New Analytical Method to Evaluate Casing Integrity during Hydraulic Fracturing of Shale Gas Wells

Figure 3

The coordinate rotation processes: (a) stress state of a horizontal well and (b) coordinate transformation system. Principal in situ stress coordinate system, ; geodetic coordinate system, ; coordinate system, after the second time rotation; coordinate system, after the third time rotation; local wellbore coordinate system, XYZ; wellbore deviation angle, α; wellbore azimuth angle, β; the maximum horizontal stress azimuth angle, φ.