A generalized neural-net kinetic rate equation

Abstract

This paper illustrates the application of a generalized neural-net kinetic rate equation to perform identification of the process conditions and dynamic simulation of batch and continuous metallurgical and mineral processing systems. The proposed approach is useful essentially to simulate ill-defined dynamic processes where the existing fundamental and empirical model fail owing to their lack of generality. The basis of the kinetic rate equation is a set {k(C)n, Cn, tn} which is derived directly from batch reactor concentration-time data or concentration-mean-residence-time kinetic data of a system of continuous stages in series and its associated pivot process conditions. The generalized kinetic rate equation is defined by using the above set and linked to a trained neural net via adjustment factors α (for adjusting the rate) and β (for adjusting the final recovery), which relate the process conditions within the reactor to the kinetics of the process under consideration. This approach permits the dynamic simulation of a variety of metallurgical and mineral processing systems at any process conditions catered for by the trained neural net. The same set of kinetic data may also be used to establish deviations from the pivot conditions quantified as α and β values. Conversely, these α and β values permit the identification of process conditions within the reactor, which could be used in process identification. In contrast to most of the existing models, no curve-fitting is required, as the kinetic rate equation utilizes experimental data directly. A number of theoretical, mineral processing and hydrometallurgical case studies are used to demonstrate the applicability of the generalized neural-net kinetic rate equation.