Rough-surfaced fracture generation with variable aperture using self-affine methods

Synthetic rough-surfaced fractures have been successfully generated using methods founded on self-affine principles, which can be based on properties obtained from fracture surface measurements. In order to generate fractures using self-affine methods, a function describing the correlation between the upper and lower surfaces is required, as well as two key parameters, the Hurst exponent H and a scaling parameter Sp. In current literature, there are several methods for determining H and Sp which are primarily adopted for measurements of 1-dimensional fracture traces. There are however comparatively few studies using these methods with measurements of surface scans and applying them to generate realistic fractures. In this work, we evaluate two methods commonly used, the root-mean-square correlation function (RMS-COR) and the Fourier Power Spectrum (FPS) approach, each with several variations of possible implementation when applied to measurements of fracture surfaces.

To obtain an accurate representation of the aperture field and rough surfaces we use high resolution surface scans of a natural fracture sample. For each method variation 100 realisations of the aperture fields are generated and their respective ensembles are evaluated against the measured aperture distribution. The most accurate method for obtaining H and Sp in terms of its ability to generate apertures that correspond with the measured fracture sample studied was the RMS-COR method. We show a linear relationship between H and Sp that provides a best fit of synthetically generated fractures when compared with the measured fracture sample. We also introduce an improved approach for representing the correlation function between two rough surfaces. Finally, using a restricted subsection of the sample, we demonstrate the developed model can successfully generate upscaled fractures. Thus, aperture fields generated using this method can be used for representing and modelling larger fractures or multiple fractures in a network, allowing for numerical flow simulations to include realistic representations of aperture internal heterogeneity based on measurements obtained from a natural rock fracture.