Methods for Estimating Fracture Abundance and Size From Borehole Observations

Abstract

Summary This study develops deterministic, exact equations relating fracture frequency (P10), density (P32), and length and width dimensions of rectangular and elliptical fractures from borehole observations. These general equations are applicable to both image logs and cores. A Monte Carlo type of simulation model generated the stochastic data used to derive the equations. The equations use five basic parameters relating frequency to density: borehole diameter, fracture length, fracture width, fracture angle with borehole axis (β), and the rotation angle of the long fracture axis within the fracture plane (γ). For both general equations, density corrections can be applied to individual fractures to find density. Fracture porosity is calculated on a per–fracture basis by applying aperture to density corrections. Both equations match the model to within the small standard deviation between simulations. In addition, the elliptical equation generally agrees with the existing exact theory. The study also develops methods for calculating fracture height (width) and length for rectangular fractures. Fracture height and length are calculated by observing the borehole–enclosed height and length and comparing them with the borehole–enclosed area. The calculation of fracture size is extended to estimate block height and length (block–face size.) These relationships cover a wide range of fracture size and orientation vs. borehole diameter. The theory is valid from small boreholes to tunnels. The general equations consider fractures as planar objects with length and width dimensions and negligible aperture compared with the other dimensions. Fracture aperture is applied, on a per–fracture basis, after the density correction to calculate fracture porosity. In addition to density and porosity calculations, an existing method for fracture–frequency prediction is improved by applying the general relationships. The methods described here are demonstrated using an image log from a vertical well from British Columbia, Canada. In this well, an image log was run over the Triassic section, including the zone of interest, the Montney Formation. Although the average fracture size in the Montney was very large, possibly on the order of tens of meters, they had a much smaller block–face size, on the order of a few meters, which could explain some of the production aspects from this formation.