Numerical model for the investigation of countercurrent chromatography

A numerical model is developed to describe the separation process of countercurrent chromatography (CCC) in this work. The theory of countercurrent extraction table (TCCET) is first proposed to calculate concentration distributions of chemical components in the CCC, which is essential for a numerical model to describe the dynamic equilibrium of mass transfer. According to the theory of countercurrent extraction, the concentration in chromatography obeys binomial distribution, while the outflow from the n-th stage is a negative binomial distribution. As a result of the central limit theorem, they will obey normal distribution for sufficiently large n. Row-stage ratio (R(RS)) is then defined to determine the K value or retention time because it has a linear relationship to K value and retention time. The stage for a certain K value can be subsequently obtained with a very simple form, n(k)=1/(2piq(k)X(2)(k, max)), which can be calculated from the peak height obtained from experiments. Finally, the actual stage for a separation chromatogram can be acquired with using this simple expression. The agreement between theoretic and experimental results is quite satisfactory in the normal-phase and reversed-phase elution mode.