CHAOS in FLUIDIZED BED COMBUSTOR

D.E. Ventzas 1 , and P. TsiakarasDpt of Mechanical & Industrial Eng, University of Thessaly,

Pedion Areos, 38334, Volos, GREECE, Email: tsiak@uth.gr

ABSTRACT:

KEYWORDS:

INTRODUCTION: Combustion in fluidized bed combustors includes mixing, reaction kinetics and bed particle motions, i.e. it is highly nonlinear dynamic process. The paper statistically correlates flow, acoustic, ultrasonic, pressure data series, i.e. these parameters with bed fluid dynamics. The data are used for statistical analysis (stationarity), state classification and combustor diagnostics. Nostationary processes behave as transport phenomena, i.e. present similar statistical properties, but in space, not in time.

exhaust

bed microcomputer

DPTsolenoid

HPF LPF

grid PT 0.1 - 40 Hz

supply airnozzle forslugging fluidizing aircontrol

Fig. . Fluidized bed instrumentation

Four distinct fluidization regimes are possible that follow each other, by increasing the gas flow, i.e. the vibrating particles, bubbling, slugging and transition to turbulence regimes, where:Umf = minimum fluidization flowUmss = maximum stable slugging flow

11 Visiting Professor, Electronics Dpt, TEI Lamia, E-mail: dventzas@uth.gr

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2 v p b standard i a udeviation b r b of ΔΡ r t b transition

a i l to1 t c i turbulence i l n n e g g s slugging 0

Umf Umss gas flow

Fig. . Standard deviation of ΔΡ in fluidized bed v.s. the fluidizing gas flow

Further gas flow increase results in decreased coherency and increased complexity of macroscopic bed behavior, giving stutters in oscillation that manifest an intermittent transition to chaos (stutters increase in frequency with increasing flow).

Fig. . Differential pressure signal of a fluidized bed under slugging conditions

(non periodicities and signal interruption corresponds to stutter, while cycle magnitude corresponds to the slug size)

As flow is increased from Umss, the slugging patterns become less regular, forming stutters that collapse and the amplitude of oscillation increases through several cycles (passage of large bubbles) until it reaches the amplitude of the regular slugging pattern. Flow stabilization control results in distinct and narrow harmonics, while flow destabilization distributes power content across many frequencies.

TIME SERIES: The time series measured from any system, here the fluidized bed combustor, are presented in time domain {x(t), t}, phase-space trajectory {x(t), y(t)}, delay return map {x(t), x(t+k)}, or mutual information map { Rxy(τ), τ}or { Rxy(τ), x(t)}. The measurements are tested by correlation integral tests,

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In a circulating fluidized bed, flow increase varies rarefication in solid fuels and pressure frequency changes in a pipe; gradual changes (drifts) and step changes are recorded and classified (i.e. related to bed states).

High speed measurements of pressure drop and particle motion

COMBUSTION and CHAOS: Flame signals produce what is called deterministic chaos (i.e. non random chaos) from which we can extract a wide range of useful information, in order to increase reliability.

CHAOTIC CONTROL of FLUIDIZED BEDS: Hydrodynamics of fluidized beds are chaotic. They determine the performance of the fluidized bed reactor (mass transfe / reaction); for instance the average bubble size of gas bubbles in the bed could be reduced, the bypass of the solids reduces, resulting in a higher conversion.

Since FB are chaotic systems, they have the general characteristics of chaotic systems, i.e. they are deterministic nonlinear systems, showing irregular (almost random) behavio; it is impossible to make long term predictions of the system development because these are extremely sensitive to initial conditions or external perurbations. However, short term predictions are possible and the sensitivity to control actions can be exploited by a chaos controller. Such a controller can change the system behavior completely at the cost of only very small control actions. This chaos control idea (1990) has not been applied to complex systems yet. To obtain experience with chaos control algorithms, a simple experimental chaotic pendulum (forced by an electromotor periodically) is studied. After a transient time, e.g. 100 s, the control suppresses the chaotic behavior. The contol algorithms developed for the pendulum are tried in a small (4 cm diameter x 20 cm height) fluidized bed to prevent slugging (a very undesired flow regime). Slugging can be reduced when a small fraction of the gasfeed is injected above the gas distributor.

