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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 axi-symmetric 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.

Oil well logging. --- Geophysical well logging. --- Logging, Geophysical well --- Well logging, Geophysical --- Logging, Oil well --- Well logging, Oil --- Mathematics. --- Geophysics. --- Functional analysis. --- Partial differential equations. --- Numerical analysis. --- Partial Differential Equations. --- Geophysics/Geodesy. --- Numerical Analysis. --- Functional Analysis. --- Prospecting --- Borings --- Geology, Stratigraphic --- Petroleum --- Petroleum engineering --- Geophysical methods --- Geology --- Differential equations, partial. --- Physical geography. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematical analysis --- Geography --- Partial differential equations --- Geological physics --- Terrestrial physics --- Earth sciences --- Physics --- Oil well logging --- Mathematical models.