In this talk an overview is presented of the Algebraic Oil project, running in Shell Research in Rijswijk, in cooperation with a number of universities.

The project is rather unusual in that it concerns applications of Commutative Algebra to industrial problems, in this case problems in production of oil – and gas, as well as problems in oil – and gas exploration. Both from the applications – and from the algebraic point of view this is a bizarre combination.

To place the project into the proper perspective the ‘traditional’ research approach is described very briefly. This provides at the same time the motivation for leaving the traditional vector space environment and move to a polynomial-ring-module setting.

The talk then concentrates on a particular problem in oil production, addressing this problem in an algebraic setting. This sort of considerations has created a – still controversial – new activity in algebra, called Approximate Commutative Algebra. One of the most important objects in this new activity is the Approximate Vanishing Ideal, which is calculated with an adapted version of the Buchberger-Möller Algorithm. In particular it is demonstrated that this leads to an algebraic modelling of the oil production, revealing interactions and flow mechanisms, which cannot be ‘observed’ with the traditional approaches.

The talk ends with an overview of current and future activities.