Question

Component	Feed(molar flowrates (kmol/hr)	Ki
CH4	20	19.92
C2H6	25	13.33
C3H8	60	6
C4H10	70	2.46
C5H12	35	1.5

The feed mixture is fed into a continuous distillation column as liquid at its bubble point . the column operates at ambient conditions to achieve a 99.2% recovery of component ethane in the distillate product and 95.7% recovery of propane in the bottoms product.

1. determine the light key (LK) and heavy key (HK) components for the system

2. complete the material balance over the distillation column and calculate the mole fraction of each component in the feed, distillate and bottoms stream

Answer 1

The feed consists of methane, ethane,.butane, propane and pentane.

Arranging the constituent in the order of increasing boiling point as below,

Methane CH4 = -161.5 °C,

Ethane C2H6 = -89°C,

Propane C3H8 = -42°C,

Butane C4H10 = -1°C,

pentane = 36° C

Heavy key

It is the heaviest compound in the distillate product and anything heavier than it will appear in bottoms.

So, with 99% present in distillate, Ethane is the heavy key

Light key

it is the lightest compound present in the bottoms and anything lighter than it will go into distillate. And it lies immediately below the heavy compound in the boiling point. Butane is the light key.

MATERIAL BALANCE

Component	Feed(molar flowrates (kmol/hr)	Percent
CH4	20	9.5
C2H6	25	11.9
C3H8	60	28.6
C4H10	70	33.3
C5H12	35	16.7

Total molar feed rate is = 20+25+60+70+35 = 210 kMol/Hour

​​​​​​Mole percentage of a component = (moles of component / total moles of feed )*100

for methane = (20/210)* 100 = 9.5%

similarly other percent are given in above table.

From statement we know 99.2% of Ethane is in Distillate, so remaining 0.8% of Ethane must be in bottoms. And 95.7% of Propane is in bottoms.

Total balance of Column

Feed in = Distillate + Bottoms

Balance on Ethane

Ethane in feed = Ethane in distillate + Ethane in bottoms

Ethane in distillate = (99.2/100)* 25 = 24.8 kMol/hr

Ethane in bottoms = 25 -24.8 = 00.2 kMol/hr

As methane is lighter than ethane, all of it will be present in distillate

to compute the distillate and bottoms rate and composition, at least the composition of one component in each must be specified