Unstable density-driven flow in heterogeneous porous media:: A stochastic study of the Elder [1967b] short heater'' problem -: art. no. 1007

The situation of a dense fluid overlying a lighter one is potentially unstable and under certain conditions may result in fingers of dense contaminant freely convecting downward. Free convection causes increased contaminant transport over larger distances and over shorter timescales than is possible by diffusion alone. Unlike free convection in homogenous porous media, free convection in heterogeneous porous media has received relatively little attention. In this study, a well-understood problem of transient free convection in homogeneous porous media, the Elder [1967b] short heater'' problem has been modified to study the effects of heterogeneity in permeability distributions on solute transport processes using a stochastic framework. A set of measurable indicator characteristics including solute fluxes, solute present, center of gravity and finger penetration depth are used in the quantitative analysis of output. Heterogeneity in the permeability distribution provides both the triggering mechanism for the onset of instabilities and also controls their subsequent growth and/or decay. Results show that (1) an increase in the standard deviation of the log permeability field results in a greater degree of instability at earlier times but promotes stability at later times, (2) an increase in the horizontal correlation length of the log permeability field creates laterally extensive low-permeability zones that dissipate upward and downward motion needed to maintain convection and therefore causes a reduction in the degree of instability, (3) a greater degree of heterogeneity causes greater uncertainty in predictions, and (4) traditional predictive methods such as the Rayleigh number (based upon an average permeability) do not generally work in their application to heterogeneous systems. Probability of exceedence analysis also demonstrates that analyses based upon homogeneous assumptions will typically underestimate, often quite significantly, the value of key measurable characteristics.