Anomalous Transport in Fracture Networks under Shear-Thinning Flow

Abstract

Seminar given at IDAEA-CSIC, Barcelona. Shear-thinning fluids are injected into fractured rock by design, in drilling and fracturing operations, in enhanced oil recovery, in remediation and in enhanced geothermal systems. This talk asks whether the rheology changes only how much fluid flows, or also how solutes spread. Flow is computed on two-dimensional discrete fracture networks with an Ellis constitutive law, lubrication within fractures and mass conservation at intersections, over 100 realisations of four network families and five fluid-forcing combinations. Shear thinning raises the conductance exponent of a fracture from the cubic law b^3 to b^(2+1/n), so wide fractures gain conductance faster than narrow ones: the flow channels, and more volume is left behind in slow branches. The low-speed exponent of the Eulerian velocity density, f_e ~ u^(alpha-1), falls from 1 to 0.79 where apertures are least variable, and from 0.79-0.84 to 0.36-0.41 where they are most variable. That exponent controls the transport. Continuous-time random walk theory turns it into breakthrough tails t^(-2-alpha) and t^(-1-alpha) for flux-weighted and uniform injection, and displacement variance growing as t^(2-alpha). An upscaled Ornstein-Uhlenbeck CTRW, whose three inputs — the velocity distribution, the advective tortuosity and one correlation length — are all measured on the flow field with no fit to transport, reproduces mean displacement, variance and breakthrough against particle tracking on the networks. The Gaussian-copula closure is shown to be useful but not exact: the measured correlation lies below the single-scale exponential in every cell, and the memory of a particle depends on how slow it is. The main conclusion is that changing the fluid changes the transport regime, not merely the time scale. Funded by the European Union. A. Lenci acknowledges funding under the Marie Skłodowska-Curie grant agreement No. 101111216 (GEONEAT); M. Dentz acknowledges funding under the European Research Council grant agreement No. 101071836 (KARST). Views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.