Start with N gmsec vapor at 80C reaching condenser and operate under full reflux taking no product

Now, increase condenser efficiency and let it cool the distillate by T°C.

This cool distillate is warmed up to 80°C when it hits the buffer zone at the top of the packing, causing

0.601.T / 220.8 gm/sec of the rising vapor to be condensed.

We can simplify that by noting that for a given drop in temperature T, the relationship 0.601T / 220.8 is a constant. We'll call that constant 'd'.

So Nd gm/sec is condensed in the buffer. This joins the N gm/sec coming down as reflux, making the total reflux

2) The vapor now reaching condenser is (N - Nd) gm/sec and this is condensed and cooled T°C. The rising vapor now condensed in buffer is now (N - Nd)d, and the total reflux is now (N - Nd) + (N -Nd)d = N - Nd + Nd - Nd2 = N - Nd2, and the reflux ratio R = (N - Nd2) / N.

3) Now the vapor reaching the condenser is (N - (N - Nd)d = N - Nd + Nd2 gm/sec and this is condensed and cooled To C. The rising vapor now condensed in buffer zone is (N - Nd + Nd2)d, the reflux is now (N - Nd + Nd2) + (Nd - Nd2 + Nd3) = N + Nd3, and the reflux ratio R = (N + Nd3) / N

4) This time the vapor reaching the condenser is N - (Nd - Nd2 + Nd3) gm/sec, and this is condensed and cooled To C. The amount of rising vapor now condensed in the buffer zone is (N - Nd + Nd2 -Nd3)d, and the reflux is now (N - Nd + Nd2 - Nd3) + (Nd - Nd2 + Nd3 - Nd4) = N -Nd4, making the reflux ratio R = (N - Nd4) / N.

etc etc etc 