Abstract
The pollution of groundwater, essential for supporting populations and agriculture, can have catastrophic consequences. Thus, accurate modeling of water pollution at the surface and in groundwater aquifers is vital. Here, we consider a density-driven groundwater flow problem with uncertain porosity and permeability. Addressing this problem is relevant for geothermal reservoir simulations, natural saline-disposal basins, modeling of contaminant plumes and subsurface flow predictions. This strongly nonlinear time-dependent problem describes the convection of a two-phase flow, whereby a liquid flows and propagates into groundwater reservoirs under the force of gravity to form so-called “fingers”. To achieve an accurate numerical solution, fine spatial resolution with an unstructured mesh and, therefore, high computational resources are required. Here we run a parallelized simulation toolbox ug4 with a geometric multigrid solver on a parallel cluster, and the parallelization is carried out in physical and stochastic spaces. Additionally, we demonstrate how the ug4 toolbox can be run in a black-box fashion for testing different scenarios in the density-driven flow. As a benchmark, we solve the Elder-like problem in a 3D domain. For approximations in the stochastic space, we use the generalized polynomial chaos expansion. We compute the mean, variance, and exceedance probabilities for the mass fraction. We use the solution obtained from the quasi-Monte Carlo method as a reference solution.
Highlights
Many techniques are used to investigate the propagation of uncertainties associated with porosity and permeability into the solution, such as classical Monte Carlo (MC) sampling
We describe the stochastic modeling, integration methods, and the generalized polynomial chaos expansion technique in Sect
We applied the generalized polynomial chaos expansion (gPC) expansion to approximate the solution of the density driven flow, which is modeled by a time-dependent, nonlinear, second order differential equation
Summary
Accurate prediction of the movement of contamination in groundwater is essential. Certain pollutants are soluble in water and can leak into groundwater systems, such as seawater into coastal aquifers or wastewater leaks. Some pollutants can change the density of a fluid and induce density-driven flows within the aquifer This causes faster propagation of the contamination due to convection. Many techniques are used to investigate the propagation of uncertainties associated with porosity and permeability into the solution, such as classical Monte Carlo (MC) sampling. Alternative, less costly techniques use collocation, sparse grid, and surrogate methods, each with their advantages and disadvantages. We validate our obtained results using the quasi-Monte Carlo (qMC ) approach Both methods require the computation of multiple simulations (scenarios) for variable porosity and permeability coefficients. Overviews of the uncertainties in modeling groundwater solute transport (Carrera 1993) and modeling soil processes (Vereecken et al 2016) have been performed, as well as reconnecting stochastic methods with hydrogeological applications (Bode et al 2018), which included recommendations for optimization and risk assessment. For problems with a large number of random variables, the methods based on a regular grid (in stochastic space) are less preferable
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