A strategy for solving a mathematical model of barium sulphate precipitation in a continuous stirred tank reactor

In a previous paper, we modelled the precipitation of barium sulphate in a continuous stirred tank reactor by computational fluid dynamics and compared our predictions with previous experimental and modelling work. Turbulent momentum transfer solutions for different process conditions were obtained using the RANS and MRF approaches whilst reactive mass transfer was simulated by solving the transport equations for the three reacting species and five moments of the crystal population balance. Micromixing effects were accounted for indirectly. In this paper, the detailed numerical aspects that led to the previous predictions are presented in detail. In particular, the way the highly nonlinear and stiff set of the transport equations was handled is discussed. The main issue is to diminish the inherent tendency for diverging iterations to be calculated during the initial stage of the mass transfer simulations. The critical elements of a successful procedure for preventing this divergence are discussed. Overall, general guidelines for an efficient strategy and a perspective on how to obtain optimized solutions are outlined, including the use of the under-relaxation factor. Even so, increases in impeller speed or feed rate significantly increase the number of iterations required for a converged solution. It is also seen that a constant BaSO4 concentration in the exit stream is not a sufficient condition for concluding the iteration process.