Multiple Steady States in Distillation

Abstract

We study multiple steady states in distillation. We first analyze the simplest case of ternary homogeneous azeotropic mixtures. We show that in the case of infinite reflux and an infinite number of trays (∞/∞ 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. We also locate in the composition triangle the feed compositions that lead to these multiple steady states. We further note that most of these results are independent of the thermodynamic model used. We show that the prediction of the existence of multiple steady states in the ∞/∞ case has relevant implications for columns operating at finite reflux and with a finite number of trays. Using numerically constructed bifurcation diagrams for specific examples, we show that these multiplicities tend to vanish for small columns and/or for low reflux flows. Nevertheless, the ∞/∞ multiplicities do exist for columns at realistic operating conditions. We comment on the effect of multiplicities on column design and operation for some specific examples. We then extend the homogeneous mixture results to ternary heterogeneous mixtures. We study the ∞/∞ case in much more depth and detail by demonstrating how the ∞/∞ analysis can be applied to different column designs. More specifically, we show how the feasible distillate and bottom product paths can be located for tray or packed columns, with or without decanter and with different types of condenser and reboiler. We derive the fully detailed, necessary and sufficient condition for the existence of these multiple steady states based on the geometry of the product paths. Simulation results for finite columns show that the predictions carry over to the finite case. The complete list of the ∞/∞ case predictions is presented. The implications of these multiplicities for column design, synthesis and simulation are demonstrated. More specifically, we show how the ∞/∞ 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 important issue of the effect of the thermodynamic phase equilibrium on the existence of multiplicities is discussed. Using the ∞/∞ analysis, we identify entire mixture classes for which multiplicities are inherent and robust. Mixtures with ambiguous VLE data are studied; we show that in some cases a slight VLE difference between models and/or experimental data may affect the existence of multiplicities while other, major VLE discrepancies do not. 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.

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