Modelling of Adsorption of Dyes from Aqueous Solution by Activated Carbon - Wong, Teck Ngin (2004)
Adsorption process has been gaining popularity as an effective alternative for separation processes. Two fundamental properties that influence the adsorption rate are the adsorption equilibrium and mass transfer limitation. The adsorption isotherm is obtained from batch studies. The mass transfer coefficients obtained from batch studies need to be extrapolated by matching the model with the experimental data. The mass transfer parameters are important in designing a fixed-bed absorber, commonly used in the industry. For dye adsorption on activated carbon, concentration dependent surface diffusivity is the most important mass transfer parameter and must be included in the study. The pore diffusivity should also be included to improve the accuracy of the simulation. Therefore, the film-pore-concentration dependent surface diffusion (FPCDSD) model is identified as the best model to describe the adsorption rate of dye onto activated carbon. In this study, a mathematical model for adsorption rate is developed based on the FPCDSD model. The governing partial differential equations (PDEs) are transformed to ordinary differential equations (ODEs) using orthogonal collocation (OC) method. These v sets of ODEs are then integrated using the numerical algorithm DIVPAG (IMSL library subroutine), which is based on variable order, variable step method implementing backward differential formula (Gear’s Method) and is suitable for stiff system of first order non-linear ODEs. Programs written in FORTRAN 90 are used to extrapolate the mass transfer parameters by matching the simulation data with the experimental data of batch studies. The FPCDSD model is sufficiently general and thus can be reduced to describe other simplified models for liquid adsorption easily, e.g. the film-concentration dependent surface diffusion (FCDSD) model and the film-pore diffusion (FPD) model. Three set of experimental data from Choy et al. (2001) based on different masses were selected to test the applicability of the FPCDSD model in simulating batch adsorption. Simulation results show that, for acid dye/activated carbon system a single set of mass transfer parameters is able to match the simulation and experimental data using the FPCDSD model and the FCDSD model. However, ignoring the pore diffusion, there resulting a 30% differences in the surface diffusion. For Methylene Blue/PKS (different larger initial concentrations) systems, only the FPCDSD model could use a single set of mass transfer parameters. The FPCDSD model is then further extended to model the fixed-bed adsorber. A computer program written in FORTRAN 90 is developed. The PDEs for the axial and radial directions are discretised into ODEs using OC method. Column results showed that the retention time increases with increasing bed length and superficial velocity. Increasing the bed porosity, the residence time will decrease. Using the equilibrium vi isotherm and mass transfer parameters obtained from batch studies and with a suitable correlation for film mass transfer coefficient, the fixed-bed model can be used to predict the breakthrough curve of column adsorption.