Modeling groundwater velocity uncertainty in nonstationary composite porous media

Despite the intensive research over the past decades in the field of stochastic subsurface hydrology, our ability to analyze and model heterogeneous groundwater systems remains limited. Most existing theories are either too restrictive to handle practical complexity or too expensive to be applied to realistic problem sizes. In this paper we present approximate, closed-form equations that allow modeling 2D nonstationary flows in statistically inhomogeneous aquifers, including composite aquifers containing multiple zones characterized by different statistical models. The composite representation has the effect of decreasing the variance of deviations from the mean, relaxing the limitation of the small-perturbation assumption. The simple formulas are illustrated with a number of examples and compared with a corresponding first-order nonstationary numerical analysis and Monte Carlo simulation. The results show that, despite the gross simplifications, the closed-form equations are robust and able to capture complex variance dynamics, reproducing surprisingly well the first-order numerical solutions and the Monte Carlo simulation even in highly nonstationary, variable situations.