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ISSN 1320-0682 | ||
| Complexity International is a
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Louis J. Mittoni and M. Philip Schwarz
G. K. Williams Cooperative Research
Centre for Extractive Metallurgy
CSIRO Division of Mineral and Process Engineering
P.O. Box 312, Rosebank MDC, Clayton VIC 3169, Australia
Email: Louis.Mittoni@dmpe.csiro.au
A method for determining the state of gas-liquid bubbling systems by constructing d-dimensional vectors using measured intervals between specific high frequency pressure events in the upstream region of the gas supply line is described. The possibility of applying pattern recognition algorithms to identify operating conditions from return maps is also explored. The feasibility of this approach for the estimation of such parameters as refractory wear, melt density, injection submergence, liquid circulation, bubble frequency and size distribution is demonstrated using a number of laboratory experiments.
Real time monitoring and control of industrial scale reactors is a challenging problem for the metallurgical industry. Monitoring vibration of the reactor vessel shell, monitoring pressure oscillations in the gas supply system, and using x-ray imaging systems are just some of the approaches that have been trialled for this purpose [1]. The pressure monitoring approach is favoured due to the relative ease with which measurements may be made and the reliability of the signal to reflect the underlying dynamics.
There have been several studies on the use of dynamic pressure signals for the interpretation of gas-melt interactions in the lab [2], and on both pilot and industrial scale systems [3]. The degree of understanding of pressure time series in some systems, however, is limited to the inference of statistical averages such as bubbling frequency and to some extent other information such as the blocked/unblocked status of injection nozzles and general operating conditions of the system. The manual interpretation of this data in conjunction with other visual information for verification of system conditions is neither convenient nor accurate in industrial systems.
It has been found by previous workers [2,3,4] that in addition to gas flow rate, the gas-liquid dynamics at the injection region is highly dependent on system conditions such as liquid stirring and circulation, melt density and temperature, gas density, gas-liquid mass transfer rate, nozzle geometry and bath geometry. In the past, this knowledge has been valuable in the design and scale-up stages of new process development, to ensure the system will perform as required and to minimise potentially harmful behaviour such as excessive splash or surface wave action.
Using a laboratory scale model of a bottom injection bubbling system and a room temperature aqueous solution, it is possible to observe single bubbling dynamics through period two and four bubbling regimes to a domain which is unpredictable for medium and long term time periods yet deterministic in the short term [5]. This behaviour is similar, though not identical, to that found in the dripping faucet system [6]. The period two and four regimes have only been found to occur under certain conditions dependent on the orifice diameter and chamber volume: they do not appear to constitute a period doubling transition to chaos. The more complex deterministic region is peculiar in that the dynamics maintain a general similarity even under varying system conditions. Also in contrast to the physics of the dripping faucet system is the presence of low pressure wakes formed behind rising bubbles, adding to the complexity in the dynamics of a gas-liquid bubbling system.
Of particular relevance to the present study is the structure of return map plots formed by plotting the time interval 
between two successive `pressure events' P1 and P2 versus the interval 
between the next pair P2 and P3. These events are defined by any significant oscillation in the derivative of the pressure transducer signal, relating to bubble appearance and delayed release or oscillation of the bubble envelope.
Return maps for different conditions could then be compared and analysed with the help of commonly used invariant extraction methods [7].
The experimental work has shown that by constructing return map vectors from the derivative of dynamic pressure in the gas supply line, it is possible to infer the state, immediate past and immediate future at the gas injection region. The experiments performed show that learning vector quantisation [8] has been effective in learning and separating some of the system conditions such as gas flow regime and injection nozzle diameter. With an improvement in the invariant calculation and choice of pattern recognition algorithm to accommodate several simultaneous parameter variations, it would be possible to monitor some metallurgical or liquid treatment systems automatically.