CHAOS IMPROVES CHEMICAL PERFORMANCE: Chaotic features and dynamic performance in small and large reactors, with bubbles giving poor mass transfer in a catalytic reaction, high reactant gas transfer resistance, high rise velocity of the bubbles and lower reaction results (i.e. reactant gas bypass) than other conventional reactors with the same contact time. We control bubble size and reaction system selectivity, including the hydro-dynamics, i.e. chaos control, leading to smaller bubbles, i.e. less reactant gas bypass.

conversion1

0.8

0.6

0.4

0.2

0.0 0 2 4 6 8 10bubblesize (cm)

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Fig. . Calculated conversion as function of bubble size for a model reaction

PRESSURE FLUCTUATIONS: Hydrodynamic conditions in a hot bubbling fluidized bed (BFB) combustor and a cold BFB model, i.e. the effect of the loaded solids above the L-valve on the flow rate, the origin of pressure fluctuations in both laboratory and industrial scale boilers. The hydrodymanic similitude in bubbling fluidized beds (600 μ round sand, fired with natural gas to 725oC, with 150 μ diameter round copper particles) is matched by dimensionless parameter D/dp , or a dimensionless . solids loading to the riser. The height of solids above the L-valve (under conditions of varied particle diameter, density and L-valve aeration rates) affects the flow rate of solids through the L-valve and into the circulating fluidized bed.

CHAOTIC FLOW: The simplest chaotic flow is defined by:dxdt

ydydt

zdzdt

x y A z where A

x A x x x

2

2

2 0168 2 0577

0

. . .

. Air-fuel mixing occurs in all combustion phenomena and industrial processes. The quantitative modeling of mixing efficiency is a fundamental prerequisite for the correct design and scale-up of chemical reactors. Chaotic nature of mixing induced by stretching and folding dynamics supported by the local mechanisms (micro-mixing), results in the existence of KAM surfaces, intrinsic local instability, topological transitivity within an invariant manifold u (the chaotic manifold), local exponential divergence of nearby trajectories within u, which are analogous to those of non-integrable area preserving (Hamiltonian) systems; these phenomena have been observed in many different systems (stirred tank reactors at low Reynolds number (Re<500), periodically excited closed flows such as cavity flow, or the flow within two eccentric cylinders, static industrial mixers, open flow systems (the vortex-pair flow) and can be simulated quantitatively by means of much simpler model flow.

By quantitative description of mixing performances at low Reynolds numbers, we define an infinitesimal vector l, evolved by:

dxdt

vdldt

l v l ltt , . , 0 0

where x is the position vector of the passive particle and v the velocity, the ll0

stretching, giving the kinematic analysis of mixing. For real systems, the velocity field v is not known (and should be calculated). For simple two dimensional systems

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(e.g. cavity flow, the fluid dynamic reduces to the solution of the vorticity ω stream function ψ equations, 2 20 , while for more complex flows (e.g. in the case of real static mixers) CFD is needed. A simpler discrete model given by the sine flow corresponding to a veloocity field described by:

v v vx

Ln T t n T

v vy

Lv n T t n T

x y

x y

02

2 2 1

20 2 1 2 2

0

0

.sin.

( ) ( )

.sin.

( ) ( )

which is a periodic flow with periodic boundary conditions, and T is its half period. The corresponding Poincare section, in dimensionless coordinates, (stroboscopic map at t = 2.n.T) is given by:

x x T f y T f x

y y T f xn n n n

n n n

1

1

. . (

. ( ))

where f(x) = sin(2πx) . The chaotic nature of the flow induces loss of information in the analysis of reaction/diffusion/advection equations, especially to local approximate models (lamellar models associated with a quenched distribution of lamellae), which may be disappear as a consequence of infinitely fast reaction, giving an iterated multi-fractal model; we want to deal with the practical case of high Peclet numbers Pe >104.

Experimentally tracer gas measurements (He) and mass spectrometer He concentration measurements, for velocities 1.2 - 4.3 m/s and silica sand (0.32 mm) as bed material were carried out.

FLUIDIZED BED GASIFIER CONTROL: Generating simple linear models from simple data and using the model for impoved control results in improved operation of the gasifier, leading to multivariable control strategy.

In the servo mode, the control system must adjust the reactor input variables so that the reactor output meets operational objectives, such as no clinkering, high carbon conversion, meet targeted gas make and bed density, high gas heating value, meet targeted fuel/non-combustible mole ratio and mean bed temperature and maintain HOC balances inventories.

In the regulatory mode, all these objectives and more are considered by operators during gasifier operation. All inlet gas flow rates are flow controlled with simple PID type controllers, gasifier backpressure is controlled via a split range controller, and MGCR pressure is controlled via a PID controller. The backpressure control is critical to steady operation of the gasifier, as fluctuations in backpressure impact inlet gas flowrates and bed density.

