This monograph, the first of its kind on the mathematical model of spontaneous potential well-logging, proves the well-posedness of the model, and proposes three efficient schemes of numerical solution, supported by a number of numerical examples. Spontaneous potential (SP) well-logging is one of the most common and useful well-logging techniques in petroleum exploitation. This monograph is the first of its kind on the mathematical model of spontaneous potential well-logging and its numerical solutions. The mathematical model established in this book shows the necessity of introducing Sobolev spaces with fractional power, which seriously increases the difficulty of proving the well-posedness and proposing numerical solution schemes. In this book, in the axisymmetric situation the well-posedness of the corresponding mathematical model is proved and three efficient schemes of numerical solution are proposed, supported by a number of numerical examples to meet practical computation needs.
Preface.- Modeling.- Properties of solutions.- Limiting behavior.- Techniques of solution.- Numerical simulation.- Bibliography.
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