Analysis of bubble flow in metallurgical operations using multivariate statistical techniques

The behaviour of bubbles within metallurgical vessels is important to crucial aspects of their operations, such as mass transfer, heat transfer and splash generation. Physical models have been used to investigate different aspects of bubbling and provide data for verification of mathematical models. In industry, spout eye area, which is formed while the gas escapes from the liquid surface during bottom gas stirring process, has been used to monitor the process. Vibration signals on the wall of vessels have also been measured in industry to monitor the gas flow. Sound signals of the bubbling have been correlated with different behaviour of the gas bubbles inside the bath, such as bubble formation, distortion, coalescence, volumetric oscillation and detachment. It is clear that these three types of signal, i.e. image from the disturbed top surface, sound of the bubbling and vibration on the wall of the vessel are all generated from the same physical process, and indicate some aspect of the bubbling phenomena. This study focuses on the investigation of the combined effect of all these three types of signals, which were collected simultaneously in well controlled cold model experiments, based on multivariate statistical analysis techniques. The aim of this study is to investigate the possibility of monitoring bubble flow with a combined signal, which depends on the variables that can be reliably measured, and if possible, how to simplify this combined signal from the large data base which carries all the information of the process. Cold modelling experiments were performed to establish techniques to analyse all these three types of signals simultaneously and quickly. A cylindrical cold model with a diameter of 420 mm and height of 500 mm, based on both dimensional and dynamic similarity criteria, was used to collect different types of signals simultaneously over a wide range of flowing conditions. The depth of the water bath which simulates steel was kept at 210 mm, and motor oil, which simulated slag, the height varied from 5 mm to 20 mm. Pressured gas were injected from the bottom of the vessel through a nozzle with a diameter of 3 mm, and the volume flow rate varied from 2.0 l/min to 20.0 l/min. Images of the disturbed top surface and sound of the bubbling signals were collected by a digital video camera installed above the vessel and vibration signals were collected by an accelerometer installed on the wall of the vessel. The size of the spout eye area was calculated by a threshold technique developed in this study, which takes approximately 0.1 second to analyse each frame of the image files in average, and the sound and vibration signals were pre-treated in both time domain and frequency domain. Principal Component Analysis (PCA) technique was applied in this study to investigate the data base collected from the cold model experiments. The results from PCA demonstrated that the three types of signals are highly correlated and can be combined into one latent variable, which explains most (about 86%) of the total variation of the cold model experiments, and this latent variable can indicate the stirring process inside the bath effectively, because there exists a clear linear relationship (R2=0.96) between this latent variable (dominant principal component) and stirring power which was calculated from the same cold model data. Since there are established relationships between the overall mass transfer coefficients and inclusion removal rate with stirring power, it should be possible to predict the metallurgical operations inside the bath using this latent variable. The possibility of indicating the stirring process by just one or two channels of signals was further investigated and the PCA results showed that the signals from just one channel can only provide limited indication of the system, however, the combined signal from sound and vibration can capture most of the variation of the process (about 88% of the total variation except the image signals), and there is also a clear linear relationship (R2=0.95) between stirring power and the latent variable which combined the signals from sound and vibration. This finding suggests new type of sensor can be developed, which can be applied to monitor the gas stirring process and provide a feedback signal for the control system, based on combination of vibration and sound signals alone. This finding is particularly important for the pyrometallurgical operations where it is difficult to install a digital camera above the vessel. The relationship between stirring power and Froude number, which is generally applied as a dynamic criteria for the gas bubbling phenomena, was investigated and the results showed that there is a clear linear relationship between the combined signal and Froude number specifically defined. A new variable 'BF (bubbling factor)' was defined in this study based on the combined signal of sound intensity and vibration magnitude. PCA results based on the cold model data showed that BF can capture most variation of the process (91.3%), and a strong linear relationship was found between bubbling factor and stirring power (R2=0.92), which demonstrate that BF can monitor the bubble flow effectively and can be applied to predict the metallurgical operations inside the bath. Additionally, statistical analysis based on the cold model data showed that the sampling period can be reduced to 2.0 seconds to collect sufficient information about the stirring process inside the bath, which means that the bubbling factor can give a feed back signal every two seconds. These findings should facilitate the development of online sensors that monitor the stirring process quickly and effectively, based on sound and vibration signals from the process.