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Non-linear singular integral representation for petroleum reservoir engineering

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Abstract

A new mathematical model is proposed in order to determine the properties of the reservoir materials, when oil reserves are moving through porous media, which is a very important problem of petroleum reservoir engineering. Thus, the above problem is reduced to the solution of a non-linear singular integral equation, which is numerically evaluated by using the singular integral operators method (SIOM). Also, several properties of the porous medium equation, which is a Helmholtz differential equation, are analyzed and investigated. An application is finally given for a well testing to be checked when an heterogeneous oil reservoir is moving in a porous medium. By using the SIOM, the pressure response from the well test conducted in the above heterogeneous oil reservoir is calculated.

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  1. Interpaper Research Organization, 8, Dimaki Str, GR-106 72, Athens, Greece

    E. G. Ladopoulos

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  1. E. G. Ladopoulos
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Ladopoulos, E.G. Non-linear singular integral representation for petroleum reservoir engineering. Acta Mech 220, 247–255 (2011). https://doi.org/10.1007/s00707-011-0476-0

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  • DOI: https://doi.org/10.1007/s00707-011-0476-0

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