Anisotropy of tracer dispersion in rough model fractures with sheared walls

arXiv:0810.0519v1 [physics.geo-ph] 2 Oct 2008 Anisotropy of tracer dispersion in rough model fractures with sheared walls. Boschan A.a,b, Auradou H.a, Ippolito I.b, ChertcoffR.b, Hulin J.P.a aUniv Pierre et Marie Curie-Paris6, Univ Paris-Sud, CNRS, F-91405. Lab FAST, Bat 502, Campus Univ, Orsay, F-91405, France. bGrupo de Medios Porosos, Departemento de F´ısica, Facultad de Ingenier´ıa, Universitad de Buenos Aires, Paseo Col´on 850, 1063 Buenos-Aires, Argentina. Abstract Dispersion experiments are compared for two transparent model fractures with identical complementary rough walls but with a relative shear displacement ⃗δ parallel (⃗δ ∥⃗U) or perpendicular (⃗δ ⊥⃗U) to the flow velocity ⃗U. The structure of the mixing front is characterized by mapping the local normalized local transit time ¯t(x, y) and dispersivity α(x, y). For ⃗δ ⊥⃗U, displacement fronts display large fingers: their geometry and the distribution of ¯t(x, y)U/x are well reproduced by assuming parallel channels of hydraulic conductance deduced from the aperture field. For ⃗δ ∥⃗U, the front is flatter and α(x, y) displays a narrow distribution and a Taylor-like variation with Pe. Channelization is a key characteristic of flow and transport in fractured rocks ([12]) and results frequently from the occurence of relative shear displacements of the two fracture surfaces during fracturation ([14, 8]). Such displacements (named ⃗δ thereafter) have been shown both experimentally and numerically ([11, 1]) to create channels and ridges perpendicular to ⃗δ. Their length depends on the multiscale geometry of the frac- ture walls and, even for small amplitudes δ, may be a significant fraction of the fracture size. The permeabil- ity is then anisotropic: both its value and the correlation length of the velocity field are higher for a mean flow parallel to these channels (i.e. perpendicular to ⃗δ). The objective of this communication is to demon- strate experimentally that this type of channelization also induces a strong anisotropy of the magnitude and properties of tracer dispersion. This is achieved by com- paring dispersion for mean flows parallel and perpendic- ular to the direction of the channels, but with identical flow parameters and geometry otherwise. A previous work ([4]) studied dispersion in one similar model (with a lower value of δ) but with the different objective of an- alyzing the influence of the fluid rheology. Here, the dy- namics of the process, i.e. the variation with distance of the geometry and thickness of the mixing front is more specifically compared in the parallel and perpendicular configurations. Many experiments on solute spreading in fractures have been reported: [13, 9, 10] observed dispersion co- efficients D increasing linearly with the mean flow ve- locity U (i.e. the dispersivity α = D/U is constant). However, these measurements were all realized at the outlet of the sample with no information on the develop- ment of the mixing front with distance. Measurements by [15] used radioactive tracers, still with a resolution too low to investigate local spreading. In all these pa- pers, the anisotropy of dispersion is not investigated and (except for [10]) little information is available on the relative position of the fracture walls. We use transparent model fractures allowing for high resolution optical concentration measurements over their full area. The models are mounted vertically be- tween a light panel and a 16 bits Roper digital camera. Fluid flow takes place between two self-affine rectangu- lar rough walls of same characteristic exponent H = 0.8 as in many fractured rocks ([16]). The mean flow ve- locity ⃗U is parallel to the length Lx = 350 mm of the walls (their width is Ly = 90 mm). The two walls are complementary and identical in the two models and they match perfectly when put in contact; then, they are pulled away normal to their mean surface and a lateral shear ⃗δ, parallel or perpendicular to ⃗U (i.e. to x) is in- troduced. In these two configurations, referred to as ⃗δ ∥⃗U and ⃗δ ⊥⃗U, the mean velocity ⃗U is therefore respectively perpendicular and parallel to the channels created by the shear. Both δ and the mean aperture a are equal to 0.75 mm. The standard deviation of the aper- ture σa = 0.144 mm is larger than for the similar models of [4] (σa = 0.11mm): as a result, the flow field is found to be more strongly channelized. The fluids are shear thinning 1000 ppm solutions of scleroglucan in water with a high constant viscos- Preprint submitted to Elsevier October 30, 2018 ity (µ0 ≈4500 mPa.s) at low shear rates ˙γ ≤˙γ0 pre- venting the appearance of unwanted buoyancy driven flows ([17]). One has ˙γ0 = 0.026 s−1: for a viscous Newtonian flow between parallel plates at a distance a, the corresponding mean velocity is U0 = a˙γ0/6 = 3 × 10−3 mm/s. At shear rates ˙γ ≥˙γ0, the viscosity de- creases as µ ∝˙γn−1 with n = 0.26 (see [4]). One of the fluids contains 0.2 g/l of blue dye and the densities are matched by adding NaCl to the o

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