Mathematical relation to find concentration profile of solid resin in Adsorption Process with isotherm models

Study of adsorption models and concentration profile is very important in order to determine efficiency and mass transfer coefficients. A non-linear partial differential equation (PDE) was obtained using mass balance on the spherical element at resin by four isotherm models (Langmuir, Freudlich, Redlich-peterson and Toth). The PDE turn to linear equation with Approximation Method and it solved with converge Implicit Method and lead to concentration profile. The most advantage of this work is presentation of general PDE that it is independent of type of isotherm models. Also, a general matrix is obtained for this type of problems. Generally, the solution of matrix presented a comparison between experimental data and mathematical calculations. Therefore, one can compute the deviation of the theoretical calculations with the experiments.