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Mathematical model and numerical method for spontaneous potential log in heterogeneous formations

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Abstract

This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has been shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.

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Correspondence to Ke-jia Pan  (潘克家).

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(Communicated by Zhe-wei ZHOU)

Project supported by the National Natural Science Foundation of China (No. 10431030) and the Shanghai Natural Science Foundation (No. 08ZR1401100)

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Pan, Kj., Tan, Yj. & Hu, Hl. Mathematical model and numerical method for spontaneous potential log in heterogeneous formations. Appl. Math. Mech.-Engl. Ed. 30, 209–219 (2009). https://doi.org/10.1007/s10483-009-0208-z

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  • DOI: https://doi.org/10.1007/s10483-009-0208-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

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