Two GSA techniques are presented in detail and computed with the PCE. The results from case studies show that GSA is able to quantify the heterogeneity of the information in PU and model structure and parameter dependencies affects significantly the final GSA result as well as output variation. Frameworks for robust process design are introduced to alleviate the adverse effect of PU on process performance. The first robust design framework is developed based on the PEM. The proposed approach has high computational efficiency and is able to take parameter dependencies into account. Then, a novel approach, in which the Gaussian mixture distribution (GMD) concept is combined with PEM, is proposed to handle non-Gaussian distribution. The resulting GMD-PEM concept provides a better trade-off between process efficiency and probability of constraint violations than other approaches. The second robust design framework is based on the iterative back-off strategy and PCE. It provides designs with the desired robustness, while the associated computational expense is independent from the optimization problem. The decoupling of optimization and UQ provides the possibility of implementing robust process design to more complex pharmaceutical manufacturing processes with large number of PU. In this thesis, the case studies include unit operations for (bio)chemical synthesis, separation (crystallization) and formulation (freeze-drying), which cover the complete production chain of pharmaceutical manufacturing. Results from the case studies reveal the significant impact of PU on process design. Also they show the efficiency and effectiveness of the proposed frameworks regarding process performance and robustness in the context of QbD.Die pharmazeutische Industrie muss sowohl den gestiegenen Wettbewerbsdruck standhalten als auch die von Regulierungsbehörden geforderte QbD-Initiative (Quality by Design) umsetzen. Modellgestützte Verfahren können einen signifikanten Beitrag leisten, aber Parameterunsicherheiten (PU) erschweren jedoch eine zuverlässige modellgestützte Prozessauslegung. Das Ziel dieser Arbeit ist daher die Erforschung von effizienten Approaches zur Sensitivitätsanalyse und robusten Prozessdesign der pharmazeutische Industrie. Methoden, Point Estimate Method (PEM) und Polynomial Chaos Expansion (PCE), wurde implementiert, um effizient Unsicherheitenquantifizierung (UQ) zu erlauben. Der globalen Sensitivitätsanalyse (GSA) ist eine systematische Quantifizierung von Parameterschwankungen auf die Simulationsergebnisse. Zwei GSA Techniken werden im Detail vorgestellt und an Beispielen demonstriert. Die Ergebnisse zeigen sowohl den Mehrwert der GSA im Kontext des robusten Prozessdesigns als auch die Relevanz zur korrekten Berücksichtigung von Parameterkorrelationen bei der GSA. Um den schädlichen Einfluss von PU auf die modellgestützte Prozessauslegung zusätzlich zu minimieren, wurden weitere Konzepte aus der robusten Optimierung untersucht. Zunächst wurde das erste Konzept basierend auf der PEM entwickelt. Das erste Konzept zeigt einen deutlich reduzierte Rechenaufwand und kann auch die Parameterkorrelationen entsprechend in der robusten Prozessauslegung berücksichtigen. In einem zweiten Schritt wurde ein neuer Ansatz, der die Gauß-Mischverteilung mit der PEM kombiniert, hierzu für nicht normalverteilte PU erfolgreich implementiert. Weiterhin wurde eine iterative Back-off-Strategie erforscht, die auch die PU entsprechend berücksichtigt aber leichte Rechenaufwand zeigt. Durch die Entkoppelung von UQ und Optimierung können wesentlich komplexere pharmazeutische Herstellungsprozesse mit einer hohen Anzahl an PU implementiert werden. Die in dieser Arbeit untersuchten verfahrenstechnische Grundoperationen decken somit einen Großteil der gesamten Produktionskette der pharmazeutischen Herstellung ab. Die Ergebnisse der untersuchten Beispiele zeigen deutlich den Einfluss von PU auf das modellgestützte Prozessdesign auf. Mithilfe der vorgeschlagenen Approaches können die PU effektiv und effizient bei einer optimalen Balance von Rechenaufwand und der geforderten Zuverlässigkeit ganz im QbD-Sinne berücksichtigt werden