Azeotropic distillation multiple steady states

Rigorous models of staged distillation processes are formulated by setting up material balance equations, equilibrium relations, summation equations, and enthalpy balance equations (MESH equations). In these models, the extent of nonlinearity may be very severe, particularly for azeotropic and reactive distillation systems. MESH system based mathematical models can thus yield multiple solutions (multiple steady states), a fact which has been observed by many researchers. 

Also included is an example of one of the important complexities in trying to deal with azeotropic distillation systems. These systems are highly nonlinear and exhibit the phenomenon of multiple steady states. 

The nonlinear algebraic equations that describe a steady-state distiUalion column consist of component balances, energy balances, and vapor-liquid phase equilibrium relationships. These equations are nonlinear, particularly those describing the phase equilibrium of azeotropic systems. Unlike a linear set of algebraic equations that have one unique solution, a nonlinear set can give multiple solutions therefore, the possibility of multiple steady states exists in azeotropic distillation. 

Reder et al. [88] have applied this analysis technique to study distillation of the methyl formate system. They report unique steady state solutions for all possible feeds, if distillation of the (hypothetical) non-reactive quaternary system MeOH/ FA/MF/W is considered. In contrast, steady state multiplicity can be found for the reactive system in the distillation region formed by MF, MeOH, Wand the binary azeotrope but not for the distillation region formed by FA, MeOH and the binary azeotrope. In fact, an infinite number of steady states with different distillate concentrations can be found for some critical bottom flow rate B. Fig. 10.4 shows the distillate concentration as a function of B varying from zero to its maximum value. 

First simulation results on steady state multiplicity of etherification processes were obtained for the MTBE process by Jacobs and Krishna [45] and Nijhuis et al. [78]. These findings attracted considerable interest and triggered further research by others (e. g., [36, 80, 93]). In these papers, a column pressure of 11 bar has been considered, where the process is close to chemical equilibrium. Further, transport processes between vapor, liquid, and catalyst phase as well as transport processes inside the porous catalyst were neglected in a first step. Consequently, the multiplicity is caused by the special properties of the simultaneous phase and reaction equilibrium in such a system and can therefore be explained by means of reactive residue curve maps using oo/< -analysis [34, 35]. A similar type of multiplicity can occur in non-reactive azeotropic distillation [8]. 

More than one steady state for the same set of specified variables (output multiplicity) is one of the interesting features of azeotropic distillation. Simple distillation columns with ideal vapor-liquid equilibrium, however, may also show MSS (Jacobsen and Skogestad, 1991). The existence of output multiplicities in distillation were first reported on the ternary ethanol-water-benzene (EWB) system. Earlier simulation-based studies had reported two distinct steady states depending on the starting guesses (Bekiaris et al.. 

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