Relating the permeability of quartz sands to their grain size and spectral induced polarization characteristics

Recently, Revil & Florsch proposed a novel mechanistic model based on the polarization of the Stern layer relating the permeability of granular media to their spectral induced polarization (SIP) characteristics based on the formation of polarized cells around individual grains. To explore the practical validity of this model, we compare it to pertinent laboratory measurements on samples of quartz sands with a wide range of granulometric characteristics. In particular, we measure the hydraulic and SIP characteristics of all samples both in their loose, non-compacted and compacted states, which might allow for the detection of polarization processes that are independent of the grain size. We first verify the underlying grain size/permeability relationship upon which the model of Revil & Florsch is based and then proceed to compare the observed and predicted permeability values for our samples by substituting the grain size characteristics by corresponding SIP parameters, notably the so-called Cole-Cole time constant. In doing so, we also asses the quantitative impact of an observed shift in the Cole-Cole time constant related to textural variations in the samples and observe that changes related to the compaction of the samples are not relevant for the corresponding permeability predictions. We find that the proposed model does indeed provide an adequate prediction of the overall trend of the observed permeability values, but underestimates their actual values by approximately one order-of-magnitude. This discrepancy in turn points to the potential importance of phenomena, which are currently not accounted for in the model and which tend to reduce the characteristic size of the prevailing polarization cells compared to the considered model, such as, for example, membrane polarization, contacts of double-layers of neighbouring grains, and incorrect estimation of the size of the polarized cells because of the irregularity of natural sand grain

Theory of transient streaming potentials associated with axial-symmetric flow in unconfined aquifers

We present a semi-analytical solution for the transient streaming potential response of an unconfined aquifer to continuous constant rate pumping. We assume that flow occurs without leakage from the unit below a transverse anisotropic aquifer and neglect flow in the unsaturated zone by treating the water-table as a moving material boundary. In the development of the solution to the streaming potential problem, we impose insulating boundary conditions at land surface and the lower boundary of the lower confining unit. We solve the problem exactly in the double Laplace—Hankel transform space and obtain the inverse transforms numerically. The solution is used to analyse transient streaming potential data collected during dipole hydraulic tests conducted at the Boise Hydrogeophysical Research Site in 2007 June. This analysis yields estimates of aquifer hydraulic parameters. The estimated hydraulic parameters, namely, hydraulic conductivity, transverse hydraulic anisotropy, specific storage and specific yield, compare well to published estimates obtained by inverting drawdown data collected at the field site

Predicting permeability from the characteristic relaxation time and intrinsic formation factor of complex conductivity spectra

Low-frequency quadrature conductivity spectra of siliclastic materials exhibit typically a characteristic relaxation time, which either corresponds to the peak frequency of the phase or the quadrature conductivity or a typical corner frequency, at which the quadrature conductivity starts to decrease rapidly toward lower frequencies. This characteristic relaxation time can be combined with the (intrinsic) formation factor and a diffusion coefficient to predict the permeability to flow of porous materials at saturation. The intrinsic formation factor can either be determined at several salinities using an electrical conductivity model or at a single salinity using a relationship between the surface and quadrature conductivities. The diffusion coefficient entering into the relationship between the permeability, the characteristic relaxation time, and the formation factor takes only two distinct values for isothermal conditions. For pure silica, the diffusion coefficient of cations, like sodium or potassium, in the Stern layer is equal to the diffusion coefficient of these ions in the bulk pore water, indicating weak sorption of these couterions. For clayey materials and clean sands and sandstones whose surface have been exposed to alumina (possibly iron), the diffusion coefficient of the cations in the Stern layer appears to be 350 times smaller than the diffusion coefficient of the same cations in the pore water. These values are consistent with the values of the ionic mobilities used to determine the amplitude of the low and high-frequency quadrature conductivities and surface conductivity. The database used to test the model comprises a total of 202 samples. Our analysis reveals that permeability prediction with the proposed model is usually within an order of magnitude from the measured value above 0.1 mD. We also discuss the relationship between the different time constants that have been considered in previous works as characteristic relaxation time, including the mean relaxation time obtained from a Debye decomposition of the spectra and the Cole-Cole time constant

