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.

We investigated systematically the micromechanics of compaction in two carbonates of porosity above 30%, Majella grainstone and Saint Maximin limestone. The composition, grain size and pore surface area of these rocks were determined. Hydrostatic compression experiments were performed under dry and wet conditions beyond the onset of grain crushing. A significant water weakening effect was observed in both rocks. A set of conventional triaxial experiments was also performed on both rocks under dry conditions at confining pressures ranging from 3 to 31 MPa. Microstructural observations were carried out on the deformed samples. The mechanical behavior of these high porosity carbonates is dominated by shear-enhanced compaction associated in most cases with strain hardening. Stress-induced cracking and grain crushing are the dominant micromechanisms of deformation in both rocks. In Majella grainstone, compactive shear bands appeared at low confinement, in qualitative agreement with the deformation bands observed in the field. At higher confining pressures, compaction localization was inhibited and homogeneous cataclastic flow developed. In Saint Maximin limestone, compaction localization was observed at all confining pressures. An increasing number of compactive shear bands at various orientations appeared with increasing strain. These new data suggest that compaction localization is important in the mechanical compaction of high porosity carbonates.

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High-quality streaming potential coupling coefficient measurements have been carried out using a newly designed cell with both a steady state methodology and a new pressure transient approach. The pressure transient approach has shown itself to be particularly good at providing high-quality streaming potential coefficient measurements as each transient increase or decrease allows thousands of measurements to be made at different pressures to which a good linear regression can be fitted. Nevertheless, the transient method can be up to 5 times as fast as the conventional measurement approaches because data from all flow rates are taken in the same transient measurement rather than separately. Test measurements have been made on samples of Berea and Boise sandstone as a function of salinity (approximately 18 salinities between 10 À5 mol/dm 3 and 2 mol/dm 3 ). The data have also been inverted to obtain the zeta potential. The streaming potential coefficient becomes greater (more negative) for fluids with lower salinities, which is consistent with existing measurements. Our measurements are also consistent with the high-salinity streaming potential coefficient measurements made by Vinogradov et al. (2010). Both the streaming potential coefficient and the zeta potential have also been modeled using the theoretical approach of . This modeling allows the microstructural, electrochemical, and fluid properties of the saturated rock to be taken into account in order to provide a relationship that is unique to each particular rock sample. In all cases, we found that the experimental data were a good match to the theoretical model.

Fluid permeability is one of the most important characteristics of a hydrocarbon reservoir, and is described by a number of empirical and theoretical models. We have taken four of the most important models, each of which is derived from a different physical approach, and have rewritten them in a generic form that implies a characteristic scale length and scaling constant for each model. The four models have been compared theoretically and using experimental data from 22 bead packs and 188 rock cores from a sand-shale sequence in the U. K. sector of the North Sea. The Kozeny-Carman model did not perform well because it takes no account of the connectedness of the pore network and should no longer be used. The other three models ͑Schwartz, Sen, and Johnson ͓SSJ͔; Katz and Thompson ͓KT͔; and the Revil, Glover, Pezard, and Zamora ͓RGPZ͔͒ all performed well when used with their respective length scales and scaling constants. Surprisingly,we found that the SSJ and KT models are extremely similar, such that their characteristic scale lengths and scaling constants are almost identical even though they are derived using extremely different approaches: The SSJ model by weighting the Kozeny-Carman model using the local electrical field, and the KT model by using entry radii from fluid imbibition measurements. The experimentally determined scaling constants for each model were found to be c SSJ Ϸ c KT Ϸ 8 / 3 Ϸ c RGPZ / 3. Use of these models with AC electrokinetic theory has also allowed us to show that these scaling constants are also related to the a value in the RGPZ model and the m* value in time-dependent electrokinetic theory and then to derive a relationship between the electrokinetic transition frequency and the RGPZ scale length, which we have validated using experimental data. The practical implication of this work for permeability prediction is that the KT model should be used when fluid imbibition data are available, whereas the RGPZ model should be used when electrical data are available. where the permeability, k KC , is expressed in terms of the KC hydraulic radius, the formation factor F, a constant c KC , and a length scale r KC , where r KC ‫ס‬ 2V p / S p , i.e., twice the ratio of the pore volume, V p ,

[1] Two triaxial compression experiments were performed on Carrara marble at high confining pressure, in creep conditions across the brittle-ductile transition. During cataclastic deformation, elastic wave velocity decrease demonstrated damage accumulation (microcracks). Keeping differential stress constant and reducing normal stress induced transient creep events (i.e., fast accelerations in strain) due to the sudden increase of microcrack growth. Tertiary creep and brittle failure followed as damage came close to criticality. Coalescence and rupture propagation were slow (60 -200 seconds with $150 MPa stress drops and millimetric slips) and radiated little energy in the e x p e r i m e n t a l f r e q u e n c y r a n g e ( 0 . 1 -1 M H z ). Microstructural analysis pointed out strong interactions between intra-crystalline plastic deformation (twinning and dislocation glide) and brittle deformation (microcracking) at the macroscopic level. Our observations highlight the dependence of acoustic efficiency on the material's rheology, at least in the ultrasonic frequency range, and the role played by pore fluid diffusion as an incubation process for delayed failure triggering. Citation: Schubnel,

A large number (1253) of high-quality streaming potential coefficient (C sp ) measurements have been carried out on Berea, Boise, Fontainebleau, and Lochaline sandstones (the latter two including both detrital and authigenic overgrowth forms), as a function of pore fluid salinity (C f ) and rock microstructure. All samples were saturated with fully equilibrated aqueous solutions of NaCl (10 −5 and 4.5 mol/dm 3 ) upon which accurate measurements of their electrical conductivity and pH were taken. These C sp measurements represent about a fivefold increase in streaming potential data available in the literature, are consistent with the pre-existing 266 measurements, and have lower experimental uncertainties. The C sp measurements follow a pH-sensitive power law behaviour with respect to C f at medium salinities (C sp = − 1.44 × 10 −9 C − 1.127 f , units: V/Pa and mol/dm 3 ) and show the effect of rock microstructure on the low salinity C sp clearly, producing a smaller decrease in C sp per decade reduction in C f for samples with (i) lower porosity, (ii) larger cementation exponents, (iii) smaller grain sizes (and hence pore and pore throat sizes), and (iv) larger surface conduction. The C sp measurements include 313 made at C f > 1 mol/dm 3 , which confirm the limiting high salinity C sp behaviour noted by Vinogradov et al., which has been ascribed to the attainment of maximum charge density in the electrical double layer occurring when the Debye length approximates to the size of the hydrated metal ion. The zeta potential (ζ ) was calculated from each C sp measurement. It was found that ζ is highly sensitive to pH but not sensitive to rock microstructure. It exhibits a pH-dependent logarithmic behaviour with respect to C f at low to medium salinities (ζ = 0.01133 log 10 (C f ) + 0.003505, units: V and mol/dm 3 ) and a limiting zeta potential (zeta potential offset) at high salinities of ζ o = − 17.36 ± 5.11 mV in the pH range 6-8, which is also pH dependent. The sensitivity of both C sp and ζ to pH and of C sp to rock microstructure indicates that C sp and ζ measurements can only be interpreted together with accurate and equilibrated measurements of pore fluid conductivity and pH and supporting microstructural and surface conduction measurements for each sample.