Aspect ratio distribution and chord length distribution driven modeling of crystallization of two-dimensional crystals for real-time model-based applications

Two-dimensional (2D) crystals, for which the shape is described by two linear sizes, are common in fine chemical and pharmaceutical industries. Since the crystal size and shape are directly related to the performance of active pharmaceutical ingredients, the simultaneous size and shape distribution control is of paramount importance in pharmaceutical crystallization engineering. To efficiently achieve simultaneous size and shape control often requires model-based control strategies; however, the increased computational cost of the process simulation and the substantial differences between the simulated and measurable quantities make the implementation of model-based control approaches challenging. This paper addresses the important problem of the real-time simulation of the most likely measurable chord length distribution (CLD) and aspect ratio distribution (ARD) as well as the concentration variations during the crystallization of 2D needle-shaped crystals. This enables the application of focused beam reflectance measurement (FBRM) and particle vision and microscopy (PVM), two routinely applied probes, as quantitative direct feedback control tools. Artificial neural network (ANN)-based FBRM and PVM soft-sensors are developed, which enable the direct and fast transformation of 2D crystal size distribution (CSD) to CLD and ARD on arbitrary 2D grids. The training data for the ANN are generated by a first principle, geometrical model-based simulation of FBRM and PVM for high aspect ratio crystals, although the ANN approach is applicable for any simulated or experimental training data sets. It is also demonstrated that the in situ imaging-based shape measurement underestimates the real aspect ratio (AR) of crystals, for which a simple correction is proposed. From the model-equation solution perspective, the soft-sensors require full population balance solution. The 2D high-resolution finite volume method is applied to simulate the full 2D CSD, which is an accurate, stable, but computationally expensive technique. The real-time applicability is achieved through various implementation improvements including grid optimization and data-type optimized hybrid central processing unit-graphical processing unit calculations

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

Chord length distribution based modeling and adaptive model predictive control of batch crystallization processes using high fidelity full population balance models

The control of batch crystallizers is an intensively investigated topic as suitable crystallizer operation can reduce considerably the downstream operation costs and produce crystals of desired properties (size, shape, purity, etc.). Nevertheless, the control of crystallizers is still challenging. In this work the development of a fixed batch time full population balance model based adaptive predictive control system for cooling batch crystallizers is presented. The model equations are solved by the high resolution finite volume algorithm involving fine discretization, which provides a high fidelity, accurate solution. A physically relevant crystal size distribution (CSD) to chord length distribution (CLD) transformation is also developed making possible the direct, real-time application of the focused beam reflectance measurement (FBRM) probe in the control system. The measured CLD and concentration values are processed by the growing horizon estimator (GHE), whose roles are to estimate the unmeasurable system states (CSD) and to readjust the kinetic parameters, providing an adaptive feature for the control system. A repeated sequential optimization algorithm is developed for the nonlinear model predictive control (NMPC) optimization, enabling the reduction of sampling time to the order of minutes for the one-day long batch. According to the simulation results, the strategy is highly robust to parametric plant-model mismatch and significant concentration measurement noise, providing very good control of the desired CLD

Experimental implementation of a Quality-by-Control (QbC) framework using a mechanistic PBM-based nonlinear model predictive control involving chord length distribution measurement for the batch cooling crystallization of L-ascorbic acid

L-ascorbic acid is synthetized in large industrial scale from glucose and marketed as an immune system strengthening agent and anti-oxidant ingredient. The overall yield of conversion of the precursor glucose to L-ascorbic acid is limited, therefore the crystallization is a critically important step of the L-ascorbic acid production from economic point of view. It is widely accepted that the crystal size distribution (CSD) influences numerous relevant macroscopic properties of the final crystalline product and it also significantly affects the downstream operations. The present paper discusses the chord length distribution (CLD, which is directly related to the CSD) control, during the crystallization of L-ascorbic acid from aqueous solution. Batch crystallization process is employed, which is the classical, and still dominant, operation in fine chemical and pharmaceutical industries. A comparative experimental study of two state-of-the-art Quality-by-Control (QbC) based crystallization design approaches are presented: (1) a model-free QbC based on direct nucleation control (DNC) and (2) a model-based QbC using a novel nonlinear model predicative control (NMPC) framework. In the first investigation, the DNC, a process analytical technology based state-of-the-art model free control strategy, is applied. Although, DNC requires minimal preliminary system information and often provides robust process control, due to the unusual crystallization behavior of L-ascorbic acid, it leads to long batch times and oscillatory operation. In a second study the benefits of model-based QbC approach are demonstrated, based on using a NMPC approach. A population balance based crystallization process model is built and calibrated by estimating the nucleation and growth kinetics from concentration and CLD measurements. A projection based CSD to CLD forward transformation is used in the estimation of nucleation and growth kinetics. For robustness and adaptive behavior, the NMPC is coupled with a growing horizon state estimator, which is aimed to continuously improve the model by re-adjusting the kinetic constants. The study demonstrates that the model-based QbC framework can lead to rapid and robust crystallization process development with the NMPC system presenting good control behavior under significant plant model mismatch (PMM) conditions

