The Algebraic Oil Research Project was a collaboration between the Department of Exploratory Research at Shell International Exploration and Production B.V. (Rijswijk / The Netherlands) and the Chair of Symbolic Computation at Universität Passau (Germany).

The research project was initiated in 2004 by personal communications between Dr. Hennie Poulisse (SIEP) and Prof. Dr. Martin Kreuzer (Passau). In a first phase which ended 4/2009, the Stichting Shell Research Foundation supported a research agreement between SIEP, Universität Passau and Universita di Genova. Since 8/2008, the project is based on a direct research agreement between SIEP and Universität Passau.

The research project addresses several topics at the heart of oil recovery and oil exploration: production optimization, production allocation, improvement of the ultimate recovery, development of production strategies, and discovery of new oil reservoirs. The basic idea was to introduce methods of of symbolic computation (computer algebra) to solve problems in these areas. More precisely, the new techniques were part of an emerging area called Approximate Computational Commutative Algebra (or hybrid computation or symbolic-numeric computation). The main activities center on the following individual topics:

• Production Optimization: Via suitable symbolic-numeric algorithms, in particular the AVI-algorithm, new polynomial models were constructed for oil production systems which permit structural insights into the interactions between different parts of those systems. These new models yielded a better understanding of internal reservoir structure and make long-term forecasts possible.
• Production Allocation: Based purely on the bottom-up approach followed in production modeling, the research project studied the question of how to attribute to the individual wells or production zones their contribution to the total production, even in the absence of direct measurements of those contributions. The mathematical methods were based on explicit approximate ideal membership, subideal border basis computations, and techniques for rational approximation of border bases.
• Improvement of the Ultimate Recovery: In view of the possibility of understanding reservoir mechanics in unprecedented detail and the availability of long-term production models, the researchers attempted to derive production strategies which take changes in the structure of the reservoir into account and delay the decrease of reservoir pressures. This part of the project was intimately connected to the development of new methods for exploration, since certain changes in the structure of the reservoir can also be detected by seismic methods.
• Dynamic Modelling of Production Systems: By using methods from differential polynomial algebra, time dependencies and dynamic changes in the production system were modeled. To this end, suitable algorithms in approximate differential polynomial algebra were developed. The new differential models could be applied to study phase transitions between distinct steady states of the production system.
• New Methods of Exploration: Traditional methods for seismic exploration impose strong assumptions about the geometry of a reservoir. New symbolic-numeric methods were used to avoid early linearization and permited novel interpretations of seismic exploration data.