Detection and Quantification of Three-Dimensional Hydraulic Fractures With Horizontal Borehole Resistivity Measurements

This paper investigates the suitability of low-frequency borehole resistivity measurements for detecting and appraising hydraulic fractures. The effects of the borehole logging tool's transmitter-receiver spacing, orientation, and operating frequency, as well as the fracture's shape, cross-sectional area, dip, and electrical-conductivity contrast with the embedding formation, are quantified using an fast Fourier transform (FFT)-accelerated integral-equation solver. Simulation results for a logging tool that consists of one transmitter and two receivers in a homogeneous shale formation of 1/3 S/m conductivity show the following: 1) Longer transmitter-receiver spacings can differentiate larger fractures, while shorter transmitter-receiver spacings can detect smaller fractures; specifically, the tool can differentiate fractures up to ~1000 m
²
in area if the receivers are 18 and 19.2 m away from the transmitter, but this long-spacing configuration cannot detect fractures smaller than ~10 m
²
in area and requires the effective electrical conductivity of the fracture to be larger than 100 S/m. In comparison, the tool can detect fractures as small as ~1 m
²
in area if the receivers are 1.2 and 1.5 m away from the transmitter even if the effective electrical conductivity of the fracture is only 10 S/m, but this short-spacing configuration cannot distinguish fractures larger than ~10 m
²
in area. 2) Coaxial measurements are sensitive to the fracture cross-sectional area but cannot differentiate fractures of the same area with different cross-sectional shapes or dips. Transverse copolarized measurements can discern axially symmetric fractures from asymmetric ones; for example, in long-spacing configuration, they can differentiate elliptical fractures with an aspect ratio of 8 from circular or square fractures if their areas are within ~1 m
²
to ~1000 m
²
. Cross-polarized measurements can quantify fracture dip and become more sensitive as the dip angle increases; for example, in long-spacing configuration, they can detect 15° dipping fractures that are larger than ~100 m
²
in area but cannot distinguish them, while they can detect and distinguish 60° dipping fractures if their areas are in the range of ~100-1000 m
²
. 3) The measurements are mostly insensitive to the operating frequency in the 10 Hz-1 kHz range in the short-spacing configuration and depend moderately on the operating frequency in the long-spacing configuration. 4) The relative strength of the measured signals is proportional to the fracture effective electrical conductivity when the fracture is more than ten times conductive compared to the embedding rock formation. 5) Short-spacing measurements exhibit higher resolution; the tool can differentiate two fractures as long as they are more than ~1 m (4 m) away from each other in the short-spacing (long-spacing) configuration. 6) In complex fracture networks, not only major branches but intermediate and small branches contribute to the shape and magnitude of measured signals; the contributions depend mainly on the area and position of the branches.