High-resolution GPU-based simulations of quasi-static poroelasticity: seismic attenuation and modulus dispersion in three-dimensional stochastic fracture networks

SUMMARY Fractures significantly impact the elastic and hydraulic properties of geological structures, influencing fields like geothermal energy, hydrocarbon exploration, nuclear waste disposal and $\mathrm{ \mathrm{CO}}_2$ storage. Characterizing these formations is challenging due to the scale disparity between seismic wavelengths and fracture sizes. This study leverages decades of analytical and numerical advancements to evaluate the effective mechanical properties of fractured solids at the mesoscopic scale. A novel numerical method for modelling quasi-static Biot’s poroelastic equations using graphics processing units (GPUs) is introduced for simulating hydromechanically coupled systems. Capable of handling up to 133 million voxel elements on a single GPU, this method offers unprecedented spatial resolution to model complex fracture networks. The GPU-accelerated solver, FastBiot_QS, delivers exceptional performance, achieving a computational speedup of approximately 520 times compared to central processing unit-based methods. The solver’s accuracy is rigorously validated in 1-D and 3-D setups. Simulations reveal that fracture clustering and spatial distribution significantly affect seismic attenuation and modulus dispersion. Clusters of interconnected fractures lead to higher attenuation at higher frequencies, while sparsely distributed fractures result in higher attenuation at lower frequencies. Simulations with log-normal and uniform distributions present intermediate behaviours between densely clustered and sparsely distributed fractures. The study can improve interpretations of seismic data and hydraulic properties in fractured media.