Dynamic Streaming Potential Coupling Coefficient in Partially Saturated Porous Media

SUMMARY Seismoelectric signals are generated by electrokinetic coupling from seismic wave propagation in fluid-filled porous media. This process is directly related to the existence of an electrical double layer at the interface between the pore fluid and minerals composing the pore walls. The seismoelectric method attracts the interest of researchers in different areas, from oil and gas reservoir characterization to hydrogeophysics, due to the sensitivity of the seismoelectric signals to medium and fluid properties. In this work, we propose a physically based model for the dynamic streaming potential coupling coefficient (SPCC) by conceptualizing a porous medium as a bundle of tortuous capillaries characterized by presenting different pore size distributions (PSD). The results show that the dynamic streaming potential coupling coefficient is a complex function depending on the properties of pore fluid, mineral–pore fluid interfaces, microstructural parameters of porous media and frequency. Parameters influencing the dynamic SPCC are investigated and explained. In particular, we show that the PSD affects the transition frequency as well as the shape of the SPCC response as a function of frequency. The proposed model is then compared with published data and previous models. It is found that the approach using the lognormal distribution is in very good agreement with experimental data as well as with previous models. Conversely, the approach that uses the fractal distribution provides a good match with published data for sandstone samples but not for sand samples. This result implies that the fractal PSD may not be pertinent for the considered sand samples, which exhibit a relatively narrow distribution of pore sizes. Our proposed approach can work for any PSD, for example, including complex ones such as double porosity or inferred from direct measurements. This makes the proposed models more versatile than models available in literature.

The classical Helmholtz-Smoluchowski equation is broadly used to characterize the relationship among the DC streaming potential coupling coefficient, the properties of the porous medium and the pore fluid, such as the zeta potential, fluid dielectric, conductivity and permittivity under the steady-state fluid flow. However, there is a frequency-dependent streaming potential through both sides of a transducer, which is one kind of porous media sintered by glass beads with different diameters and embedded in the liquid circular angular accelerometer. In order to increase the streaming potential signal, broaden the bandwidth of the accelerometer, and analyze the influence factors, we present a novel measurement system to determine streaming potential coupling coefficient of those transducers, which provides a sinusoidal pressure-driven fluid flow for transducers below 320 Hz. We have measured dynamic streaming potential coupling coefficients of 4 types of transducers by this device, and the results are well consistent with the theoretic model. For magnitude anomalies of the frequency response of the streaming potential coupling coefficient, we analyze the relationship among the cut-off frequency, permeability, and the mean particle size. It is proved that the cut-off frequency is inversely proportional to the mean particle size or permeability.

A series of experiments were performed to characterize the permeability, the specific storage, the capillary pressure, the streaming potential coupling coefficient, and the electrical conductivity of a very low permeability Callovo‐Oxfordian clay rock at different water saturations. The Callovo‐Oxfordian formation is presently investigated as a potential host to store nuclear wastes because of its very low permeability (typically 10 nd at saturation) and high specific surface area. We first present the constitutive transport equations including an electrokinetic cross‐coupling term in the generalized Darcy and Ohm constitutive equations. Then we present new experimental results using measurements of transient weight losses of samples submitted to a change in the relative humidity imposed by an automated humidity system in a hermetic chamber. These experiments are interpreted with a 1‐D analytical model of the coupled hydromechanical and transport equations. The hydromechanical transport properties (relative permeability and specific storage) of this clay rock are investigated in the relative saturation range from 0.23 to 0.70. We demonstrate that below 30% in relative humidity, the flux of the vapor phase with respect to the flux of the liquid water phase cannot be neglected. The relative apparent permeability can be described by a simple power law relationship with the saturation. In addition, we measure the electrical conductivity and the streaming potential coupling coefficient at various saturations. The electrical conductivity is described by a model accounting for electrical double‐layer contributions to surface conductivity. The measurement of the streaming potential coupling coefficient agrees with a power law model for the coupling coefficient versus the relative water saturation. A relationship between the exponent used to characterize the relative permeability and the second Archie's exponent used to describe the dependence of the electrical conductivity of the material with respect to the saturation is discussed.

