Computers & Chemical Engineering, Vol.21, No.9, 1031-1042, 1997
Solution Techniques for Population Balance-Equations as Applied to Heterogeneous Aqueous Processes in Stirred-Tank Reactors
In this paper, a combination of analytical and numerical methods for solving the dynamic population balance equations associated with simultaneous leaching-precipitation reactions with size-independent rates is developed. An analytical solution suitable for both dissolving and precipitating phases in either continuous or batch reactors is derived assuming that concentrations of aqueous reactant are known a priori. When these concentrations are unknown, the population balance equations are combined with molar balances for aqueous reactants. The resulting system of equations is solved by converting the population balance equations into systems of ordinary differential equations. This is achieved by applying the moment transformation for the precipitation phases, whereas an original application of the numerical method of lines is developed for the leaching phases. The use of the proposed techniques is demonstrated by solving equations that arise in modelling batch and continuous transient reactors. The application of the numerical method of lines is also generalized for the case of size-dependent rates for either leaching or precipitating phases.