Extraction efficiency is determined by mass and heat transfer processes in the liquid-solid system. In order to determine the optimal conditions for the extracting process, it is necessary to make up a mathematical model which reliably describes mass and heat exchange processes. In our study there are equations of mass and heat transfer, which occur during extracting process. They allow to determine numerically the process parameters and describe the resistance shares of external mass transfer much easier than in other methods of calculation. Further development of the outlined ideas leads to a new content of the concepts of kinetic coefficients of mass and heat transfer. To prove the accuracy of the calculation method, the share of external mass transfer resistance was calculated when extracting soybean oil with extraction gasoline and dichloroethane. The described calculation method for extracting process features may be used for designing extraction equipment, technology development and technological characterizing of process. Taking into account the identified system features, it is possible to reduce the solution to a particular form and mathematically describe a specific mass and heat exchange process. This makes it possible to determine the optimal conditions and increase the efficiency of the extracting process.

Optimization of extracting food products from plant raw materials using a mathematical model is suggested. The model has been derived for the analysis of extracting pectin from Jerusalem artichoke. Multistage anti-cyclic extraction, non-stationary diffusion for the initial element of the processed raw material in the form of plates is considered. The calculations take into account the effect of reverse solvent change, the time of the solvent drain from the solid phase, among other process parameters. The derived equation makes it possible to analyze the effect of the impregnation of a part of the miscella at an intermediate stage of a countercurrent multistage extraction on the efficiency of the process. The correctness of the mass conductivity coefficient calculations was confirmed using the performance indicators of the extractor. Based on the data obtained, a mathematical model was created that describes the extraction process with a variable coefficient of mass conductivity. Thus, it is possible to determine the optimal parameters of the process including the rate of fluid flow through the material, the crushed material particle size, the thickness of the particles, and the processing time.