Non-isothermal Fluidized Bed Research Articles

Burning of Sulfur-Containing Liquid Fuels in Fluidized Catalyst Bed

Results are presented of the process of burning of sulfur-containing liquid fuels in a nonisothermal fluidized bed of a ShchKZ-1 industrial catalyst for the example of sulfurous and heavy high-sulfur oil. The optimal (“dropdown”) temperature profile in the bed was determined. This profile is characterized by a downstream decrease in temperature from 700 to 500°C. A mathematical simulation based on the description of experimental data on the variation of the sulfur concentration at the exit from the adsorbent (calcite) bed at its varied charge was used to calculate the specific capacity of the sorbent to be (14.2-15.9) x 103 g cm3. It was shown that the potential capacity of calcite in fluidized bed exceeds by an order magnitude that in a fixed bed.

A reduced-order model for heat transfer in multiphase flow and practical aspects of the proper orthogonal decomposition

This paper discusses two practical aspects of reduced-order models (ROMs) based on proper orthogonal decomposition (POD) and presents the derivation and implementation of a ROM for non-isothermal multiphase flow. The POD method calculates basis functions for a reduced-order representation of two-phase flow by calculating the eigenvectors of an autocorrelation matrix composed of snapshots of the flow. The flow is divided into transient and quasi-steady regions and two methods are shown for clustering snapshots in the transient region. Both methods reduce error as compared to the constant sampling case. The ROM for non-isothermal flow was developed using numerical results from a full-order computational fluid dynamics model for a two-dimensional non-isothermal fluidized bed. Excellent agreement is shown between the reduced- and full-order models. The composition of the autocorrelation matrix is also considered for an isothermal case. An approach treating field variables separately is shown to produce less error than a coupled approach.

Mathematical model of unsteady gas to solid particles heat transfer in fluidized bed

The mathematical model of unsteady one-dimensional gas to particles heat transfer for non-isothermal fluidized bed with periodic heating of solid particles has been described. The method of numerical solution of governing differential equations, the algorithm and the computer program, have been presented. By using mathematical model and computer program, the temperature profiles for interstitial gas, gas in bubbles, and solid particles along the height of fluidized bed in function of time, have been determined. The results obtained on the basis of prediction method are compared to the experimental results of the authors; the satisfactory agreement has been found for interstitial gas temperature and solid particle temperature. On the basis of this comparison, the mathematical model has been verified.

Dynamic Characteristics of a Periodically Forced Fluidized Bed Catalytic Reactor under Conventional PI Control

A two-phase model of a non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions A → B → C is used to investigate the dynamic characteristics of this industrially important unit when it is periodically forced. The investigation concentrates on forcing a periodic regime of the autonomous system with a relatively high forcing frequency. It is shown that by periodic forcing of the feed temperature, chaotic regimes occur for small amplitudes of forcing. For constant frequency and with the change in the forcing amplitude the behavior of the unit alternates between periodic and chaotic regimes via period doubling and period adding mechanisms. When on the other hand the amplitude is fixed chaotic regimes also appear for small changes in the forcing frequency. The effects of these parametric perturbations on the yield of the desired intermediate product B is also investigated. It is shown that the yield can be improved by an appropriate selection of the forcing frequency.

O-Xylene oxidation to phthalic anhydride over unsteady state catalysts

o-Xylene oxidation in a non-isothermal fluidized bed has been studied. Phthalic anhydride yield appears to be significantly higher than in an isothermal fluidized bed or in ideal mixing and plug flow reactors. A higher yield is caused by an unsteady state of the catalyst resulting from a chaotic particle movement in the temperature field.

EXISTENCE OF COMPLEX ATTRACTORS IN FLUIDIZED BED CATALYTIC REACTORS

A relatively simple two-phase model for the non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions has been used to investigate the complex oscillatory behaviour of this industrially important unit. Relaxation oscillations are produced by distortion of limit cycles which have fast and slow motion in the phase space. The new type of period-adding bifurcation has been uncovered, analysed and is shown to generate periodic bursting with high periodicity. The period-adding mechanism presented is classified as a third kind of period-adding. The complex oscillatory trajectory is conjectured to terminate by a boundary crisis.

Complex Non-Chaotic Attractors in Fluidized Bed Catalytic Reactors

A two-phase model for the non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions used earlier to investigate the chaotic behaviour of this system 1 is used in this investigation to explore the behaviour in a different region of parameters to demonstrate the existence of complex non-chaotic behaviour. It is found that relaxation oscillations develop through distortion of limit cycles which have fast and slow motion in the different region of the phase space. A new type of period-adding bifurcation of the Poincare’ return points is uncovered and is shown to generate periodic bursting with a complex ‘strange’ geometrical structure. The period-adding mechanism presented is classified as a third kind of period-adding according to the classification of Holden and Fan 27 . It is conjecture that the complex oscillatory trajectory is terminated by a boundary crisis.

