[S-CG56] Dynamics in mobile belts

[SCG56-P09] Numerical experiments on electrical conduction in fluid-saturated tight rocks

*Tohru Watanabe¹ (1.Faculty of Sustainable Design, University of Toyama)

Keywords:electrical conductivity, fluid, crack

Numerical experiments were conducted to understand the electrical conduction in fluid-saturated tight rocks. We consider tight rocks like granites, in which the electrical current can flow through interconnected grain boundary cracks. Our problems are following: (1) When open grain boundaries have the same conductance, how does the bulk conductance depend on the fraction of open grain boundary? (2) How is the bulk conductance affected by the variation in the open grain boundary conductance? For simplicity, a 2D 50×50 square lattice is used to model a network of grain boundaries. Grain boundaries are randomly opened to a given fraction (0.5~0.8), and the interconnection of open grain boundaries is examined. The electrical current in the lattice is calculated with the finite difference method. The conductance ratio of the open to closed grain boundaries is assumed to be 10⁴. The electrical current flows preferentially through open grain boundaries. For a fraction of open grain boundary, 50 distributions of open grain boundaries are examined. When the fraction of open grain boundary is smaller than 0.55, no interconnected path over a system is formed from open grain boundaries. When the fraction is 0.55, open grain boundaries rarely form an interconnected path over a system. When the fraction is larger than 0.65, open grain boundaries form a connected path over a system. Most open grain boundaries are incorporated in the connected path. The bulk conductance is close to the open grain boundary conductance and its variance is quite small. The bulk conductance is insensitive to the conductance change in a small fraction of open grain boundaries. Between the fraction of 0.55 and 0.65, large variances of bulk conductance are observed. The conductance is low without an interconnected path over a system, while it is relatively high with an interconnected path. However, a lot of open grain boundaries are still isolated from the interconnected path. When the conductance is dropped in a fraction of open grain boundaries, it can lead to a large drop in the bulk conductance. The critical fraction for the interconnection varies with the geometry of lattice. It decreases with increasing coordination number of a network. However, qualitatively similar behavior of the bulk conductance is expected in other lattices. Numerical experiments on 3D lattices and implications for measured electrical conductivity in brine-saturated granitic rocks will also be discussed in this presentation.