A one-parameter model for describing the residence time distribution of closed continuous flow systems characterized by nonlinear reaction kinetics: Rod and ball mills

• The model is simple to use and very accurate.
• Value of the model parameter can be directly estimated from the variance of the RTD.
• Model demonstrated for laboratory, pilot and industrial-scale rod and ball mills
• Model well suited to systems characterized by composition dependent reaction kinetics

For evaluation of the performance of a continuous flow reactor, a description of the residence time distribution (RTD) of the reactants is required in the form of a suitable mathematical expression. For closed reactors, the analytic expression obtained from the well known axial dispersion model is too complicated for practical use. The \two-parameter empirical model that involves one large and two small perfectly mixed sub-reactors along with a small plug flow sub-reactor provides an accurate description of RTD in the form of a relatively much simpler mathematical expression. However, due to the lack of specification of the sequence in which the sub-reactors are arranged, this model cannot be used for modeling of systems characterized by nonlinear reaction kinetics. Therefore, in this paper we propose a new one-parameter empirical model that meets both the requirements. The model involves partitioning the process unit into a number of unequal-volume perfect mixers arranged in a definite order. The first perfect mixer at the feed end is the largest, and the volumes of the successive smaller perfect mixers form a geometric progression, the inverse of the common ratio being the sole parameter of the model. Several sets of available experimental RTD data on two closed reactors, rod mills and ball mills, were analyzed using the proposed model. In most cases the model was found to fit the experimental data on a par with the dispersion and two-parameter models. Moreover, the proposed order of arrangement of different perfect mixers could be validated by demonstrating that the simulated trend of variation in the particle size distribution along the mill matches closely with that observed in practice.

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