## Stage and Column Models

A rigorous method describes a column as a group of equations and is the mathematical engine to solve and satisfy these equations to calculate the operating conditions of the column.

Column design and performance calculations present the column at steady state, that is, what enters the column matches what leaves it (material and energy balances), i.e.:

helpful to consider properties other than the boiling point. For example, if a mixture of intermolecularly bound substances is to be separated by distillation, their partition is likely to be more difficult than the differentials between their boiling points would indicate. On the other hand, a mixture of alkanes may well be more easily separable than comparison of their boiling points would otherwise indicate. In any case practice is necessary, both conducting distillations and selecting systems for distillation. Once experience has been gained it is satisfying to be able to rationalize the results of a fractionation in terms of physico-chemical principles. One positive note: since distillation does not result in loss of product, in the worst case one can recombine all the fractions and redistill using different conditions and, if necessary, a different system.

£ (moles of any component in the feeds)

= £ (moles of the component in the products)

Feed enthalpy + Heat added

= Product enthalpy + Heat removed

Figure 1 shows a complex column with one feed and one side product. The top stage of the column is a partial condenser, with a vapour product, D, and a liquid product, d. The reflux is the liquid, L0, and the reflux ratio is L0/(D + d). The bottoms product, B, leaves stage N + 1, the reboiler. The stages are numbered from the top, with the condenser as stage 0, the top tray in the column, stage 1, the bottom tray, stage N, and the reboiler, as stage N + 1.

An ideal or equilibrium stage is where vapour and liquid entering and leaving the stage are perfectly mixed and there are no inhibitions to material transfer between the phases. The material and energy flows in and out of a simple stage, with no feeds or side products, is stage j depicted in Figure 2, and i represents the component number. Components are numbered from 1 to the last, C.

The enthalpy terms, Hj and hj, are molar enthalpies of the vapour and liquid leaving the stage, respectively. These molar enthalpies are multiplied by the total flow rates, Vj and Lj, leaving the stage to give the total energy leaving the stage in each phase.

The feed stage model (stage f in Figure 2) for an equilibrium stage assumes that the feed liquid mixes

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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