New line-source solution and scaling relations for diffusive leakage of brine from an infinite aquifer-caprock composite domain during geological storage of CO2

Abstract

Diffusive leakage of heat or chemical species from the storage layers is ubiquitous in engineering systems. Understanding the measure of diffusive fields around the target layer may be used to better design a prospective engineering system and characterize anomalies in the observed pressure, chemicals, and temperature. We report a novel analytical solution to a widely occurring yet unsolved diffusion type problem where a storage layer with a line-source at the inner boundary is embedded in an infinite medium. The analytical difficulty posed by two-dimensional flow and mutual interaction between surrounding formations and storage layer is handled by successively applying Hankel and Laplace transforms. The obtained solution was verified analytically and compared with the classical Theis solution. Afterwards, we focus our discussion around CO2 storage problem and analyze the pressure perturbation behavior, temporally and spatially, to identify the degree of dependency of model parameters. We identify that the diffusive leakage rate scales with the square root of nondimensional time. The distance to the maximum local radial leakage (Rmax) is found to be nonvariant to the model parameters and scales with the square root of the nondimensional time. It was found that more than 99% of the total leakage takes place within 5Rmax radius from the injection point. We also identify a simple scaling relation for the leakage-influenced radius as Rinf≈4.34td. The presented solution and scaling relation will find their usefulness in numerous diffusive problems such as CO2 and waste chemical disposal in deep geological formations and enhanced geothermal energy extraction.