Modelling the induced polarization of bentonite-sand mixtures

International audienceSpectral induced polarization (SIP) has become an increasingly popular geophysical method for hydrogeological and environmental applications. These applications include for instance the non-intrusive characterization of the textural and interfacial physicochemical properties of bentonites used as permeability barriers in landfills or to store various types of contaminants including radioactive wastes. Bentonites are mainly constituted of smectites, which have very high specific surface areas (SSA) and cation exchange capacities (CEC). Therefore, these minerals have very high electromigration and polarization current densities responsible for very high in phase and quadrature conductivities, respectively. In addition, in diluted water, the diffuse layer of smectites occupies a large fraction of the pore space and may be therefore considered as part of the pore space. In our approach [1], complex electrical conductivities of saturated unconsolidated bentonite and bentonite-sand mixtures are modeled at different salinities (NaCl) of the bulk pore water using a Donnan equilibrium model coupled to the revisited SIP model of Leroy and Revil [2]. Our complex surface conductivity model considers the DC contribution of the diffuse and Stern layers as well as the electrochemical polarization of the Stern layer coating the grains with different sizes. The macroscopic SIP model is based on the differential effective medium theory and considers the complex surface conductivity of the sand and smectite grains and the complex conductivity of the pore space. In our model, the diffuse layer of quartz sands occupies a small fraction of the pore space and is considered therefore as part of the surface of the grains. Our SIP model predicts very well the low frequency (0.1 Hz - kHz) complex electrical conductivities of bentonite and bentonite-sand mixtures, except for very low frequencies (< 0.1 Hz) where membrane polarization may occur (Figure 1). The in phase conductivity of the sample with a high clay content (20 % in volume) increases slowly with salinity because of the very high DC surface conductivity of smectite. The observed large increase of the in phase and quadrature conductivity of the samples with the clay content (1, 20 and 100% in volume) is also predicted by our model. The quadrature conductivity of the samples with a high clay content is fairly independent on the pore fluid salinity because it is strongly connected with the SSA, CEC and Stern layer of smectite (Figure 1). The in phase conductivity of the sample with a low clay content (1% in volume) increases quickly with the salinity because of its low DC surface conductivity. Its quadrature conductivity also increases quickly with salinity because of the formation of the Stern layer at the surface of quartz sand. Nevertheless, our SIP model can't predict the quadrature conductivity spectra observed at very low frequencies (< 10-1 Hz). The missing polarization mechanism may correspond to membrane polarization and there is an effort to be done to incorporate this contribution in a unified model

Modeling the evolution of spectral induced polarization during calcite precipitation on glass beads

International audienceWhen pH and alkalinity increase, calcite frequently precipitates and hence modifies the petrophysical properties of porous media. The complex conductivity method can be used to directly monitor calcite precipitation in porous media because it is very sensitive to the evolution of the pore structure and its connectivity. We have developed a mechanistic grain polarization model considering the electrochemical polarization of the Stern layer surrounding calcite particles. This model depends on the surface charge density and mobility of the counter-ions in the Stern layer. Our induced polarization model predicts the evolution of the size of calcite particles, of the pore structure and connectivity during spectral induced polarization experiments of calcite precipitation on glass beads pack. Model predictions are in very good agreement with the complex conductivity measurements. During the first phase of calcite precipitation experiment, calcite crystals growth, and the inverted particle size distribution moves towards larger calcite particles. When calcite continues to precipitate and during pore clogging, inverted particle size distribution moves towards smaller particles because large particles do not polarize sufficiently. The pore clogging is also responsible for the decrease of the connectivity of the pores, which is observed through the increasing electrical formation factor of the porous medium

Importance of structural history in the summit area of Stromboli during the 2002–2003 eruptive crisis inferred from temperature, soil CO2, self-potential, and electrical resistivity tomography

