Abstract. Electrokinetic phenomena are responsible for several electrical properties of fluidsaturated porous materials. Geophysical applications of these phenomena could include the use of streaming potentials for mapping subsurface fluid flow, the study of hydrothermal activity of geothermal areas, and in the context of earthquake prediction and volcanic activity forecasting, for example. The key parameter of electrokinetic phenomena is the •' potential, which represents roughly the electrical potential at the mineral/water interface. We consider silica-dominated porous materials filled with a binary symmetric 1:1 electrolyte such as NaC1. When in contact with this electrolyte, the silica/water interface gets an excess of charge through chemical reactions.Starting with these chemical reactions, we derive analytical equations for the •' potential and the specific surface conductance. These equations can be used to predict the variations of these parameters with the pore fluid salinity, temperature, and pH (within a pH range of 6-8). The input parameters to these equations fall into two categories: (1) mineral/fluid interaction geochemistry (including mineral surface site density and surface equilibrium constants of mineral/fluid reactions), and (2) pore fluid pH, salinity, and temperature. The •'potential is shown to increase with increasing temperature and pH and to decrease with increasing salinity. The proposed model is in agreement with available experimental data. The application of this model to electric potentials generated in porous media by fluid flow is explored in the companion paper.

Abstract.The electrical conductivity of rocks results from conduction through the bulk solution occupying the pores and from surface conduction occurring at the fluid/grain interface. The nature of the surface electrical conductivity of shaly and clean sands and sandstones is examined.Surface conduction is characterized by the specific surface conductance which is the sum of three contributions: (i) Conduction within the electrical diffuse layer, which makes a negligible contribution to the total specific surface conductance. (ii) Conduction in the Stern layer, which is shown to vary significantly with the salinity of the pore fluid at low salinities (10 -6 to 10 -3 mol 1-1), but becomes independent of salinity at higher salinities. (iii) A mechanism operating directly on the mineral surface, independent of salinity, and perhaps associated with proton transfer. At salinities higher than 10 -3 mol 1 -I and at 25øC, the specific surface conductance of quartz and clays is equal to 8.9x10 -9 S and 2.5x10 -9 S respectively. Equations describing the influence of surface conductivity and microstructure upon the macroscopic electrical conductivity of sands, sandstones, and shales are also developed.

We present a model describing ionic electrical conduction in porous media, with particular emphasis given to surface conduction. The porous medium is assumed to consist of an insulating matrix and an interconnected pore volume that is saturated with an electrolyte. When in contact with an electrolyte, mineral surfaces get an excess of charge that is balanced by mobile ions in an electrical diffuse layer above the surface. Electrical conduction in this diffuse layer can contribute substantially to the effective electrical conductivity of the porous medium. Our surface conduction model is based on a description of surface chemical reactions and electrical diffuse layer processes. For this purpose, we consider an amphoteric mineral surface described by a five-sitetype model. We derive the fractional occupancies of positive, negative, and neutral sites on the surface, and the fractional ionic diffuse layer densities, as a function of the salinity and the pH. Finally, the specific surface conductance used to describe the surface electrical conduction is related to the previously mentioned properties, via the electrical surface potential, and is found to be dependent on the electrolyte concentration and pH.

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The streaming potential is that electrical potential which develops when an ionic fluid flows through the pores of a rock. It is an old concept that is recently being applied in many fields from monitoring water fronts in oil reservoirs to understanding the mechanisms behind synthetic earthquakes. We have carried out fundamental theoretical modeling of the streaming-potential coefficient as a function of pore fluid salinity, pH, and temperature by modifying the HS equation for use with porous rocks and using input parameters from established fundamental theory (the Debye screening length, the Stern-plane potential, the zeta potential, and the surface conductance). The model also requires the density, electrical conductivity, relative electric permittivity and dynamic viscosity of the bulk fluid, for which empirical models are used so that the temperature of the model may be varied. These parameters are then combined with parameters that describe the rock microstructure. The resulting theoretical values have been compared with a compilation of data for siliceous materials comprising 290 streaming-potential coefficient measurements and 269 zeta-potential measurements obtained experimentally for 17 matrix-fluid combinations (e.g., sandstone saturated with KCl), using data from 29 publications. The theoretical model was found to ably describe the main features of the data, whether taken together or on a sample by sample basis. The low-salinity regime was found to be controlled by surface conduction and rock microstructure, and was sensitive to changes in porosity, cementation exponent, formation factor, grain size, pore size and pore throat size as well as specific surface conductivity. The high-salinity regime was found to be subject to a zeta-potential offset that allows the streaming-potential coefficient to remain significant even as the saturation limit is approached.

