Application of Chaos Theory to Gas Injection

"It is well known that gas injection systems can exhibit a wide range of dynamical behaviours, ranging from linear periodic bubbling through to highly complex turbulent jetting. Recently, it has been observed that an important intermediate regime exists under certain system conditions, where the dynamics are complex in nature yet predictable for short time periods. This paper reviews the evidence to support the above hypothesis, and discusses the invariant quantitative measures such as density, return maps, Lyapunov exponent and dimension which may be used as pattern recognition features in a mOnitoring and control strategy.INTRODUCTIONThere has been a great deal of research on the submerged injection of gases into liquids. This interest is primarily due to the large number of applications in the pyrometallurgical and chemical engineering industries. Gases are typically injected into liquids to achieve goals such as heat and mass transfer, or physical mixing and agitation. Only recently though has the possibility of using the evolution of the gas dynamics as a probe to internal system conditions been raised [1, 2].At very low gas injection rates and small upstream chamber volumes, gas normally disperses in the form of stable bubbles of constant volume [3]. With increases in gas flow rate, the dynamics become more complex, bifurcating into double bubbling, multiple bubbling and complex coalescence behaviour. Irregularities measured in pressuretime series acquired upstream of the injection port under these complex conditions have usually been treated as bothersome noise or contamination to be filtered from the signal and ignored in the analysis. These irregularities, however, may contain physically interesting and useful information on the system from which they were produced if the system may be classified as deterministically chaotic [4]."