Abstract. The paper shows that an attainability region of a binary fractionating column depends on two parameters. These parameters are expressed through kinetic coefficients and mixture properties. The paper also considers a problem of finding the maximal productivity of the ternary distillation. Selection conditions for an optimal separation order and expressions for the maximal productivity of this process were obtained.

The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how these problems are linked to the field of finite-time thermodynamics.

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In this paper an estimate for the reversible molar heat supply needed for fully separating a certain mixture is given on the basis of thermodynamic balance equations. It is shown that in order to estimate this heat supply one should solve the problem of selecting the optimal separation sequence. The algorithm solving this task is given. This algorithm allows to select the separation sequence on the basis of preliminary calculations, knowing only the properties of the component that one wants to separate. The solution algorithm is demonstrated for an exemplary system: a gas-fractionation plant.

An estimate has been obtained of the energy consumption on 1 mol of separated mixture based on thermodynamic balances for processes that use mechanical and heat energy. Only irreversible losses depend on the order of separation for mixtures in mechanical systems, while for the systems using the heat, the order of separation also affects the reversible energy consumption. In the latter case, in order to obtain a reversible estimate of the heat consumption, one should solve the problem of selecting the order of separation. An algo rithm has been obtained for its solution that enables one to approximately choose the order of separation at the stage of preliminary calculations knowing only the properties of the feed.