Influence of grain size and shape on dielectric permittivity and its implications for water-saturation assessment

Dielectric permittivity mixture models commonly assume simple geometries for the constituting rock components, which affect their reliability in rocks with complex pore geometry and rock fabric such as carbonates. The combined influence of pore geometry, grain shape, and grain size on the performance of those models in water saturation assessment remains to be tested. Frequency-domain dielectric permittivity simulations can model the influence of pore and grain geometries on dielectric permittivity without a need for explicitly defining those parameters. Individual impacts of the aforementioned properties can be quantified and separated in the pore-scale domain via dielectric permittivity simulations. Therefore, the objectives of this paper are to (a) design pore-scale rock samples with different grain shapes and sizes, (b) investigate the influence of grain shape, grain size, and pore connectivity on the dielectric permittivity of the pore-scale rock samples as well as rock images from carbonate and sandstone formations, and (c) evaluate the performance of multiple dielectric permittivity mixture models in the quantification of water saturation. We construct three-dimensional (3D) synthetic rock models with spheroidal grains. We use different aspect ratios (i.e., the ratio of the radius of the major axis to the radius of the minor axis) and grain sizes for spheroids. Next, we numerically alter the water saturation. We perform frequency-domain dielectric permittivity simulations (through the solution of Maxwell’s equations in the frequency domain) in actual and synthetic samples in the frequency range of 100 Hz to 5 GHz. Finally, we test the performance of multiple dielectric permittivity mixture models (e.g., Maxwell-Garnett, Hanai-Bruggeman, CRIM, etc.) in the estimation of water saturation from dielectric permittivity measurements. We observed that the relative permittivity (i.e., the real part of the dielectric permittivity) increased with an increase in the aspect ratio of the spheroid grains. The electrical conductivity (which is associated with the imaginary part of the dielectric permittivity) decreased as the grains became flatter, which is due to the decreasing efficiency in electrical current flow. The dielectric permittivity dispersion is much less significant for rounder spheroid grains. The dispersion and absolute values of the relative permittivity and electrical conductivity decreased with the decreasing water saturation. We documented that overlooking the influence of pore and grain geometries can lead to average relative errors in water saturation up to 100% in the sandstone and carbonate samples. Taking into account the grain geometry and using Maxwell-Garnett formulation with the background medium properties estimated with the CRIM equation resulted in the lowest average relative errors (10%) in water saturation quantification. The documented results quantified the impacts of grain size, grain shape, and pore connectivity on dielectric permittivity. This analysis was possible through pore-scale modeling of dielectric permittivity dispersion. The outcomes demonstrate the limitations of the current dielectric permittivity mixture models in the calculation of dielectric permittivity and assessment of water saturation under different conditions. Therefore, the results of this work can help in quantifying the uncertainty associated with the use of existing dielectric permittivity mixture models depending on the pore and grain geometry of any given rock.

