1,720,970 research outputs found
On the prediction of PSD in antisolvent mediated crystallization processes based on Fokker-Planck equations
No full textA phenomenological model for the description of antisolvent mediated crystal growth processes is presented. The crystal size growth dynamics is supposed to be driven by a deterministic growth factor coupled to a stochastic component. Two different models for the stochastic component are investigated: a Linear and a Geometric Brownian motion terms. The evolution in time of the particle size distribution is then described in terms of the Fokker-Planck equation. Validations against experimental data are presented for the NaCl-water-ethanol anti-solvent crystallization system. It was found that a proper modeling of the stochastic component does have an impact on the model capabilities to fit the experimental data. In particular, the GBM assumption is better suited to describe the antisolvent crystal growth process under examination
On the influence of hydrogen bond interactions in isothermal and nonisothermal antisolvent crystallization processes
No full textThe effect of the temperature on the Crystal Size Distribution (CSD) in antisolvent crystallization operation, for systems where the solubility is weakly dependent on the temperature, is analyzed. The hydrogen bonding properties of the solvents used that in␣uence the supersaturation of the solution and consequently the growth and the nucleation dynamic can explain this e␣ect on the CSD. To verify and quantify these e␣ects, experiments were conducted and the Fokker␣Planck modeling equations were used to obtain the quantifying parameters (growth velocity, the asymptotic mean size, and the di␣usivity). Results are provided through investigations into the nonisothermal antisolvent crystallization of sodium chloride (NaCl), in which the solubility is practically independent of temperature for the range of operating conditions considered
A Stochastic Formulation for the Prediction of PSD in Crystallization Processes: Comparative Assessment of Alternative Model Formulations
No full textA stochastic formulation for the description of antisolvent mediated crystal growth processes is discussed. In the proposed approach the crystal size growth dynamics is driven by a deterministic growth factor coupled to a stochastic component. The evolution in time of the particle size distribution is then described in terms of a Fokker-Planck equation. In this formulation the specific form of the stochastic model leads to different shapes for the probability density function. I this work we investigate and assess comparatively the performance of the FPE approach to model the crystal size distribution based on different expressions for the stochastic component. In particular, we consider the Langevin equation with a multiplicative noise term that depends on the crystal size (time and space). It is shown and corroborated via experimentation that the best stochastic model is given by the Geometric Brownian Motion (GBM). Excellent quantitative agreement between experiments and the predictions from the FPE- GBM model were obtained for a range of conditions. Validations against experimental data are presented for the NaCl-water-ethanol anti-solvent crystallization system
Data-derived analysis and inference for an industrial deethanizer
No full textThis paper presents an application of data-derived approaches for analyzing and monitoring industrial processes. The discussed methods are used in visualizing process measurements, extracting operational information, and designing estimation models for primary process variables otherwise difficult to measure in real-time. Emphasis is given to the modeling of the data with two classical machine learning paradigms; the self-organizing map (SOM) and the multi-layer perceptron (MLP). The effectiveness of the proposed approach is validated on an industrial deethanizer, where the goal is to identify operational modes and most sensitive variables for this full-scale unit, as well as design an inferential model for a critical process variable, the bottom ethane concentration. The study led to the definition of a fully automated monitoring tool to be implemented online in the plant's distributed control system. The results confirmed the potential of the data-derived approach, and based on the analysis, the existing control configuration of the unit could be redefined toward more consistent operations. Because it is general and modular by design, the tool can be easily used for other processes
On the topological modeling and analysis of industrial process data using the SOM
No full textIn this paper, we overview and discuss the implementation of topology-based approaches to modeling and analyzing industrial process data. Emphasis is given to the representation of the data obtained with the self-organizing map (SOM). The methods are used in visualizing process measurements and extracting relevant information by exploiting the topological structure of the observations. Benefits of the SOM with industrial data are presented for a set of process measurements measured in an industrial gas treatment plant. The practical goal is to identify significant operational modes and most sensitive process variables before developing an alternative control strategy. The results confirmed that the SOM-based approach is capable of providing valuable information and offers possibilities for direct application to other process monitoring tasks. (C) 2010 Elsevier Ltd. All rights reserved
