Mathematical Modeling of Reactive Extraction of Solute from Slab Solid Material

Abstract

Reactive extraction is gaining higher attention due its wide application in various solute separation processes. Here, a mathematical model of reactive extraction in slab has been proposed. The model was developed by considering simultaneous processes of active compound intra particle diffusion, second order elemental reaction of solute-active compound, and intra-particle product diffusion. The obtained partial differential equations (PDEs) were solved using Finite Difference Approximation (FDA) method by using realistic parameters. Concentration profile as well as product yield were evaluated as a function of time. As a result, the model proposed here may serve as a basis design for reactive extraction unit. Sensitivity analyses was conducted to inspect the influence of slab thickness, diffusivity and reaction rate constant to the product yield. Eventually, model validation was conducted by comparing the simulation results with analytical solutions for special cases. Validation results showed that the model gave good agreement with the analytical solution.