On reliability of stress determined by hydraulic fracturing stress measurement using transverse fractures

Hydraulic fracturing stress measurement using a set of transverse fractures is a powerful tool for estimating stress at a great depth. Qualitatively speaking, reliability of evaluated stress improves when orientation of fractures in the set differs significantly from each other. In order to express the circumstance quantitatively, we introduce so-called condition number defined for linear algebraic equations to measure the proximity of a problem to ill-condition. In the present case, condition number is determined completely by the orientation of fractures used to evaluate stress. We employ thirty sets of artificial data of the orientation of fractures, instead of field data. Each set consists of ten fractures, the orientation of which is generated by random sampling. By using these artificial data, we examine the reliability and the condition number for two artificial stress states. It is revealed that the reliability and the condition number have strong correlation to each other and thus the condition number is very helpful for measuring reliability of evaluated stress.