The behaviour of gas injected through a submerged orifice into a liquid is highly dependent on the geometrical configuration of the injection region and the gas supply system. An appreciable gas volume directly upstream of the injection nozzle acts as a spring to which energy may be stored and retrieved during the evolution of a single bubble. In general, for a given liquid, static pressure and chamber volume, the frequency of chamber oscillations is only marginally dependent on the growth stage of the bubble [2]. Bubbles detach approximately at the point where upwardly acting forces, such as buoyancy and gas inertia, exceed those which are downward acting such as line tension forces at the nozzle-gas-liquid interface.
Under conditions where the chamber oscillation frequency is of the order of the natural bubbling frequency defined by the balance of forces, the bubbling dynamics may change from single bubbling to multiple bubbling or coalescence behaviour when injection flow rate is increased. Complicating this coupling are the appreciable effects of bubble wakes. The added wake pressure at a distance s behind a bubble of radius r may be expressed as
where 
is liquid density, U is bubble rise velocity and g is the acceleration due to gravity.
As a new bubble appears and grows at the nozzle, the preceding bubble wake affects its rate of growth and detachment, subsequently leaving the chamber at a particular phase of oscillation.
Also affected is the rise velocity of the newly formed bubble, which in turn determines the wake force on future bubbles.
A detailed numerical model of bubble-bubble interactions, although interesting, is beyond the scope of the current presentation.
Plotting the time between successive bubbles in the form of a return map gives a convenient representation of bubbling behaviour.
Comparable to the approach taken by previous workers in similar systems [6], an arrangement consisting of an electrical circuit which measures the time 
between successive events in the transducer signal may be used to construct the return map plots. Functional moments M may be computed using
where d is the dimension of the return map vector 
and 
.
These moments may be used as an input into pattern recognition routines. Functional moments have been chosen in the present demonstration as an invariant due to their simplicity and ability to contain some information on the dynamics for a system which may have high noise levels. As noted earlier, learning vector quantisation [8] has been used to distinguish between different return maps by constructing vectors with the moments and using nearest neighbour classification to estimate the conditions under which the data was acquired.
Figure 1 shows a schematic of the experimental setup. The experimental room temperature apparatus used was a 250 mm diameter cylindrical tank constructed from perspex, normally filled to a level of 100 mm with a 70% glycerol/water solution. The perspex was chosen to facilitate visual supervision and the glycerol mixture proved beneficial due to the increased bubble envelope stability. A high speed camera (Hycam) recording at 400 frames/s was used for visual-signal comparisons. The Hycam frame pulse signal was then used to digitally trigger a 386 PC computer which stored the pressure signal at a rate of 10 kHz. Transfer of the high speed recording to a time coded VHS video tape allowed every frame to be matched with its signal counterpart.
The submerged gas injection orifice was placed near the base of the vessel on top of an inverted cup 38 mm in diameter so that the injection point was approximately 35 mm above the tank floor. This arrangement significantly reduced the effects of re-circulation induced by rising bubbles. To realistically model a generic gas-liquid injection system, the experimental apparatus included a chamber volume fitted directly below the injection orifice. The pressure transducer and gas supply line were positioned adjacent to one another in the chamber, so as to minimise any effects of the supply blowing directly onto the transducer port. The precise volume in the chamber was maintained at 359 ml by partially filling the bottom with water.
Nitrogen as the injection gas was supplied from a vertical cylinder via a mass flow controller (MFC), which allowed accurate control of injection conditions and precise flow measurement. The computer was used to control the MFC which varied the gas flow rate repeatable to within 
FS including linearity for the range 0-10 standard l/min.
This arrangement allowed the injection rate to be slowly varied during the course of an experiment.
A high response silicon based bridge transducer was used to monitor the dynamic pressure in the chamber volume cylinder. The output of the transducer was then amplified and filtered to give a voltage proportional to the derivative of the pressure fluctuations.
Comparison of the signal derivative with a preset voltage, set to include all pulses in the signal, gave rise to a digital signal which was high when the derivative exceeded the preset value and low otherwise. Immediately following the comparator was a one shot multivibrator which produced a fixed width pulse at the rising edge of the signal.
