Tracer dispersion in 2‐D fractures with flat and rough walls in a radial flow geometry

IPPOLITO, I.; HINCH, E. J.; DACCORD, G.; HULIN, J. P.

Physics of Fluids A: Fluid Dynamics

AIP

Año: 1993 vol. 5 p. 1952 - 1962

0899-8213

Tracer dispersion is studied in a plane fracture geometry with a radial flow between closelyspaced parallel walls with either two smooth surfaces or one smooth and one rough surface. Anecho dispersion technique in which the fluid is first injected into the fracture during a time Tbvand then pumped back through a detector is used in the experiments and is complemented byMonte-Carlo-type numerical simulations, For the smooth wall case, the Taylor dispersionmechanism is dominant when longitudinal molecular diffusion is negligible: it is verifiednumerically and experimentally that its transition to irreversibility only depends on the ratio ofTi, to the transverse diffusion time 7, across the fracture thickness. In addition, the variationof AT2/(4Ti,,rm) with respect to Tiny/rm is the same as for a flow of parallel geometry(AT2 being the mean square deviation of the transit time). Longitudinal molecular diffusionincreases the global dispersion like T,,/( PeQrm) at low P&let numbers PeQ and long times dueto the longitudinal velocity gradient. When one of the walls is rough, one expects to have ageometrical dispersion locally proportional to the velocity. A corresponding linear variation ofAT2/(4Ti,vT,) with respect to dm is observed experimentally.