Upscaling fracture aperture fields using self-affine methods with evaluation against laboratory flow measurements

ABSTRACT: Many subsurface formations in igneous rocks have low permeability, with fluid flow primarily occurring through variable aperture rough-surfaced fractures. We use high-resolution 3D scans of a 200 x 200 mm2 natural rock fracture to determine the Hurst exponent (H), scaling parameter (Sp) and correlation function for self-affine aperture field generation. Stochastic realisations of 60 aperture fields are generated from the full fracture and subsections of varying sizes (252 mm2, 502 mm2, 1002 mm2, 1502 mm2) as well as 1D profiles (25 mm, 50 mm, 100 mm, 150 mm and 200 mm) are upscaled to 2002 mm2 aperture fields. Flow simulations through the generated aperture fields using a modified cubic law with Modflow 6 are evaluated against a laboratory measured flowrate. Apertures generated on the same scale as the measured sample, with no upscaling, result in a median simulated flowrate which slightly exceeds the measured value, with an absolute difference of 0.006 ml/s and relative difference of 0.14. Linear regression analysis of the H and Sp parameter space shows a slightly smaller intercept for flow best fit than previous geometrical analysis. Flow predictions from upscaled aperture fields based on the subsections remain within one order of magnitude for measured values, demonstrating reasonable precision. This study also shows that 1D trace profiles can be used to generate and upscale aperture fields. The approach on individual profiles yield ensembles that produce flowrates from 0.001 to ~0.08 ml/s. Shorter profiles (25 mm and 50 mm) provide accurate flow predictions when averaged, while longer traces improve precision but reduce accuracy. However, multiple short trace profiles must be used to constrain the predicted flowrates. Overall, 1D trace profiles with roughness analysis and implementation of the self-affine generation methodology can generate 2D fracture apertures with comparative length scales and be used for meaningful flow predictions.