• Algebraic Oil Research Project

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    Project Description

    This project ended April 30th 2009.
    Please go to Algebraic-Oil Research Project.

    The Algebraic Oil / CoCoA Research Agreement is a cooperation between Shell International Exploration & Production (Rijswijk/NLD), the Department of Mathematics of Genova University (Italy), and the Faculty of Informatics and Mathematics of Passau University (Germany). The figure below gives a schematic overview of this cooperation.


    Although this project is a purely scientific development, certain relations between algebra and practical results have been formulated as {Algebra, E&P Application} pair. These pairs form a substantial part of the study.

    Algebraic Subject

    E&P Application
    Syzygies Interrelationships
    Sub-survace ⇔ Surface Relationship: Ultimate Recovery
    Differential Gröbner Basis Dynamical Systems
    Including long-term changes ⇒ Forecasting, Reservoir management. Special activity: Good Slugs, using the energy generated by slugs for production — and exploration (see last pair) applications
    Elimination Theory www2.m
    Acronym for `Where, when, what to measure'. Minimal requirements technical infra structure.
    Invariant Theory Generic elements
    Global exchange of information
    Homotopy Test versus Production
    The change from the test — to the production situation for a well is viewed as a continuous deformation of the well test model
    Automated Theorem Proving Diagnostics and Decisions
    Including relationships between processes that run on different time scales, e.g. early recognition of building-up water break through. Subject may be considered as next generation Artificial Intelligence.
    Computational Homology Surface characterization
    Surface characterization of sub-surface through computation of homology groups. Of particular importance for last pair.
    D–Modules Non–seismic Exploration
    This application is possible since this algebraic subject allows the consideration of spatial variation. This pair is coupled with the first — and second pair.

    Since it would go beyond the scope of this overview to describe these pairs here in detail, a high-level description is presented of the first pair of this sequence.
    The {Syzygy, Interrelationships} pair is a direct attack on one of the most fundamental problems in oil production operations: increasing the ultimate recovery of a reservoir. The idea is to give a decomposition of the total production of a group of wells or a collection of zones (measured at the surface, i.e. at the output of the separator) as a polynomial combination of separate productions from the wells or zones.
    The ambiguities in this decomposition are called Syzygies. These syzygies are functions of the indeterminates, i.e. of the measured quantities involved. The appearance of certain sub-surface quantities in the syzygies reveals sub-surface interrelationships. The structure of a syzygy may moreover reveal the mechanism causing this interrelation. Thus there exists a natural synergy between production and, what may be called, production-exploration.

    ApCoCoA Development

    Besides the {Algebra, E&P Application} pairs, a further emphasis of the project is the continued development of the computer algebra system CoCoA, specifically the new ApCoCoA C++ library. This library allows researchers to implement new low-level functions and include ApCoCoA functions in their special purpose software. Moreover, ApCoCoA supports both symbolic and numerical computations. The following figure gives a first impression of the contours of the change that is associated with this coupling.



    Algebra meets E&P Applications

    As this figure suggests, essentially all applications that are contructed via the digital computer have to pass through the gate titled Numerical Linear Algebra. The interfaces between numerical and symbolic calculations are still in their infancy. For E&P applications, the numerical/symbolic interface is very important, because it makes it possible to use the measurements from an E&P application for symbolic algebraic manipulations.
    The symbolic/numerical interface allows passing the algebraic results back to the E&P application, notably for control actions. It is also crucial in the interpretation of the algebraic results in terms of the language of the E&P application: first for all monitoring purposes, and secondly to generate from the set of all algebraic solutions the (and this is a conjecture) only one that is physically realizable.
    The development of these interfaces is an enormous endeavour, and hence an important element of the project.
    The importance of these developments has been acknowledged by the Shell Foundation which sponsors the first four-year period 2005-2009 of the project by an amount of 400.000 Euros. An extension of the project to further applications in production-exploration and oil exploration is in preparation.
    This page was last modified 21, November 2007.