Summary Broadband dielectric dispersion measurements are attractive options for the assessment of water-filled porosity. Dielectric permittivity is influenced by salinity as well as other rock/fluid properties. However, the effect of salinity on Maxwell-Wagner polarization (i.e., interfacial polarization) and dielectric permittivity in rock samples with complex pore structures requires further investigation. The objectives of this work are (a) to perform frequency-domain dielectric permittivity numerical simulations on 3D pore-scale rock samples at different salt concentration levels, (b) to quantify the effect of salinity on dielectric permittivity and interfacial polarization in the frequency range between 20 MHz and 5 GHz, and (c) to quantify the critical frequency (i.e., the frequency at which the relative permittivity becomes frequency-independent). We first perform pore-scale frequency domain dielectric permittivity simulations in fully water-saturated carbonate samples with complex pore structures to obtain the complex dielectric permittivity in the frequency range of 0.01–5 GHz and at different salinity levels. Next, we numerically create partially water/hydrocarbon-saturated water-wet samples and perform simulations at different salinity and water saturation levels to investigate the combined effect of salinity and water saturation on dielectric permittivity. Finally, we investigate how reliable conventional mixing models, such as the complex refractive index model (CRIM) and Hanai-Bruggeman (HB), are in the assessment of water saturation at different salinity levels. We used 3D pore-scale rock samples with complex pore structures from Austin Chalk, Estaillades Limestone, and Happy Spraberry formations. The increase in salinity from 2 to 50 parts per thousand (PPT) resulted in the relative permittivity to increase by 18% at 20 MHz. Similarly, an increase in salinity from 2 PPT to 50 PPT resulted in electrical conductivity to increase by 15 times at 20 MHz. However, at 5 GHz, the difference between the relative permittivity of the samples at different salinities was negligible. We demonstrated that the critical frequency was above 1 GHz. Thus, if complex dielectric permittivity at 1 GHz is being used, an accurate salinity assumption is required in the interpretation of conventional dielectric mixture models in carbonate formations. Finally, we observed 52% and 42% average relative errors in water saturation quantification when applying CRIM and HB models at all the frequencies of interest, respectively. The results also indicated that conventional models should not be used in the presence of uncertainty in salinity at lower frequencies. The results of this work quantified the frequency at which the water-filled pore volume rather than the Maxwell-Wagner polarization controls the relative permittivity of rock samples saturated with a wide range of brine salinity. Moreover, the results demonstrated that the relative permittivity of the rock samples with complex pore structures may still be significantly affected by the interfacial polarization even at 1 GHz. Moreover, the results suggested that the conventional mixture methods cannot reliably take into account the salt concentration of formation water, and this can lead to significant errors in reserves assessment.

Fluid saturations and distributions, water salinity, pore structure, and porosity affect dielectric permittivity measurements. However, the conventional dielectric permittivity mixture models, such as Complex Refractive Index Model (CRIM) and Hanai-Bruggeman (HB) do not quantitatively include the cumulative effect of the aforementioned petrophysical properties. Moreover, the effect of salt concentration on multi-frequency dielectric permittivity measurements still needs to be investigated. The objectives of this paper are (a) to investigate the effect of salt concentration on complex multi-frequency dielectric permittivity responses in rocks with complex pore structure, (b) to develop a new workflow for estimating multi-frequency dielectric permittivity of rock samples taking into account the complexity of pore structure, different polarization mechanisms, porosity, water saturation, and salt concentration, and (c) to develop an inversion algorithm to simultaneously estimate water saturation and salinity from dielectric dispersion data. First, we conduct dielectric permittivity experiments on fully brine-saturated rock samples. Then, we change the salinity of the samples and perform dielectric permittivity experiments on the rock samples at different water salinity levels. Next, we develop a new rock-physics workflow which includes the combined effect of the aforementioned petrophysical properties. The new workflow calculates the multi-frequency complex dielectric permittivity responses of synthetic rock samples. Then, we use an automated inversion algorithm to simultaneously estimate water saturation and salinity of actual rock samples from the joint interpretation of the real and imaginary parts of multi-frequency dielectric permittivity measurements. We successfully verified the reliability of the new workflow in the core-scale domain using 12 different rock samples in the Barra Velha formation. The new workflow simultaneously estimated water saturation and salinity with average relative errors less than 12% and 14%, respectively. Moreover, we observed that the average relative errors between the experimentally observed and calculated dielectric permittivity that are obtained from the introduced mixture model, CRIM, and HB are 11%, 121%, and 26%, respectively. We demonstrated that the effect of salt concentration could have significant effects on dielectric permittivity responses up to 3 GHz and has to be reliably taken into account in interpretation of dielectric measurements. The multi-frequency joint interpretation of the real and imaginary parts of dielectric permittivity measurements makes the introduced workflow a robust interpretation technique in the presence of uncertainties in the estimates of the formation water salinity. Moreover, unlike the conventional dielectric mixture models, the introduced workflow honors the complexity of pore structure and composition, water salinity, and different polarization mechanisms.

