Finite element optimization method of boundary load of in-situ stress field

The constrained optimization model based on the least square method is established. According to the fundamental equations of elastic mechanics, an optimization inversion method of the boundary load of in-situ stress field of CBM reservoir is proposed. The method combines the finite element and the finite-difference methods together to optimize and approximate the objective function through the variation of boundary load on the basis of the stress value of partial measured points, and eventually the inverse boundary load is obtained. The optimization calculation is performed on the basis of the method which makes the calculated results agree well with the measured data of in-situ stress. This method can overcome the shortage of common back analysis method such as adjusting boundary loads and regression method, so it can improve the calculation precision. Taking the numerical magnitude and azimuth of in-situ stress in a typical well for Qinshui Basin as a constraint, the in-situ stress field has been calculated. The example shows that the proposed method is credible and has high precision, and can effectively solve the boundary load inversion of in-situ stress field.