Improving the computational efficiency of first arrival time uncertainty estimation using a connectivity-based ranking Monte Carlo method

Abstract

The first arrival time of a solute plume migrating from its source to an environmentally sensitive target is one of the key quantities of interest when assessing the risks of groundwater contamination. First arrival times are correlated with the hydraulic connectivity properties of spatially heterogeneous porous formations. Hydraulic connectivity leads to the presence of preferential flow paths which in turn control the transport dynamics of the leading edge of the solute plume and therefore first arrival times. In applications, these arrival times are subject to uncertainty given the lack of a detailed site characterization. The Monte Carlo method is commonly adopted to estimate the uncertainty of solute arrival times, however it leads to a computational burden. In this work, we build upon the existing knowledge regarding the correlation between connectivity and first arrival times to propose an innovative connectivity-based ranking Monte Carlo approach to quantify the uncertainty of first arrival times. The proposed method is tailored to predict first arrival times and allows to alleviate the computational costs when compared to the traditional Monte Carlo method. Our method consists of ranking the randomly generated spatially heterogeneous hydraulic conductivity fields according to their connectivity. The connectivity metric adopted is based on the concept of the minimum hydraulic resistance and can be obtained at a very low computational cost through the use of graph theory. We illustrate the methodology by analyzing the convergence rate of the first arrival time means and standard deviations. We compare the convergence rate of the first arrival times statistics obtained through the proposed methodology with those computed through the traditional Monte Carlo method. Overall, our results indicate the that the proposed methodology ensures a faster convergence of the considered quantities, thus reducing the time required for their estimation and the associated computational burden.