The measured spectral-induced polarization (SIP) response of highly porous granular materials can be modeled by upscaling the Nernst-Planck equation for a single grain and performing a convolution product with the particle size distribution. The distribution of relaxation times associated with the polarization of consolidated porous media seems, intuitively, to be controlled by the pore size distribution because of the radius of curvature of the interface between the solid and the pore water. We have explored a mechanistic model connecting the SIP response of consolidated media to mercury injection capillary porosimetry (MICP) data. First, we developed a mechanistic electric double layer (EDL) polarization model for porous media, which considered the polarization of the Stern layer, which was possibly enhanced by the polarization of the diffuse layer and the effect of the pore size distribution. The new model revealed that the relaxation time of porous media such as sandstones could be overestimated if the enhancement of the overall polarization by the diffuse layer was not considered. Second, we have developed an empirical method to obtain the pore size distribution from MICP data by assuming a linear relation between the pore size and the pore throat size using a pore aspect ratio. Then, we compared the measured quadrature conductivities of nine samples with the theoretical quadrature conductivity obtained by convoluting the pore size distribution with the Warburg model. The Warburg model is considered to represent the quadrature conductivity response of a consolidated porous material characterized by an infinitively narrow unimodal pore size distribution coated by an EDL. The position of the peak of the phase was well-reproduced from the MICP data. In addition, the calculated broadness of the phase spectra was usually well-reproduced by convolving the Warburg function with the pore size distribution.

Coupled physical and chemical processes occur along the injected CO2 pathway in a reservoir (in CCS or CO2-based EOR) and may have consequences on the reservoir petrophysical properties. The work is based on the study of two carbonate rocks, all measurements were done using steady state method in the core flooding system. Petrophysical studies were performed on the two samples. The streaming potential coupling coefficient is basically defined as a sensitivity coefficient between the electrical potential and the variation of capillary pressure. In unsaturated porous medium this streaming potential coupling coefficient is controlled by CO2/N2-brine saturation and can be related to the CO2-brine relative permeability.

Harmonic pumping tests performed in an unconfined aquifer are responsible for a non-linear and phase shifted behavior of the self-potential response recorded at the ground surface with respect to the change in the pressure heads of the aquifer. The observed non-linearity of the transfer function can be reproduced with a petrophysical model in which the permeability, the capillary pressure curve, and the streaming potential coupling coefficient are modelled inside a unified framework approach based on the van Genuchten parametrization including a hysteretic behaviour with the water saturation. The field equations for the hydraulic heads and the self-potential signals are solved with a finite-element code, which is used to compute the time variation of the self-potential variations over time for two numerical experiments accounting or not for hysteresis. Only the model with hysteresis can reproduce the field observations.

