Distillation column: How to fix temperature and pressure

A distillation column can be illustrated as follows:

Pressure Profile

In a distillation column there exists a pressure gradient. The pressure at the bottom is higher and lowers towards the top of the column. This pressure gradient occurs due to the trickling liquid that restricts the upward flow of vapour thus creating a pressure loss on the flow. 

In steady-state distillation processes, the column pressure is kept constant and the temperature is varied to control the composition of the product streams.
In normal situations, the vapor pressure of the liquid on the top tray fixes the pressure at that location before the vapor enters the overhead condenser. This parameter fixes the column pressure. The pressure in the other sites in the column depends on the ability of the vapors and liquids to distribute themselves up and down the column with minimum pressure drops. 

It is the liquid composition on the top tray that defines the expected column operating pressure. 
The external reflux ratio (L/D) has a bearing on fixing that composition – as the various L/V’s (internal reflux ratios) that are generated down the column have on the various trays’ compositions. 

The bottom pressure will be determined by the pressure drop along the column. This depends on the relevant selected technology and the load of vapor and liquid inside the column. The corresponding bubble point of bottom pressure will specify the bottom temperature. 

The purpose of the reflux is to provide down-flowing liquid throughout the rectification section to contact with the up-flowing vapor in order to achieve stage-by-stage equilibrium heat and mass transfer thus purifying the top product. When sub-cooled reflux is introduced to the top tray, it must be heated up to its bubble point before the lighter components will vaporize.

Temperature Profile

The temperature distribution in a distillation column is warmer at the bottom and cooler at the top. For a binary feed mixture, the temperature at the bottom is just lower than the boiling point of the heavier component while the temperature at the top is just above the boiling point of the lighter component. 

At the bottom of the column, it is desired that the heavy component remains as a liquid and the lighter component remains as a gas, thus the temperature at the bottom should match this requirement. The temperature of the bottom is controlled by a reboiler. The heat added at the bottom is easy to control through steam or hot oil flow rates. 

It is the opposite at the top of the column, i.e., the light component is required to remain a gas while the heavier component is condensed and trickles down the column. The temperature at the top is set above the boiling point of the lighter component. The top product is usually needed in liquid form for easy storage hence the gaseous products need to be condensed. This liquid stream is then split into two where one stream is returned to the column and the other is sent to storage. 

The temperature at the top is controlled by adjusting the reflux rate. The Reflux Rate is the flow rate of the liquid sent back to the top of the column. A higher reflux rate results in more cooler liquid falling down the column against the rising warmer gas, and the top temperature is lower.

Overall heat is added at the bottom of the column awhile heat is extracted at the top of the column. Inside the column the temperature balance is created between the hot gas rising up the column and the cooler liquid falling down the column.

Inside the column, the temperature is set by the relative volatility or the partial pressure of the feed according to Raoult’s law. The volatility of components in the column is different. If P is the total pressure in the column, this is equal to the sum of P1 + P2 + P3 + ---- partial pressures at a different height. 

While total pressure is constant in the column, the partial pressures of the feed components are different along with the height. 

Partial pressure = Mole fraction x Vapor pressure of pure component at a height 

Since volatility of hydrocarbon increases as you go up, the vapor pressure increases, and consequently, saturation temperature gets lower. Therefore, the column gets cooler as we go up. In a steady-state, the partial pressures do not change much.

Remember: 

Raoult's law states that the vapor pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent present

What is L/D?

It is the external reflux ratio: It is the ratio of the liquid returned to the column divided by the liquid removed as product, i.e., R = L/D.  

As the external reflux cools the top of the tower, vapors consisting of heavier fraction condense and flow down the tower and it's referred to as internal reflux. The liquid/vapor flow ratio inside the upper section of the column.is referred to as the internal reflux ratio i.e., L/V.