Now take off product between condenser and buffer at rate r gmsec

Vapor initially reaching condenser is N gm/sec Cooled distillate reaching buffer is (N - r) gm/sec Rising vapor condensed in buffer is (N - r)d gm/sec Reflux ratio R = (N + Nd - rd - r) / N = [N - r]+N + [(N - r)d] / N

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 - Nd2 + rd2 - rd)] / N = [N - r - Nd2 + rd2] / N = [N - r ]+N - [(N - r)d2] / N

Vapor now reaching condenser is N - (N - Nd + rd - r)d = N - Nd + Nd2 - rd2 + rd

Cooled distillate reaching buffer is N - Nd + Nd2 - rd2 + rd - r

Amount condensed by this is (N - Nd + Nd2 - rd2 + rd - r)d

Reflux ratio R = [N - Nd + Nd2 - rd2 + rd - r] + [Nd - Nd2 + Nd3 - rd3 + rd2 - rd]

etc etc etc

Summary:

Reflux ratio is

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.

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