Broadband dielectric dispersion measurements are attractive options for assessment of water-filled Dielectric permittivity is influenced by salinity as well as other rock/fluid properties. However, the effect of salinity on Maxwell-Wagner polarization (i.e., interfacial polarization) and dielectric permittivity in rock samples with complex pore structure requires further investigation. The objectives of this work are (a) to perform frequency domain dielectric permittivity numerical simulations on 3-dimensional (3D) pore-scale rock samples at different salt concentration levels, (b) to quantify the effect of salinity on dielectric permittivity and interfacial polarization in the frequency range between 20 MHz to 5 GHz, and (c) to quantify the frequency at which the interfacial polarization diminishes. We first perform pore-scale frequency domain dielectric permittivity simulations in fully water-saturated carbonate samples with complex pore structure to obtain the complex dielectric permittivity in the frequency range of 0.02-5 GHz and at different salinity levels. Next, we numerically create partially water/hydrocarbon-saturated water-wet samples and perform simulations at different salinity and water saturation levels to investigate the combined effect of salinity and water saturation on dielectric permittivity. Finally, we investigate how reliable conventional mixing models, such as Complex Refractive Index Model (CRIM) and Hanai-Bruggeman (HB), are in assessment of water saturation at different salinity levels. We used 3D pore-scale rock samples with complex pore structure from Austin Chalk, Estaillades Limestone, and Happy Spraberry formations. The increase in the salinity from 2 PPT to 50 PPT resulted in the dielectric constant to increase by 25% at 20 MHz. Similarly, an increase in salinity from 2 PPT to 50 PPT resulted in electrical conductivity to increase 10 times at 20 MHz. However, at 5 GHz the difference between the dielectric constants of the samples at different salinities was negligible. We demonstrated that the frequency at which the interfacial polarization becomes negligible is above 1 GHz. Thus, an accurate salinity assumption is required in the interpretation of conventional dielectric mixture models in carbonate formations. Finally, we observed 52% and 42% average relative errors in water saturation quantification when applying CRIM and HB models, respectively. The results also indicated that conventional models should not be used in the presence of uncertainty in salinity at lower frequencies. The results of this work quantified the frequency at which the water-filled pore volume rather than the Maxwell-Wagner polarization controls the dielectric constant of rock samples saturated with wide range of brine salinity. Moreover, results demonstrated that unlike the samples with relatively simple pore geometry (e.g., sandstone formations), the dielectric constant of the rock samples with complex pore structure may still be affected by the interfacial polarization even at 1 GHz. Moreover, the results suggested that the conventional mixture methods cannot reliably take into account salt concentration of formation water, and this can lead to significant errors in reserves assessment.

Complex pore geometry and composition as well as heterogeneous and anisotropic behavior of organic-rich source rocks significantly affects physical properties of the rock measured by well logs such as electrical resistivity and dielectric permittivity. These physical properties are used to estimate in situ petrophysical properties of the formation such as hydrocarbon saturation. Conventional methods for assessment of hydrocarbon saturation include interpretation of (a) electrical resistivity logs through resistivity-porosity-saturation models (e.g., Archie's equation and the dual-water model) and (b) dielectric permittivity measurements using volumetric techniques such as the Complex Refractive Index Model (CRIM). In the application of these approaches to formations with complex pore structure and mineral composition such as organic-rich formations, the impact of complex pore-structure (e.g., kerogen porosity and inter-granular pores), pyrite, and conductive mature kerogen have not been taken into account. The aforementioned limitations cause significant uncertainty in estimates of water saturation. The method proposed in this paper improves the assessment of hydrocarbon saturation using combined interpretation of dielectric and electrical resistivity measurements. We start with pore-scale numerical simulations of electrical resistivity and dielectric permittivity of fluid-bearing porous media to investigate the impact of structure of pore and matrix constituents on these measurements. The inputs to these simulators are three-dimensional (3D) pore-scale rock images. We then introduce an analytical model that combines conductivity and permittivity measurements for assessment of water-filled porosity and hydrocarbon saturation. We applied the new method on actual sandstone and synthetic organic-rich source rock samples. We observed an improvement in estimates of water-filled porosity compared to conventional methods in both cases of conventional and unconventional rock samples. This improvement was more significant in the case of organic-rich source rocks with complex pore structure. In the case of synthetic organic-rich source rock samples, the simulation results confirmed that not only the pore structure, but also spatial distribution and tortuosity of water, kerogen, and pyrite networks, affect the dielectric permittivity and electrical resistivity. Taking into account these parameters through the joint interpretation of dielectric and electrical resistivity measurements significantly improves assessment of hydrocarbon saturation.