Chaotic, non-chaotic strange attractors and bistability in non-isothermal fluidized bed catalytic reactors under PI control

In this paper which is an extension of Ajbar and Elnashaie [ Chaos, Solitons & Fractals 7, 1317–1331 (1996)] new results are presented for the bifurcation and chaotic characteristics of a PI controlled non-isothermal fluidized bed catalytic reactor. The system is characterized by the existence of strange non-chaotic attractors in certain regions of the parameter space. The system also exhibits complex bistability over a wide range of parameters.

Period-adding and chaos in fluidized bed catalytic reactors

A conventional Proportional-Integral-Derivative (PID) controller is considered for the stabilization of a non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions, modeled using the two-phase theory of fluidization. The investigation, although in a restricted region of the parameter space, has uncovered a good part of the rich dynamic characteristics of the controlled unit, including sequences of burst patterns that undergo transition from simple to complex oscillatory behavior. The alternation between the period-doubling sequence and the saddle-node bifurcation creates the chaotic regime while the generation and persistence of complex bursting are associated with the period-adding bifurcation.

On the chaotic behaviour of forced fluidized bed catalytic reactors

The response of a non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions to high frequency forcing is investigated. The present investigation concentrates on the effect of the forcing amplitude on the behaviour of the system at a number of chosen positions of the centre of forcing. The behaviour of the system over the wide range of forcing amplitudes covered is found to be very sensitive to the position of the centre of forcing relative to the homoclinical orbit (infinite period bifurcation point) of the unforced system. A new type of intermittency with two laminar phases of different periodicities has been uncovered, analysed and is shown to form a transitional region between two ordinary intermittencies each with its single laminar channel. Different mechanisms of the transition between chaotic regions and periodic windows has been indentified and analysed in some details, these mechanisms include: period doubling, period halving, period adding and tangent bifurcation. The system exhibited one-dimensional stroboscopic maps which resemble the logistic map, the Rose-Hindmarsh model maps as well as the experimental one-dimensional map of bromide concentration for the Belousov-Zhabotinsky reaction in a continuous stirred tank reactor.

Bifurcation, instability and chaos in fluidized bed catalytic reactors with consecutive exothermic chemical reactions

A two-phase model for the non-isothermal fluidized bed catalytic reactor with consecutive exothermic reactions has been used to investigate the bifurcation, instability and chaotic characteristics of this industrially important unit. The investigation, although in a restricted region of the parameter space, has uncovered a good part of the rich dynamic characteristics of this system, including; 2 n and 2 n k period doubling sequences leading to chaos, banded and fully developed chaos, interior crises, tangent bifurcation leading to intermittency, periodic windows interrupting chaotic regions and alternating periodic-chaotic sequences. Within the chaotic region a new type of periodic windows (termed periodic horns) which differ quantitatively and qualitatively from ordinary periodic windows have been discovered.

Modelling of fluidized bed reactors—VI(b): The nonisothermal bed with stochastic bubbles

Two stochastic nonisothermal fluidized bed reactor models are developed to investigate the significance of the fluctuating nature of fluidized beds on reactor performance. Fluctuating bubble size distributions within the bed are simulated by stochastic mass and heat transfer coefficients. Results of hybrid computer simulations indicate that randomness can enhance or inhibit reactor performance depending on the operating parameters of the nonisothermal model. Bubble and dense phase concentration statistics are fairly similar to those of corresponding isothermal models because dense phase temperatures are relatively insensitive to transfer coefficient fluctuations due to the high dense phase beat capacity. However, the corresponding stochastic isothermal models predict decreases in conversion with increasing variance in the transfer coefficients for all operating conditions. Results indicate that a deterministic system with two stable steady states may have fewer stable random stationary solutions. The existence of the stationary states is dependent on fluctuation frequency and variance of the transfer coefficients.

Multiplicity of steady states in fluidized bed reactors—V: The effect of catalyst decay

A simplified two-phase model is used to investigate the behaviour of non-isothermal fluidized bed reactors experiencing catalyst decay. The investigation shows that for highly exothermic reaction it is almost always desirable to operate the reactor at the middle unstable steady state, since it gives higher accumulative yield than both the high and the low temperature steady states. A simple feedback control scheme with time varying set point is suggested to stabilize the middle steady state. The dynamic behaviour and stability of the system is investigated for the open-loop reactor (uncontrolled) and the closed loop reactor (controlled).

Modelling of fluidized bed reactors—II: Uniform catalyst temperature and concentration

A model based on the simple two phase theory of fluidization including the catalyst particles as a third phase has been developed for a nonisothermal fluidized bed catalytic reactor with continuous circulation of catalyst particles. The dilute phase is assumed to be in plug flow, the emulsion phase gas is considered to be perfectly mixed and the particles are assumed to be perfectly mixed and uniform. Exact criteria for uniqueness and multiplicity of the steady state solutions are presented and some conclusions derived therefrom. Several examples illustrating the influence of some parameters on the steady state multiplicity are reported. The steady states are analyzed for local asymptatic stability using Liapunov's direct method, but the sufficient conditions for stability are found to be rather conservative. Numerical examples illustrating the transient behavior of the system are presented, and it has been found that the initial temperature of the catalyst particles is a predominant factor in determining which steady state will be approached.