Development of a First-principle Model of a Semi-batch Rhodium Dissolution Process

Abstract

First-principle modelling of chemical processes and their unit operations has been of great interest in the chemical process, as well as the control and allied industries over the past decades. This is because it offers the opportunity to develop virtual representations (models) of real process systems, which can be used to describe and predict the dynamic behaviour of those systems. These models are based on the fundamentals of the transport phenomena of fluid dynamics (involving momentum transfer), mass transfer, and energy transfer of the systems they describe. A first-principle model of a semi-batch rhodium dissolution chemical process has been developed. It describes the dynamic behaviour of two exothermic reactions, occurring simultaneously in a semi-batch process. The dissolution of 29 kg of solid crude rhodium sponge (Rh) into 546 L of a solution of hydrochloric acid (HCl(aq)), to produce a solution of aqueous rhodium(III) chloride (RhCl3.H2O), as well as the reaction of chlorine (Cl2(aq)) with water (H2O(l)) to produce some more HCl(aq) in the reactor. The model was formulated as a system of explicit ordinary differential equations (ODEs), which demonstrated some good and stable qualitative tracking of the temperature and pressure data of the real reactor. The molar responses of all chemical species, as well as the heats of reactions, showed to be consistent with the description of the process, and no negative values of those variables were generated. Estimates of the key parameters of heat and mass transfer coefficients, arrhenius constants, and activation energies of reactions were assumed and tuned to satisfaction by trial-and-error, but not optimised. This is because during simulations, the numerical solver would often fail to integrate the equations, due to the appearance of large derivatives in some model equations whenever those parameters varied, thereby stopping simulations. Finally, the model was validated with a set of data from 45 batches. For all simulations done, the simulated temperature responses showed better prediction of data than the simulated pressure responses did, with an average percentage accuracy of 80% against 60 percent, respectively.