A numerical assessment of local strain measurements on the attenuation and modulus dispersion in rocks with fluid heterogeneities

Abstract

SUMMARY The forced oscillation method is widely used to investigate intrinsic seismic wave dispersion and attenuation in rock samples by measuring their dynamic stress–strain response. However, using strain gauges to locally measure the strains on samples surfaces can result in errors in determining the attenuation and moduli of rocks with mesoscopic scale heterogeneities. In this study, we developed a 3-D numerical model based on Biot's poroelastic theory to investigate the effect of strain gauge location, number and size on attenuation and dispersion in response to wave-induced fluid flow. Our results show that increasing the strain gauge length, number, and size can reduce the error between local and bulk responses. In a homogeneous and isotropic rock with a quasi-fractal fluid heterogeneity at 12 per cent gas saturation, the relative error between local and bulk responses stays below 6 per cent when the strain gauge length surpasses 8.6 times the correlation length. As the gas saturation becomes larger, the ratio minimally changes non-monotonically, initially increasing and then decreasing. We also used the Monte Carlo method to demonstrate that local laboratory measurements can approximate the reservoir-scale response with a minimum relative error of 1.5 per cent as the sample number increases. Our findings provide guidance for (i) interpreting local low-frequency measurements in terms of bulk properties of rock and (ii) upscaling lab measurements to reservoir-scale properties.