First we have to understand the question. The question is What is the impact on energy consumption during the separation of a mixture using distillation at different pressures? Let us consider a binary case of two components with fixed feed composition. So the question is what should be the pressure of distillation column for a desired recovery & purity of top & bottom products, so that energy consumption is low.
When you talk about energy consumption let us consider the gross energy required site wide so that overall impact can be assessed, I mean that every component of energy consumer should be converted finally to the fossil fuels.
Now starting from top, for maintaining the purity, you need to have higher amount of reflux or more no of stages in case of P2. Since discussion is not concerned about the capital investment it is better to consider more no of stages by keeping the same reflux amount. When reflux amount is same your vapor & liquid loads will remain same in the rectifying section of the column.
In such case, by internal heat balance, you will find that bottom vapors generation will also be more or less same and therefore, stripping section loads will also remain same.
After establishing the loads, let us focus on different energy consumption points.
- Downstream system may generally be at higher pressure & accordingly you need more energy for pumping in case of P1.
- When you decrease the pressure to P1, the latent heat of bottom product will go up & then you need more energy for the same amount of vaporization in the reboiler.
- At lower pressure vapor densities goes down & you need bigger dia column at P1. Though it is not a concern in this case, but is applicable resulting in more cost.
- At lower pressure saturation temperature goes low & you can use low level heat e.g. LP steam in place of HP steam. So if you compare with same HP steam at P2, you can generate power (Theoretically) & then use LP steam for reboiler.
- But this is often misunderstood by energy saving, which is not true. In this case actual Kcal energy requirement goes up due to higher latent heat.
- In case of low pressure you may need chilled water etc for condenser as condensing utility which is a costlier proportion than saving from HP to LP steam because of cascading effect of efficiencies in the process.
- In such case, one should not limit himself to chilled water requirement but he should also consider its - generation cost including LP for absorption chilling / Power for compression chilling / pumping cost / system losses etc. In totality chilled water usage cost is much higher than LP steam generally.
- If system is under vacuum, than the energy required for the operation of vacuum system is to be added in total energy requirement.
- Total energy should be considered based on front end fossil fuel consumption e.g. for power we should consider fossil fuels consumed in the power plant at generation site than eqv transmission losses etc. Then only you will be able to truely compare the energy consumption
My view however is that if you have Alpha of more than 2.0 then you practically should avoid distillation as the preferred choice for separation. Other methods may be more cost & energy effective.
In above post, please make sure that you do not get confused by energy requirement, energy consumption & cost as all of them are different. You may consume more LP but still your cost may be lower if your steam generation cost is cheaper. At some plant sites power is cheaper than steam on the other hand steam is cheper than power in case of some specific sites. So overall site wide analysis is necessary before selecting the distillation column pressure.