Abstract. We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous at the scale of a representative elementary volume. The wetting phase for the grains is water and the non-wetting phase is assumed to be an electrically insulating viscous fluid. We use a volume averaging approach to derive the linear constitutive equations for the electrical current density as well as and the seepage velocities of the wetting and non-wetting phases at the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as a function of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability function, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various level of saturation, and the permeability at saturation of the rock samples. We found a very good agreement between these experimental data and the model predictions.

[1] Self-potential (SP) signals that are generated under two-phase flow conditions could be used to study vadose zone dynamics and to monitor petroleum production. These streaming-potentials may also act as an error source in SP monitoring of vulcanological activity and in magnetotelluric studies. We propose a two-phase flow SP theory that predicts streaming currents as a function of the pore water velocity, the excess of charge in the pore water, and the porosity. The source currents that create the SP signals are given by the divergence of the streaming currents, and contributions are likely to be located at infiltration fronts, at the water table, or at geological boundaries. Our theory was implemented in a hydrogeological modeling code to calculate the SP distribution during primary drainage. Forward and inverse modeling of a well-calibrated 1D drainage experiment suggest that our theory can predict streaming potentials in the vadose zone. Citation: Linde, N.,

— The central uplift of the 40‐km wide Araguainha impact structure, Brazil, consists of a ring, about 8 km in diameter, of up to 150‐m high blocks of Devonian Furnas sandstone, which surround a central depression of elliptical shape (4.5 × 3.0 km). The depression is occupied by a pre‐Devonian alkali‐feldspar granite, shocked by pressures of 20–25 GPa and permeated by cataclastic shear zones and dikes of shocked granitic material. The granite is flanked and partly covered by several impact breccias: (1) Impact breccia with melt matrix overlies the granite in places and forms hills, bordering the granitic center in the S and SW. It is chemically identical with the granite and consists of thermally altered granitic clasts in a matrix of sanidine, quartz, biotite, muscovite, chlorite and riebeckite. (2) Polymict breccias form hills which border the central depression in the N and NW. Components are unshocked and shocked sediments, shock‐melted sandstone, shocked granite and shock melt rocks in irregular masses and individual bodies, embedded in a fine‐grained matrix. 40Ar/39Ar analyses show that the melt rocks solidified 246 Ma ago, indicating that the impact occurred at near the Permian‐Triassic boundary, possibly when the area was covered by a shallow sea. The present chemistry and petrography of the melt rocks suggest that by reacting with seawater granitic impact melt was depleted of K and Rb and enriched in Na, and that later diagenetic processes produced replacement of feldspar by quartz and deposition of hematite. (3) Monomict breccias, consisting of unshocked, shocked and shock‐fused quartz sandstones, form hills which surround the central depression in the SE and S. The Araguainha structure is an eroded complex crater, produced by an impact, 246 Ma ago. The depth of excavation was about 2.4 km, comprising Permian, Permo‐Carboniferous and Devonian sediments and the granitic basement. The diameter of the transient crater was about 24 km. Erosion and weathering have removed most of the original crater fill and ejecta deposits, with the exception of remnants, preserved in the central uplift.

The permeability of the Earth's crust commonly varies over many orders of magnitude. Flow velocity can range over several orders of magnitude in structures of interest that vary in scale from centimeters to kilometers. To accurately and efficiently model multiphase flow in geologic media, we introduce a fully conservative node-centered finite volume method coupled with a Galerkin finite element method on an unstructured triangular grid with a complementary finite volume subgrid. The effectiveness of this approach is demonstrated by comparison with traditional solution methods and by multiphase flow simulations for heterogeneous permeability fields including complex geometries that produce transport parameters and lengths scales varying over four orders of magnitude.

Field data‐based finite‐element simulations of flow partitioning between fractures and a permeable rock matrix reveal critical fracture aperture values that mark the transition from matrix to fracture dominated flow. For matrix permeabilities of 0.00 1–1 D, the matrix either dominates or contributes significantly to the total flow. The percentage of the flow‐normal cross‐section that is occupied by fractures, Af, strongly influences the fracture‐matrix permeability ratio, above which fractures will dominate flow. This ratio is 102–104 for Af = 10−4–10−3 (mean = 5 × 10−3), but also depends on the proportion of fractures which fully penetrate the representative elementary volume. Fluid‐velocity spectra for the fractured rock have three important characteristics: (1) Darcy velocity is only poorly correlated with permeability, (2) flow velocities have characteristic values, even if fracture‐length frequency relations are self similar, and (3) fracture and matrix velocities overlap.