Ecological Systems and Devices Annotation << Back Analytical Calculation of a Packed Extraction Column Taking Into account Longitudinal Mixing of the Extractant Golovanchikov A.B., Prokhorenko N.A., Merentsov N.A., Shibitova N.V. The differential equations of the fi rst order material balance and the second order mass transfer are derived taking into account the longitudinal mixing of the extractant. It is shown that for the equilibrium equation of the described proportional mass transfer equation is transformed into a non-homogeneous differential equation of the second order with constant coefficients, which has an analytical solution. Numerical calculations with an iteration number of up to 10,000 of the differential equation of mass transfer and analytical calculations by a simple algebraic equation are carried out. Relative errors in the calculations of the main parameters do not exceed 1–2 %. Thus, with the same calculated column diameter, the coefficient of increase in the packing height at the Pecle number Pe = 30 compared to the typical calculation that does not take into account the longitudinal mixing is 1.17 for numerical calculations, and 1.16 for the analytical calculation. Keywords: extraction, longitudinal diffusion coefficient, extractant, concentration, Peclet number, boundary conditions, analytical solution, equilibrium dependence, working line, number of transfer units. DOI: 10.25791/esip.7.2025.1534 Pp. 22-33.