A breakthrough curve analysis of unstable density‐driven flow and transport in homogeneous porous media

Abstract

In certain hydrogeological situations, density variations occur because of changes in solute concentration, temperature, and pressure of the fluid. These include seawater intrusion, high‐level radioactive waste disposal, groundwater contamination, and geothermal energy production. Under certain conditions, when the density of the invading fluid is greater than that of the ambient one, gravitational instabilities or fingers may lead to transport over larger spatial scales and significantly shorter timescales than compared with diffusion alone. This study has two key objectives: (1) to explore how the nature of a breakthrough curve changes as the density of the invading fluid changes and there is a subsequent transition from stable to unstable behavior and (2) to examine the feasibility of using 1‐D advection‐dispersion fitting models to fit the experimental data as the density of the invading fluid increases. Thirty‐six breakthrough curve experiments were carried out in fully saturated, homogeneous sand columns. Results show that an increase in the density of the source solutions leads to breakthrough curves with lower peak concentrations at breakthrough, earlier peak breakthrough pore volume and time, and an increase in positive skewness of the breakthrough curve. Visual experiments conducted in transparent columns confirm that a transition from stable to unstable behavior occurs as the density of the injectant increases and that backward convective reflux in the high‐density cases leads to dilution of the trailing edge of the pulse as evidenced by positively skewed breakthrough curves. These mixed convective systems (controlled by both forced and free convection) are characterized by a mixed convective ratio. Parameter estimation using a 1‐D advection‐dispersion fitting model suggests that unstable plume migration can be fitted with an apparent pore flow velocity and dispersivity at low‐density gradients. However, as the density of the injectant increases, it becomes progressively difficult to estimate parameters that fit the experimental curves with a model that does not explicitly account for density effects. Significantly poorer matches are obtained when the invading solution concentration is equal to, or exceeds, the solution concentration denoted by ML (the medium‐ to low‐density solution), i.e., invading solutions greater than approximately 13,000 mg/L in this study. Care must therefore be taken in applying standard advection‐dispersion models to breakthrough curve analyses where even modest density differences are encountered.