Attenuation by squirt flow in undersaturated gas sands

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Abstract
In unconsolidated sand at low saturations, water exists in pendular rings at grain contact points. As the grains are pressed together by a passing wave, the squirt flow will contribute to wave attenuation. In a model which consists of a sphere‐pack framework, fluid flow equations are solved under certain approximations to calculate the viscous losses and, hence, attenuation. Attenuation is negligible for a sphere‐pack composed of equal‐sized spherical grains. The model is extended to include a spectrum of grain contact geometries, in particular a log‐normal spectrum of aspect ratios. The attenuation is substantial and depends markedly upon a lower limit imposed on the aspect ratios. For contacts of Type B (water separating two grains) only, results at 1 Hz are consistent with those of Mavko and Nur (1979) based on two‐dimensional (2-D) cracks. If contacts of Type A (two grains in contact) and Type B are present, the attenuation is greater by 2–3 orders of magnitude. The model with Type B contacts displays a dependence of attenuation on water saturation in the range 1–10 percent; the model with Type A and B contacts does not. When the results were fitted to the measurements of absolute attenuation and saturation dependence at kHz frequencies by Gardner et al. (1964), only the model with Type B contacts with aspect ratios [Formula: see text] could fit the data.

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