Investigation of Numerical Solution Approaches to Multicomponent Batch Distillation in Packed Beds

Abstract

Finite difference and orthogonal collocation techniques are used to obtain numerical solution of the differential contactor model that represents a packed column. In the orthogonal collocation approach, polynomial approximation to the model equations results in a sparse system of equations that is much smaller in dimension than with the other methods. Exploiting this sparsity and choosing the proper order for approximating polynomial are the critical issues. Higher CPU time associated with higher order of the polynomial necessitates use of finite elements in the collocation techniques. We study the accuracy and efficiency issues underlying all these approaches with the help of hydrocarbon mixture and ethanol esterification examples. The later case study is considered with both with and without the presence of reaction.

An Optimal Campaign Structure for Multicomponent Batch Distillation with Reversible Reaction

“…The value of the integer p depends on the number of products that are of interest. The reflux optimization for distillations A and B differs only in the number of cuts (n) and hence in p. Gradients are evaluated numerically by the finite difference approximation since function evaluation is very expensive computationally (around 50 min of CPU on Sparc 5 (Wajge et al, 1997)). Though such an approximation has the potential for introducing numerical errors, good accuracy can be obtained by a careful selection of the step size for the approximation (Rosen and Luus, 1991).…”

“…This not only allows the use of the simple stoichiometric constraint for the off-cuts but also allows the formulation of the distillation model with reaction occurring only in the reboiler. The resulting distributed model has been described by Wajge et al (1997).…”

“…Typically, the reflux profile is assumed to undergo step-wise changes, where both the timing of these step changes and the reflux level between changes are taken as optimization variables. Using suitable numerical approximations of the ODE (staged column) or PDE (packed column) model (Wajge et al, 1997), the resulting problem can be converted and solved as a large, structured nonlinear programming problem.…”

Improving Batch Reactive Distillation Processes with Off-Cut

“…Cuille and Reklaitis, Wajge et al, Bollyn and Wright, and Brüggemann et al discuss the development and numerical solution of dynamic models for BREAD systems. The feasibility of BREAD processes is investigated by Lee and co-workers − using RCMs and Steger et al using a graphical method.…”

Optimization of a Semibatch Distillation Process with Model Validation on the Industrial Site

“…Previous and recent studies of batch distillation have focused on simulation (Ahmad and Barton, 1996;Skogestad et al, 1997;Wajge et al, 1997;Li et al, 1997a) and optimization (Logsdon and Biegler, 1989;Fahart et al, 1990;Diwekar and Madhavan, 1991;Mujtaba and Macchietto, 1992a) of such processes. To facilitate both the distillation and the reaction, reactive batch distillation has been proposed and investigated (Albet et al, 1991;Mujtaba and Macchietto, 1992b;Sørensen et al, 1996), in which usually a reversible reaction, which takes place in the reboiler, is considered.…”