Multiple steady states in distillation

We study multiple steady states in distillation. We first analyze ternary homogeneous azeotropic mixtures. We show that in the case of infinite reflux and an infinite number of trays ({dollar}infty{dollar}/{dollar}infty{dollar} case) one can construct bifurcation diagrams on physical grounds with the distillate flow as the bifurcation parameter. Multiple steady states exist when the distillate flow varies non-monotonically along the continuation path of the bifurcation diagram. We derive a necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the distillation region boundaries. The feed compositions that lead to these multiplicities are located in the composition space.; The homogeneous mixture results are extended to heterogeneous mixtures. We demonstrate how the {dollar}infty{dollar}/{dollar}infty{dollar} analysis can be applied to different column designs (tray or packed columns, with or without decanter and with different types of condenser and reboiler). The fully detailed, necessary and sufficient multiplicity condition is derived. We show that the prediction of the existence of multiplicities in the {dollar}infty{dollar}/{dollar}infty{dollar} case has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams, we show that these multiplicities tend to vanish for small columns and/or for low reflux flows. Nevertheless, the {dollar}infty{dollar}/{dollar}infty{dollar} multiplicities do exist for columns at realistic operating conditions.; The complete list of the {dollar}infty{dollar}/{dollar}infty{dollar} case predictions is presented. The implications of these predictions for column design, synthesis and simulation are demonstrated. We show how the {dollar}infty{dollar}/{dollar}infty{dollar} predictions can be useful for the selection of the entrainer, the equipment and the separation scheme. We show that, in some cases, the column operation at an unstable steady state may have some advantages. The effect of phase equilibrium on the existence of multiplicities is discussed. Finally, we identify the key issues and the pitfalls one should be cautious about when designing or computing the composition profile of an azeotropic distillation column with a commercial simulator.