Ferroelectric Bi4Ti3O12 thin films with single phase and nanosized microstructure were prepared on Pt/Ti/SiO2/Si(111) substrate by metalorganic solution deposition using titanium butoxide and bismuth nitrate at relatively low annealing temperatures. The internal strain in Bi4Ti3O12 thin films was calculated from the peak shifts and broadening of XRD patterns. With increase in annealing temperature, the uniform strain decreased from positive to zero and then to negative, and the non-uniform strain decreased and was negative. The total strain was negative and in the range of -0.2%–-1.0%, from which the stress of the films was calculated to be about -1.4×109 N/m2. The mode values of strain decreased with increase in annealing temperature and increased with increase in film thickness. The dielectric constant increased with increase in annealing temperature and film thickness. The dielectric properties were interpreted by considering the influence of strain, grain size, and grain boundaries. The strain lowered the polarization and increased the dielectric constant. The larger the grain size and the thinner the grain boundary, the greater the dielectric constant. The influence of grain size and grain boundary was stronger than that of the strain.

Ionic properties and concentration significantly influence the response of brine-saturated rock samples to electromagnetic disturbance. However, the dielectric permittivity response of rock samples under different ionic conditions is poorly described. This significantly limits the potential information that could be gained from dielectric permittivity measurements about the pore geometry and fluid content. Therefore, the influence of salt concentration and type on broadband dielectric permittivity must be quantified in the pore- and core-scale domains to develop analytical dielectric permittivity models. The objectives of this paper are to (a) investigate the influence of salt type and concentration on dielectric permittivity via experimental measurements and pore-scale simulations and (b) identify the limitations of current effective medium theories in the interpretation of dielectric permittivity measurements in samples with different ionic conditions. We investigate the influence of salt concentration and type on the dielectric permittivity of pore- and core-scale Berea sandstone samples. First, we perform frequency-domain dielectric permittivity simulations to quantify the response of the pore-scale models to electric field excitation. The frequency-domain dielectric permittivity simulator solves Maxwell’s equations under quasi-static conditions at discrete frequencies. We simulate the dielectric permittivity in the frequency range of 20 MHz to 3 GHz. We run the simulations in samples saturated with NaCl, KCl, and MgCl2 brines. The salt concentration of the brine solutions ranges between 2 to 100 PPT. For the core-scale analysis, we fully saturate the samples with different brine solutions at varying salt concentrations. In the core-scale domain, we use the exact brine solutions and salt concentrations defined for the pore-scale analysis. The dielectric permittivity measurements were conducted using a network analyzer with a high-temperature coaxial probe setup in the frequency range of 200 MHz to 3 GHz. We observed that relative permittivity at 1 GHz decreases with increasing salt concentration, irrespective of the brine type. However, the type of salt significantly controls the magnitude of the decrease in relative permittivity. After increasing the salt concentration from 10,000 to 100,000 PPM, relative permittivity at 1 GHz decreased by 7% and 11% when the samples were saturated with KCl and NaCl brine solutions, respectively. Furthermore, this behavior was enhanced as the frequency decreased. The impact of salt type on relative permittivity was negligible in samples saturated with 10,000 PPM brine solutions. Finally, we examined the potential errors that could arise from assuming an inaccurate salt type in the interpretation of dielectric permittivity measurements. We observed that incorrect assumptions about the brine type could result in up to 20% relative errors in water saturation assessment via dielectric permittivity measurements. Therefore, taking the influence of salt concentration and type into account is critical for a reliable interpretation of dielectric permittivity. The outcomes of this work will be helpful in the interpretation of dielectric permittivity measurements in formations with variable salt concentrations of formation water. Additionally, in the cases where the salinity of the formation water is unreliable, this work will illuminate the extent to which the dielectric permittivity measurements can be used for petrophysical analysis.

