THE PURPOSE. The purpose of this work was to use the associated paradigm for a correct quantum-chemical description of non-catalytic and catalytic supercritical fluid processes of transesterification of triglycerides with alcohols and hydrolysis of triglycerides and to model a one-stage process for obtaining biodiesel fuel, carried out under supercritical fluid conditions with its subsequent scaling to the commercial level.METHODS. The Gaussian09 software product was used to describe quantum chemical studies. The process modeling was carried out using the ASPEN Plus® v2006 software product. The behavior of thermodynamic systems at high temperatures and pressures is modeled using "RK ASPEN EOS". For modeling processes carried out at low pressures, mathematical models UNIQUAC and UNIFAC-LL were used. The scaling of the process was carried out in the VMGSim program.RESULTS. The third part of the review focuses on the quantum-chemical modeling of the transesterification reaction carried out under supercritical fluid conditions. It is shown that taking into account the associative paradigm makes it possible to obtain calculated reaction rate constants that agree in order with the experimental values. And also an analysis was carried out and the results of modeling the process of obtaining biodiesel fuel and scaling it to a commercial level, with a capacity of up to 9000 tons / year, were presented.CONCLUSION. The conducted analysis showed that biodiesel fuel can be a competitive fuel in our and the world market.