Kerosene

Refinery Optimization

An oil refinery purchases two crude oils (crude 1 and crude 2). These crude oils are put through four processes: distillation, reforming, cracking, and blending, to produce petrols and fuels which are sold.

Distillation

Distillation separates each crude oil into fractions known as light naphtha, medium naphtha, heavy naphtha, light oil, heavy oil and residuum according to their boiling points. Light, medium and heavy naphthas have octane numbers of 90, 80, and 70, respectively. The fractions into which one barrel of each type of crude splits are given in the table above.

Reforming

The naphthas can be used immediately for blending into different grades of petrol or can go through a process known as reforming. Reforming produces a product known as reformed gasoline with an octane number of 115. The yields of reformed gasoline from each barrel of the different naphthas are given below:

1 barrel of light naphtha yields 0.6 barrels of reformed gasoline;

1 barrel of medium naphtha yields 0.52 barrels of reformed gasoline;

1 barrel of heavy naphtha yields 0.45 barrels of reformed gasoline.

Cracking

The oils (light and heavy) can either be used directly for blending into jet fuel or fuel oil or be put through a process known as catalytic cracking. The catalytic cracking produces cracked oil and cracked gasoline. Cracked gasoline has an octane number of 105.

1 barrel of light oil yields 0.68 barrels of cracked oil and 0.28 barrels of cracked gasoline;

1 barrel of heavy oil yields 0.75 barrels of cracked oil and 0.2 barrels of cracked gasoline.

Cracked oil is used for blending fuel oil and jet fuel; cracked gasoline is used for blending petrol

Residuum can be used for either producing lube-oil or blending into jet fuel and fuel oil;

1 barrel of residuum yields 0.5 barrels of lube-oil.

Blending

Petrols (Motor Fuel)

There are two sorts of petrol, regular and premium, obtained by blending the naphtha, reformed gasoline and cracked gasoline. The only stipulations concerning them are that regular must have an octane number of at least 84 and that premium must have an octane number of at least 94. It is assumed that octane numbers blend linearly by volume.

Jet Fuel

The stipulation concerning jet fuel is that its vapor pressure must not exceed 1 kilogram per square centimeter. The vapor pressures for light, heavy and cracked oils and residuum are 1.0, 0.6, 1.5, and 0.05 kilograms per square centimeter respectively. It may again be assumed that vapor pressures blend linearly by volume.

Fuel Oil

To produce fuel oil, light oil, cracked oil, and heavy oil and residuum must be blended in the ratio 10:4:3:1.

There are availability and capacity limitations on the quantities and processes used:

The daily availability of crude 1 is 20,000 barrels.

The daily availability of crude 2 is 30,000 barrels.

At most 45,000 barrels of crude can be distilled per day.

At most 10,000 barrels of naphtha can be reformed per day.

At most 8000 barrels of oil can be cracked per day.

The daily production of lube oil must be between 500 and 1000 barrels.

Premium moto fuel product must be at least 40% of regular moto fuel product.

The profit contributions from the sale of the final products are (in pence per barrel)

Premium petrol 700

Regular petrol 600

Jet Fuel 400

Fuel oil 350

Lube-oil 150