Through-Casing Hydraulic Fracture Evaluation by Induction Logging II: The Inversion Algorithm and Experimental Validations

Evaluation of hydraulic fractures has been under intensive study since the last decade. Among published works, only a few have included casing effects. This paper focuses on the through-casing electromagnetic (EM) induction imaging method that evaluates hydraulic fractures with enhanced contrasts. An experimental system and an inverse scattering algorithm are presented. The laboratory scaled experimental system is built for the feasibility study of the EM induction imaging method for the through-casing hydraulic fracture evaluation. To develop the inverse scattering algorithm, fractures outside boreholes with metallic casing are modeled by a novel hybrid approximation method. This method combines the distorted Born approximation and the mixed order stabilized bi-conjugate gradient fast Fourier transform method to solve the forward scattering problem. The variational Born iterative method is applied to solve the nonlinear inverse problem iteratively. Experimental results show that the inverse scattering algorithm is effective for EM contrast enhanced through-casing hydraulic fracture evaluation.