Three-phase reactive distillation offers a challenging case for process modeling and design. It is the inherent complexity of the system arising from the appearance of a second liquid phase that makes process modeling both mathematically strenuous and computationally demanding. Optimal design assisted by mathematical programming techniques of such columns becomes an even more laborious task as alternating three-phase and two-phase columns regions can be identified only at the final solution.

This work combines the predictive power of nonequilibrium (NEQ) models with the approximating properties of orthogonal collocation on finite elements (OCFE) model formulation for the development of an accurate and reliable process model for three-phase reactive distillation columns. Following Higler et al. (2004) the NEQ model is based on mass and energy balances for each phase present while the thin film model is utilized for the description of the transport phenomena and chemical reactions around the three possible interfaces (vapor-liquid I, vapor-liquid II, liquid I-liquid II). Mass and heat transfer in the film region are expressed in terms of the multicomponent Maxwell-Stefan equations.

A key feature in the modeling of three-phase reactive distillation is the accurate identification of the boundaries between three-phase and two-phase column regions. The location of the phase boundary may vary as column conditions change. In particular, when the optimal column configuration and operating points are sought, phase boundaries are not known a priori and may be difficult to estimate. Therefore the model structure should be able to adapt accordingly. The model reduction capabilities of the OCFE model formulation greatly facilitate the tracking of the phase boundary (Swartz and Stewart, 1987) and ultimately the development of a compact in size model that encompasses the rigorous description of the occurring phenomena (Dalaouti and Seferlis, 2006). Phase boundary tracking is achieved with the performance of a thermodynamic phase stability test and the position of a finite element breakpoint at each phase boundary.

Optimal design using a NEQ/OCFE model enables the calculation of the column configuration as described by the number of stages for staged columns or packing height for packed columns, location of feed streams, sizes of reactive and non-reactive column sections, stage holdups, and column operating conditions such as reflux and reboil ratios, catalyst load, and reactant stream ratio using conventional nonlinear programming techniques. Due to the continuous nature of the resulting NEQ/OCFE model, staged columns are transformed into continuous domains thus avoiding the use of integer/binary variables associated with the existence of column stages; a feature that facilitates the design optimization significantly.

The proposed modeling framework has been applied in the optimal design of a staged column for the production of butyl acetate via the esterification reaction of butanol and acetic acid.

Dalaouti N, Seferlis, P., (2006). A unified modeling framework for the optimal design and dynamic simulation of staged reactive separation processes, Comput. Chem. Eng., 30, 1264.

Higler A., Chande R., Taylor R., Baur R, Krishna R. (2004). Nonequilibrium modeling of three-phase distillation. Comput. Chem. Eng., 28, 2021.

Swartz C.L.E., Stewart W.E. (1987). Finite-element steady state simulation of multiphase distillation. AIChE J., 33, 1977.