Modeling and control of a packed distillation column

A rigorous dynamic model based on fundamental material and energy balances, thermodynamic relationships and mass transfer expressions was formulated for a packed distillation test system separating cyclohexane and n-heptane at atmospheric pressure. The model contains six nonlinear partial differential equations and five nonlinear algebraic equations for the packing in addition to equations modeling the overhead accumulator, sump, total reboiler and feed section. Several simplifying assumptions enabled reduction of the rigorous model to a form suitable for use in on-line model-predictive control calculations. The effect of each simplifying assumption was evaluated with respect to accuracy, dimensionality and speed of solution. Dynamic model predictions compared well with experimental data obtained from step-tests conducted on the large-scale packed distillation test system at the Separations Research Program's facility at the Balcones Research Center, UT Austin.;An investigation into the influence of effective interfacial area on the operation and control of packed columns revealed that aggressive surface treatment of structured packings gives rise to input multiplicity and gain-sign changes, even in ideal binary distillation. Packed columns were also found to exhibit output multiplicity and bifurcations. Steady-state stability conditions were developed, and model characteristics which led to output multiplicity and bifurcations were identified. An examination of the dependence of the dominant column time constant on operating conditions revealed that the holdup that undergoes the greatest composition change in response to a change in input governs the speed of response of the column.;Nonlinear Model-Predictive Control (NMPC), a strategy for feedback control of constrained nonlinear processes, was developed. The algorithm can be used to control open-loop stable and unstable processes described by a wide variety of model equations, and addresses input, state and output constraints in an explicit manner. The advantages of the algorithm were demonstrated by simulating the start-up of a CSTR, and control of a packed distillation column with infeasible set-points. In each case, NMPC proved to be superior to traditional controllers. NMPC, in conjunction with a nonlinear model-based state/parameter estimation scheme, was used to control the packed column at the Balcones Research Center. When an infeasible set-point was specified as the control objective, NMPC took the process as close to the set-point as possible, in a least-squares sense, thus proving superior to linear control.