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Coupled Electro-hydrodynamic Transport in Geological Fractures,

Abstract : Fractures are very common features in subsurface crystalline rocks, where they are organized in networks of interconnected elements [1]. A number of essential mechanical properties of the rock formations, such as their mechanical strength and their transport properties (hydraulic and electri- cal conductivities), are dictated by the behavior of the fracture networks. Within these networks, individual geological fractures are the basic structural unit controlling the ow of uids and the trans- port of solute chemical species. Their length is distributed over a very large range, which strongly constrains the connectivity and hydraulic behavior of the network [2]. Fracture wall roughness is responsible for ow channeling (and therefore, heterogeneity) within the fracture plane, which, at the fracture scale, impacts the fracture's transmissivitty [3, 4]. The characteristic length scale Lc at which the two fracture walls are matched [5, 6], plays a crucial role as it is the upper limit scale for ow heterogeneities [7]. When Lc is suciently large with respect to the distance between two intersections with other fractures, fracture wall roughness also impacts the distribution of uxes in-between fractures of the network [8]. The most prevalent way of computing the transport properties and transmissivitty of a rough fracture in an ecient way and without resorting to a full three-dimensional ow simulation, is to use the lubrication approximation, which leads to a Darcy ow type equation for the pressure, the Reynolds equation [3]. This method has been used extensively to simulate the ow [3, 9], as well as the electric current (without ow) through a rough fracture [10]. However, the e ect of the electrical properties of the fracture walls on the transport properties of a fracture still remains an open question, to the best of our knowledge. Since dissolved minerals and salts are ever present in the uids inside the fracture, Electrical Double Layers (EDL) almost inevitably form at the uid-solid interface [11], and their strength depends on the chemical properties of the rock and ionic strength of the uid. Therefore, the ocurrence, at the fracture scale, of externally-imposed or naturally-occurring gradients in electrical potential and/or ionic concentration, can lead to signi cant changes in the uid motion through the fracture, as compared to ows driven primarily by hydraulic head di erences. In this work, we attempt to explore the ow dynamics that result from such coupled electro- hydrodynamic forcings. To this end, we generalize the standard lubrication theory for ow, to include a description of the coupled transport of uid massn, solutes, and electrical current under application of xed di erences in hydraulic head (or pressure), electrical potential and concentration across the fracture. By invoking the requirement of conservation of volumetric ow rate, ions and electrical charge uxes, a coupled system of equations can be derived, which governs the spatial distribution of electrical potential, pressure and concentration in the bulk uid within the fracture. This system of equations is the generalization of the Reynolds equation to the coupled transport of uid mass, solutes, and electrical charges. It is solved using an iterative Finite Volume Method to gain insight into the dynamics of the coupled transport processes, in geological fractures with a realistic aperture field. We investigate in particular the role of the characteristic length scale Lc.
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Submitted on : Monday, March 25, 2019 - 4:08:31 PM
Last modification on : Friday, April 5, 2019 - 8:18:08 PM


  • HAL Id : insu-02078818, version 1


Uddipta Ghosh, Tanguy Le Borgne, Yves Méheust. Coupled Electro-hydrodynamic Transport in Geological Fractures,. Computer Methods in Water Resources (CMWR) 2018, Jun 2018, Saint-Malo, France. ⟨insu-02078818⟩



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