On the detectability and appraisal of hydraulic fractures in layered media using borehole resistivity measurements

Summary form only given. Hydro-fracturing is a widely used technique to enhance hydrocarbon production from organic shales and tight-gas sands. To assess the flow efficiency in the treated area, the geometrical properties of induced fractures, including their location, orientation, and size, must be determined. Recent simulation results show that low-frequency borehole resistivity measurements are promising candidates for detecting fractures, especially when they are injected with electrically conductive proppant that increases the conductivity contrast between the fracture and the background (D. Pardo and C. Torres-Verdin, SEG Expanded Abstracts, 2012; K. Yang et al., SEG Expanded Abstracts, 545-550, 2013; K. Yang and A. E. Yılmaz, IEEE APS Int. Symp., 2013). These and similar studies, however, assume that the fracture resides in a homogeneous and isotropic background. It is necessary to quantify the validity of this method for detecting more general fractures, including the common case of irregularly-shaped, arbitrarily-oriented fractures in the presence of multiple layers, anisotropic layers, and mechanically weak surfaces. In this article, the effects of background earth formations on the detectability of hydrofractures, including complex three-dimensional (3D) networks of them, are studied by simulating multi-component low-frequency borehole resistivity measurements in a planar layered medium. An integral-equation approach is used to perform the simulations; as a result, only the borehole and the fracture models are meshed, the background is modeled using layered-medium Green functions, and the logging tool is modeled as an impressed transmitter and two receivers that are moved in the borehole. Specifically, the frequencydomain volume electric-field integral-equation (VEFIE) is constructed and is converted into a matrix equation using the method-of-moments procedure. At each tool position, (i) the matrix equation is solved for a different excitation/ri- ht-hand side, (ii) the solution is accelerated using an iterative FFT-based procedure tailored for efficient analysis of scattering from 3D structures in layered media (K. Yang and A. E. Yılmaz, CEM Int. Workshop, 4-8, 2013), and (iii) the solution is used to compute the scattered fields at the receivers. Using this approach, the effects of conductivity contrast, background anisotropy, fracture geometry, and transmitter-receiver spacing on the detectability of 3D hydro-fractures in planar layered media can be investigated. Simulations indicate that (i) coaxial measurements are sensitive to the fracture cross-section area; (ii) cross-polarized measurements can quantify fracture dip; (iii) maximum fracture area that can be differentiated is larger for longer transmitter-receiver spacing but a higher conductivity contrast is required; (iv) measured signal strength is more sensitive to the component of the background conductivity parallel to the fracture plane when the background is anisotropic; and (v) irregular fracture shapes such as those arising in the presence of weakness planes and highly-heterogeneous rock formations can be assessed. The presentation also compares the detectability of hydro-fractures in homogeneous and layered backgrounds.