FRACTALS: In the attempt to study and simulate (by virtual reality) the fluidized bed, fractals are produced by using a initiating signal (shape) and a fractal generator (signal). In fluidized bed case the initiating shape is the bed’s conditions (shape, loading, fuel, etc) and the fractal generator is the agitating air/gas stream and/or the released heat. This is in close conformity with the universal speculation, that the morphology of systems and organisms have a fractal-like appearance and their shape (or operation) is encoded according to fractal generators. Fractals allow the storage of large number of data as mathematical formulae, achieving very high compression ratios (over 100:1).

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The bed dynamics is a noisy but low-dimensional nonlinear (periodic and regular) oscillator that undergoes transitions (including slugging), involving a fixed point, i.e. two limit cycles and chaotic motion. Plots of sequential windows of signals (Ti, Ti+1, Ti+2) reveal dynamic structure in slugging sequences, by progressing from disordered oscillations to noisy limit cycles, see fig. . The stable state corresponds to:

116 155. . U

U mf

Ti

Ti+1 Ti+1

Ti+1

Fig. . Chaotic curves in 2D phase domain (3D projections)

Fractal is a set which is self-similar under magnification; they can be magnified infinitely and expressed mathematically with small sets of data; they are structures possessing similar-looking forms of many different sizes, extensions of classical Euclidean shapes. Fluidized bed turbulence under certain conditions could be considered a fractal image. By the periodic-doubling route to chaos, we access chaotic behavior by doubling the velocity profile peaks, i.e. by flow pulsation, or by momentary perturbations (short burst) to achieve large scale changes in slugging patterns in order to enhance or disrupt slug formation. 15 % duty cycle pulse, just after the rising crossing of the pressure variation, drives the solenoid, see fig. ,

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injecting 5% of total bed gas flow. Optimal parameters for bed operating conditions is acquired by a an expert monitoring, or manually. Fractal transform expresses mathematically any real world image, i.e. the fluidized bed condition and substitutes the limited resolution (detail) pixel-by-pixel (color intensity) photography; this is the so-called Fractal Image Format (FIF) that is resolution independent and consists of domain and range blocks.

Fig. . Slugging in fluidized bed

CONCLUSIONS: All the above signals characteristic parameters correspond to chaotic indices in fluidized bed combustor characterization, that assist us in characterizing states and conditions of the fluidized bed, control it more efficiently in combustion or heat treatment (circulating) applications. The bed is sensitive to small perturbations in air flow that alter the bed behavior, leading to sophisticated control algorithms that achieve better control results, more economically (in terms of bed operation and combustion efficiency).

REFERENCES1. Ajbar A., Elnashaieh S.S.E.H, Controlling chaos by periodic perturbations in non-isothermal fluidized-bed reactor, AIChE Journal 42:11, 3008-19, 19962. Bai D., Bi H.T., Grace J.R, Chaotic behavior of fluidized beds based on pressure and voidage fluctuations, AIChE Journal 43:5, 1357-1361, 19973. Bayliss A., Matkowsky B.J, Two routes to chaos in solid fuel combustion, SIAM Journal of Applied Mathematics 50, 437-459, 19904. Bleek C.M. van den, Schouten J.C, Deterministic chaos: a new tool in fluidized bed design and operation, Chemical Engineering Journal 53, 75-87, 19935. Bouillard X., Miller A.L, Experimental investigations of chaotic hydrodynamic attractors in circulating fluidized beds, Powder Technology 79, 211-5, 19946. Caputo E., Sello S., Marcolongo V, Nonlinear analysis of experimental noisy time series in fluidized bed systems, Chaos, Solitons & Fractals, 19947. Crutchfield J.P., Packard N.H, Symbolic dynamics of noisy chaos, Physica D 7, 201-223, 19838. Daw C.S., Finney C.E.A., Vasudevan M., Goor N.A, Self-organization and chaos in a fluidized bed, Physical Review Letters 75:12, 2308-2311, 1995

