Sir, In one of your videos you've said that in a continuous counter current distillation every tray is at different boiling temperature (i.e. my guess:at any tray,incoming vapour which was in equilibrium from which tray it is coming from, so when it arrives at a new tray the vapor sees a new temp. So it again it brings itself to new equilibrium according to temp., and so on the separation occurs),my doubt is what i am guessing is it true?? And if it is true then which graph follows as its governing graph Pxy or Txy in a distillation column?? And what about the movement of coordinates on these graphs:is it vertical or horizontal??
What actually happens in the real world is, as nearly always, complicated, but let's try to break it down a bit into simpler questions. Your question is interesting and it may be of interest to my students so I'll give it some extra attention in a rather long answer: A continuous distillation column is (essentially always) run at constant pressure, meaning that we have the same pressure in the entire column (I'll soon come back to why this is not really true…) and different temperatures at different heights. Theoretically it could have been possible to create a distillation column that runs at a constant temperature and different pressures at different heights, but that is way more complicated than running a distillation column at constant pressure. Hence, a T-xy diagram (drawn for constant pressure) is more suitable to describe what happens in the column than a P-xy diagram (drawn for constant temperature). Note: A continuous distillation column operated at constant pressure does not, however, have exactly the same pressure everywhere. When we say that we operate a continous distillation column at constant pressure we are simplifying. In all flow systems there is friction and where there is friction there is a pressure drop. We see the same effect when we experience that it is easier to drink liquid water using a 10 cm straw than using a 100 cm straw. Even if we neglect the pressure drop in the column, the T-xy diagram will be difficult to use. What happens at a tray is that _a_ mole of vapour with one composition condenses and releases energy that goes into heat losses and in to evporation of _b_ mole of liquid of another composition. Even if we ignore heat losses and assume that evaporation enthalpy is independent of composition (which together implies that a=b and that we thus have equimolar counter diffusion) it is still tricky to display that mass balance in a meaningful way in a T-xy diagram. In a x-y diagram, however, that is simple. The mass balance is just a straight line and that's why x-y-diagrams (drawn for a specified constant pressure) is used in McCabe-Thieles graphical method. There is, however, one case when you can use a T-xy diagram to illustrate what happens in the continuous distillation column and that's when you have * 100% efficient trays (which is practically impossible, so this is only theoretical) and * total reflux (which means the distillation column is not producing anything) For such a (theoretical) system you simply draw a staircase in the T-xy-diagram where each step in the staircase is one ideal tray. This means that you can use a T-xy diagram to determine the minimum number of ideal trays needed to achieve a certain separation (i.e. the minimum number of ideal trays to achieve a separation for which the composition in the distillate, xD, and the composition in the bottoms, xW, are both given). The horisontal lines in a T-xy diagram tell you which condensing vapour composition is in equilibrium with which boiling liquid composition while the vertical lines tell you the composition of the flows (in this case the composition of the liqud running downwards will be identical to the composition of the vapour flowing upwards. Compare the McCabe-Thiele solution where the horisontal lines tell you the composition of the gas fluxes (from ideal trays) going upwards and the vertical lines tell you the composition of the liquid fluxes flowing down. Also compare the x-y-diagram for the total reflux case. If you have total reflux the McCabe-Thiele operating line (i.e. the mass balance) is the x=y line. This means that you get the same composition in the gas fluxes and the liquid fluxes. In trying to think of what actually happens at each tray, I find it helpful to simplify and assume that the heat capacity (Cp) is small in comparison with the evaporation enthalpy and that the evaporation enthalpy is constant. So, when the vapour rises up to the tray it is slightly warmer than the temperature at the tray. At the same time, the liquid pouring down to the tray is slightly cooler than the temperature at the tray. We get a heat balance (at steady-state, i.e. when the temperature on the tray is constant in time) Q from vapour = Q to liquid + Q to surrounding where Q from vapour = (decrease in temperature)*Cp_gas +∆Hvap*(amount of vapour that condenses) Q to liquid = (increase in temperature)*Cp_liquid + ∆Hvap*(amount of liquid that evaporates) and where hopefully the heat losses Q to surrounding ≈ 0 This heat balance is what governs the temperature at each tray. In the real case ∆Hvap is dependent on composition and heat capacities vary with temperature and it all becomes rather messy. On top of that there is no guarantee that the composition at different places on the very same tray are the same e.g. because of the heat losses that might give a higher temperature in the centre and a lower temperature towards the edges. I hope my answer helped you rather than confused you
Sir, In one of your videos you've said that in a continuous counter current distillation every tray is at different boiling temperature (i.e. my guess:at any tray,incoming vapour which was in equilibrium from which tray it is coming from, so when it arrives at a new tray the vapor sees a new temp. So it again it brings itself to new equilibrium according to temp., and so on the separation occurs),my doubt is what i am guessing is it true?? And if it is true then which graph follows as its governing graph Pxy or Txy in a distillation column??
