Mass transfer process for prolate spheroidal drops in rotating disc contactor column

Abstract

A rotating disc contactor (RDC) column is one of the equipments that is commonly used in the chemical industry. This column is used for the liquid-liquid extraction process where it is a method to separate compounds based on their insolubility differences. The mass transfer process in the RDC column occurs due to the counter-current motion of the drop and continuous phases. The mass transfer process that occurs in the RDC column is also can be modelled mathematically. Previously, this process is modelled by assuming that the drops were spherical. After considering the research done on the distribution of drops and column properties, the drops have shapes closer to spheroidal rather than spherical. Therefore, a new model of the mass transfer process in the RDC column is proposed. This new model is developed by assuming that the drops are taking prolate spheroidal shape instead of oblate due to the properties of the column. The mass transfer process of the prolate spheroidal drops is determined by using Fick's second law in Cartesian coordinates to predict the diffusion for rectangular shape body. By using a suitable transformation equation, a three-dimensional partial differential equation is obtained. However, instead of solving Fick's second law analytically, the numerical approach is used. In this study, the finite difference method (FDM) is chosen. Since FDM is one of the methods that engineers usually use to solve modelling problems, the algorithm for this three-dimensional partial differential equation would help engineers increase the capability of the RDC column only by simulation, thus reducing the experimental cost. The algorithm developed in this study can be adjusted depending on the initial value and the boundary value of the system. This new model shows that the results obtained are satisfying the profile of concentration in the RDC column. After comparing the numerical results with the experimental results, this model's relative error was between 0.1% until 9%, which varied due to some stages. In conclusion, the results from the new model are closer to the experimental results compared to the older model. The algorithm obtained in this study can be used for references in solving the threedimensional partial differential equation and this model would help engineers in improving the RDC column performance.