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10. Daw C.S., Finney C.E.A., Vasudevan M, Measuring and controlling chaotic dynamics in a slugging fluidized bed, Proceedings of the Third Experimental Chaos Conference, Edinburgh, 1995, 83-91, 199511. Daw C.S., Halow J.S, Evaluation and control of fluidization quality through chaotic time series analysis of pressure-drop measurements, AIChE Symposium Series 89:296, 103-122, 199312. Daw C.S., Lawkins W.F., Downing D.J., Clapp N.E. Jr, Chaotic characteristics of a complex gas-solids flow, Physical Review A 41:2, 1179-81, 199013. Ding J., Tam S.W, Asymptotic power spectrum analysis of chaotic behavior in fluidized beds, International Journal of Bifurcation and Chaos 4:2,327-341199414. Elnashaie S.S., Abashar M.E., Teymour F.A, Bifurcation, instability and chaos in fluidized bed catalytic reactors with consecutive exothermic chemical reactions, Chaos, Solitons & Fractals 3:1, 1-33, 199315. Flook, A, Fractals, Sensor Review, Vol.16, No. 3, pp. 42-7, MCB Press, 199616. Franca F., Acigoz M., Lahey R.T. Jr., The use of fractal techniques for flow regime identification, International Journal of Multiphase Flow 17:4, 545-52, 199117. Fuller T.A., Flynn T.J., Daw C.S, Enhancing burner diagnostics and control with chaos-based signal analysis techniques , Proceedings of the International Mechanical Eng. Congress & Exposition (ASME), Paper HT-15, Vol. 4, 281-91, 199618. Gorman M., el-Hamdi M., Robbins K.A, Four types of chaotic dynamics in cellular flames, Combustion Science and Technology 98, 79-93, 199419. Hay J.M., Nelson B.H., The calculation of the characteristics of a chaotic attractor in a gas-solid fluidized bed, Chemical Eng. Science 50:3, 373-380, 199520. Karamavrun A.I., Clark N.N., Halow J.S, Application of mutual information theory to fluid bed temperature and differential pressure signal analysis, Powder Technology 84, 247-257, 199521. Karamavrun A.I., Clark N.N, Local differential pressure analysis in a slugging fluidized bed using deterministic chaos theory, Chemical Eng. Sci. 52:3, 357-70, 199722. Karamavrun A.I., Clark N.N, Application of deterministic chaos theory to local instantaneous temperature, pressure, and heat transfer coefficients in a gas fluidized bed, Journal of Energy Resources Technology 118:3, 214-220, 199623. Lehrman M., Rechester A.B., White R.B, Symbolic analysis of chaotic signals and turbulent fluctuations, Physical Review Letters 78:1, 54-57, 199724. Margolis S.B, A new route to chaos in gasless combustion, Combustion Science and Technology 88, 223-246, 199225. F. J, Muzzio, D. M. Hobbs, D. J. Lamberto, C, Fractal and Chaos in Chemical Engineering, Ed: M. Giona, G. Biardi, World Scientific, Singapore, 199726. Nguyen K., Daw C.S., Chakka P., Cheng M., Bruns D.D., Finney C.E.A., Kennel M.B, Spatio-temporal dynamics in a train of rising bubbles , Chemical Engineering Journal, 64:1, 191-197, 199627. J. M, Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport, Cambridge University Press, Cambridge, 198928. Pence D.V., Beasley D.E., Riester J.B, Deterministic chaotic behavior of heat transfer in gas fluidized beds, Journal of Heat Transfer 117, 465-472, 199529. Pence D.V., Beasley D.E, Multi-fractal signal simulation of local, instantaneous pressure in a bubbling gas-fluidized bed: Part 1. Signal Simulation, Journal of Fluids Engineering, 1997

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30. Pence D.V., Beasley D.E, Multi-fractal signal simulation of local, instantaneous pressure in a bubbling gas-fluidized bed: Part 2. chaos assessment, Journal of Fluids Engineering, 199731. Pence D.V., Beasley D.E., Chaos analysis and contact dynamics of heat transfer in a gas-fluidized bed, Proceedings of the Heat Transfer Division, 1997 ASME International Mechanical Engineering Congress and Exposition, Dallas, 199732. Schouten J.C., Stappen M.L.M. vander, Bleek C.M. van den, Scale-up of chaotic fluidized bed hydrodynamics, Chemical Eng. Science 51:10, 1991-2000.33. Segarra M.A., Aragσn J.M., Palancar M.C, Chaotic fluidodynamic in fluidized beds, 7th Mediterranean Congress of Chemical Eng, Barcelona, 199634. Stappen M.L.M. vander, Schouten J.C., Bleek C.M. van den, The gas-solids fluidized bed as a spatio-temporal chaotic system, 1st International Particle Technology Forum, Denver, 1994, AIChE, Part I, 446-45135. Sterling J.D, Nonlinear analysis and modelling of combustion instabilities in a laboratory combustor, Combustion Science & Technology 89, 167-7936. Tam S.W., Devine M.K, A study of fluidized-bed dynamical behavior: a chaos perspective, in Applied Chaos, Wiley-Interscience, 1992, 381-391

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