The econometric secret of blending

It is February 2016, it is 10 degrees below zero and you are on your way to Utrecht, to visit your family. You are lucky because you do not have to take into account the winter regulations of NS. That is because you have used your well-earned pay check to purchase a second hand diesel car and your car always gets you from A to B safely. You just have to scrub the windows free of frost and then… yes, luckily the motor starts. Once you finally arrive in Utrecht you stop to think to yourself: ‘environmental zone’ you hear yourself say. Luckily, there is nothing to worry about because your car is from 2002.

As a car owner you are completely sure that your steel steed will perform under any circumstances. Warmth and cold need to be faced up to, and of course you are also thinking a bit about the environment. Next to the condition of the car, the quality of the fuel is an important factor here. Luckily, you don’t have to worry about the quality of the fuel, the government and the oil companies do that for you. Octane number, sulphur emission, density, flash point, cloud point, oxygen, aromatics content and benzene content are examples of properties that specify fuel. For example, Euro95 has an octane number of at least 95, a density of about 0.75 kg/l and the sulphur content may not be higher than 10 ppm.

Now you are probably asking yourself, why am I reading this piece in the Estimator? You have maybe also already come up with the answer to this question: there is a very interesting case on optimisation in the production of diesel and petrol!

 "What is economically the most profitable blend, so that the demand is fulfilled and also al of the product specifications are met?"

In a refinery, raw oil is made into semi-finished products that subsequently are reworked into end products, like Euro95. The production of these end products is sometimes called ‘blending’. While you might be looking for the optimal blending recipe for cocktails, a refinery looks for the optimal blending recipe for the end products. In a market with many competitors, this has to be done as cheaply as possible. The question is: what is economically the most profitable blend, so that the demand is fulfilled and also al of the product specifications are met?

At first, this seems like extending a simple LP with some constraints for recipes (for e.g. use at maximum 10% ethanol, or in cocktails: use at least 10% ethanol). However, as you would expect, there are several factors that make the situation more complicated. The property of the octane does not blend linearly. To be able to predict the octane number of a blend regardless, blending rules have been developed. A blending rule describes how a property behaves when it is mixed. These blending rules are derived by applying statistical techniques. The use of blending rules in optimisation allows the refinery to better predict what the properties of a blend will be. The result of this, is that the blending can be done closer to the specifications. Of course, it would be a pity to make a blend with octane number 96, when 95 is the minimum. On the other hand, when your blend has an octane number of 94.8, then you have got a problem. Either you have to blend your blend again or you have to downgrade it to a ‘worse’ product and thus also sell it for a lower price. An off spec product cannot enter the market as Euro95.

The oil industry is helped a lot by blend models such as described above. The questions that are addressed:

  • Is there added value to buying a semi-finished product on the market?
  • How do I correct my off spec product?
  • How can I blend away a component of low quality?
  • What is the impact of strict regulations on the blend that I can make?
  • Can I also blend away 20% alcohol? What impact does that have on my product and on the semi-finished products that I make in my refinery?

From the questions above you can derive that blend models can be used operationally as well as for strategical studies. As result of this:

  • A higher margin is achieved
  • No ‘too good’ products are made
  • More blends are good in one attempt
  • Cases can be analysed easily
  • More value is obtained out of semi-finished products

The typical OR (Ondernemingsraad) companies have been working on developing and supporting the mathematical models described in this article for years. Partially due to this, the fuel prices are as low as possible and you know that the fuel is not the reason why your car does not want to start on a winter’s day.

This article has been written by Bart Mateman and is submitted by Bart Mooij, graduated econometrician and FAECTOR Alumnus.

About this article

Written by:
  • Bart Mooij
| Published on: Nov 01, 2016