Summary Ionic properties and concentration significantly influence the response of brine-saturated rocks to electromagnetic disturbance. However, the dielectric permittivity response of rocks under different ionic conditions is poorly described. This significantly limits the potential information that could be gained from dielectric permittivity measurements about the pore geometry and fluid content. The influence of salt concentration and type on broadband dielectric permittivity must be reliably quantified to enhance interpretation of dielectric permittivity measurements. The main objective of this paper is to quantify the influence of salt type and concentration on dielectric permittivity via experimental measurements and pore-scale simulations. We examine the impact of salt concentration and type on the dielectric permittivity of pore- and core-scale Berea sandstone (BS) samples. First, we perform frequency-domain dielectric permittivity simulations to quantify the response of the pore-scale models to electric field excitation. The frequency-domain dielectric permittivity simulator solves Maxwell’s equations under quasistatic conditions at discrete frequencies. We simulate the dielectric permittivity in the frequency range of 20 MHz to 3 GHz. We perform the simulations in samples saturated with NaCl, KCl, and MgCl2 brines. The salt concentration of the brine solutions ranges between 10 PPT and 100 PPT (parts per thousand). We fully saturate the samples with different brine solutions at varying salt concentrations for the core-scale analysis. In the core-scale domain, we use the brine solutions and salt concentrations assumed in the pore-scale analysis. The dielectric permittivity measurements were conducted using a network analyzer with a high-temperature coaxial probe setup in the frequency range of 300 MHz to 3 GHz. We observed that relative permittivity at 1 GHz increases with increasing salt concentration, irrespective of the brine type. However, the type of salt significantly controls the magnitude of the decrease in relative permittivity. After increasing the salt concentration from 10 PPT to 100 PPT, relative permittivity at 1 GHz increased by 11% and 7% when the samples were saturated with KCl and NaCl brine solutions, respectively; at 20 MHz, the same increase in salt concentration caused rock relative permittivity to increase by only 1% and 5% in the samples saturated with KCl and NaCl brines, respectively. The lower sensitivity of relative permittivity to salt concentration at 20 MHz compared to 1 GHz can be attributed to the combined influence of interfacial and orientational polarizations on rock dielectric permittivity. The impact of salt type on relative permittivity was negligible in samples saturated with 10 PPT brine solutions. Results demonstrated that taking the influence of salt concentration and type into account is critical for reliable interpretation of dielectric permittivity measurements. The novel contribution of this work is the documentation of how the saturating brine type influences the complex dielectric permittivity of the rocks. This work illuminates the extent to which the relative permittivity can be used for petrophysical analysis in cases where the formation brine salt concentration is uncertain. Additionally, the outcomes of this work will contribute to enhanced interpretation of dielectric permittivity measurements in formations with variable salt concentrations of formation water.

