Recent extensions of the residence time distribution concept: unsteady state conditions and hydrodynamic model developments

Claudel, S.; Leclerc, Jean; Tétar, L.; Lintz, H.‐G.; Bernard, Anthony

doi:10.1590/s0104-66322000000400059

Cited by 9 publications

(7 citation statements)

References 10 publications

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“…que podem ser úteis para avaliar a formação das "zonas mortas" no interior do equipamento [17,18]. Este tipo de análise também se baseia em um monitoramento constante de um traçador e, desta forma, o método proposto neste trabalho, o de medidas off-line de luminância, também pode ser aplicado para este tipo de investigação.…”

Section: Agradecimentosunclassified

Método Simples Para Determinar Distribuição De Tempo De Residência De Polímeros Em Extrusora a Partir De Medidas De Luminância

Silva¹,

Yoshida²,

Takimoto³

et al. 2017

Tecnol. Metal. Mater. Min.

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ResumoA distribuição de tempo de residência (RTD) é uma ferramenta poderosa que pode ser usada para a análise das condições do processo de extrusão. Quando se trata de polímeros, a qualidade do produto acabado é fortemente afetada pelos parâmetros de processamento a que estes materiais são submetidos. Desta forma, a RTD tem sido amplamente empregada para avaliar a extrusão destes materiais. Neste trabalho foi determinada a RTD do polipropileno processado em extrusora monorrosca e, além disso, foi avaliada a influência da velocidade de rotação da rosca sobre o tempo médio de residência e a capacidade de mistura da extrusora. Nas condições de processamento utilizadas, os resultados mostraram que o aumento da rotação reduz o tempo de residência e, ao mesmo tempo, favorece uma melhor homogeneização do fundido. Palavras-chave: Extrusão; Distribuição de tempo de residência; Luminância; Polímeros. SIMPLE METHOD FOR DETERMINATION OF THE RESIDENCE TIME DISTRIBUTION OF POLYMERS IN EXTRUDER FROM LUMINANCE MEASUREMENTS AbstractThe residence time distribution (RTD) is a powerful tool and it can be used to analyze the conditions of the extrusion process. For polymers, the quality of the products is strongly affected by the processing parameters that are applied to such materials. Thus RTD has been widely used to evaluate their extrusion. In this work, RTD of polypropylene extrusion in a single screw extruder was determined and the influence of the rotation speed of the screw on the mean residence time and the mixing ability of the extruder were evaluated. Under the range of the extrusion conditions, the results have shown that the increment of the rotation speed reduces the residence time and, at the same time, enhances the homogeneity of the melt.

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Section: Agradecimentosunclassified

Método Simples Para Determinar Distribuição De Tempo De Residência De Polímeros Em Extrusora a Partir De Medidas De Luminância

Silva¹,

Yoshida²,

Takimoto³

et al. 2017

Tecnol. Metal. Mater. Min.

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“…Therefore, some attempts to use this approach in the transient state were made [9][10][11]. For more than 70 years, this method has been used for process optimization [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Optimization of the Solution of a Dispersion Model

et al. 2020

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The study of the combination of chemical kinetics with transport phenomena is the main step for reactor design. It is possible to deviate from the model behaviour, the cause of which may be fluid channelling, fluid recirculation, or creation of stagnant regions in the vessel, by using a dispersion model. In this paper, the known general solution of the dispersion model for closed vessels is given in a new, straightforward form. In order to improve the classical theoretical solution, a hybrid of analytical and numerical methods is used. It is based on the general analytic solution and the least-squares method by fitting the results of a tracer test carried out on the vessel with the values of the analytic solution. Thus, the accuracy of the estimation for the vessel dispersion number is increased. The presented method can be used to similar problems modelled by a partial differential equation and some boundary conditions which are not sufficient to ensure the uniqueness of the solution.

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“…The transport function results in the use of perfectly mixed slices in series not resulting in plug flow. The RTD models are not used in this 73 work because they have a main limiting assumption that the studied process is in steady-state during the tracer experiment (Claudel, Leclerc, Té tar, Lintz, & Bernard, 2000). Although RTD models were extended to unsteady state conditions by some researchers (Claudel et al, 2000;Rawatlal & Starzak, 2003), they are too complicated to be integrated into a generic dynamic model structure.…”

Section: Transport Functionmentioning

confidence: 99%

A generic dynamic model structure for tumbling mills

Yu¹

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In order to develop a common mathematical and simulation platform for tumbling mills, the key aspects of grinding and both slurry and solids transport which are common to all tumbling mills are identified based on a review of existing mechanistic models and milling mechanics. Three versions of generic model structures for tumbling mills (the Generic Tumbling Mill Model Structure Versions 1 to 3: GTMMS I, GTMMS II, and GTMMS III) have been developed based on the population balance framework by incorporating sub-models for breakage characteristics, energy distribution, slurry and solids transport, and discharge.GTMMS I firstly integrates the transport function into a dynamic model structure. As an upgrade of GTMMS I, GTMMS II incorporates a 4D (four dimensional) appearance function sub-model derived from the JK Rotary Breakage Test (JKRBT) data to substitute the existing JK M-p-q t 10 -t n based appearance function model and applies the Discrete Element Method (DEM) energy distribution model, which can replace the traditional selection function, into the model structure.To obtain a 4D appearance function with wider applicable ranges, the JK Mini drop weight tester (JK Mini DWT) was used to conduct drop weight tests for smaller particles with sizes ranging from 16 mm to 0.45 mm. The test results, together with the existing data from JK Standard Drop Weight Tests (JK DWT), were analysed and the wide-range (Ore particle sizes ranging from 425 μm to 63 mm and the input specific energy from 0.1 kWh/t ~ 2.5 kWh/t) 4D appearance function models, namely the wide-range P80-m based 4D model and the wide-range P80-m-q based 4D model, were developed. All the 4D models have better performance in comparison with other t 10 based models.The wide-range 4D appearance function model, together with the DEM energy distribution model corrected by probability-based energy split scheme with both volume ratio and stiffness ratio considered, and the multicomponent sub-model were successfully applied to GTMMS III.All three versions of GTMMS were validated against plant data, and the predictions agree well with plant data. GTMMS I, II and III can work independently depending on the availability of plant data.Because of the harmonic integration of the 4D appearance function, DEM energy distribution model, transport function, discharge function, power model, dynamic modelling and multicomponent modelling, GTMMS I, II and III are more mechanistic, generic, reliable, scalable and applicable and can be treated as vital milestones towards the goal of mechanistic grinding mill modelling and forming a platform for future models such as the unified comminution models (UCM).ii Declaration by authorThis thesis is composed of my original work and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis.

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Recent extensions of the residence time distribution concept: unsteady state conditions and hydrodynamic model developments

Cited by 9 publications

References 10 publications

Método Simples Para Determinar Distribuição De Tempo De Residência De Polímeros Em Extrusora a Partir De Medidas De Luminância

Método Simples Para Determinar Distribuição De Tempo De Residência De Polímeros Em Extrusora a Partir De Medidas De Luminância

Optimization of the Solution of a Dispersion Model

A generic dynamic model structure for tumbling mills

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