Electrochemical double-layer capacitors (EDLCs) store energy at the interface of the electrode and electrolyte, known as the electrical double layer. One of the challenges facing EDLC technology is their moderate energy density compared to batteries and fuel cells. Therefore, improving EDLC performance requires identification of the key electrode and electrolyte parameters that affect energy density. Some of the key parameters that are known to impact the energy density of an electrode material are the material’s specific surface area (SSA), its pore size distribution, the macroscopic morphology, and the material’s chemical composition, relating to the wettability of the material and the faradaic reactions that may occur during charging. However, published research to date has not isolated the intercoupled relationship between specific surface area and pore size distribution. While high surface area materials often have high microporosity (pores less than 2 nm in diameter) due to the high surface to volume ratio of these small pores, as the pore size is increased into the mesopores range (2-50 nm diameter pores), the material’s SSA tends to decrease, since mesopores have a lower surface to volume ratio [1, 2]. As such, there remains an ongoing unresolved debate as to the relationship between pore size and SSA-normalized capacitance [2], with some researchers demonstrating an increased SSA-normalized capacitance in pores with diameters less than 1 nm [3], some researchers suggesting that there is no correlation between pore size and SSA-normalized capacitance [4], and some researchers demonstrating that there is a relationship between SSA-normalized capacitance and pores greater than 2 nm in diameter [5]. One of the main challenges to unravel the correlation between pore size and SSA-normalized capacitance is the variation in a material’s structural features, including total SSA, and its chemical composition. This makes it challenging to determine the effect of a single parameter [2]. In order to investigate the effect of pore size on SSA-normalized capacitance, the ideal materials for comparison would be those of similar specific surface area, and chemical composition, but differing pore size distribution. This approach ensures that the effects of the material’s total SSA are constant. When materials have different total SSA values, it is difficult to determine if the variations in performance are associated to differing pore size or differing surface area. Additionally, the relationship is more complicated in a sample with multiple pore sizes, which is common in activated carbon materials. It is critical to determine the relationship between pore size and capacitance in materials with narrow pore size distributions, and materials that have broad pore size distributions. By identifying the key structural features that improve the energy density of a material, the overall performance of EDLCs may also be improved. This study investigates the relationship between SSA-normalized capacitance and pore size distribution. Activated carbon materials were prepared with various pore size, but with similar specific surface area and chemical composition. The relationship between pore size and both SSA-normalized capacitance and gravimetric capacitance as well as the rate performance of the activated carbon materials is reported. Finally, the dependence of capacitance on maximum operating voltage is discussed in order to better elucidate the relationship between porosity and capacitance. Initial results have demonstrated that as the pore size increases, the SSA-normalized capacitance decreases. However, a similar decrease was not observed in the gravimetric capacitance. This indicates that the variation in bulk density of broad pore size distribution carbon materials may mask the effects of enhanced SSA-normalized capacitance in sub-nanometer pores. The results suggest that there may be a critical pore size distribution that will maximize both SSA-normalized capacitance and gravimetric capacitance.

Ultramicroporous carbons with extremely narrow pore size distribution via in-situ ionic activation for efficient gas-mixture separation

Pore-scale network modeling of microporosity in low-resistivity pay zones of carbonate reservoir

A combined interfacial polymerization and in-situ sol-gel strategy to construct composite nanofiltration membrane with improved pore size distribution and anti-protein-fouling property

Spherical carbon molecular sieves (CMS) have selective adsorptive properties which are suitable for separation and purification of gas mixtures. Precise methods of characterization are needed to understand the performance of CMS in separation processes. To this end, the pore size distribution (PSD) of four carbon molecular sieves were evaluated experimentally using immersion calorimetry and complemented with gas adsorption measurements at cryogenic temperatures for N2, O2 and Ar, and at 273 K for CO2. Theoretical pore size distributions were estimated using two-dimensional non-local Density Functional Theory (2D-NLDFT) models. Calorimetry results showed that B and C samples had a narrow pore size distribution with pores below 0.7 nm. Meanwhile, the pore size distributions calculated from O2 and Ar adsorption isotherms, gave an apex in the 0.5–0.6 nm region for all the carbons together with a growing development of porosity at around 0.8 nm and above for carbons A and D. The agreement observed between experiments and theory confirmed the validity of the theoretical 2D-NLDFT models to anticipate the PSD. Carbon C with pores exclusively below 0.7 nm separated CO2 and CH4 while carbon D with pores in the supermicroporous region separated propane and propylene chromatographically.

A model for liquid‐phase sintering is presented that explicitly considers the effect that the pore size distribution of the sintering compact has on the capillary forces that drive densification. In particular, the effect that liquid redistribution in the pore structure has on the driving force for sintering is considered under the assumption that the liquid can easily move to find a low‐energy configuration in the pore structure. It is shown that, for a powder compact that has a narrow pore size distribution, densification exhibits approximately the same time dependencies as those predicted by the Kingery model for liquid‐phase sintering. However, systematic changes in the absolute densification rate with the volume fraction of liquid, and the mean and breadth of the pore size distribution, are predicted. With more extreme pore size distributions, such as a bimodal distribution, behavior significantly different from that predicted by Kingery is found. In particular, it is predicted that, without there being a change in sintering mechanism, abrupt changes in densification rate may occur if the peaks in the bimodal distribution are well separated. The model provides a rational basis for interpreting how powder packing and processing steps can influence densification by liquid‐phase sintering.