International audienceThe 2002-2003 eruptive crisis of Stromboli volcano in the Aeolian Islands raised the question of how to assess the stability of the flanks of this volcanic edifice during such a crisis. To provide a response to this question, we analyzed a detailed fluid flow mapping plus the reiteration of a profile located in the vicinity of the active vents using the self-potential method, temperature data, soil-gas (CO2) measurements, and electric resistivity tomography. Coupling the interpretation of these methods that are sensitive to the flow of gas and water in the ground indicates the position of areas of mechanical weakness. In addition, they can be used to monitor the change in the discharge of fluids associated with these features before and during the 2002-2003 eruptive crisis. Our results emphasize the importance of old structural boundaries, such as the Large Fossa crater, in the development of the new set of fractures observed during the 2002-2003 eruptive crisis. Between October 2002 and January 2003, the use of CO2 soil-gas technique evidenced an increase in the discharge of CO2 outside the Large Fossa crater boundaries, along the failure boundary of the southern Sciara del Fuoco area. Self-potential and temperature measurements made before the 2002-2003 eruptive crisis reveal significant changes along the main structural boundaries of the Fossa area. The development of these anomalies is interpreted as an increase of the permeability of the structure from May 2000 to May 2002. Between January 2003 and March 2003 the reiteration of self-potential, temperature, and CO2 measurements shows an increase of fluid discharge along weakness planes located inside the Large Fossa crater boundary. They evidence no change outside this structural boundary. The importance of the Large Fossa crater boundary in controlling the deformation and fluid flow from January to March 2003 has been attested by the development of the fractures inside the Large Fossa crater boundary, and also with a network of electrooptical distance measurement stations located inside and outside this ancient crater. This multidisciplinary approach to fluid flow assessment before and during an eruptive crisis is complementary to geodetic measurements of the deformation of the edifice. It demonstrates for the first time the powerful potential of combining electrical resistivity tomography, self-potential, temperature, and soil CO2 measurements in assessing the position of the planes of mechanical weakness in a volcanic edifice

Quadrature conductivity: A quantitative indicator of bacterial abundance in porous media

The abundance and growth stages of bacteria in subsurface porous media affect the concentrations and distributions of charged species within the solid-solution interfaces. Therefore, spectral induced polarization (SIP) measurements can be used to monitor changes in bacterial biomass and growth stage. Our goal was to gain a better understanding of the SIP response of bacteria present in a porous material. Bacterial cell surfaces possess an electric double layer and therefore become polarized in an electric field. We performed SIP measurements over the frequency range of 0.1–1 kHz on cell suspensions alone and cell suspensions mixed with sand at four pore water conductivities. We used Zymomonas mobilis at four different cell densities (including the background). The quadrature conductivity spectra exhibited two peaks, one around 0.05–0.10 Hz and the other around 1–10 Hz. Because SIP measurements on bacterial suspensions are typically made at frequencies greater than 1 Hz, these peaks have not been previously reported. In the bacterial suspensions in growth medium, the quadrature conductivity at peak I was linearly proportional to the density of the bacteria. For the case of the suspensions mixed with sands, we observed that peak II presented a smaller increase in the quadrature conductivity with the cell density. A comparison of the experiments with and without sand grains illustrated the effect of the porous medium on the overall quadrature conductivity response (decrease in the amplitude and shift of the peaks to the lower frequencies). Our results indicate that for a given porous medium, time-lapse SIP has potential for monitoring changes in bacterial abundance within porous media

Near-Surface Imaging of a Hydrogeothermal System at Mount Princeton, Colorado Using 3D Seismic, Self-Potential, and DC Resistivity Data

The Upper Arkansas Valley in the Rocky Mountains of central Colorado is the northernmost extensional basin of the Rio Grande Rift(Figure 1). The valley is a half graben bordered to the east and west by the Mosquito and Sawatch ranges,respectively. The Sawatch Range is home to the Collegiate Peaks,which include some of the highest summits in the Rocky Mountains. Some Collegiate Peaks over 4250 m (14,000 ft) from north to south include Mount Harvard, Mount Yale, Mount Princeton,and Mount Antero. The Sawatch range-front normal fault strikes north-northwest along the eastern margin of the Collegiate Peaks and is characterized by a right-lateral offset between the Mount Princeton batholith and Mount Antero. This offset in basin-bounding faults is accommodated by a northeast-southwest dextral strike-slip transfer fault (Richards et al.,2010) and coincides with an area of hydrogeothermal activity and Mount Princeton Hot Springs. This transfer fault is here termed the Chalk Creek fault due to it\u27s alignment with the Chalk Creek valley. A 250-m high erosional scarp, called the Chalk Cliffs, lies along the northern boundary of this valley.The cliffs are geothermally altered quartz monzonite and not chalk.These cliffs coincide with the Chalk Creek fault, whose intersection with the Sawatch range-front normal fault results in a primary pathway for upwelling geothermal waters

