Correction of linear fracture density and error analysis using underground borehole data

Fracture data acquired from drill core and borehole image logs require corrections for the bias due to fracture orientation, that are usually achieved by the Terzaghi correction technique. Previous studies often approximate the wellbore as a one-dimensional scanline, assuming that the length of the core axis within the sampling range is equal to the scanline length. This study refers to the commonly used workflow as the original Terzaghi correction method which is known to perform poorly when the angle (θ) between the core axis and the fracture is small. To address this issue, we propose an extension of the Terzaghi correction method that also considers the core diameter and is a function of both the fractures and the host layer dipping angle. The new method resolves the fracture density problem by selecting a new direction for the scanline perpendicular to the fracture and calculating the projection length of the sampling space in this direction. The fracture spatial arrangements and observed number of sampled fractures mainly affect the performance of this new approach. However, possible errors in the new correction method pertaining to the equidistant fracture density should decrease with increasing number of sampled fractures. It is found that an acceptable correction range exists for equidistant fracture density, though, when the corrected density is not within the acceptable correction range, the observed sampled fractures will not be equal to the true observed value. This means the corrected fracture density would be in an unacceptable range of errors. Moreover, the new method can provide results within the acceptable range when the angle between the fracture and the core axis is less than 20°. At the same time, this new method is free from other disadvantages in the original Terzaghi correction method, particularly, when the ratio of layers’ thickness to the core diameter is low. Therefore, the improved approach presented here is especially applicable to thin layers (no more than two times the core diameter) and conditions where the angle between the fracture and the core axis is less than 20°, which can contribute to fracture density characterization in the subsurface.