Multiscale Hydraulic Fracture Modeling With Discontinuous Galerkin Frequency-Domain Method and Impedance Transition Boundary Condition

Abstract

To facilitate the detection of hydraulic fractures by electromagnetic survey, a discontinuous Galerkin frequency-domain (DGFD) method is introduced in this paper to efficiently model the fracture responses under complicated geophysical environments. In the proposed DGFD method, the computational domain can be split into multiple subdomains with nonconformal meshes. The Riemann solver (upwind flux) is introduced to evaluate the numerical flux. The impedance transition boundary condition (ITBC) is employed to facilitate fracture modeling by approximating fractures as surfaces. Numerical results show that the ITBC works well for different fracture conductivities, dipping angles, operation frequencies, as well as different sources. For both small- and large-scale fractures, it also shows good agreement with the references. The responses of fractures increase as their conductivities become larger. Large dipping angles can cause spikes on the responses in a borehole. For a magnetic source, higher operation frequencies can enhance the signal level, while for an electric source, the sensitivity to frequency is small. When no borehole is considered, the responses due to an electric source are in general larger than those due to a magnetic one. However, when a borehole with conductive mud is included, the responses can be reversed for the electric and magnetic sources. For multiple fractures outside a cased borehole, the signal level of an electric source is significantly reduced, while that of a magnetic source remains at a similar level compared with the scenario without a casing. With the proposed technique, multiscale modeling of hydraulic fractures in complicated geophysical environments becomes possible.