Most permeability models use effective grain size or effective pore size as an input parameter. Until now, an efficacious way of converting between the two has not been available. We propose a simple conversion method for effective grain diameter and effective pore radius using a relationship derived by comparing two independent equations for permeability, based on the electrokinetic properties of porous media. The relationship, which we call the theta function, is not dependent upon a particular geometry and implicitly allows for the widely varying style of microstructures exhibited by porous media by using porosity, cementation exponent, formation factor, and a packing constant. The method is validated using 22 glass bead packs, for which the effective grain diameter is known accurately, and a set of 188 samples from a sand-shale sequence in the North Sea. This validation uses measurements of effective grain size from image analysis, pore size from mercury injection capillary pressure (MICP) measurements, and effective pore radius calculated from permeability experiments, all of which are independent. Validation tests agree that the technique accurately converts an effective grain diameter into an effective pore radius. Furthermore, for the clastic data set, there exists a power law relationship in porosity between effective grain size and effective pore size. The theta function also can be used to predict the fluid permeability of a sample, based on effective pore radius. The result is extremely good predictions over seven orders of magnitude.

Archie's law has been the standard method for relating the conductivity of a clean reservoir rock to its porosity and the conductivity of its pore fluid for more than 60 years. However, it is applicable only when the matrix is nonconducting. A modified version that allows a conductive matrix was published in 2000. A generalized form of Archie's law is studied for any number of phases for which the classical Archie's law and modified Archie's law for two phases are special cases. The generalized Archie's law contains a phase conductivity, a phase volume fraction, and phase exponent for each of its n phases. The connectedness of each of the phases is considered, and the principle of conservation of connectedness in a three-dimensional multiphase mixture is introduced. It is confirmed that the general law is formally the same as the classical Archie's law and modified Archie's law for one and two conducting phases, respectively. The classical second Archie's law is compared with the generalized law, which leads to the definition of a saturation exponent for each phase. This process has enabled the derivation of relationships between the phase exponents and saturation exponents for each phase. The relationship between percolation theory and the generalized model is also considered. The generalized law is examined in detail for two and three phases and semiquantitatively for four phases. Unfortunately, the law in its most general form is very difficult to prove experimentally. Instead, numerical modeling in three dimensions is carried out to demonstrate that it behaves well for a system consisting of four interacting conducting phases.

The Helmholtz-Smoluchowski (HS) equation is commonly used to relate the streaming potential coupling coefficient of rocks to their zeta potential, pore fluid dielectric permittivity, conductivity, and viscosity despite it being known for almost [Formula: see text] that it does not work well for porous media. One of the problems is that the HS equation contains no implicit dependence on grain size, pore size, or pore throat size. Another has been the lack of high-quality data relating the streaming potential coupling coefficient to rock microstructural parameters. In this, predominantly experimental work, we have measured the streaming potential coupling coefficient for 12 sizes of quartz glass beads and two fluid salinities. A comparison of the new data and the existing data with the conventional HS equation and Revil’s grain size-dependent HS model shows the grain size-dependent model to be far superior in describing the data. Recognizing their utility in reservoir characterization, we have developed new equations that describe how the streaming potential coupling coefficient varies with pore diameter and pore throat diameter. We have compared experimental determinations as a function of pore throat diameter with these new relationships and found them to work very well if the ratio of the mean pore diameter to the pore throat diameter is 1.662, which is valid for random arrangement of monodisperse spheres. The zeta potential has also been calculated from the grain size-dependent HS equations and are found to be approximately constant and in agreement with the theoretically predicted values. The equations presented in this paper allow the streaming potential coupling coefficient of a reservoir rock to be calculated as a function of grain size, pore size, and pore throat size.