## More on Crude Blend Optimization

I’ve got some feedback from careful readers noting that I did not explain the crude blending optimization problem very well. I thought I would get away with it 🙂  I’ll try to do better, becoming a bit more technical. By the way, I love feedback! If something is not correct, some explanation is a bit vague, or you just want to know more about a topic, then use the handy comment function, or send me an email (if you are shy about using comments).

Now back to the blending problem. We’ll simplify the problem a bit, without losing the key features. Assume we have a distillation unit with a design throughput of 1200 tons for a crude oil which produces 1/3 gasoline (400 tons), 1/6 kerosene (200 tons), 1/4 diesel (300 tons) and 1/4 fuel oil (300 tons) in the distillation. The draw off pipes for the different fractions (cuts) are the limiting factor, i.e. we can not get more than 400 tons of gasoline from the unit, regardless of  crude composition.

If we feed a crude with a different composition, say 40% gasoline, 10% kerosene, 20% diesel and 30% fuel oil, we are limited by the gasoline fraction, and the throughput will only be 1000 tons (40% of 1000 is 400, the limit on the gasoline cut).

Consider a second crude with a (for simplicity) 25% gasoline, 25% kerosene, 25% diesel and 25% fuel oil. The throughput is limited by the kerosene cut to 800 tons (25% of 800 is 200, the capacity limit of the kerosene fraction).

We can compute the maximal throughput for the unit and each crude with a very simple LP model with a single variable, maximizing the value of that variable.

What happens if we mix the two crudes? We now have to solve an LP model with two variables:

$\max X+Y$

s.t.

$0.4 * X +0.25*Y \leq 400$

$0.1 * X +0.25*Y \leq 200$

$0.2 * X +0.25*Y \leq 300$

$0.3 * X +0.25*Y \leq 300$

Solving this model tells us that the optimal value is 1100, better than each of the two ingredients alone! We have to mix 500 tons of crude X and 600 tons of crude Y. This gives us

Gasoline: 200+150 = 350 tons

Kerosene: 50+150 = 200 tons

Diesel: 100+150 = 250 tons

Fuel Oil: 150+150=300 tons

The mix does not achieve the full design throughput though, the properties of the crudes do not allow it. But if we were to take two other crudes, or perhaps add a third one, we might achieve the optimal result. Still, an increase of throughput by 10% can be quite important, given that this drives the operation of everything else in the refinery.

In the scheduling system, the decisions are a bit more complex:

• We don’t know the percentages of the fractions that can be achieved for a given crude, we have to compute that with the simulation tool, assuming the best setpoint for the unit.
• At any given point in time, we are limited in the crudes that can be mixed by the arrival schedule of tankers and pipeline operations.
• We have to use up the crude oils which are delivered in order to free storage tanks for new arrivals. The strategy is to empty tanks as far as possible as quickly as possible.

A much more detailed, but still accessible description of the problem is given in

J.D. Kelly, J.L. Mann. Crude Oil Blend Scheduling Optimization. Hydrocarbon Processing, June/July 2003.

In case you want a bit more background on oil refineries, I was very pleased to discover the following video on YouTube:

The video discusses more than just crude distillation, it goes through all major units in the refinery.

If you rather read a book on the topic, I can recommend:

William Leffler. Petroleum Refining in Nontechnical Language. PennWell Books; 4th Revised edition (1 Nov 2008), ISBN-13: 978-1593701581

I’ve read an earlier edition as my introduction to oil refining,  it gives a good introduction to the topic without requiring a degree in process engineering. There is also a 10 CD video series by the same author, very good, but way too expensive.