A 2D Markov chain for modelling powder mixing in alternately revolving static mixers of Sysmix® type

Ponomarev, Denis; Mizonov, Vadim E.; Berthiaux, Henri; Gatumel, Cendrine; Gyenis, János; Barantseva, Elena

doi:10.1016/j.cep.2009.10.004

Cited by 8 publications

(7 citation statements)

References 18 publications

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“…If components do not exhibit the same transition probabilities in the mixing zone, one must consider as many transition matrices as there are different component flow behaviors. 19 For example, in the binary mixture case A/B, there will be four model parameters p sA , p sB , p dA , and p dB that depend on the flow behavior inside the mixer. proposed in this study, we can obtain the evolution process of the mixture state and calculate the evolution of overall standard deviation of the mixture with the number of mixing elements.…”

Section: Resultsmentioning

confidence: 99%

“…The results were different from those reported by some previous literature. 18,19 It indicated that the physical properties had little effect on the transition probability of particles in the continuous colliding static mixer, and the matrix of transition probability depended mainly on the type of mixing elements. The results showed that large different particles with a segregation potential could make good mixing in the continuous colliding static mixer.…”

Section: Resultsmentioning

confidence: 99%

“…However, these models belong to a one-dimensional cell model which only describes the mixing of particles in one direction through the mixer. On the basis of previous studies, Ponomarev 19 proposed a two-dimensional model based on the Markov chain theory for an alternately revolving static mixer of Sysmix type. In this model, mixing occurs in both horizontal and vertical directions.…”

Section: Introductionmentioning

confidence: 99%

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Markov Chain Modeling the Mixing of Coal and Solid Heat Carriers in a Continuous Colliding Static Mixer

Zhan

Liu

Zhang

et al. 2014

Ind. Eng. Chem. Res.

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The mixing of coal and solid heat carriers on the coal pyrolysis process was studied with a continuous colliding static mixer. A two-dimensional Markov chain model of both single-element and multielement has been developed to describe the mixing process of coal and solid heat carriers on the free surface. Some simulations were presented to investigate the evolution of the mixture state, as well as the influence of the initial distribution and the feeding ratio of the components on the mixing kinetics. Mixing experiments with coal and ceramic balls were carried out to validate the single-element Markov chain model proposed in this work. The experimental results of mixing coal and ceramic balls were in good agreement with those predicted from the model, demonstrating that the model was able to effectively describe the mixing process in the continuous colliding static mixer. The multielement model gave guidance and direction of mixing optimization for the application of the continuous colliding static mixing in large-scale coal pyrolysis industry. The results indicated that the transition matrices depended mainly on the type of mixing elements in a continuous colliding static mixer and had little relation with the property of particles. The present study justified that a continuous colliding static mixer was suitable for mixing binary inhomogeneous particle systems.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Markov Chain Modeling the Mixing of Coal and Solid Heat Carriers in a Continuous Colliding Static Mixer

Zhan

Liu

Zhang

et al. 2014

Ind. Eng. Chem. Res.

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“…The transition matrix was determined experimentally and allowed to describe the concentration profiles for each system. More recently, a two-dimensional model of the flow and mixing of particulate solids has been developed on the basis of the Markov chain theory for an alternately revolving static mixer [12]. This model represented the distribution of component during mixing operation, in both vertical and horizontal directions.…”

Section: A Quick State-of-the-artmentioning

confidence: 99%

Transitory powder flow dynamics during emptying of a continuous mixer

Ammarcha

Gatumel

Dirion

et al. 2013

Chemical Engineering and Processing: Process Intensification

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International audienceThis article investigates the emptying process of a continuous powder mixer, from both experimental and modelling points of view. The apparatus used in this work is a pilot scale commercial mixer Gericke GCM500, for which a specific experimental protocol has been developed to determine the hold up in the mixer and the real outflow. We demonstrate that the dynamics of the process is governed by the rotational speed of the stirrer, as it fixes characteristic values of the hold-up weight, such as a threshold hold-up weight. This is integrated into a Markov chain matrix representation that can predict the evolution of the hold-up weight, as well as that of the outflow rate during emptying the mixer. Depending on the advancement of the process, the Markov chain must be considered as non-homogeneous. The comparison of model results with experimental data not used in the estimation procedure of the parameters contributes to validating the viability of this model. In particular, we report results obtained when emptying the mixer at variable rotational speed, through step changes

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“…In the past, Markovian models have been applied to various powder mixers. One can refer to the following works: Chen et al [10], Lai and Fan [11], Wang and Fan [12,13], Fan and Shin [14], Aoun-Habbache et al [15], Berthiaux et al [16], Ponomarev et al [17]. As all these papers described the process under steady conditions, only homogeneous Markov chains have ever been considered for mixing.…”

Section: A Simple Markov Chain Representation Of Continuous Mixingmentioning

confidence: 99%

Predicting bulk powder flow dynamics in a continuous mixer operating in transitory regimes

Ammarcha

Gatumel

Dirion

et al. 2012

Advanced Powder Technology

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 9970 a b s t r a c tOver recent years there has been increasing interest in continuous powder mixing processes, due mainly to the development of on-line measurement techniques. However, our understanding of these processes remains limited, particularly with regard to their flow and mixing dynamics. In the present work, we study the behaviour of a pilot-scale continuous mixer during transitory regimes, in terms of hold-up weight and outflow changes. We present and discuss experimental results concerning the start-up dynamics of a Gericke GCM 500 mixer, for which a specific experimental protocol has been developed to determine the evolution of the hold-up in the mixer and the real outflow. Empirical relationships are derived so as to link hold-up weight variations with operating conditions. A simple stochastic approach, based on a non-homogeneous Markov chain, is developed to simulate the bulk particle flow and transport in the continuous mixer at a macroscopic level. Although this simple model is only based on the start-up behaviour, it provides a full description of the mixer dynamics in response to strong perturbations on the flow rate or on the rotational speed of the stirring device, such as negative or positive steps. This model is validated experimentally for a wide range of operating conditions, and constitutes a first approach to process control.

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A 2D Markov chain for modelling powder mixing in alternately revolving static mixers of Sysmix® type

Cited by 8 publications

References 18 publications

Markov Chain Modeling the Mixing of Coal and Solid Heat Carriers in a Continuous Colliding Static Mixer

Markov Chain Modeling the Mixing of Coal and Solid Heat Carriers in a Continuous Colliding Static Mixer

Transitory powder flow dynamics during emptying of a continuous mixer

Predicting bulk powder flow dynamics in a continuous mixer operating in transitory regimes

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