Relationship between Elastic wave Velocity and Permeability of Rock Model with penny-shaped cracks

Estimating underground fluid-flow is of great importance in petroleum engineering and carbon capture and storage (CCS). Permeability is one of the most important parameters which show how easily fluid passes through rock mass. It could be acquired just by measuring rock samples near borehole in lab-experiments. It means that permeability except near borehole should be estimated, considering other information. In this research, elastic wave velocity is focused as a tool of estimating permeability, because it is one of the most popular parameter which has underground information. The relationship between permeability and elastic wave velocities should be revealed, in order to establish a methodology to estimate rock permeability from elastic wave velocity. These two parameters are controlled by pore geometry of rock. Therefore, we focused on pore geometry as connecting bridge between the two parameters: permeability, elastic wave velocity. We modeled the considering rock as a solid mass containing a lot of same-sized penny-shaped cracks randomly. LBM (Lattice Boltzmann Method), which is one of the computational fluid dynamics methods, is adopted for calculating permeability in our study. This method has a storing point especially under complicated fluid-solid boundary condition. Elastic wave velocities are derived from effective elastic moduli (i.e., bulk modulus, stiffness). They are estimated by self-consistent approximation, which needs porosity of rock model, aspect ratio of penny-shaped cracks and volume fraction of each phase. In this research, we assume that solid phase is composed only by quartz and rock's pore space is filled with water. The simulated results demonstrate that aspect ratio of crack can be estimated by P- and S-wave velocity, and aspect ratio and P-wave velocity can determine porosity. Whereas, the relationship between porosity and permeability is dependent on aspect ratio, which means permeability can be estimated by aspect ratio and porosity. Therefore, this research reveals that permeability can be estimated by P-wave velocity and S-wave velocity if the rock is composed by same-sized penny cracks.