A stochastic formulation for the description of the crystal size distribution in antisolvent crystallization processes

A stochastic approach to describe the crystal size distribution dynamics in antisolvent based crystal growth processes is here introduced. Fluctuations in the process dynamics are taken into account by embedding a deterministic model into a Fokker‐Planck equation, which describes the evolution in time of the particle size distribution. The deterministic model used in this application is based on the logistic model, which shows to be adequate to suit the dynamics characteristic of the growth process. Validations against experimental data are presented for the NaCl–water–ethanol antisolvent crystallization system in a bench‐scale fed‐batch crystallization unit. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Kinetic Modeling of the Gas Antisolvent Process for Synthesis of 5‐Fluorouracil Nanoparticles

Mathematical modeling for 5‐fluorouracil (5‐FU) nanoparticle synthesis via gas antisolvent (GAS) process was investigated. 5‐FU was precipitated from a dimethyl sulfoxide (DMSO) solution using CO₂ as antisolvent. The particle size was controlled by nucleation and growth rates, therefore, the kinetic modeling study is essential. Thermodynamic modeling was applied to determine optimal operating conditions for experimental 5‐FU synthesis. Kinetic parameters were evaluated by fitting the particle size distribution predicted by the model to experimental data. The experimental and modeling results indicated that the particle size decreased with increasing the antisolvent addition rate.     

Formation of biodegradable polymeric fine particles by supercritical antisolvent precipitation process

The supercritical antisolvent (SAS) precipitation process as a “green” alternative to specialty particles recrystallization was successfully used to generate poly(L ‐lactide) acid (L‐PLA) from dichloromethane (DCM) solution using CO₂ as antisolvent. The influence of main operating parameters on the synthesis of L‐PLA particles in the SAS process was methodically examined. In particular, antisolvent addition rate (30, 40, 50, and 60 g/min), temperature (35, 40°C, 45°C, and 50°C), solute concentration (50, 75, 100, and 150 mg/10 ml), and solution addition rate (1, 2.5, 5, and 7.5 ml/min). These parameters could be tuned to give a mean particle diameter of 0.62 μm. It was found using scanning electron microscopy and laser diffraction that increasing the antisolvent addition rate and the solution addition rate, while decreasing the temperature and solute concentration, led to a decrease in the L‐PLA mean particle diameter. Furthermore, a unimodal particle size distribution was obtained at the higher solution and antisolvent addition rates. Spherical‐like primary particles have been obtained in all the experimental runs; thus, no change of particle morphology with the process parameters has been noticed. These results manifested that SAS recrystallization process is a valuable technique to generate reproducibly polymer particles with controlled size and size distribution. POLYM. ENG. SCI. 2013. © 2012 Society of Plastics Engineers     

Multivariable real‐time optimal control of a cooling and antisolvent semibatch crystallization process

This article presents an experimental study of simultaneous optimization with respect to two variables (cooling rate and flow‐rate of antisolvent) in an offline and online (real‐time) manner on a semibatch crystallizer. The nucleation and growth kinetic parameters of paracetamol in an isopropanol‐water cooling, antisolvent batch crystallizer were estimated by nonlinear regression in terms of the moments of the crystal population density. Moments of crystal population were estimated from the measured chord length distribution, generated by the FBRM®, and the supersaturation was calculated from the measured concentration by attenuated total reflectance‐fourier transform infrared spectroscopy. The results of real‐time optimization showed a substantial improvement of the end of batch properties (the volume‐weighted mean size and yield). For the same objective function, the real‐time optimization method resulted in an increase in the volume‐weighted mean size by ～100 μm and 15% of theoretical yield compared with the best result obtained in an offline optimization manner. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Influence of Mixing on the Precipitation of Organic Nanoparticles: A Lagrangian Perspective on Scale‐up Based on Self‐Similar Distributions

Precipitation of nanoparticles is applied in various fields with a rising interest in the formulation of poorly soluble drugs. The impact of fluid mixing on the precipitation of organic nanoparticles is analyzed. Direct numerical simulations are applied to determine the spatiotemporal evolution of the liquid phase composition and to estimate the particle evolution along Langragian trajectories. The simulation results are compared with laboratory experiments of mixing and particle size evolution, which use a recently developed approach to rapidly stabilize the precipitated nanoparticles. The impact of mixing on precipitation is revealed, thereby enabling a parameter‐free estimation of the mean particle sizes and the particle size distributions. The distributions of residence time, supersaturation time, and particle size are self‐similar for Reynolds numbers in the turbulent regime and allow the derivation of scale‐up rules.     

Evaluation of Ultrasonic Treatment for the Size Reduction of HNS and HMX in Comparison to Solvent‐Antisolvent Crystallization

The paper presents and compares two methods for the synthesis of fine particles of the high explosives HNS and HMX by ultrasonic treatment and solvent/antisolvent crystallization. The effect of ultrasonic treatment on the particle size of explosives was studied by varying the amplitude and frequency of ultrasonication for different time periods using an ultrasonic probe and an ultrasonic bath. Solvent/antisolvent recrystallization was performed by varying the process parameters including stirring rate, antisolvent temperature etc. In addition to FT‐IR spectroscopy and thermal analysis by TGA/DSC; the particle size and shape of fine powders of the explosives HMX and HNS were determined using particle size analysis and scanning electron microscopy (SEM). Ultrasonic treatment of the probes resulted in the finer grains of HMX compared to solvent‐antisolvent crystallization. However in the case of HNS, solvent‐antisolvent crystallization produced finer particles compared to ultrasonication.     

