## W

dxw xD!xw

Since the cumulative vapour produced is V = 6V, the time 6 necessary for a run is calculated from the above equation as:

In Wf"

Wi xwi xD!xw

The total amount of distillate produced can be found by integration of eqn [18]:

The above can be differentiated to give the following result:

Eqns [20]-[22] provide an efficient way of calculating the total amounts of vapour and distillate produced and the time necessary for the separation without having to solve the system of equations comprised by eqns [1]-[13]. This calculation provides an economic benchmark since it defines the optimum time for a run, based on the recovered product value and the operating costs. As the run time increases, the cumulative revenues given by the total amount of recovered product multiplied by its value will first increase but then approach an asymptotic value. The decreased economic benefit results either because the amount of distillate decreases (as in the case of constant composition distillate) or because the product stream becomes progressively less pure (as in the case of constant reflux ratio operation). The operating costs on the other hand increase steadily with time and the profit function, which combines these two costs, undergoes a maximum, after which the profit will decrease, as illustrated by Figure 2.

An analytical solution can be found for a limiting case which assumes an infinite number of stages (corresponding to minimum reflux) and constant relative volatility. At minimum reflux the operating line ends at a pinch zone and xw is located in the equilibrium

 Recovered product value / Profit Operating cost

Distillation time

Figure 2 Optimum profit profile: operating costs versus length of time. Recovered product increases rapidly at first but then levels off.

Distillation time

Figure 2 Optimum profit profile: operating costs versus length of time. Recovered product increases rapidly at first but then levels off.

line. The slope of the operating line is then given by: of eqn [31] into [30] to yield:

## 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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