Jc Jaap Schouten

Characterization of fluidization regimes by time-series analysis of pressure fluctuations

Abstract This work compares time, frequency and state-space analyses of pressure measurements from fluidized beds. The experiments were carried out in a circulating fluidized bed, operated under ambient conditions and under different fluidization regimes. Interpretation of results in time domain, such as standard deviation of the pressure fluctuations, may lead to erroneous conclusions about the flow regime. The results from the frequency domain (power spectra) and state-space analyses (correlation dimension, D ML , and Kolmogorov entropy, K ML , together with a non-linearity test) of the pressure fluctuations are generally in agreement and can be used complementary to each other. The power spectra can be divided into three regions, a region corresponding to the macro-structure (due to the bubble flow) and, at higher frequencies, two regions representing finer structures that are not predominantly governed by the macro structure of the flow. In all fluidization regimes, the measured pressure fluctuations exhibited an intermittent structure, which is not revealed by power spectral analysis of the original signals. Fluctuations with pronounced peaks in the power spectrum and in the auto-correlation function, corresponding to passage of single bubbles through the bed, are non-linear with a low dimension ( D ML D ML D ML >5.5 both K ML (bits/cycle) and D ML are insensitive to changes in the distribution of energy in power spectra. Thus, the state-space analysis reflects that non-linearity is mostly found in the macro-structure of the flow. Fluidized bed time series treated in this work are available at http://www.entek.chalmers.se/∼fijo

Characterization of regimes and regime transitions in bubble columns by chaos analysis of pressure signals

In this study it is shown that the transition from the homogeneous to the heterogeneous flow regime in bubble columns can be quantitatively found with high accuracy by analysing the chaotic characteristics of the pressure fluctuation signal (PFS). In previous work (van den Bleek and Schouten, 1993; Schouten et al., 1996), the authors have already applied this technique to time series from gas-solid fluid beds. Also, it was shown (Krishna et al., 1993, Ellenberger and Krishna, 1994) that hydrodynamics of bubble columns and fluid beds can be described in an analogous manner. Therefore in this work, the method of chaos analysis is applied to bubble columns. A distinctive feature of the pressure signal from bubble columns is that it is composed of two different parts: a low frequency part resulting from the motion of the large bubbles and a high frequency part resulting from all other processes (coalescence, collapse, breakup) that take place in the column. From the phase of the cross spectrum of two pressure probes, placed at different axial positions, it was possible to identify the bands in the spectrum of the PFS that show a significant time delay. This time delay is of the order of the passage time of bubbles between the measurement locations. This band in the spectrum of the PFS was used to estimate the Kolmogorov entropy to quantify the chaotic dynamics in the bubble column. The Kolmogorov entropy as a function of gas velocity indicates a sharp transition from the homogeneous to the churn-turbulent flow regime. From other methods considered (e.g. holdup and other properties of the signal such as variance), this transition was less clear. Therefore chaos analysis of PFSs is believed to be a powerful technique for on-line identification of flow regimes.

Gas holdup and mass transfer in bubble column reactors operated at elevated pressure

Abstract Measurements of the total gas holdup, e , have been made in a 0.15xa0m diameter bubble column operated at pressures ranging from 0.1 up to 1.3xa0MPa. The influence of the increasing system pressure is twofold: (1) a shift of the flow regime transition point to higher gas fractions, and (2) a decrease of the rise velocity of “large” bubbles in the heterogeneous regime. The large bubble rise velocity is seen to decrease with the square root of the gas density, ρ G . This square root dependence can be rationalized by means of a Kelvin–Helmholtz stability analysis. The total gas holdup model of Krishna and Ellenberger (1996, A.I.Ch.E. J. 42, 2627–2634), when modified to incorporate the ρ G correction for the large bubble rise velocity, is found to be in good agreement with the experimental results. The influence of system pressure on the volumetric mass transfer coefficient, k L a , is determined using the dynamic pressure-step method of Linek et al. (1993, Chem. Engng Sci. 48, 1593–1599). This pressure step method was adapted for application at higher system pressures. The ratio ( k L a/e ) is found to be practically independent of superficial gas velocity and system pressure up to 1.0 MPa; the value of this ratio is approximately equal to one half. This result provides a simple method for predicting k L a using the model developed for estimation of e .

Origin, propagation and attenuation of pressure waves in gas-solid fluidized beds

Abstract Recently reported results on the origin, propagation and attenuation of pressure waves in bubbling gas—solid fluidized beds are re-evaluated and the results are compared with additional experiments reported here. It is found that the measured pressure fluctuations are a result of slow and fast propagating pressure waves. Pressure waves with high propagation velocities (> 10 m/s) are unambiguously identified as compression waves, which move upwards and downwards. Upward moving compression waves originate from gas bubble formation and gas bubble coalescence. The amplitude of upward moving pressure waves is linearly dependent on the distance to the bed surface. Downward moving compression waves are caused by gas bubble eruptions at the fluidized bed surface, bubble coalescence and by changes in bed voidage. In this case the pressure wave amplitude is independent of the distance to the bed surface. Pressure waves with propagation velocities of less than 2 m/s are caused by rising gas bubbles. These pressure waves move upwards only, with an amplitude proportional to the bubble size. The average wave propagation velocity measured in a freely bubbling bed is lower than that predicted from the pseudo-homogeneous compressible wave theory owing to the presence of slowly rising gas bubbles. The average propagation velocity of pressure waves in a gas—solid circulating fluidized bed is adequately described as a function of local voidage by pseudo-homogeneous compressible wave theory. At low voidages in the bottom of the riser, the propagation velocity is lowered by the presence of gas bubbles or large gas voids.