Broadband dielectric dispersion measurements are attractive options for assessment of water-filled pore volume, especially when quantifying salt concentration is challenging. However, conventional models for interpretation of dielectric measurements such as Complex Refractive Index Model (CRIM) and Maxwell Garnett (MG) model require oversimplifying assumptions about pore structure and distribution of constituting fluids/minerals. Therefore, dielectric-based estimates of water saturation are often not reliable in the presence of complex pore structure, rock composition, and rock fabric (i.e., spatial distribution of solid/fluid components). The objectives of this paper are (a) to propose a simple workflow for interpretation of dielectric permittivity measurements in log-scale domain, which takes the impacts of complex pore geometry and distribution of minerals into account, (b) to experimentally verify the reliability of the introduced workflow in the core-scale domain, and (c) to apply the introduced workflow for well-log-based assessment of water saturation. The dielectric permittivity model includes tortuosity-dependent parameters to honor the complexity of the pore structure and rock fabric for interpretation of broadband dielectric dispersion measurements. We estimate tortuosity-dependent parameters for each rock type from dielectric permittivity measurements conducted on core samples. To verify the reliability of dielectric-based water saturation model, we conduct experimental measurements on core plugs taken from a carbonate formation with complex pore structures. We also introduce a workflow for applying the introduced model to dielectric dispersion well logs for depth-by-depth assessment of water saturation. The tortuosity-dependent parameters in log-scale domain can be estimated either via experimental core-scale calibration, well logs in fully water-saturated zones, or pore-scale evaluation in each rock type. The first approach is adopted in this paper. We successfully applied the introduced model on core samples and well logs from a pre-salt formation in Santos Basin. In the core-scale domain, the estimated water saturation using the introduced model resulted in an average relative error of less than 11% (compared to gravimetric measurements). The introduced workflow improved water saturation estimates by 91% compared to CRIM. Results confirmed the reliability of the new dielectric model. In application to well logs, we observed significant improvements in water saturation estimates compared to cases where a conventional effective medium model (i.e., CRIM) was used. The documented results from both core-scale and well-log-scale applications of the introduced method emphasize on the importance of honoring pore structure in the interpretation of dielectric measurements.

Broadband relative dielectric dispersion measurements are considered interesting options for assessment of water-filled pore volume. Conventional models such as Complex Refractive Index Model (CRIM) and Maxwell Garnett (MG), often overlook or oversimplify the complexity of pore structure, geometrical distribution of the constituting fluids, and spatial distribution of minerals. This yields to significant errors in assessment of water saturation especially in rocks with complex pore structure. Therefore, it becomes important to quantify the impacts of pore structure and spatial distribution of minerals on broadband relative dielectric dispersion measurements to be able to make decisions about reliability of water saturation estimates from these measurements in a given formation. The objectives of this paper are (a) to quantify the impacts of pore structure and spatial distribution of minerals on relative dielectric permittivity measurements in a wide range of frequencies, (b) to propose a new simple and physically meaningful workflow, which honors pore geometry and spatial distribution of minerals to enhance fluid saturation assessment using relative dielectric permittivity measurements, (c) to verify the reliability of the introduced model in the pore-scale domain. First, we perform numerical simulations of relative dielectric dispersion measurements in the frequency range of 20 MHz to 1 GHz in the pore-scale domain. The input to the numerical simulator includes pore-scale images of actual complex carbonate rock samples. We use a physically meaningful model which honors spatial distribution of the rock constituents for the multi-frequency interpretation of relative dielectric response. To verify the reliability of the model in multiple frequencies, we apply the model to the results of relative dielectric simulations in the pore-scale domain on 3D computed tomography scan (CT-scan) images of carbonate rock samples, which are synthetically saturated to obtain a wide range of water saturation. We successfully verified the reliability of the introduced model in the pore-scale domain using carbonate rock samples with multi-modal pore-size distribution. Estimated water saturations from the results of simulations at 1 GHz resulted in an average relative error of less than 4%. We observed measurable improvements in fluid saturation estimates compared to the cases which CRIM or MG models are used. Results demonstrated that application of conventional models to estimate water saturation from relative dielectric response is not reliable in frequencies below 1 GHz.

