Computer methods distillation columns

General Properties of Computerized Physical Property System. Flow-sheeting calculations tend to have voracious appetites for physical property estimations. To model a distillation column one may request estimates for chemical potential (or fugacity) and for enthalpies 10,000 or more times. Depending on the complexity of the property methods used, these calculations could represent 80% or more of the computer time requited to do a simulation. The design of the physical property estimation system must therefore be done with extreme care. 

Distillation is a well-known process and scale-up methods have been well established. Many computer programs for the simulation of continuous distillation columns that are operated at steady state are available. In fine chemicals manufacture, this concerns separations of products in the production of bulk fine chemicals and for solvent recovery/purification. In the past decade, software for modelling of distillation columns operated at non-steady state, including batch distillation, has been developed. In the fine chemicals business, usually batch distillation is applied. 

Relaxation methods are not competitive with the steady-state methods in the use of computer time, because of slow convergence. However, because they model the actual operation of the column, convergence should be achieved for all practical problems. The method has the potential of development for the study of the transient behaviour of column designs, and for the analysis and design of batch distillation columns. 

However, in a more complex case with many equations where analytical solution would be diflicult, the equations can be solved numerically. All the and simultaneous equation solving packages available in most digital-computer libraries can be used. Keep in mind, however, that these are complex-variable simultaneous equations. A special-purpose method for solving the equations Tor a distillation column will be presented in the next example. 

However, the products cannot be calculated exactly and the procedure outlined is difficult to accomplish. Instead, calculations are made from both ends of the column to a match on an internal stage, perhaps first neglecting certain components, and later correcting the calculation by adding those components. The method has been well described by Robinson and Gilliland, and is certainly useful for simple distillation columns. Greenstadt et al. (Gl) have shown its application to computers. 

Operation of a batch distillation is an unsteady state process whose mathematical formulation is in terms of differential equations since the compositions in the still and of the holdups on individual trays change with time. This problem and methods of solution are treated at length in the literature, for instance, by Holland and Liapis (Computer Methods for Solving Dynamic Separation Problems, 1983, pp. 177-213). In the present section, a simplified analysis will be made of batch distillation of binary mixtures in columns with negligible holdup on the trays. Two principal modes of operating batch distillation columns may be employed ... 

The variables most commonly fixed in operations of distillation columns are listed in Section 13.6. Detailed calculation processes of column performance may require other intermediate or tentative specifications whose nature depends on the particular computer algorithm used. These specifications are identified with the descriptions of the three chief methods of this section. 

For single separation duty, Al-Tuwaim and Luyben (1991) proposed a shortcut method to design and operate multicomponent batch distillation columns. Their method, however, required a great number of simulations, which must be computationally very expensive, before they could arrive at an optimum design and find an optimum reflux ratio. Further details are in Chapter 7. 

Example 4 Calculation of the BP Method Use the BP method with the SRK equation-of-state for K values and enthalpy departures to compute stage temperatures, interstage vapor and liquid flow rates and compositions, and reboiler and condenser duties for the light-hydrocarbon distillation-column specifications shown in Fig. 13-51 with feed at 260 psia. The specifications are selected to obtain three products a vapor distillate rich in Cg and C3, a vapor side-stream rich in TI-C4, and a bottoms rich in n-Cj and n-Ce. 

Newton and quasi-Newton methods are used for more difficult convergence problems, for example, when there are many recycle streams, or many recycles that include operations that must be converged at each iteration, such as distillation columns. The Newton and quasi-Newton methods are also often used when there are many recycles and control blocks (see Section 4.8.1). The Newton method should not normally be used unless the other methods have failed, as it is more computationally intensive and can be slower to converge for simple problems. 

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