The paper shows the expediency of supplementing the balance simplex method by calculating the number of free variables of separation flowsheets containing recycle flows. The need to determine and set the free variables that provide lower energy consumption when calculating the material balance of flowsheets with recycling is justified. The problem of material balance multivariance is illustrated, and ways to solve it are shown with the example of separation flowsheets for two ternary mixtures: n-butanol + water + toluene and n-butanol + butyl acetate + water. Separation flowsheets containing three distillation columns and a liquid–liquid separator are proposed for both systems. The dependence of the recycle flow values and the energy consumption of distillation columns and separation flowsheets on the selection and setting of values of free variables in solving the balance problem is shown. The dependence of energy consumption on the composition of the original mixture is studied for an n-butanol + butyl acetate + water system. Recommendations for setting free variables for flowsheets of the separation of ternary mixtures with three binary (and one ternary) azeotropes are formulated. The technique of highlighting the region of separation flowsheet operability is illustrated. The column operating parameters that ensure the production of products of a given quality with minimal energy consumption are determined. It is shown that with the incorrect selection and setting of variables (during balance task solvation), the energy consumption for mixture separation can be overestimated by more than 40%.