Semi-analytical solution for pressure change and leakage rate through aquifer leaks or fractures considering both Darcy and non-Darcy phenomena

Study of potential leakage of hazardous liquid waste into deep aquifer or abandoned wells is very important research work in recent days. CO2 sequestration into the brine media is not an exception of that. The saline aquifer is always overlain by a leaky aquitard or seal which may allow the migration of the injected CO2 or any kind of hazardous liquid waste to the upper aquifer through some leaks or fractures. The scope of study includes how the migration through the seal or aquitard causes the pressure change in the upper aquifer because of that injection into the target storage aquifer. Such pressure change is used to infer the leakage pathway location and characteristics of the leak or fractures. In this complex issue both Darcian and non-Darcian flow has been taken care of combindly. The Izbash equation has been used to describe the non-Darcian flow in the aquifer. A semi-analytical solution is obtained in Laplace domain and finally it has been solved numerically. Afterwards different parameters have been evaluated (leak or fracture size, injection rate, conductivity) to see how they directly affect the upper aquifer pressure and leakage rate independently.