Abstract

Summary Geophysical measurements can obtain seismic wave velocities and fluid saturation in partially saturated media for monitoring fluid spatial variations during injection and extraction from porous rocks, and this is of great relevance for underground hydrogen storage and carbon sequestration. However, the P-wave velocities are not only governed by the overall saturation, but also depend on the fluid patches and their size. The patch size variation as saturation changes is commonly ignored in modelling investigations, even though it is natural to assume that fluid patches will form larger as saturation progresses and that percolating clusters will form at some critical saturation levels. To capture the evolution of patch size with saturation implied in the velocity-saturation relations, we are inspired by percolation theory. By incorporating the connectivity of water-filled patches in the continuous random medium model, we develop a critical saturation model. We apply this critical saturation model to examine recently reported experimental measurements, specifically analyzing the patch size changes. And the new model predictions are in reasonable agreement with experimental observations. Our approach enhances the interpretation accuracy of the velocity-saturation relations and forms the basis for understanding the elastic response features of fluid clustering in porous rocks.