A multiple mechanism model for measuring extra- and intraparticle mass transport in ion exchange resins

A diffusion-based kinetic model for resin-based ion exchange is proposed that simultaneously describes extra- and intraparticle diffusion for the purpose of predicting batch transient adsorption rates during resin operation. The extraparticle diffusion is simulated through Newton's-law-of-cooling assuming a stagnant laminar layer, while the intraparticle simulation assumes a homogeneous internal pore environment and uses the Nernst–Planck equation to describe multi-ion diffusion. The key parameters of the model are the mass transfer coefficient, the intrinsic diffusivities of the adsorbing and desorbing ions and the equilibrium coefficient associated with the Mass-Action-Law, which is assumed to be applicable at the liquid/resin interface. A novel method is described to determine the critically important ion concentration at the interface from experiment. Kinetic tests are undertaken in a closed circuit system, adsorbing Na, Mg, and Ba ions separately onto gel type acid resin, and the simulation is fitted to the measured raw data using the Hook–Jeeves search algorithm. The intraparticle diffusivities of the three ions are hence measured and reported.