Mathematical modelling of mass transfer in a multi-stage rotating disc contactor column

Abstract

In this study, the development of an improved forward and inverse models for the mass transfer process in the Rotating Disc Contactor (RDC) column were carried out. The existing mass transfer model with constant boundary condition does not accurately represent the mass transfer process. Thus, a time-varying boundary condition was formulated and consequently the new fractional approach to equilibrium was derived. This derivation initiated the formulation of the modified quadratic driving force, called Time-dependent Quadratic Driving Force (TQDF). Based on this formulation, a Mass Transfer of A Single Drop (MTASD) Algorithm was designed, followed by a more realistic Mass Transfer of Multiple Drops (MTMD) Algorithm which was later refined to become another algorithm named the Mass Transfer Steady State (MTSS) Algorithm. The improved forward models, consisting of a system of multivariate equations, successfully calculate the amount of mass transfer from the continuous phase to the dispersed phase and was validated by the simulation results. The multivariate system is further simplified as the Multiple Input Multiple Output (MIMO) system of a functional from a space of functions to a plane. This system serves as the basis for the inverse models of the mass transfer process in which fuzzy approach was used in solving the problems. In particular, two dimensional fuzzy number concept and the pyramidal membership functions were adopted along with the use of a triangular plane as the induced output parameter. A series of algorithms in solving the inverse problem were then developed corresponding to the forward models. This eventually brought the study to the implementation of the Inverse Single Drop Multistage (ISDMS)-2D Fuzzy Algorithm on the Mass Transfer of Multiple Drops in Multistage System. This new modelling approach gives useful information and provides a faster tool for decision-makers in determining the optimal input parameter for mass