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

Szilágyi, Botond; Nagy, Zoltán K.

doi:10.1016/j.compchemeng.2016.03.023

Cited by 38 publications

(30 citation statements)

References 28 publications

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“…Uniformly distributed mesh was used with N = 1000 elements, which ensured the high-fidelity model solution. The crysiv MATLAB based function was used to solve the model equations (Szilágyi and Nagy, 2016). The material related constants are listed in Table 1.…”

Section: Model Developmentmentioning

confidence: 99%

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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

Szilágyi

Borsos

Pal

2019

Chemical Engineering Science

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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 2 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 readjusting 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.

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Section: Model Developmentmentioning

confidence: 99%

“…FVM is a discretization based technique: finer discretization entails higher accuracy but this also translates into higher computational costs. Significant reduction in the time to solve PBEs based on FVM can be achieved by efficient computer implementation (Majumder et al, 2010;Szilágyi and Nagy, 2016).…”

Section: Introductionmentioning

confidence: 99%

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

Szilágyi

Borsos

Pal

2019

Chemical Engineering Science

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“…Polydisperse multiphase flows are present in several industrial technologies, such as spray combustion, bubble column reactor, fluidized bed reactor, and so on . This is one of the reasons why the academia has been devoting a significant amount of effort on this topic . Basically, there are three main approaches to predict the polydisperse multiphase flow behaviour: the fully resolved, the Lagrangian point‐particle, and the Eulerian‐Eulerian (E‐E) models …”

Section: Introductionmentioning

confidence: 99%

GPU‐accelerated simulation of polydisperse multiphase flows using dual‐quadrature‐based moment methods

et al. 2020

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Polydisperse multiphase flows can be simulated by coupling a population balance model to the multi-fluid model. For the first time, this simulation is carried out using the dual-quadrature method of generalized moments (DuQMoGeM) and its direct version to solve the population balance model. The main disadvantage of these methods is the high computational cost of the embedded cubature. Herein, this challenge was addressed by parallelization on graphics processing units, which resulted in a significant acceleration of the simulations, with speedups that can be larger than 1000. Numerical simulations considering simultaneous particles breakage and aggregation were conducted with direct DuQMoGeM-FC and DQMoM-FC, whose results were different due to the existence of quadrature error in the latter. K E Y W O R D S moment methods, multiphase flow, particulate systems, population balance

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“…The high resolution finite volume method (HR-FVM) is an efficient algorithm to compute the CSD without significant numerical diffusion and/or oscillations 14 . The solution speed can be improved to meet the real time applicability with efficient implementations 15 .…”

Section: Introductionmentioning

confidence: 99%

Chord Length Distribution Based Modeling and Adaptive Model Predictive Control of Batch Crystallization Processes Using High Fidelity Full Population Balance Models

Szilágyi

Agachi

2018

Ind. Eng. Chem. Res.

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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 un-measurable system states (CSD) and to re-adjust 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.Nucleation activation energy 39760, J mol -1 K -1Growth rate constant 11266, µm s -1

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

Cited by 38 publications

References 28 publications

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

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

GPU‐accelerated simulation of polydisperse multiphase flows using dual‐quadrature‐based moment methods

Chord Length Distribution Based Modeling and Adaptive Model Predictive Control of Batch Crystallization Processes Using High Fidelity Full Population Balance Models

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