: This paper presents the general theory for determining the in-situ stress state from multiple fracturing data. The complete exact non-linear solution is presented. This cannot be solved explicitly, therefore a semi-linearized version is also presented, as well as a linear version. It is shown that the fracturing equation takes the form of an hyperbolic equation, an elliptic equation or a parabolic equation. A solution can be obtained with a minimum of two data sets. However, using an inversion technique, a solution can be obtained with any number of data sets as the solution is over determined. Comparison is made between the solutions. Field data is used to compare the results.


The application of rock mechanics in the petroleum industry has increased in later years. Due to the increasing complexity of petroleum wells, borehole stability issues have become challenges that have to be handled. Borehole collapse is one class of problem, whereas circulation losses due to unexpected fracturing accounts for significant additional expenditures. In general, drilling cannot proceed before mud losses are healed.

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