[S-EM12] Electric, magnetic and electromagnetic survey technologies and scientific achievements

[SEM12-02] Improvement of empirical equations for estimating the electrical conductivity of smectite-bearing rocks: A numerical simulation approach

*青山 健太郎¹、橋本 武志¹ (1.北海道大学)

キーワード：電気伝導度、スメクタイト

Previous studies have proposed equations to calculate the bulk electrical conductivity of rock from temperature, salinity, porosity, and clay mineral content to interpret the conductivity of rocks containing clay minerals. However, in many cases, those equations have only been validated under limited conditions. To overcome this problem, we performed numerical simulations computing the electrical conductivity of ternary mixtures of aqueous NaCl solution, quartz, and smectite in arbitrary proportions over a wide range of temperatures and salinities and verified whether the equations proposed in the previous studies could reproduce the synthetic data. In our simulations, the conductivity tensor of each element and the surface conductance of the solid-liquid boundary were calculated based on previous studies, such as electrical double-layer models, and those elements were randomly or anisotropically assigned to a discretized three-dimensional model space to compute the DC conductivity by the finite element method. Using this simulator, we computed the bulk conductivity at various temperatures (0–200°C), salinities (10^-4–5 mol kg-1), porosities (0–1), and volume fractions of smectite in the solid phase (0–1). Since the conductivity of each element can be calculated accurately at those temperature and salinity ranges, and the simulator was able to reproduce the experimental data of electrical conductivity measurements from the previous studies, the synthetic data are deemed valid. Using this simulator, we found a region of decreasing bulk conductivity with increasing salt concentration and porosity below 1 mol kg^-1 NaCl if rocks contain smectites. Then, those synthetic data were fitted by the empirical equations. We found that the constant clay conductivity (σ_c) in the empirical equation of Qi and Wu (2022) based on the effective medium theory can be modified to a quadratic function of fluid conductivity (σ_w); i.e., σ_c∝aσ_w²+bσ_w+c where a, b, and c are free parameters. This modification gives a better fit with a smaller AIC, and is also supported by the molecular dynamics simulation and the analysis using the effective medium theory. The modified equation is expected to be widely applicable in interpreting low-resistivity structures in shallow subsurface.