Multiple Steady States in Homogeneous Separation Sequences

Abstract

In this article, multiple steady states are studied in sequences of interlinked columns commonly used to separate azeotropes in ternary homogeneous distillation. More specifically, two major separation schemes were concerned: the intermediate entrainer scheme and the “boundary separation” scheme. On the basis of the results on multiplicities in single columns for the case of infinite reflux and infinite column length (infinite number of trays) similar criteria for separation sequences were developed. It is shown how to construct bifurcation diagrams on physical grounds with one product flow rate as the bifurcation parameter and how the product paths of a sequence can be located. Moreover, a necessary and sufficient condition for the existence of multiple steady states in column sequences is derived on the basis of the geometry of the product paths. The overall feed compositions that lead to multiple steady states in the composition space are also located. For the intermediate entrainer scheme multiplicities occur for all feed compositions. For the boundary separation scheme multiplicities may disappear when a single column is integrated into a sequence. By use of examples of the two separation schemes, it is shown that the prediction of the existence of multiple steady states in the ∞/∞ case has relevant implications for columns with finite length (finite number of trays) operated at finite reflux.

Multiple Steady-States Analysis and Unstable Operating Point Stabilization in Homogeneous Azeotropic Distillation with Intermediate Entrainer

“…Strategies for Identifying Multiple Steady States Using Aspen Plus. In Guẗtinger and Morari's work, 21 Aspen Plus was used to detect the multiple solutions in the intermediate entrainer separation sequences. Their results confirmed that the steady-state multiplicities may exist in the column operating at realistic conditions, and the two stable solutions on the LSS and HSS, respectively, were found.…”

“…Thus, if the entrainer recycle is not closed, multiple steady states are expected for the first column of the direct or the indirect split sequence. Guẗtinger's work 21 proved that the existence of multiple steady states in intermediate entrainer separation sequence does neither depend on the external feed composition nor on the location of the azeotrope. Aspen Plus was utilized by Guẗtinger 21 to detect the multiple solutions in the acetone/benzene/n-heptane ternary system separation sequence.…”

“…Guẗtinger's work 21 proved that the existence of multiple steady states in intermediate entrainer separation sequence does neither depend on the external feed composition nor on the location of the azeotrope. Aspen Plus was utilized by Guẗtinger 21 to detect the multiple solutions in the acetone/benzene/n-heptane ternary system separation sequence. In Guẗtinger's work, the higher and lower stable steady states (HSS and LSS, respectively) have been traced by rigorous process simulations, but the unstable steadystate solutions were still missed.…”

∞/∞-Analysis of heterogeneous distillation processes

“…Therefore, it has been systematically used for studying homogeneous and heterogeneous azeotropic distillation (Bekiaris et al, 1993;Müller and Marquardt, 1997;Müller, 1998). Further, it has successfully been applied to processes with more than one unit operation in a flow sheet (see e.g., Laroche et al, 1992;Esbjerg et al, 1998;Güttinger and Morari, 1996;Blagov et al, 2000;Nazanskii et al, 2001;Ulrich, 2002;Ulrich and Morari, 2003;Bonet et al, 2007). The stream table of a process resulting from ∞/∞ -analysis is, despite its inherent strong assumptions, often a good approximation of the stream table obtained from corresponding simulations based on the equilibrium stage model (Ryll et al, 2006;Grützner et al, 2007;Burger and Hasse, 2013).…”

On the multiple solutions of the flash equations

“…Güttinger and Morari (1996) state that the general notion of multiplicity is that a system with specified variables that meet its degrees of freedom exhibits different solutions at steady-state. The multiplicity is called input multiplicity when two or more sets of input variables (flows) provide the same output condition.…”