Distillation rigorous solution procedures

SEPARATION COLUMNS (DISTILLATION, ABSORPTION AND EXTRACTION) The basic steps in any rigorous solution procedure will be ... 

Rigorous and stiff batch distillation models considering mass and energy balances, column holdup and physical properties result in a coupled system of DAEs. Solution of such model equations without any reformulation was developed by Gear (1971) and Hindmarsh (1980) based on Backward Differentiation Formula (BDF). BDF methods are basically predictor-corrector methods. At each step a prediction is made of the differential variable at the next point in time. A correction procedure corrects the prediction. If the difference between the predicted and corrected states is less than the required local error, the step is accepted. Otherwise the step length is reduced and another attempt is made. The step length may also be increased if possible and the order of prediction is changed when this seems useful. 

Distillation is a widely used and important separation operation in the chemical industries. Rigorous model for the distillation process involves the MESH system of equations. Since the model is nonlinear, it may have more than one (feasible) solution. Simulation packages do not provide any systematic procedure to find multiple solutions. In the absence of complete information on MSS, wrong conclusions might be drawn on various aspects of design, operation, and control. Thus, a need exists for a systematic approach to find all feasible solutions for the distillation process. 

The holdup effects can be neglected in a number of cases where this model approximates the column behavior accmately. This model provides a close approximation to the Rayleigh equation, and for complex systems (e.g., azeotropic systems) the synthesis procedures can be easily derived based on the simple distillation residue curve maps (trajectories of composition). However, note that this model involves an iterative solution of nonlinear plate-to-plate algebraic equations, which can be computationally less efficient than the rigorous model. 

---