Reliability of In Situ Stress Due to Similarity of Crack Orientation in Hydraulic Fracturing Stress Measurement

Abstract

Hydraulic fracturing rock stress measurement utilizing shut-in pressures of transverse cracks, the reliability of evaluated in situ stress state depends upon the independence of crack orientation, qualitatively speaking, the reliability improves when orientation of cracks differs significantly from each other. In order to evaluate the relationship between independence and reliability, we introduced the condition number of a matrix which is completely determined by the orientation of transverse cracks induced by hydraulic fracturing. We examined 30 sets of artificial data, each set of which consisted of ten cracks generated by random sampling, under two given stress states, and investigated the relationship between the condition number and the reliability of the estimated stress state. It was revealed that the reliability and the condition number had strong correlation and, thus, the condition number is a very useful measure of the reliability of the estimated stress state.