Eulerian simulations of bubbling behaviour in gas-solid fluidised beds

Abstract In literature little attempt has been made to verify experimentally Eulerian-Eulerian gas-solid model simulations of bubbling fluidised beds with existing correlations for bubble size or bubble velocity. In the present study, a CFD model for a free bubbling fluidised bed was implemented in the commercial code CFX of AEA Technology. This CFD model is based on a two fluid model including the kinetic theory of granular flow. Simulations of the bubble behaviour in fluidised beds at different superficial gas velocities and at different column diameters are compared to the Darton et al. (1977) equation for the bubble diameter versus the height in the column and to the Hilligardt and Werther (1986) equation, corrected for the two dimensional geometry using the bubble rise velocity correlation of Pyle and Harrison (1967). It is shown that the predicted bubble sizes are in agreement with the Darton et al. (1977) bubble size equation. Comparison of the predicted bubble velocity with the Hilligardt and Werther (1986) equation shows a deviation for the velocity of smaller bubbles. To explain this, the predicted bubbles are divided into two bubble classes : bubbles that have either coalesced, broken-up or have touched the wall, and bubbles without these occurrences. The bubbles of this second class are in agreement with the Hilligardt and Werther (1986) equation. Fit parameters of Hilligardt and Werther (1986) are compared to the fit parameters obtained in this work. It is shown that coalescence, break-up, and direct wall interactions are very important effects, often dominating the dynamic bubble behaviour, but these effects are not accounted for by the Hilligardt and Werther (1986) equation.

Deterministic chaos: a new tool in fluidized bed design and operation

Abstract Deterministic chaos theory offers new and useful quantitative tools to characterize the non-linear dynamic behaviour of fluidized beds. The dimension and entropy of the fluidized beds strange attractor can be used for various purposes, such as the classification of fluidization regimes or fluidized bed scale-up. This is illustrated by experimental and model simulation examples of deterministic chaotic behaviour in ambient gas-solids fluidized beds of Geldart B particles. It is shown that the Kolmogorov entropy is dependent on, amongst other parameters, the gas velocity and the bed aspect ratio. In dimensionless scaling of fluidized bed reactors this type of relationship can probably be of use in establishing full dynamic similarity.

Validation of the Eulerian simulated dynamic behaviour of gas-solid fluidised beds

In this paper, a Eulerian–Eulerian CFD model for a freely bubbling gas–solid fluidised bed containing Geldart-B particles is developed for studying its dynamic characteristics. This CFD model is based on the kinetic theory of granular flow. Van Wachem et al. (1998a) Comput. Chem. Engng 22 (Suppl.), S299–S307 have shown that this model is capable of providing reasonable predictions of the time-averaged properties. In this paper, the dynamic characteristics of the gas–solids behaviour at different superficial gas velocities, at different column diameters, and at different pressures are evaluated, namely (A) the velocity of pressure and voidage waves through the bed, (B) the power of the low and high frequencies of the pressure and voidage fluctuations, (C) the reorientation of the gas–solids flow just above minimum fluidisation and the effect of elevated pressure upon this reorientation, and (D) the Kolmogorov entropy. The CFD simulation results for items (A)–(D) are compared with published experimental data and with appropriate correlations from the literature. A good agreement is found between the Eulerian–Eulerian CFD simulations of bubbling fluidised-bed dynamics, and the data from experiments in the literature. This is a strong incentive for the further development of this type of simulation models in fluidised-bed reactor design and scale-up.

Fluidization regimes and transitions from fixed bed to dilute transport flow

Characterization by means of Kolmogorov entropy shows that the dynamics of the bottom bed in small size circulating fluidized bed risers are significantly different from the dynamics of the dense bottom bed in large size risers and, as a consequence, two types of circulating regimes are introduced: the exploding bubble bed for large risers and the circulating ‘slugging’ bed for small risers, the latter at high superficial gas velocities. In a pictorial fluidization diagram ten gas—solid fluidization regimes are given, seven of which are experimentally identified with the Kolmogorov entropy by varying the superficial gas velocity, riser solids holdup and diameter (or width) of the riser: bubbling bed, slugging bed, exploding bubble bed, intermediate turbulent bed, circulating ‘slugging’ bed, intermediate dilute flow, and dilute transport flow. No transition could be identified between the exploding bubble bed at captive conditions and the exploding bubble bed at circulating conditions in the dense bottom bed of the two largest facilities in this study. This suggests that the dense bottom bed in large size risers can be considered as a bubbling bed. A turbulent bed was found in none of the facilities of this study with the Geldart B solids used. As well as by the Kolmogorov entropy (chaos analysis), the hydrodynamics have been characterized by amplitude of pressure fluctuations, while a solids distribution analysis has also been carried out. The study has been made in four (circulating) fluidized beds of different size and design, all operated with 0.30 mm silica sand. The dimensions of the fluidized bed risers are 1.47 × 1.42 × 13.5 m, 0.70 × 0.12 × 8.5 m, 0.12 m i.d. × 5.8 m, and 0.083 m i.d. × 4.0 m.

