Mathematical model and numerical method for spontaneous potential log in heterogeneous formations |
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Authors: | Ke-jia Pan Yong-ji Tan Hong-ling Hu |
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Affiliation: | School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China; College of Mathematics and Computer Science, Hunan Normal University,Changsha 410081, P. R. China |
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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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Keywords: | spontaneous potential log elliptic interface problems mathematical model numerical simulation |
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