And what about the movement of coordinates on these graphs:is it vertical or horizontal??
What actually happens in the real world is, as nearly always, complicated, but let's try to break it down a bit into simpler questions. Your question is interesting and it may be of interest to my students so I'll give it some extra attention in a rather long answer:
A continuous distillation column is (essentially always) run at constant pressure, meaning that we have the same pressure in the entire column (I'll soon come back to why this is not really true…) and different temperatures at different heights. Theoretically it could have been possible to create a distillation column that runs at a constant temperature and different pressures at different heights, but that is way more complicated than running a distillation column at constant pressure. Hence, a T-xy diagram (drawn for constant pressure) is more suitable to describe what happens in the column than a P-xy diagram (drawn for constant temperature).
Note: A continuous distillation column operated at constant pressure does not, however, have exactly the same pressure everywhere. When we say that we operate a continous distillation column at constant pressure we are simplifying. In all flow systems there is friction and where there is friction there is a pressure drop. We see the same effect when we experience that it is easier to drink liquid water using a 10 cm straw than using a 100 cm straw.
Even if we neglect the pressure drop in the column, the T-xy diagram will be difficult to use. What happens at a tray is that _a_ mole of vapour with one composition condenses and releases energy that goes into heat losses and in to evporation of _b_ mole of liquid of another composition. Even if we ignore heat losses and assume that evaporation enthalpy is independent of composition (which together implies that a=b and that we thus have equimolar counter diffusion) it is still tricky to display that mass balance in a meaningful way in a T-xy diagram. In a x-y diagram, however, that is simple. The mass balance is just a straight line and that's why x-y-diagrams (drawn for a specified constant pressure) is used in McCabe-Thieles graphical method.
There is, however, one case when you can use a T-xy diagram to illustrate what happens in the continuous distillation column and that's when you have
* 100% efficient trays (which is practically impossible, so this is only theoretical) and
* total reflux (which means the distillation column is not producing anything)
For such a (theoretical) system you simply draw a staircase in the T-xy-diagram where each step in the staircase is one ideal tray. This means that you can use a T-xy diagram to determine the minimum number of ideal trays needed to achieve a certain separation (i.e. the minimum number of ideal trays to achieve a separation for which the composition in the distillate, xD, and the composition in the bottoms, xW, are both given). The horisontal lines in a T-xy diagram tell you which condensing vapour composition is in equilibrium with which boiling liquid composition while the vertical lines tell you the composition of the flows (in this case the composition of the liqud running downwards will be identical to the composition of the vapour flowing upwards. Compare the McCabe-Thiele solution where the horisontal lines tell you the composition of the gas fluxes (from ideal trays) going upwards and the vertical lines tell you the composition of the liquid fluxes flowing down.
Also compare the x-y-diagram for the total reflux case. If you have total reflux the McCabe-Thiele operating line (i.e. the mass balance) is the x=y line. This means that you get the same composition in the gas fluxes and the liquid fluxes.
In trying to think of what actually happens at each tray, I find it helpful to simplify and assume that the heat capacity (Cp) is small in comparison with the evaporation enthalpy and that the evaporation enthalpy is constant. So, when the vapour rises up to the tray it is slightly warmer than the temperature at the tray. At the same time, the liquid pouring down to the tray is slightly cooler than the temperature at the tray. We get a heat balance (at steady-state, i.e. when the temperature on the tray is constant in time)
Q from vapour = Q to liquid + Q to surrounding
where
Q from vapour = (decrease in temperature)*Cp_gas +∆Hvap*(amount of vapour that condenses)
Q to liquid = (increase in temperature)*Cp_liquid + ∆Hvap*(amount of liquid that evaporates)
and where hopefully the heat losses
Q to surrounding ≈ 0
This heat balance is what governs the temperature at each tray. In the real case ∆Hvap is dependent on composition and heat capacities vary with temperature and it all becomes rather messy. On top of that there is no guarantee that the composition at different places on the very same tray are the same e.g. because of the heat losses that might give a higher temperature in the centre and a lower temperature towards the edges.
I hope my answer helped you rather than confused you