Darcy’s model with optimized permeability distribution for the simulation of Stokes flow and contaminant transport in karst aquifers

Simulation of fluid flow in karst aquifers is challenging because of the presence of porous and free-flow regions within a single aquifer system. One simple but less accurate approach to model such a system is to use Darcy’s model. This model has much lower computational overhead than many other more rigorous approaches. The results obtained from the Darcy model are accurate for the porous regions of the aquifer, but it produces inaccurate results inside the caves. An approach is proposed called the Darcy model with optimized permeability distribution (DMOPD) for modeling accurate pressure and velocity distributions within the aquifer while retaining almost the same computational cost as the Darcy model. This method comprises three main steps. First, at the first time-step, the pressure and velocity distribution of the entire aquifer is solved using the Brinkman model. Then each cave is divided into an odd number of zones, with the middle zone assigned a maximum permeability value. Subsequently, the permeability ratios of the other surrounding zones are estimated using a global optimization technique. The permeability ratio is the ratio of permeability in that zone to the maximum permeability within the cave. Finally, the Darcy model is run for the remaining time steps using the optimized values of permeability obtained in the second step. Example applications presented show that this method is able to approximate the Brinkman model very well and much faster when compared to the Brinkman model.