Cor M. van den Bleek

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.

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.

Application of chaos analysis to multiphase reactors

It is shown that chaos analysis provides valuable tools to improve the design and operation of multiphase reactors, the most useful tools being the systems attractor and the Kolmogorov entropy. Applications of chaos analysis are based upon examining the attractor shape and/or on a characterization of the attractor by the Kolmogorov entropy. Examples are given by the characterization of regimes and regime transitions, scale up, control of the bubble pattern in the reactor to influence selectivity and conversion of chemical reactions, and the development of a tool to early detect agglomeration in fluidized beds.

Learning Chaotic Attractors by Neural Networks

An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time series. During training, the algorithm learns to short-term predict the time series. At the same time a criterion, developed by Diks, van Zwet, Takens, and de Goede (1996) is monitored that tests the hypothesis that the reconstructed attractors of model-generated and measured data are the same. Training is stopped when the prediction error is low and the model passes this test. Two other features of the algorithm are (1) the way the state of the system, consisting of delays from the time series, has its dimension reduced by weighted principal component analysis data reduction, and (2) the user-adjustable prediction horizon obtained by error propagationpartially propagating prediction errors to the next time step. The algorithm is first applied to data from an experimental-driven chaotic pendulum, of which two of the three state variables are known. This is a comprehensive example that shows how well the Diks test can distinguish between slightly different attractors. Second, the algorithm is applied to the same problem, but now one of the two known state variables is ignored. Finally, we present a model for the laser data from the Santa Fe time-series competition (set A). It is the first model for these data that is not only useful for short-term predictions but also generates time series with similar chaotic characteristics as the measured data.

Can deterministic chaos create order in fluidized-bed scale-up?

Abstract A characteristic property of a dynamic system is how fast it generates information in time. The information connected to a dynamic system is expressed in bits; it is a profound primitive concept and, therefore, cannot be defined as a combination of elemental constituents. The rate of generation of information in a dynamic system is measured by the Kolmogorov entropy in bits per second. This measure can be computed from a time series of one of the independent variables of the dynamic system; in the case of a fluidized bed, this may, for example, be pressure or voidage. The entropy is finite and positive in the case of a deterministic chaotic system, as, for example, a gas—solids fluidized bed. This means that, beside the laws of conservation of mass, energy and momentum, in dimensionless scaling of fluidized-bed reactors, the law of conservation of information should be also taken into account. This implies that two fluidized-bed reactors that are properly scaled will exhibit the same non-dimensional rate of information loss, expressed as Kd p / U O . This entropy measure should, therefore, be used to assess the dynamic similarity of scaled fluidized-bed reactors.

IR mechanistic studies on NO reduction with NH3 in the presence of oxygen over cerium-exchanged mordenite

An in situ IR study on NO reduction with ammonia in the presence of oxygen has been performed with cerium-exchanged mordenite (CeNaMOR) in order to examine the reaction intermediates involved in the reaction. Co-adsorption of NO and O2 on fresh CeNaMOR resulted in the formation of NO+(nitrosonium ion: 2161 cm–1), NO2–(nitrito: 1416 cm–1) and NO3–(nitrato: 1510, 1487 and 1337 cm–1), while NH3 adsorption on fresh CeNaMOR led to the formation of NH4+(1470, 1730, 2500–3500 cm–1) and coordinatively bonded NH3 species (1603, 2500–3500 cm–1). Under a flow of the three reactants (NO, NH3 and O2) as the case for the selective catalytic reduction (SCR) reaction in practice, the adsorbed ammonia species turned out to be dominantly present on CeNaMOR. The admission of NO and O2 over NH3-preadsorbed CeNaMOR at 100 °C led to the preferred disappearance of coordinatively bonded NH3 species, prior to NH4+, and at the same time, the appearance of the bands due to water and NO2– was observed. The admission of NH3 at 100 °C over CeNaMOR containing preadsorbed NOx species (NO+, NO3– and NO2–) resulted in a substantial reduction of the NO+ band, while the NOx– species were found to disappear simultaneously with NH4+ only at and above 300 °C, leaving water as a product. Based on these results, a nitrosation reaction scheme is proposed, where NO+ and NH3 react easily, and the less reactive adsorbed species, NO2– and NH4+, react with each other only at a higher temperature. The proposed scheme can agree with the reaction stoichiometry and reaction orders known for NO reduction with NH3 over CeNaMOR.

Prediction of NOx Emissions from a Transiently Operating Diesel Engine Using an Artificial Neural Network

For an adequate control of the reductant flow in selective catalytic reduction of NO x in diesel exhaust, a tool has to be available to accurately and quickly predict the engines NO x emission. For these purposes, elaborate computer models and expensive NO x analyzers are not feasible. The application of a neural network is proposed instead. Measurements were performed on a transient operating diesel engine. One part of the data was used to train the network for NO x emission prediction, the other part was used to test. The average absolute deviation between the predicted and measured NO x emission is 6.7 %. The reductant buffering capacity of the deNOx catalyst will diminish the effect of the deviation on the overall NO x removal efficiency. The high accuracy of the neural network predictions, combined with the short computation times (0.2 ms/data point), makes the neural network a very promising tool in automotive NO x control.

Monitoring fluidization dynamics for detection of changes in fluidized bed composition and operating conditions

In many industrial applications of gas-solids fluidized beds, it is worthwhile to have an on-line monitoring method for detecting changes in the hydrodynamics of the bed (due for example to agglomeration) quickly. In this paper, such a method, based on the short-term predictability of fluidized bed pressure fluctuations, is examined. Its sensitivity is shown by experiments with small step changes in the superficial gas velocity and by experiments with a gradual change in the particle size distribution of the solids in the bed. Furthermore, it is demonstrated that the method is well able to indicate if a stationary hydrodynamic state has been reached after a change in the particle size distribution (a ‘grade change’).

Modelling SO2 and NOx emissions in fluidized bed combustion of coal

The catalytic activity of calcined limestone and sulphated limestone on the oxidation for NH3 to NO were tested in a fixed bed, which simulates the interactions between SO2 and NOx emissions from a fluidized bed combustor caused by the CaO based sorbents. The calcined limestone is very active for oxidation of NH3 to NO, while the sulphated lime is almost an inert for this reaction. A model is proposed to describe the SO2 and NOx emissions and their interactions, in which the unsulphated CaO based sorbents capture the SO2 from coal and catalytically oxidize intermediate N compounds (NH3) to NOx. The sulphation of limestone is based on an approximate analytical solution of the general gas-solid reaction model with structure change of the particle. A simple scheme of NOx formation and destruction is used to describe the NOx emissions. The results of the model are compared with different sources of experimental data from fluidized bed combustion in literature. The comparisons show a good agreement.

Prediction of NOx and SOx emissions in FBC of coal using easy to determine coal and sorbent characteristics

Abstract A simple model is presented to predict the sulfur retention and the NOx emission during fluidized bed combustion of coal by using basic coal and sorbent characterization parameters. The work is an extension of D.U.T. SURE model to NOx emission. Based on a simple kinetic model and on one phase ideally mixed hydrodynamics a set of analytical expressions is derived. The results from the model are in agreement with experimental observations.