On-board hydrogen storage is one of the major hurdles for success of hydrogen economy. Hydrogen storage using physisorption technique demands highly porous materials. Carbide derived carbons (CDC), a new class of porous carbons produced by thermo chemical etching of metal atoms from carbides were selected as a method for producing highly porous material for hydrogen storage. In order to synthesize tunable nanoporous carbon and to establish a structure-property relation between initial metal carbide and resultant nanoporous carbon, CDCs were synthesized from four metal carbides, two that have uniform carbon to carbon distance in the lattice structure (ZrC, TiC and SiC) and one that has a non-uniform carbon distribution in the lattice (B4C). It was shown that a uniform distribution of carbon atoms in the carbide is important for obtaining a narrow pore size distribution (PSD). CDC derived from B4C had a relatively broad PSD and contained mesopores even at the lowest synthesis temperature, while the CDC produced from SiC maintained a narrow PSD even at the synthesis temperature of 1200oC. CDC produced from ZrC and TiC has a narrow PSD at low synthesis temperature and pores gets wider at higher temperatures. Comparison of CDCs produced from ZrC, TiC and B4C shows that CDCs produced from ZrC and TiC show a lower degree of ordering than that from B4C at high temperatures. Unlike CDCs produced from ZrC and TiC, the PSD of CDCs from B4C does not change appreciably in the 600-1200oC range. CDCs produced from ZrC and TiC can have both narrowly distributed micropores (pores smaller than 2 nm) and mesopores (pores larger than 2 nm), depending on synthesis temperature. In this work, it is demonstrated that porosity of CDC can be fine tuned with a high accuracy by using different starting carbides and varying the synthesis temperatures. This is very important in many applications of porous carbon, especially for gas storage. CDC from ZrC, TiC, B4C and SiC resulted in a family of high surface area nanoporous carbons (300 to 2300 m2/g) of average pore size ranging from 0.5 to 1.4 nm, A systematic study on hydrogen storage capacity of CDCs and comparison with other materials including metal organic framework (MOF-5), single (SWCNT) and multiwalled carbon nanotubes (MWCNT) dispelled the popular myth that hydrogen physisorption is directly proportional to SSA, and provided guidance for optimal design by showing that a large volume of small open pores is the key to high hydrogen uptake at cryogenic temperatures and ambient pressure. Values up to 3 wt.% and 30 kg/m3 have been demonstrated in CDCs; these are twice what can be stored in MOF-5 and several times higher than has been achieved in SWCNT or MWCNT at 77 K and atmospheric pressure. The isosteric heat of hydrogen adsorption up to 11 kJ/mole of CDCs is higher than that reported for activated carbon, CNT and MOF.

The role of adsorbent pore size distribution in multicomponent adsorption on activated carbon

We report on the results of extensive computer simulation of the effect of deformation on the morphology of a porous medium and its fluid flow properties. The porous medium is represented by packings of spherical particles. Both random and regular as well as dense and nondense packings are used. A quasistatic model based on Hertz's contact theory is used to model the mechanical deformation of the packings, while the evolution of the permeability with the deformation is computed by the lattice-Boltzmann approach. The evolution of the pore-size and pore-length distributions, the porosity, the particles' contacts, the permeability, and the distribution of the stresses that the fluid exerts in the pore space are all studied in detail. The distribution of the pores' lengths, the porosity, and the particles' connectivity change strongly with the application of an external strain to the porous media, whereas the pore-size distribution is not affected as strongly. The permeability of the porous media strongly reduces even when the applied strain is small. When the permeabilities and porosities of the random packings are normalized with respect to their predeformation values, they all collapse onto a single curve, independent of the particle-size distribution. The porosity reduces as a power law with the external strain. The fluid stresses in the pore space follow roughly a log-normal distribution, both before and after deformation.