Efficient Electromagnetic Simulation and Experiment Tools for Hydraulic Fracture Evaluation

Hydraulic fracturing is an essential way to improve the production of unconventional oil and gas, especially shale gas. Therefore, it is important to characterize the produced fractures using either acoustic or electromagnetic (EM) methods, and evaluation of hydraulic fractures has been under intensive study since last decade. Electromagnetic techniques, including induction logging and galvanic techniques, have the advantages of nondestructive measurements and high sensitivity to the formation and fracture resistivity. They are widely used for produced fracture evaluation.

However, conventional forward and inverse methods in low frequency range face significant challenges by such multiscale problems where the fracture width (<1cm) is orders of magnitude smaller than its diameters (>100 m). The problem becomes much more complicated when the effects of borehole, casing, and planar stratified medium need to be considered for realistic oil field application.

This dissertation focuses on three aspects. First of all, the application of newly developed efficient forward electromagnetic solvers, hybrid distorted Born approximation and mixed ordered stabilized bi-conjugate gradient FFT (DBA-BCGS-FFT) method, and hybrid numerical mode matching with the stabilized bi-conjugate gradient FFT (NMM-BCGS-FFT) method, are illustrated. For the DBA-BCGS-FFT method, the two components of the solver, distorted Born approximation (DBA) and mixed ordered stabilized bi-conjugate gradient FFT (BCGS-FFT), are separately discussed with their advantages and disadvantages. Then the hybrid DBA-BCGS-FFT will be introduced and explained, including how the combination of the advantages of the two solvers and overcome their disadvantages. For the second forward method, the numerical mode matching (NMM) method is introduced with the procedures of the NMM-BCGS-FFT method for analyzing the effects of the complex cased borehole and planar stratified medium.

Second, the inverse solver, variational Born iterative method (VBIM), is introduced for hydraulic fracture reconstruction. The box constraints in the inversion process is introduced to enhance the fracture reconstruction resolution and avoid unrealistic parameter in the inversion. In the procedures of the inverse solver, the forward solvers are applied to construct the system matrix. In this application, the inverse solvers are applied to process the secondary field data obtained by field scanners and laboratory detectors.

The results will be separate into three sections. First, the validation of the forward and inverse solvers is demonstrated. The commercial software, COMSOL, is used for the validation. Then, induction logging detection and galvanic detection model results show the capability of the forward and inverse solvers. Last, two established experiment systems will be described with details. The laboratory scaled experimental system is established for feasibility study of the electromagnetic induction detection, and the field test control source electromagnetic system is designed and built for hydraulic fracture evaluation. In induction logging detection model, experimental results show that the inverse scattering algorithm is effective for electromagnetic contrast enhanced through-casing hydraulic fracture evaluation. In galvanic detection model, the impact of different hydraulic fracturing material and choices of transmitter/receiver locations on signal response will be discussed to show the application of the forward solvers in field configuration design. Both fracture reconstruction results by the inverse solvers with the experimental data will be discussed in these two chapters.