Non-Darcian flow experiments of shear-thinning fluids through rough-walled rock fractures

Understanding non-Darcian flow of shear-thinning fluids through rough-walled rock fractures is of vital importance in a number of industrial applications such as hydrogeology or petroleum engineering. Different laws are available to express the deviations from linear Darcy law due to inertial pressure losses. In particular, Darcy’s law is often extended through addition of quadratic and cubic terms weighted by two inertial coefficients depending on the strength of the inertia regime. The relations between the effective shear viscosity of the fluid and the apparent viscosity in porous media when inertial deviations are negligible were extensively studied in the past. However, only recent numerical works have investigated the superposition of both inertial and shear-thinning effects, finding that the same inertial coefficients obtained for non-Darcian Newtonian flow applied in the case of shear-thinning fluids. The objective of this work is to experimentally validate these results, extending their applicability to the case of rough-walled rock fractures. To do so, flow experiments with aqueous polymer solutions have been conducted using replicas of natural fractures, and the effects of polymer concentration, which determine the shear rheology of the injected fluid, have been evaluated. Our findings show that the experimental pressure loss-flow rate data for inertial flow of shear-thinning fluids can be successfully predicted from the empirical parameters obtained during non-Darcian Newtonian flow and Darcian shear-thinning flow in a given porous medium

Les Institutions internationales régionales en Afrique occidentale et centrale , par Francis Wodie,..

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From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation

This work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The structures under concern, representative of real systems for many applications, are composed of cylinders of square cross section for values of the porosity ranging from 15% to 96%. The critical Reynolds number at the bifurcation is determined for incompressible isothermal Newtonian fluid flow by Direct Numerical Simulations (DNS) based on a finite volume discretization method that is second order accurate in space and time. It is shown that for ordered square periodic structures, the critical Reynolds number increases when the porosity decreases and strongly depends on the choice of the Representative Elementary Volume on which periodic boundary conditions are employed. The flow orientation with respect to the principal axes of the structure is also shown to have a very important impact on the value of the Reynolds number of the bifurcation. When structural disorder is introduced, the critical Reynolds number decreases very significantly in comparison to the ordered structure having the same porosity. Correlations between the critical Reynolds number and the porosity are obtained on both ordered and disordered structures over wide range of porosities. A frequency analysis is performed on one of the velocity components to investigate pre- and post-bifurcation flow characteristics