Population balance modeling of particle size distribution in monomer‐starved semibatch emulsion polymerization

The evolution of particle size distribution (PSD) in the monomer‐starved semibatch emulsion polymerization of styrene with a neat monomer feed is investigated using a population balance model. The system under study ranges from conventional batch emulsion to semicontinuous (micro)emulsion polymerization depending on the rate of monomer addition. It is shown that, contrary to what is often believed, the broadness of PSD is not necessarily associated with the length of nucleation period. The PSDs at the end of nucleation are found to be independent of surfactant concentration. Simulation results indicate that at the completion of nucleation the particle size is reduced and the PSD narrows with decreasing rate of monomer addition despite nucleation time increasing. The broad distribution of particles frequently encountered in semibatch emulsion polymerizations is therefore attributed to stochastic broadening during the growth stage. The zero‐one‐two‐three model developed in this article allows perceiving that the dominant kinetic mechanism may be different for particles with different sizes. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Application of The Splitting Approach to Solve Population Balance Equations in Chemical Processes

Different processes in chemical industries deal with particles and multiphase flow. In such processes, particle or bubble size distribution (PSD) influences the final product quality and also process design. On the other hand, solutions to the dominant hydrodynamic and thermo‐kinetic equations ignoring these distributions will make it impossible to accurately simulate these processes. Solutions to population balance equations (PBE's) are needed to attain the PSD. One of the most common methods for the solution of a PBE is the classes method (CM). However, as this method requires a large number of classes to give a reasonable result, it needs a huge amount of calculations and time. To overcome this problem, in this paper, a variant of the CM is proposed in which particles in different classes are transformed to new classes in two steps with the application of the operator splitting technique. In the first step, the particles are aggregated and broken up to form three parallel types of groups, namely: groups formed from aggregated particles, groups formed from broken‐up particles, and finally, a group formed from non‐altered particles. In the second step, these parallel groups are combined to redefine classes for the next time step. Finally, results of this method, which could be called the parallel groups classes method (PGCM), for different coalescence and breakage kernels are compared with those obtained using the analytical solution and the CM. Excellent agreement of the results from the PGCM with the analytical solution reveals its effectiveness and accuracy; which will give it an advantage over the CM.     

Regularized maximum likelihood estimation of sparse stochastic monomolecular biochemical reaction networks

A sparse parameter matrix estimation method is proposed for identifying a stochastic monomolecular biochemical reaction network system. Identification of a reaction network can be achieved by estimating a sparse parameter matrix containing the reaction network structure and kinetics information. Stochastic dynamics of a biochemical reaction network system is usually modeled by a chemical master equation (CME) describing the time evolution of probability distributions for all possible states. This paper considers closed monomolecular reaction systems for which an exact analytical solution of the corresponding chemical master equation can be derived. The estimation method presented in this paper incorporates the closed-form solution into a regularized maximum likelihood estimation (MLE) for which model complexity is penalized. A simulation result is provided to verify performance improvement of regularized MLE over least-square estimation (LSE), which is based on a deterministic mass-average model, in the case of a small population size.     

ASTRO‐FOLD 2.0: An enhanced framework for protein structure prediction

The three‐dimensional (3‐D) structure prediction of proteins, given their amino acid sequence, is addressed using the first principles–based approach ASTRO‐FOLD 2.0. The key features presented are: (1) Secondary structure prediction using a novel optimization‐based consensus approach, (2) β‐sheet topology prediction using mixed‐integer linear optimization (MILP), (3) Residue‐to‐residue contact prediction using a high‐resolution distance‐dependent force field and MILP formulation, (4) Tight dihedral angle and distance bound generation for loop residues using dihedral angle clustering and non‐linear optimization (NLP), (5) 3‐D structure prediction using deterministic global optimization, stochastic conformational space annealing, and the full‐atomistic ECEPP/3 potential, (6) Near‐native structure selection using a traveling salesman problem‐based clustering approach, ICON, and (7) Improved bound generation using chemical shifts of subsets of heavy atoms, generated by SPARTA and CS23D. Computational results of ASTRO‐FOLD 2.0 on 47 blind targets of the recently concluded CASP9 experiment are presented. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

An Artificial Neural Network approximation based decomposition approach for parameter estimation of system of ordinary differential equations

In this work a new approach for parameter estimation which is based upon decomposing the problem into two subproblems is proposed, the first subproblem generates an Artificial Neural Network (ANN) model from the given data and then the second subproblem uses the ANN model to obtain an estimate of the parameters. The analytical derivates from the ANN model obtained from the first subproblem are used for obtaining the differential terms in the formulation of the second subproblem. This greatly simplifies the parameter estimation problem. The key advantage of the proposed approach is that solution of a large optimization problem requiring high computational resources is avoided and instead two smaller problems are solved. This approach is particularly useful for large and noisy data sets and nonlinear models where ANN models are known to perform quite well and therefore plays an important role in the solution of the overall parameter estimation problem.     