The resulting digital signal was then fed into an Am9513A timing circuit inside the control computer which measured the interval between events to an accuracy of 
for the largest periods encountered.
Figure 1: Schematic diagram of the experimental apparatus used to monitor and record the gas-liquid bubbling interactions.
Experimental runs were performed using nozzle diameters of 
and 
mm. A study of the effect of nozzle diameter on the return maps was chosen for this preliminary investigation in order to demonstrate the basic principles of the approach.
Other parameters such as liquid density and system pressure would require identical analyses, whereas distinguishing liquid circulation effects would most likely need additional invariants such as maximum Lyapunov exponent or dimension as an input into the pattern recognition stage.
Due to space limitations in this paper and the very large number of results acquired, only a small subset of observations is displayed in Figure 2 using two-dimensional return maps.
Figures 2(a)-(c), plotted on an arbitrary scale, show return maps corresponding to the period one, two and four regimes found at 
and 
l/min respectively using a 
mm diameter nozzle and 300 mm of distilled water as the liquid.
Figure 2: Return map embeddings for conditions (a) 
mm nozzle, 
l/min, (b) 
mm nozzle, 
l/min, (c) 
mm nozzle, 
l/min. For a fixed flow rate of 
l/min, displayed are nozzle diameters (d) 
mm, (e) 
mm, (f) 
mm, (g) 
mm and (h) 
mm.
The period one return map corresponding to single bubbling was found to be common for nozzle diameters greater than 
mm, and only occurred up until a certain flow rate which increased proportional to nozzle diameter. For smaller nozzle diameters, the period two return map extended to lower and lower flow rate values.
It was found that the 
mm diameter nozzle clearly displayed period one, two and four regimes as shown for low viscosity liquids only.
The short period doubling cascade is due to the interaction between the chamber volume oscillations and natural bubbling frequency, and the low branch of the bifurcation (lower interval value) equals the time for one full period of the pressure oscillation. It is probable that period four and higher periodicities are not permitted at small nozzles due to frictional damping or high viscosities due to viscous damping mechanisms.
For larger injection orifice diameters, it was found that the single bubbling to complex dynamics transition was more sudden. 
and 
mm diameter nozzles showed no signs of period two or higher return maps since the more complex dynamics due to bubble wake forces occurred first at lower flow rates, dominating the dynamics.
Figures 2(d)-(h) obtained using nozzle diameters
of 
and 
mm respectively at 
l/min
are typical examples of the results obtained under conditions
described in Section 3. These return maps are
plotted on the same scale, where the full width of each display
represents 80 ms. Whilst the general form of the return maps
for different orifices is similar due to the otherwise identical
conditions, it is apparent that higher line tension forces around
the nozzle increase the bubble volumes,
and hence have resulted in a higher mean value for the inter-event intervals.
The first and most important point to explore in the results, is the precise connection between points in the return maps and behaviour of gas at the nozzle. For this purpose, return map vectors 
were again formed using d = 4. As an example, neighbouring vectors in the return maps were selected, which had a Euclidean separation of approximately 8 ms in the four-dimensional space. Figure 3 shows the exact high speed camera frames corresponding to the two near-neighbour vectors.
Close examination of Figure 3 reveals that there are three fully developed and detached bubbles in each frame with identical volumes and positions. The first bubble in this series formed and detached to rise at a "moderate" velocity. The second bubble originally grew explosively as a thin column due to the previous bubble's wake, experienced a short delay due to the chamber pressure oscillations and then continued to grow, detach and rise to merge with the preceding bubble. A third bubble influenced by the wake of the previous two bubbles initially grew rapidly with an elongated form, but as the second (previous) bubble's wake became less significant, it detached and rose with a moderate velocity similar to that of the first bubble.
