This work is focused on the modelling of the absorption phenomenon accompanied by several chemical reactions occurred in stage column, the chosen method of resolution is a model which couple between two others methods Levenberg-Marquardt and Thomas algorithms. The model is a set up of material and energy balances; the constants of balance thermodynamics permit to give the function joining the molar fractions in the two phases, the constraints of the system are satisfied while respecting the normalization of the molar fractions in the phases liquid and steam. The example chosen for validation of the model is about absorption of carbone dioxide and hydrogen sulfide by alkanolamine solution.