Real time image processing based on-line feedback control system for cooling batch crystallization

The direct nucleation control (DNC) is a process analytical technique (PAT) based model free feedback control strategy for batch and continuous crystallization processes, which has been successfully applied in numerous cases. The basic principle of DNC is the use of controlled dissolution cycles to control a measurement directly related to the particle number in the system. During the DNC, in the case of cooling crystallization fines are dissolved by repeated heating-cooling loops. In this context, the controlled variable is the (relative) particle number, which is manipulated using a feedback control approach through the temperature. The particle number is traditionally measured with focused beam reflectance measurement (FBRM), however other PAT tools can also be employed in a similar feedback control setup. Often crystallization processes are also monitored by real-time imaging systems. In the current work a novel DNC setup is proposed in which microscopy images are captured and processed by the means of image analysis in real time. The images are used to extract the relative particle number, which is controlled using the DNC framework. The robustness of the new image analysis based direct nucleation control (IA-DNC) is presented via three case studies with materials having different crystallization properties. The IA-DNC approach uses a Particle Vision probe although other in situ or in line imaging systems can also be used in the framework. The systems are monitored with FBRM for comparison purposes. The setup achieved stable, converged control in most cases and is demonstrated that the IA-DNC has several advantages over the classical FBRM based DNC. The IA-DNC can also be used for real time feedback control of crystal shape

Enabling mechanical separation of enantiomers through controlled batchwise concomitant crystallization : digital design and experimental validation

In the pharmaceutical industry the separation of chiral molecules is important due to the different physiochemical properties that the enantiomers of a chiral drug possess. Therefore, resolution techniques are used to separate such enantiomers from one another. In particular, preferential crystallization is a common technique used to separate conglomerate-forming compounds, due to its high selectivity. However, the efficient separation of enantiomers in a batchwise preferential crystallization process through seeding with the preferred enantiomer alone is still inefficient, since unwanted nucleation of the counter enantiomer is inevitable. Here, we demonstrate a model-based digital design for the separation of enantiomers for a conglomerate-forming compound (asparagine monohydrate), by using mechanical separation by sieving after crystallization, whereby the separation is enabled by a designed bias in the crystal size distributions of each enantiomer. This bias is created by a concomitant crystallization of both enantiomers using optimized seeding and cooling profiles obtained from a population balance model. In this way, a high level of control is achieved over a batchwise preferential crystallization process, since the crystallization of both enantiomers is controlled. We show that, through this separation method, material with impurity levels as low as 6 wt % can be obtained. To our knowledge this is the first demonstration of modeling such a process to separate enantiomers of a conglomerate-forming compound

Design and baseline characteristics of the finerenone in reducing cardiovascular mortality and morbidity in diabetic kidney disease trial

Background: Among people with diabetes, those with kidney disease have exceptionally high rates of cardiovascular (CV) morbidity and mortality and progression of their underlying kidney disease. Finerenone is a novel, nonsteroidal, selective mineralocorticoid receptor antagonist that has shown to reduce albuminuria in type 2 diabetes (T2D) patients with chronic kidney disease (CKD) while revealing only a low risk of hyperkalemia. However, the effect of finerenone on CV and renal outcomes has not yet been investigated in long-term trials. Patients and Methods: The Finerenone in Reducing CV Mortality and Morbidity in Diabetic Kidney Disease (FIGARO-DKD) trial aims to assess the efficacy and safety of finerenone compared to placebo at reducing clinically important CV and renal outcomes in T2D patients with CKD. FIGARO-DKD is a randomized, double-blind, placebo-controlled, parallel-group, event-driven trial running in 47 countries with an expected duration of approximately 6 years. FIGARO-DKD randomized 7,437 patients with an estimated glomerular filtration rate >= 25 mL/min/1.73 m(2) and albuminuria (urinary albumin-to-creatinine ratio >= 30 to <= 5,000 mg/g). The study has at least 90% power to detect a 20% reduction in the risk of the primary outcome (overall two-sided significance level alpha = 0.05), the composite of time to first occurrence of CV death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for heart failure. Conclusions: FIGARO-DKD will determine whether an optimally treated cohort of T2D patients with CKD at high risk of CV and renal events will experience cardiorenal benefits with the addition of finerenone to their treatment regimen. Trial Registration: EudraCT number: 2015-000950-39; ClinicalTrials.gov identifier: NCT02545049