On the stochastic simulation of particulate systems

The stochastic chemical kinetics approach provides one method of formulating the stochastic crystallization population balance equation (PBE). In this formulation, crystal nucleation and growth are modelled as sequential additions of solubilized ions or molecules (units) to either other units or an assembly of any number of units. Monte Carlo methods provide one means of solving this problem. In this paper, we assess the limitations of such methods by both (1) simulating models for isothermal and nonisothermal size-independent nucleation, growth and agglomeration; and (2) performing parameter estimation using these models. We also derive the macroscopic (deterministic) PBE from the stochastic formulation, and compare the numerical solutions of the stochastic and deterministic PBEs. The results demonstrate that even as we approach the thermodynamic limit, in which the deterministic model becomes valid, stochastic simulation provides a general, flexible solution technique for examining many possible mechanisms. Thus the stochastic simulation permits the user to focus more on modelling issues as opposed to solution techniques.     

Design of quadratic estimators using covariance information in linear discrete‐time stochastic systems

Abstract. This article describes a polynomial estimation technique based on the state‐space model and develops an estimation method for the quadratic estimation problem by applying the multivariate recursive least squares (RLS) Wiener estimator to the quadratic estimation of a stochastic signal in linear discrete‐time stochastic systems. The augmented signal vector includes the signal to be estimated and its quadratic quantity. The augmented signal vector is modelled in terms of an autoregressive model of appropriate order. A numerical simulation example for the speech signal as a practical stochastic signal is implemented and its estimation accuracy is found to be considerably improved in comparison with the existing RLS Wiener estimators. The proposed method may be applied advantageously to the quadratic estimations of wide‐sense stationary stochastic signals in general.     

On‐line control of crystal properties in nonisothermal antisolvent crystallization

The issues regarding the design and implementation of on‐line optimal control strategies of crystal properties in nonisothermal antisolvent crystallization processes to control particles’ mean size and standard deviation are dealt. The one‐dimensional Fokker–Planck equation is used to represent the dynamic characteristics of the crystal growth and generate iso‐mean and iso‐standard deviation curves. Using controllability tools it is demonstrated that the system is ill conditioned in the whole operational range, posing limitations on the achievable control performance. To circumvent the problem, a control strategy is formulated by pairing crystals’ mean size with antisolvent feed rate and manipulating temperature to control the standard deviation. A novel digital image‐texturing analysis approach is discussed and implemented to track crystals’ size distribution along the experiment and providing the on‐line information for further feedback control action. Subsequently, alternative control strategies are implemented and tested to achieve a desired crystal size distribution. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2188–2201, 2015     

处理多分散颗粒凝并和冷凝/蒸发问题的多重Monte Carlo算法

提出一个新的多重Monte Carlo (MMC) 算法来求解同时考虑凝并和冷凝/蒸发的通用动力学方程 (GDE),该算法基于时间驱动, 模拟过程中保持模拟颗粒数目不变和计算区域体积不变. 描述了时间步长确定方法, 同时处理凝并和冷凝/蒸发的方案. 针对常凝并核和常冷凝核, 常凝并核和线性冷凝核, 线性凝并核和线性冷凝核三种特殊工况, MMC算法模拟了颗粒尺度分布函数的时间演变, 与理论分析解进行了比较, 表明MMC算法能解决普通Monte Carlo算法的计算精度和计算代价不能协调的矛盾, 具有较小的计算代价和较高的计算精度, 能够适用于工程应用.     

Controlled liquid antisolvent precipitation using a rapid mixing device

Particle formation by the liquid antisolvent (LAS) process involves two steps: mixing of solution–antisolvent streams to generate supersaturation and precipitation (which includes nucleation and growth by coagulation and condensation) of particles. Uniform mixing conditions ensure rapid and uniform supersaturation, making it a precipitation controlled process where the particle size is not further affected by mixing conditions and results in precipitation of ultra-fine particles with narrow particle size distribution (PSD). In this work, we demonstrate that the use of an ultrasonically driven T-shaped mixing device significantly improves mixing of solution and antisolvent streams for precipitation of ultra-fine particles in a continuous operation mode. LAS precipitation of ultra-fine particles of multiple active pharmaceutical ingredients (APIs) such as itraconazole (ITZ), ascorbyl palmitate (ASC), fenofibrate (FNB), griseofulvin (GF), and sulfamethoxazole (SFMZ) in the size range 0.1–30 μm has been carried out from their organic solutions in acetone, dimethyl sulfoxide (DMSO), tetrahydrofuran (THF), and ethanol (EtOH). Classical theory of homogeneous nucleation has been used to analyze the result, which suggests that higher nucleation rate results in finer particle size. Interestingly, experimental determination of degree of supersaturation indicates that higher supersaturation does not necessarily result in higher nucleation rate and nucleation rates can be correlated to solvent polarity.