Prediction and uncertainty of free convection phenomena in porous media

Abstract

Over the past few decades, groundwater flow and solute transport models have been commonly used to make predictions of complex, highly nonlinear, semichaotic free convective processes in various hydrogeologic settings. However, there has been much confusion in the literature about the ability of models to make reliable predictions of free convection phenomena. Particularly, different model codes and numerical schemes have been observed to give different solutions to the same problem. Attempts to match the precise nature of finger patterns in space and time have been somewhat unsuccessful. The classical notion of grid convergence appears to be nonmeaningful in the context of these processes when attempting to compare the complex fingering patterns. This study examines the predictability of a highly unstable free convective flow system by quantitatively investigating several representative plume characteristics. These characteristics include “microscopic” features such as the number of fingers and deepest plume front, and “macroscopic” features such as vertical center of solute mass, total solute mass, and solute flux through the source zone. Surprisingly, both microscopic and macroscopic variables can be estimated with a small degree of uncertainty. It is shown that the microscopic variables have slightly greater uncertainty than macroscopic variables. This indicates a greater degree of predictability in free convection systems than may have been previously thought to exist. It also suggests that a paradigm shift which analyses free convection in a stochastic rather than deterministic framework is required. This has significant consequences for model simulation and testing as well as process prediction.