Analysis of steady state multiplicity in kinetically controlled reactive distillation
Reactive distillation systems combine chemical reaction and distillation, which are traditionally done separately. Combining different unit operations into one consolidated system (whenever feasible) is based on the idea that the properties of the new system will make the process more profitable than traditional systems of separate reaction and separation. However, the dynamic behavior of reactive distillation columns can be complicated as multiple steady states occur commonly in reactive distillation columns. In some reactive distillation columns, many branches of steady states with different stability are close to each other leading to complex dynamic behavior in those regions. Furthermore, the degrees of freedom available for control of a reactive distillation column can be significantly smaller than those in more traditional systems consisting of separate subsystems for reaction and separation. Despite significant progress on design and dynamic simulation of reactive distillation systems, more general results are needed concerning their steady state and dynamic behavior.
Through the application of bifurcation and singularity theory, necessary conditions have been found for the existence of multiplicity in these systems and for the stability of the solutions. From this analysis, several key relationships have been found to determine the possibility of steady state multiplicity; they involve the vapor liquid equilibrium of the system as well as other physical properties such as the activation energy and the heat of reaction and vaporization.
First, the analysis focused on the study of the reactive flash. The understanding of the multiplicity there paved the way for the understanding of the multiplicity in columns. It was found that multiple solutions in the reactive flash and reactive distillation columns are generated by similar mechanisms. The mathematical conditions that determine the multiplicity in the case of columns also incorporate the effects of having multiple stages in the device. Multiplicity is possible in endothermic systems as well as those with a small heat of reaction. The number of steady states in reactive distillation systems is usually 2 n+1, where n is the number of reaction separation stages. Increasing the number of reactive-separation stages in the device generally increases the number of steady states. The results also suggest that multiplicity in columns is more easily achieved than in the flash due to the larger composition differences available in columns. Multiplicity in the reactive flash means that the column can have multiple solutions for some conditions. However, the column can have multiple solutions while the flash does not.