(574k) Modeling and Control of a Packed Distillation Column

The vast majority of industrial processes have as final operation separation stages. Distillation represents 95% of the operations in chemical industries having a major impact on product quality and energy use. The control of distillation columns presents a major challenge because of its non-linearities, its non-stationary behavior, the relationship between the control of two compositions, and the large amount of disturbances. One way to simulate the control of a unit operation is by developing a theoretical model that presents the performance of this operation. This work presents a model based on the equilibrium for the distillation of the solution water ? ethanol in the packed column of the Chemical Engineering Laboratory at the Universidad de los Andes, a sensitivity analysis a PI control for the compositions of bottoms and distillate, and the comparison of such control with the Ideal Free Distribution (IFD) model.

First of all, it is necessary to simulate the packed column in a stable state. For that, we assume that the column is in thermodynamic equilibrium in each stage, a partial condenser, a liquid feed in its saturation temperature, constant pressure, negligible heat losses with the surroundings and a five columns stage with its feed in the third theoretical plate. With these assumptions, the model is formulated, using the MESH equations and the Wilson model for the equilibrium of the solution, and the solution is provided based on the model of the tridiagonal matrix. This model solves in a rigorous way the distillation column, but it is necessary to divide the column in theoretical plates. Five theoretical equilibrium stages are found, and a total condenser. Then, a sensitivity analysis is performed in order to find which and in what magnitude the disturbances in the feed alter the stable state response. This result shows that the disturbance that generates the biggest modification in the response in the stable condition is the feed composition. Further, this simulation provides the needed information to find some indispensable values for the dynamic simulation and some constants needed to find a transfer function of the system.

With the obtained results, a dynamic state model is developed primarily in the mass balances at each theoretical stage using the Wilson thermodynamic model. The results give the temperature and composition profile for a given period of time. This model assumes a binary non-ideal mixture, constant pressure along the column, constant molar flows without steam retention, linear liquid dynamic, thermodynamic equilibrium at every stage, and a total condenser. With this model, it is found the required time to obtain the stable state and the possibility to make a proper simulation control. Besides, we can get a transfer function for the system that relates every composition or temperature in each stage with two inlets, specifically the distillate and reboil reflux.

Using the dynamic state model we develop two PI controllers tuned in order to control the distillate and bottoms temperature with L-V configuration giving very good results with pulse and step signals in the feed properties (i.e., the feed concentration, flow and the state in which it is entering to the column). The control gives stabilization in around ten minutes but it generates great changes in the manipulated variables and in high frequencies it presents an oscillation with large amplitude generating enormous energy losses and very distant concentration with the set point. Outside these disadvantages, the controllers yield a stable response in a wide range of specified set points and the columns acquire high molar concentrations of ethanol in the distillate with values around the 78%. In addition, the model gives the possibility to control every single stage if it is necessary.

Even though we get a reasonably good performance with the PI controllers, the amount of energy lost is big. In order to improve this, a behavioral ecology model is developed to keep the enthalpy loss in the entire column constant using the concept of the minimum thermodynamic condition (MTC). Using the bioinspired model based on the Ideal Free Distribution (IFD) concept, and the replicator dynamics, we guarantee that the performance is better than for a linear controller (i.e., the energy lost is improved, and the response is faster).