Analytical and numerical solutions of linear and nonlinear chromatography column models

The advection-convection models (ACM) have practical applications in the investigation of separation processes, where mass (heat) is transferred by convection and diffusion (dispersion) along mass/heat exchanger, eq. adsorption, chromatography column, tubular reactor, etc. The ACM consists of nonlinear partial differential equations which can be solved only with numerical methods. In the article, a comparison of the volume method (VM) and orthogonal collocation on finite elements (OCFE) is presented in terms of their reliability, accuracy of calculations, and speed of calculation. The OCFE proved to be more robust than VM.

The linear ACM model for the chromatography column has an analytical solution in the form of the equation for the number of theoretical plates (N). This equation is often applied in the interpretation and evaluation of model parameters. However, the versions of N equation published in the literature are not correct. The error can lead to significant imprecision for specific cases. Here, in the paper, the revised equations are presented and discussed for the most frequently used chromatography column models.