The Compleat Distiller

THE COMPLEAT DISTILLER 111
2)
Vapor now reaching condenser is N - (Nd - rd) = N - Nd + rd
Cooled distillate reaching buffer is N - Nd + rd - r
Rising vapor condensed in buffer is (N - Nd + rd - r)d
Reflux ratio R = [(N - Nd + rd - r) + (Nd - Nd 2 + rd 2 - rd)] / N
= [N - r - Nd 2 + rd 2 ] / N
= [N - r ]÷N - [(N - r)d 2 ] / N
3)
Vapor now reaching condenser is N - (N - Nd + rd - r)d = N - Nd + Nd 2 - rd 2 + rd
Cooled distillate reaching buffer is N - Nd + Nd 2 - rd 2 + rd - r
Amount condensed by this is (N - Nd + Nd 2 - rd 2 + rd - r)d
Reflux ratio R = [N - Nd + Nd 2 - rd 2 + rd - r] + [Nd - Nd 2 + Nd 3 - rd 3 + rd 2 - rd]
= [N - r +Nd 3 - rd 3 ] / N
= [N - r]÷N + [(N - r)d 3 ] / N
etc etc etc
Summary:
Reflux ratio is
1. [N - r]÷N + [(N - r)d] / N
2. [N - r ]÷N - [(N - r)d 2 ] / N
3. [N - r ]÷N + [(N - r)d 3 ] / N
........................
n. [N - r ]÷N - (-1) n [(N - r)d n ] / N
Once again, since d < 1, then this is a converging series with limit [N - r] / N
The reflux oscillates around a mean of [N - r], and this is a rapidly damped oscillation and stable as
before.
This shows that the system exhibits damped oscillation should a sudden change in cooling be imposed,
but rapidly settles down to the "default" reflux ratio that would exist should no cooling occur. It also
shows that this occurs no matter how severe the initial cooling may be, large oscillations taking only a
little more time to damp out.
They were wrong!
A compound column is inherently stable in respect of the temperature of the reflux returned by the
head condenser, so no special precautions need be taken to control the flow of coolant in that
condenser, other than keeping it steady at a rate that ensures complete condensation of all vapor
reaching it. Many people have spent needless hours worrying and struggling to design systems that
avoid cooling the condensate, and all the time they were pursuing the wrong goal. Some time spent up
front studying theory can save many hours of fruitless toil.
(If you’re using Cooling or Vapor Management (Chapter 4) to control reflux, then of course you don’t
want complete condensation, but the key point is that the stability of the system ensures that whatever
reflux ratio you do impose will remain constant.