Time evolution of psd in crystallization operations: an analytical solution based on Ornstein-Uhlenbeck process
No full textA new formulation of the recent stochastic approach for the description of the particle-size distribution (PSD) time evolution in antisolvent crystal-growth processes is presented. In this new approach, the crystals size is modeled as a random variable driven by a Gompertz growth term and the corresponding Fokker-Planck equation is carried out. This proposed formulation, allows an analytical solution to describe the time evolution of the PSD as a function of the model parameters. The analytical solution is obtained by exploiting the typical properties of linear partial differential equations with linear coefficients, and using the analogy with Kalman filter, in terms of the first two stochastic moments: mean and variance of the PSD. Furthermore, an alternative way for the parameters estimation based on the maximum likelihood estimation is also introduced. Validations against experimental data are provided for the NaCl-water-ethanol antisolvent crystallization system
On-line control of crystal properties in nonisothermal antisolvent crystallization
No full textThe issues regarding the design and implementation of on-line optimal control strategies of crystal properties in noniso- thermal 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 condi- tioned 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 imple- mented to track crystals’ size distribution along the experiment and providing the on-line information for further feed- back control action. Subsequently, alternative control strategies are implemented and tested to achieve a desired crystal size distribution
A stochastic approach for the prediction of PSD in crystallization processes: Analytical solution for the asymptotic behavior and parameter estimation
No full textRecently, a novel stochastic formulation based on the Fokker–Planck equation (FPE) for the description of anti-solvent mediated crystal growth process was proposed. Here, we further expand these results by analyzing the asymptotic (end of the batch) solution of the FPE for the CSD. In this regard, the analytical solution of the stationary FPE is exploited for predicting the end of the batch CSD as function of the model parameters. Furthermore, the availability of such analytical solution is used to simplify and diminish the computational burden of the parameter estimation problem. Two alternative approaches for parameter estimation are discussed based on the use of the analytical solution of the FPE and of the dynamic of the logistic equation (deterministic component of the FPE approach). Validations against experimental data for the NaCl–water–ethanol anti-solvent crystallization system are presented
Stochastic Approach for the Prediction of PSD in Crystallization Processes: Formulation and Comparative Assessment of Different Stochastic Models
No full textA stochastic formulation for the description of antisolvent mediated crystal growth processes is discussed. In the proposed approach, the crystal size growth dynamics is driven by a deterministic growth factor coupled to a stochastic component. The evolution in time of the particle size distribution (PSD) is then described in terms of a Fokker-Planck equation. In this work, we investigate and assess comparatively the performance of the FPE approach to model the crystal size distribution based on different expressions for the stochastic component. In particular, we investigate the one-dimensional Fokker-Planck equation with a nonlinear diffusion coefficient to represent the crystal growth process. Validations against experimental data are presented for the NaCl water ethanol antisolvent crystallization system. It is shown that the stochastic model better suited to describe the experiments is given by the Geometric Brownian Motion (GBM), which gives an excellent agreement, with the experiments for a wide range of process conditions (i.e., antisolvent feed rate)
Dynamic evolution of PSD modelled using an Ornstein-Uhlenbeck process approach
No full textIn this paper a new stochastic approach for the description of antisolvent crystal growth processes is presented. In this approach, the trajectory of crystals mean size is modeled as a Gompertz equation and the time evolution of the Particle Size Distribution (PSD) is modeled as a Fokker-Planck equation. In the new formulation the problem is reformulated as an Ornstein Uhlenbeck process and using Fourier transformation an analytical solution is then obtained to describe the time evolution of the PSD as function of the model parameters. Validations against experimental data are provided for the NaCl-water-ethanol antisolvent crystallization system
- …