The important conclusion from this example and other similar observations is that vectors in the return maps do give an accurate and non-degenerate representation of the bubbling dynamics. Following the future of neighbouring vectors in the return maps results in agreement for a short period until the two trajectories finally diverge. If enough verifiable information can be gathered on any gas-liquid injection system, it should be possible to confidently describe those states encountered in the future operation of the system. Extrapolation of room temperature model behaviour to pilot plant and industrial systems may also be possible if the correct scaling criterion and operating limitations are observed.
Figure 3: Time-coded high speed camera frames for two neighbouring return map vectors for 70% glycerol / water solution using 
mm nozzle and gas flow rate of 
l/min. Points marked 1-3 indicate fully formed bubbles, whereas point 4 marks the position of an expanding bubble cap.
To implement a fully automated control system for a metallurgical reactor, it is necessary to explore the recognition of the operating conditions under which data is acquired. The mere fact that there are visible changes in return maps supports the probability of success.
Just three functional moments for i = 0, 1 and 2 were calculated for the case of recognising nozzle diameter from the return maps using Equation (2) with different values of k, l and m. k=l=m=0 corresponding to the mean inter-event interval also proved effective for the return maps displayed in Figure 2.
Using the moments of four return maps for each of the nozzles at a flow rate of 
l/min as training vectors, and two other sets of moments for an accuracy test, it was found that the learning vector quantisation algorithm correctly estimated the gas flow and nozzle diameter parameters on every occasion. On application to an industrial vessel, this information would be useful in determining the orifice diameter and detect whether there is unacceptable refractory wear around the tuyeres.
As other parameters such as liquid re-circulation and, to a smaller extent, bath depth have also revealed variations in their return maps [5], it is possible to use the pattern recognition concept for their evaluation by employing a more sophisticated preprocessing stage.
The ultimate success of the return map pattern recognition procedure will depend on a number of factors. If the metallurgical reactor is operating under conditions of subsonic injection rates so that the pressure fluctuations can be obtained, it would be possible to implement a monitoring or control system which classifies individual vectors in the return maps formed from the inter-event time periods 
.
By using this method in conjunction with a training period, it would be possible to monitor shifts across familiar operating conditions. Therefore, the bubble behaviour would be known and changes could be automatically detected.
In the case where estimates of individual parameters are desired, it would also be possible to track the values of invariants of the return maps, such as dimension and maximum Lyapunov exponent. For instance, an increase in the rate of liquid re-circulation results in a higher level of noise and hence a larger maximum Lyapunov exponent, whereas higher liquid density does not introduce additional noise to the system. Figure 4 displays a schematic diagram of the possible implementation structure of the pattern recognition monitoring and control approach.
Figure 4: Monitoring and control loop schematic for a generic bath smelting system.
As it is necessary to have a knowledge of the phase interactions in gas dispersion vessels to guarantee efficient operation, upstream pressure fluctuations need to be dissected for any information contained within. It has been visually verified, with the aid of high speed films, that return maps generated from the derivative of pressure fluctuations are a reliable and accurate means for estimating the conditions at the nozzle-gas-liquid interface region.
It has also been illustrated that with appropriate pre-processing stages and pattern recognition techniques, it is possible to make an estimation of individual parameters which influence the evolution of bubbles, and hence change the appearance of return maps. With a wider scope of laboratory experiments, including variation of parameters such as liquid density, gas density, temperature and liquid re-circulation rates, a better understanding of the full potential to recognise individual parameters could be obtained. From the results acquired so far, this method shows great potential for the monitoring and control of some gas-liquid systems operating under discrete bubbling conditions.
The G.K. Williams Cooperative Research Centre for Extractive Metallurgy is a joint venture for basic metallurgical research between the Department of Chemical Engineering at the University of Melbourne and the CSIRO Division of Mineral and Process Engineering and is supported by the Australian Government Cooperative Research Centre Program.
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Monitoring Complex Metallurgical Systems using Pattern Recognition Techniques
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