Estimation of the particle diffusivity in a liquid-solids fluidized bed based on a stochastic model

Yutani, N.; Ototake, Naoshi; Too, J. R.; Fan, Liang‐Shih

doi:10.1016/0009-2509(82)80138-3

Cited by 36 publications

(20 citation statements)

References 8 publications

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“…In liquid-solid fluidized beds, the movement of fluidized particles appears to be irregular and random, which is assumed to be essentially stochastic [11]. Recent work demonstrated that some of the phenomena taking place in liquid- solid fluidized beds are amenable to the analysis couched in the parlance of the fractional Brownian motion (FBM) [12,13].…”

Section: Fractal Analysismentioning

confidence: 99%

Radial Particle Profiles in a Liquid‐Solid CFB with Varying Viscosity

Zheng¹

2004

Chem Eng & Technol

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Flow structure was characterized in a 76 mm diameter by 2.0 m high liquid-solid circulating fluidized bed (LSCFB) with different viscous liquids ranging from 1.0 mPa´s to 4.8 mPa´s. Measurements of mean and local solids holdup were carried out in the axial and the radial direction, respectively. The results showed that a uniform axial and a nonuniform radial distribution of the time-averaged solids holdup appeared in the LSCFB. The viscosity of the liquid phase reduces the nonuniform distribution of solid particles in the radial direction. By examining the instantaneous data signals, flow behavior in a viscous system was found to be more uniform and less vigorous. To further understand the hydrodynamics in a LSCFB, Hurst's rescaled range (R/S) analysis was also adopted to analyze its stochastic characteristics and the local flow properties.

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Section: Fractal Analysismentioning

confidence: 99%

Radial Particle Profiles in a Liquid‐Solid CFB with Varying Viscosity

Zheng¹

2004

Chem Eng & Technol

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“…Nevertheless, the performance of a liquidsolid fluidized bed as a contactor or reactor is influenced appreciably by various factors, such as the flow regime (Volpicelli et al, 1966;Kang and Kim, 1988), the motion of fluidized particles (Handley et al, 1966;Kmiec, 1978;Yutani et al, 1983), and voidage distribution (Fan et al, 1985); this gives rise to highly complicated, nonlinear and stochastic behavior of the bed. While some attempts had been made to stochastically analyze and model such behavior, they were mostly based on the Markovian assumptions and notion of classical Brownian motion (Yutani et al, 1982(Yutani et al, , 1983Yutani and Fan, 1985;Fan et al, 1990a;Kang et al, 1990).Our recent works on multiphase flow systems (Fan et al, 1989(Fan et al, , 1990b have indicated that the concept of fractional Brownian motion (fBm), which can be characterized by the Hunt exponent, H , may be applicable to the analysis of liquidsolid fluidized beds. The model based on this concept has been proposed by Mandelbrot and van Ness (1968) to identify the long-term correlation in a time series, which is self-affine.…”

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confidence: 97%

Fractal analysis of fluidized particle behavior in liquid‐solid fluidized beds

et al. 1993

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Liquid-solid fluidized beds have been adopted widely for catalytic liquid-phase reactions, separation and recovery of materials with ion exchange resin, adsorption, sedimentation, and wastewater treatment. Their unique features are the effective liquid-solid contact and the high rates of heat and mass transfer (Morooka et al., 1980;Muroyama et al., 1986;Kang and Kim, 1987). Nevertheless, the performance of a liquidsolid fluidized bed as a contactor or reactor is influenced appreciably by various factors, such as the flow regime (Volpicelli et al., 1966;Kang and Kim, 1988), the motion of fluidized particles (Handley et al., 1966;Kmiec, 1978;Yutani et al., 1983), and voidage distribution (Fan et al., 1985); this gives rise to highly complicated, nonlinear and stochastic behavior of the bed. While some attempts had been made to stochastically analyze and model such behavior, they were mostly based on the Markovian assumptions and notion of classical Brownian motion (Yutani et al., 1982(Yutani et al., , 1983Yutani and Fan, 1985;Fan et al., 1990a;Kang et al., 1990).Our recent works on multiphase flow systems (Fan et al., 1989(Fan et al., , 1990b have indicated that the concept of fractional Brownian motion (fBm), which can be characterized by the Hunt exponent, H , may be applicable to the analysis of liquidsolid fluidized beds. The model based on this concept has been proposed by Mandelbrot and van Ness (1968) to identify the long-term correlation in a time series, which is self-affine. It has been postulated that the rescaled range (R/S) analysis can be a means of estimating H for a given time series (Mandelbrot and Wallis, 1969a,b;Feder, 1988).In this work, pressure fluctuations in a liquid-solid fluidized bed have been examined by resorting to the R/S analysis; the effects of fluidized particle size, axial position, and liquid flow rate on the Hurst exponent, H, or the local fractal dimension, dpL, have been examined. The results have revealed that the pressure fluctuations in the bed, exhibiting long-term corre- Pressure taps were installed on the wall of the column at six different heights from the distributor. Each pressure tap was connected to one of the two input channels of a differential pressure transducer (Enterprise Model CJ3D), which produced an output voltage proportional to the pressure difference between the two channels. The remaining channel was exposed to the atmosphere.Signals were processed by an oscilloscope, a personal computer (Zenith 386), and a mainframe computer (IBM 3084). The voltage-time signal, corresponding to the pressure-time signal, from the transducer was fed to the recorder at the selected sampling rate of 0.005 s. A typical sample comprised 4,000 points. This combination of the sampling rate and sample length ensured that the full spectrum of hydrodynamic signals were captured from the liquid-solid fluidized bed; the signals were processed off-line. Results and DiscussionThe experimental results indicated that, in general, the amplitude of pressure fluctuations in the liquid-s...

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“…Despite it does not seem very realistic to assume that upward and backward transitions are equal in an upward fl ow under gravity, these two models gave a fi rst insight on the fl uidised bed modelling with Markov chains. Professor Fan's research team also investigated particle diffusivity (Yutani et al, 1982;Yutani and Fan, 1985), radial particle mixing and bubble behaviour (Yutani et al, 1983;Yutani et al, 1986) in fl uidized beds using a stochastic analysis. However, this approach was more relevant to Markov processes rather than Markov chains and is thus outside of the scope of our paper.…”

Section: Flow In Fl Uidized Bedsmentioning

confidence: 99%

Applications of Markov Chains in Particulate Process Engineering: A Review

Berthiaux

Mizonov

2004

Can J Chem Eng

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Processes involving particles, are known to exhibit extremely unpredictable behaviour, mainly due to the mesoscopic nature of granular media. Understanding particulate processes, not only for intellectual satisfaction, but also for process design and operation, basically requires a systems approach in modelling. Because they combine simplicity and flexibility, the stochastic models based on the Markov chain theory are very valuable mathematical tools to this respect. However, they are still largely ignored by the whole core of chemical engineering researchers. This motivates the existence of this review paper, in which we examine the three traditional issues: mixing and transport, separation and transformation.

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Estimation of the particle diffusivity in a liquid-solids fluidized bed based on a stochastic model

Cited by 36 publications

References 8 publications

Radial Particle Profiles in a Liquid‐Solid CFB with Varying Viscosity

Radial Particle Profiles in a Liquid‐Solid CFB with Varying Viscosity

Fractal analysis of fluidized particle behavior in liquid‐solid fluidized beds

Applications of Markov Chains in Particulate Process Engineering: A Review

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