Induced polarization of clay-sand mixtures: experiments and modelling

Frequency-domain induced polarization (IP) measurements consist of imposing an alternative sinusoidal electrical current (AC) at a given frequency and measuring the resulting electrical potential difference between two other non-polarizing electrodes. The magnitude of the conductivity and the phase lag between the current and the difference of potential can be expressed into a complex conductivity with the in-phase representing electromigration and a quadrature conductivity representing the reversible storage of electrical charges (capacitive effect) of the porous material. Induced polarization has become an increasingly popular geophysical method for hydrogeological and environmental applications [1]. These applications include for instance the characterization of clay materials used as permeability barriers in landfills or to contain various types of contaminants including radioactive wastes [2]. The goal of our study is to get a better understanding of the influence of the clay content, clay mineralogy, and pore water salinity upon complex conductivity measurements of saturated clay-sand mixtures in the frequency range ~ 1 mHz-12 kHz. The complex conductivity of saturated unconsolidated sand-clay mixtures was experimentally investigated using two types of clay minerals, kaolinite and smectite in the frequency range 1.4 mHz - 12 kHz. Four different types of sample were used, two containing mainly kaolinite (80% of the mass, the remaining containing 15% of smectite and 5% of illite/muscovite; 95% of kaolinite, 5% of illite/muscovite), and the two others containing mainly Na-smectite or Na-Ca-smectite (95% of the mass; bentonite). The experiments were performed with various clay contents (1, 5, 20, and 100 % in volume of the sand-clay mixture) and salinities (distilled water, 0.1 g/L, 1 g/L, and 10 g/L NaCl solution). In total, 44 saturated clay or clay-sand mixtures were prepared. Induced polarization measurements were performed with a cylindrical four-electrode sample-holder (cylinder made of PVC with 30 cm in length and 19 cm in diameter) associated with a SIP-Fuchs II impedance meter and non-polarizing Cu/CuSO4 electrodes (Figure 1). These electrodes were installed at 10 cm from the base of the sample holder and regularly spaced (each 90 degree). The results illustrate the strong impact of the Cationic Exchange Capacity (CEC) of the clay minerals upon the complex conductivity. The amplitude of the in-phase conductivity of the kaolinite-clay samples is strongly dependent to saturating fluid salinity (Figure 2) for all volumetric clay fractions, whereas the in-phase conductivity of the smectite-clay samples is quite independent on the salinity, except at the low clay content (5% and 1% of clay in volume). This is due to the strong and constant surface conductivity of smectite associated with its very high CEC. The quadrature conductivity increases steadily with the CEC and the clay content. We observe that the dependence on frequency of the quadrature conductivity of sand-kaolinite mixtures is more important than for sand-bentonite mixtures. For both types of clay, the quadrature conductivity seems to be fairly independent on the pore fluid salinity (Figure 2) except at very low clay contents (1% kaolinite-clay in volume). This is due to the constant surface site density of Na counter-ions in the Stern layer of clay materials [3]. At the lowest clay content (1%), the magnitude of the quadrature conductivity increases with the salinity, as expected for silica sands. In this case, the surface site density of Na counter-ions in the Stern layer increases with salinity [4]. The experimental data show good agreement with predicted values given by our Spectral Induced Polarization (SIP) model [4]. This complex conductivity model considers the electrochemical polarization of the Stern layer coating the clay particles and the Maxwell-Wagner polarization. We use the differential effective medium theory to calculate the complex conductivity of the porous medium constituted of the grains and the electrolyte. The SIP model includes also the effect of the grain size distribution upon the complex conductivity spectra. Interfacial parameters are estimated using the TLM of Sverjensky [5] for silica and the Donnan model of Tournassat and Appelo [6] for smectite