Buoyancy-Driven Chaotic Regimes During Solute Dispersion in Pore Networks

Abstract

In an attempt to investigate gravity effects on solute dispersion at the scale of a pore network, single source-solute transport visualization experiments are performed on glass-etched pore networks of varying morphology and degree of pore-scale heterogeneities. The (lighter) low solute concentration aqueous solution flows steadily through the porous medium and the (heavier) high solute concentration solution is injected at a very low and constant flow rate through an inner port. The transient evolution of the solute concentration distribution over various regions of the pore network is determined at different scales by capturing and video-recording snapshots of the dispersion on PC, measuring automatically the spatial variation of the color intensity of the solution, and transforming the color intensities to solute concentrations. Without the action of gravity, the steady-state dispersion regime changes with Peclet (Pe) number, and the longitudinal and transverse dispersivities are estimated by fitting the experimental datasets to approximate analytic solutions of the advection-dispersion equation. Under the action of gravity, multiple of steady-state solute dispersion regimes is developed at each Pe value, and lobe-shaped instabilities of the solute concentration are observed across the pore network, as the downward flow of the denser (higher solute concentration) fluid is counterbalanced by the upward flow of the less dense (lower solute concentration) fluid. The steady-state dispersion regimes may be periodic, quasi-periodic or chaotic depending on the system parameters. The nature of the transient fluctuations of the average solute concentration is analyzed by identifying the periodicity of the fluctuations, determining the autocorrelation function and the statistical moments of the time series, and inspecting the FFT (fast Fourier transform) power spectra. It is found that the mixing zone tends to be stabilized at higher values of the Peclet (Pe) number. Periodic and quasi-periodic solute dispersion regimes are favored by relatively high Pe values and low degree of pore scale heterogeneities, whereas chaotic regimes are favored by low Pe values and high degree of pore-scale heterogeneities. Some ambiguity concerning the classification of the observed solute dispersion regimes is due to the fact that the short length of the time series does not allow the processing of datasets with the nonlinear methods of state-space analysis.