SCALING STRUCTURE OF TRACER DISPERSION FRONTS IN POROUS-MEDIA

Experiments on the miscible displacement of a clear fluid by a dyed fluid of the same viscosity and density in a rectangular quasi-two-dimensional porous medium are presented. Equiconcentration dispersion fronts were identified using computer image processing. The fronts taken at three different concentrations are fractal curves with approximately the same box fractal dimension D congruent-to 1.45. In an alternative analysis the fronts were reduced to single valued functions and the dynamic scaling behavior investigated using a self-affine scaling formalism. The Hurst exponent H = 0.55 and the dynamic exponent beta = 0.5, found by collapsing height difference correlation function data, are consistent with the results obtained through other analysis methods. The average concentration profile across the dispersion front was found to follow the classical solution of the diffusion-convection equation. The dependence of the width of the equiconcentration dispersion front sigma on time yields dispersion coefficients D(sigma) over one order of magnitude less than the longitudinal dispersion coefficient D(parallel-to).