Distillation columns, energy balance

For many pieces of equipment, such as heat exchangers and distillation columns, stand-alone programs are available that calculate material and energy balances around that piece of equipment, size the equipment, and calculate or rate its performance. 

Distillation Columns. Distillation is by far the most common separation technique in the chemical process industries. Tray and packed columns are employed as strippers, absorbers, and their combinations in a wide range of diverse appHcations. Although the components to be separated and distillation equipment may be different, the mathematical model of the material and energy balances and of the vapor—Hquid equiUbria are similar and equally appHcable to all distillation operations. Computation of multicomponent systems are extremely complex. Computers, right from their eadiest avadabihties, have been used for making plate-to-plate calculations. 

Himmelbau (1995) or any of the general texts on material and energy balances listed at the end of Chapter 2. The Ponchon-Savarit graphical method used in the design of distillation columns, described in Volume 2, Chapter 11, is a further example of the application of the lever rule, and the use of enthalpy-concentration diagrams. 

Ranzi E, Rovaglio M, Faravelli T, Biardi G. Role of energy balances in dynamic simulation of multicomponent distillation columns. Computers Chem Eng 1988 ... 

Interaction is unavoidable between the material and energy balances in a distillation column. The severity of this interaction is a function of feed composition, product specification, and the pairing of the selected manipulated and controlled variables. It has been found that the composition controller for the component with the shorter residence time should adjust vapor flow, and the composition controller for the component with the longer residence time should adjust the liquid-to-vapor ratio, because severe interaction is likely to occur when the composition controllers of both products are configured to manipulate the energy balance of the column and thereby "fight" each other. 

However, in batch distillation, the system is frequently very stiff, owing either to wide ranges in relative volatilities or large differences in tray and reboiler holdups. Therefore, if methods for non-stiff problems are applied to stiff problems (ODE models but having column holdup and/or energy balances), a very small integration step must be used to ensure that the solution remains stable (Meadow, 1963 Distefano, 1968 Boston et al., 1980 Holland and Liapis 1983, etc.). 

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. 

In alternative (a) pure products are obtained in each column. Since the relative volatility diminishes with the pressure, higher reflux is needed in the H P column. The balance of duties can be obtained by adjusting the split of the feed. Roughly speaking, by double-effect distillation the energy consumption is divided by two. In alternative (b) there is a large temperature difference between top and bottom that may be exploited by a sloppy split in the HP column with the heavy component, while in alternative (c) this is done with the light component. Alternative (c) is the best for the present case study since it allows a lower temperature of the hot utility. 

The SR method can be applied to distillation columns, but the equations of the algorithm do not allow the solution of the condenser and the reboiler with the other stages in the column. Because only the energy balances are used as independent functions, reboiler and condenser duties, reflux ratio, and the boilup ratio have to be specified. This overspecifies the column and the solution cannot be found. The condenser and the reboiler can be solved as separate unit operations in a flowsheet as demonstrated by Fonyo et al. (39). The SR method is used in the ABSBR step of FLOWTRAN of Monsanto, St. Louis, Missouri, and also in both the public release version of ASPEN and in ASPENPlus of AspenTech, Cambridge, Massachusetts. 

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