Xd Xwf 1 X

XD XwiJ V 1 Xwf

Eqns [34] and [37] were developed by Bauerle and Sandall, assuming the ideal pinched columns operating at minimum reflux. None the less, their application to real columns yields good approximated results if the equipment operates in a near-pinched zone at the bottom. This is often the case for columns with five or more theoretical stages.

[33] Design

Substitution of eqn [33] into the general mass balance expression, eqn [29] and subsequent integration produces an analytical form for the mass balance given by:

If the column is operated at constant distillate composition, direct integration of eqn [29] produces the expression for the mass balance:

The integration of eqn [20], however, requires the development of an expression for the time-dependent operating line, which is accomplished by substitution

The operation of a batch distillation column, even pilot-scale equipment, is often as technically involved as operation of an industrial-scale column, and the same amount of care in start-up and safety procedures should be taken. Whether designing a new column or revamping an existing one, the necessary safety and physical properties data such as flash and ignition points, flammability and toxicity must be compiled for each component in the mixture. Predictive equations or experimental values for the vapour pressures of all components and binary equilibrium data should be compiled together with parameters of equations of state or activity coefficient models whenever available. Other physical properties to be included are liquid and vapour heat capacities, heats of vaporization and viscosities.

Once the physical property data bank has been put together, preliminary design calculations can be performed. For a multicomponent distillation column a light-key and a heavy-key component should be chosen in order to reduce the preliminary design to a pseudo-binary system. At this point it is possible to use graphical methods like McCabe-Thiele or even something more involved like Ponchon-Savarit to carry our a case study to find out the system response in terms of required number of theoretical stages for a specified purity at different reflux ratios. To accomplish this, the optimization techniques described later can be useful, but since they are also hard to implement. The alternative approach of using a simplified calculation method such as presented in the section on column operation might be more desirable. This initial set (reflux ratio — number of theoretical stages) will permit the preliminary design.

Depending on the intended purpose of the laboratory-scale column, these initial calculations are likely to be sufficient for specifying the details of column design. Reboiler and condenser heat loads permit sizing of steam and condensation coils. Environmental concerns have introduced complexities in design which were not previously an issue for pilot-scale distillation. Current regulations at our site require condensate return to steam generation facilities to recover waste heat. Even a moderate condenser heat load can require prohibitively large quantities of cold tap water and the condenser heat load for even a small distillation column will typically be substantially larger than can be handled by laboratory-scale recirculated chillers. Much of the final decisions on absolute sizing will be dependent upon available facilities and the anticipated intensity of column use. It is important to get to a reasonably accurate preliminary design early in the design process, so that such practical constraints can be considered.

In many situations, a laboratory-scale distillation column will be used for multiple separations, or as a testing ground for additional full-scale design data. Under these circumstances, design for flexibility is a primary concern. Instead of focusing on detailed physical property information, the data collection should focus on obtaining ranges of anticipated physical properties as well as ranges in batch size. The actual design should then reflect the appropriate bounds of properties and separations that may be encountered. It should be kept in mind that there is a practical minimum volume that can be handled, due to tray hold-up, while larger volumes can be handled with multiple batches. Undersizing either reboiler or condenser heat transfer capacity may render the column useless for a specific separation.

In most batch distillation operations, the lighter component is the desired product and the actual column is the rectifying section of a continuous tower. The preceding discussion in this section as well as in the next section implicitly assume this situation. Nevertheless, there might arise design situations where the economical interest lies in the heavier compounds. In more complex operations the designer might even be faced with the task of devising a separ ation sequence involving two or more columns. For the case where it is desired to recover the heavy component, the calculations for the number of stages should be performed as a stripping column instead.

Since the principles and computational basis of distillation are quite advanced, additional assumptions allow the derivation of simple expressions for the distillate composition and flow rate and the amount of material left in the feed drum. These assumptions render the evaluation of columns with recycle amenable to straightforward solutions.

The remainder of this section includes a description of a versatile laboratory distillation column and its instrumentation and safety systems.

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