In layers of limited thickness and high resistance, the amplitude of the spontaneous potential (SP) logs differs significantly from the amplitude corresponding to the layer of unlimited thickness. For a more accurate determination of reservoir properties by the SP method it is necessary to move from the apparent values of the curve to the static potential of the reservoir, that is, to solve the inverse problem.

The article presents an analytical solution for a direct problem of the SP method in case of rocks in a well crossing an electrically inhomogeneous layer of limited thickness with a zone of drilling mud penetration. The analytical solution of a similar problem proposed by Schlumberger-Doll Research (M.R. Taherian, at al.) for an impenetrable formation in the absence of penetration zone is discussed. It is shown Schlumberger’s solution is a subcase of the analytical solution regarded in present article. On the basis of the analytical solution of the direct problem the inverse problem of the SP method was solved taking into account the potentials of rock matrix. Solving the inverse problem in conjunction with the electric logging data is shown on the example of middle Cretaceous reservoirs (Achimov deposits) in Western Siberia. For this purpose we used algorithms of numerical solution of the direct problem in case of well crossing an electrically inhomogeneous layer of limited thickness with a zone of drilling mud penetration by the integro-interpolation method, and the analytical solution of the direct problem for a layer of limited thickness with regard to the potential of rock matrix. The results of numerical and analytical solutions of the inverse problem are almost identical. Proposed algorithms are intended to use in the Rosneft corporate software for petrophysical modeling.

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