Response characteristics of probe-transducer systems for pressure measurements in gas-solid fluidized beds: how to prevent pitfalls in dynamic pressure measurements

Abstract It is long known already that the pressure probe–transducer systems applied in gas–solid fluidized beds can distort the measured pressure fluctuations. Several rules of thumb have been proposed to determine probe length and internal diameter required to prevent this. Recently, Xie and Geldart [H.-Y. Xie, D. Geldart, Powder Technol. 90 (1997) 149] proposed 4 mm i.d. probes as a panacea for all practical situations encountered. However, almost no information is available in the literature that relates possible distortions to characteristics to be extracted from the pressure signal. This paper reports the influence of probe dimensions on the outcomes of different data analysis methods for fluidized bed pressure signals (spectral analysis, statistical analysis, and chaos analysis). It reviews the most important probe–transducer models and compares them on the basis of experiments with both noisy (i.e., highly turbulent gas phase) pressure time-series, and pressure time-series measured in a bench-scale fluidized bed. The comparison is carried out by determining the frequency response function in the frequency domain. It is shown, that the Bergh and Tijdeman model [H. Bergh, H. Tijdeman, Theoretical and experimental results for the dynamic response of pressure measuring systems, Report NLR-TR F.238, National Aero- and Astronautical Research Institute, Amsterdam, the Netherlands, 1965] is superior to all other models reported in literature. The Bergh and Tijdeman model, originally developed for wind-tunnel testing, is the only model that gives a good prediction of the frequency response characteristics of a probe–transducer system for a wide range of probe dimensions. In this paper, rules of the thumb supported by this model will be given. It is found that for statistical analysis and chaos analysis, probes up to 2.5 m length with an internal diameter ranging from 2 to 5 mm do not severely effect the analysis results, since these are mainly focused on frequencies up to about 20 Hz. However, in general, it is preferable to keep the probe length as short as possible. In the case of spectral analysis, the demands on the probe dimensions depend on the frequency range of interest: if one is interested in a frequency range up to 200 Hz (e.g., when studying the power-law fall-off in the power spectral density), the probe length should be limited to about 20 cm. The results reported in this paper are obtained using a transducer with an internal volume of 1500 mm3, but it is shown that the conclusions on the probe dimensions are valid for a wide range of transducer volumes. The experiments are carried out in an 80-cm i.d. bench-scale fluidized bed of sand (median diameter 470 μm, Geldart type B); for smaller particles and smaller scale installations, the frequency range of interest will shift to higher frequencies. In that case, the optimal probe diameter stays in the range from 2 to 5 mm, but it will become even more important to keep the probe length limited; this can be calculated with the Bergh and Tijdeman model [H. Bergh, H. Tijdeman, Theoretical and experimental results for the dynamic response of pressure measuring systems, Report NLR-TR F.238, National Aero- and Astronautical Research Institute, Amsterdam, the Netherlands, 1965]. The experiments presented in this paper are carried out at ambient pressure and temperature. However, since the Bergh and Tijdeman model contains no fitted parameters, it is expected to give a reliable estimate for the probe–transducer characteristics at other operating conditions as well; the effect of the temperature is shown in this paper.

SCALE-UP OF CHAOTIC FLUIDIZED BED HYDRODYNAMICS

This paper focuses on scale-up of the dynamic behavior of gas-solids fluidized bubbling reactors. An empirical approach is followed that is based on the observation that the non-linear, hydrodynamic behavior of bubbling fluidized beds is of a chaotic nature. The degree of chaos is quantified by the Kolmogorov entropy, which is a measure of the rate of loss of information in the system (expressed in bits of information per second). The basic idea of the ‘chaos scale-up methodology’ proposed in this paper is that the rate of information loss 3hould be kept similar when scaling up a bubbling bed from the small scale to the larger scale, in order to ensure dynamic (i.e. chaotic) similarity between the scaled beds. For a set of Geldart-B and -D particle systems, and for a range of bed diameters (from 0.1 m ID up to 0.8 m ID), an empirical correlation (Equation 4 in the paper) is derived that relates Kolmogorov entropy to main bubbling bed design parameters, viz. (i) fluidization conditions (superficial gas velocity, settled bed height), (ii) particle properties (minimum fluidization velocity), and (iii) bed size (diameter). It is illustrated by numerical examples how this correlation might be used in scaling up the chaotic dynamics of bubbling fluidized reactors. It is further shown that a similar type of correlation for Kolmogorov entropy can also be derived theoretically (Equations 1 and 5 in the paper).