Dynamics and reversibility of tracer dispersion in time dependent flows inside rough fractures

ROHT, Y. L.; CHERTCOFF, R.; HULIN, J. P.; AURADOU, H.; IPPOLITO, I.

Valencia

Congreso; Interpore 2019; 2019

Fundación Interpore y Universidad politecnica de Valencia

We compare the mixing of a dyed and a clear fluid by constant and time-dependent flows inside a transparent Hele-Shaw cell (length: 400 mm, width 50 mm, aperture H = 0.4 mm) with randomly distributed circular obstacles (diameter d = 1.4 mm, height H) covering 20% of the area of the cell walls^{5}. A dyed and atransparent solution of same viscosity (1.8 mPa.s) and density (1.95 g/cm^{3}) with a dye diffusion coefficientD_{m} = 4.06 10-4 mm^{2}/s are initially separated by a linear front perpendicular to the mean flow parallelto the length. Three types of experiments are performed: transmission in which the mean flow velocity Uis constant, echo^{2} in which flow is reversed after a preset time Tinv (penetration distance T_{inv} U) andoscillating flow^{4} with a sinusoidal flow rate variation of period T, amplitude A and zero mean value. Theinstantaneous concentration map is obtained by measuring light absorption through the cell with a suitablecalibration. One determines at any given time the mean location and width of the front: their variation withtime over a chosen time lapse provides a global dispersivity l_{d} = D/U and mean velocity U.Reference transmission experiments performed at different Péclet numbers (Pe = UH/D_{m}) show, for 1 \ltPe \lt 30 a geometrical dispersion regime (ld \eqsim cst)^{1,3} associated to the flow disorder introduced bythe obstacles and, for Pe \gt 30, Taylor dispersion with ld \propto Pe (for Pe \lt 1 molecular diffusion would bedominant with ld \propto 1/Pe).Echo dispersion experiments with only one injection?suction cycle provide a dispersivity significantly largerat the end of the injection (t = T_{inv}) than of the cycle (t = 2 T_{inv}), implying a partial reversibility ofdispersion with respect to the flow reversal. Both ld(T_{inv}) and ld(2 T_{inv}) increase with Tinv and reachdifferent limits l_{d}^{trans}> l_{d}^{eco} at long times This is illustrated by comparing the the displacementfronts contours at t = T_{inv} and 2 T_{inv}For oscillating flows, geometrical dispersion only occurs for large oscillation amplitudes (A = 8 and 40 mm)and up to Péclet numbers Pec = 80 and 300 increasing with A: the corresponding dispersivity is smaller thanfor transmission and increases with A. Above Pe_{c}(A), the results are similar to those obtained for flat cellwalls^{4} and depend of the ratio \tau_{m}/T of the transverse diffusion time H^{2}/D_{m} and the period T. For\tau_{m}/T \ll 1 one has quasi-stationary Taylor dispersion modulated with the period T and, for \tau_{m}/T\gg 1, partly reversible Taylor dispersion in which the periodic distortions of the front follow those of thePoiseuille profile. Compared to echo experiments, oscillating flows provide additional information when thenumber of oscillations increases: l_{d} oscillates and reaches a limit intermediate between l_{d}^{trans} andl_{d}^{eco}.