SummaryThe wettability of rocks can be assessed from interpretation of borehole geophysical measurements, such as electrical resistivity and nuclear magnetic resonance (NMR). These wettability models often require additional inputs (e.g., water saturation, porosity, and pore-geometry- related parameters), which are difficult to obtain independently. Consequently, a multiphysics workflow that integrates resistivity and NMR measurements can reduce the number of input parameters, resulting in a more accurate and robust wettability assessment. The objectives of this paper are to introduce a new workflow for joint interpretation of resistivity and NMR measurements to simultaneously estimate wettability and water saturation, and to verify the reliability of wettability and water-saturation estimates by comparison with experimentally measured contact angles, Amott Indices, and gravimetrically assessed water saturation.This new workflow for assessing wettability and water saturation combines nonlinear resistivity- and NMR-based rock physics models. The inputs to the resistivity-based wettability model include the resistivity of the rock–fluid system and brine, porosity, and pore-geometry-related parameters. The NMR-based wettability model requires the transverse (T2) response of the rock–fluid system, saturating fluids, and water-wet water-saturated and hydrocarbon-wet hydrocarbon-saturated rocks. To verify the reliability of the new integrated workflow, we perform resistivity and NMR measurements on core samples from different rock types, covering a range of wettability and water-saturation levels. These measurements are inputs to the nonlinear models, which are simultaneously solved to estimate wettability and water saturation for each core sample. We verify the reliability of wettability estimates by comparison with the Amott Index (IA) and contact-angle measurements, and the water-saturation estimates by comparison with the gravimetric water-saturation estimates.We successfully verified the reliability of the new method for this joint interpretation of resistivity and NMR measurements to estimate wettability and water saturation of limestone and sandstone core samples. For water-saturation levels ranging from irreducible water saturation to residual oil saturation, we observed an average relative error of 11% between the gravimetrically assessed and the model-estimated water saturation. It is challenging to estimate water saturation in rocks with multimodal pore-size distribution uniquely from the interpretation of NMR measurements. One contribution of the introduced workflow is improving the accuracy of water-saturation estimates (in addition to wettability) in rocks with complex pore structure and wettability states. For the wettability ranging from hydrocarbon-wet to water-wet, we observed an average absolute difference of 0.15 between the experimentally measured IA and the model-estimated wettability. These model-estimated wettability values were also consistent with the contact-angle measurements. It should be noted that the new workflow relies on physically meaningful and measurable parameters, which minimizes calibration efforts. Furthermore, the multiphysics workflow eliminates the nonuniqueness associated with wettability and water-saturation estimates obtained from independent interpretation of NMR and resistivity measurements.

Summary Complex pore geometry and composition, as well as anisotropic behavior and heterogeneity, can affect physical properties of rocks such as electrical resistivity and dielectric permittivity. The aforementioned physical properties are used to estimate in-situ petrophysical properties of the formation such as hydrocarbon saturation. In the application of conventional methods for interpretation of electrical-resistivity (e.g., Archie's equation and the dual-water model) and dielectric-permittivity measurements [e.g., complex refractive index model (CRIM)], the impacts of complex pore structure (e.g., kerogen porosity and intergranular pores), pyrite, and conductive mature kerogen have not been taken into account. These limitations cause significant uncertainty in estimates of water saturation. In this paper, we introduce a new method that combines interpretation of dielectric-permittivity and electrical-resistivity measurements to improve assessment of hydrocarbon saturation. The combined interpretation of dielectric-permittivity and electrical-resistivity measurements enables assimilating spatial distribution of rock components (e.g., pore, kerogen, and pyrite networks) in conventional models. We start with pore-scale numerical simulations of electrical resistivity and dielectric permittivity of fluid-bearing porous media to investigate the structure of pore and matrix constituents in these measurements. The inputs to these simulators are 3D pore-scale images. We then introduce an analytical model that combines resistivity and permittivity measurements to assess water-filled porosity and hydrocarbon saturation. We apply the new method to actual digital sandstones and synthetic digital organic-rich mudrock samples. The relative errors (compared with actual values estimated from image processing) in the estimate of water-filled porosity through our new method are all within the 10% range. In the case of digital sandstone samples, CRIM provided reasonable estimates of water-filled porosity, with only four out of twenty-one estimates beyond 10% relative error, with the maximum error of 30%. However, in the case of synthetic digital organic-rich mudrocks, six out of ten estimates for water-filled porosity were beyond 10% with CRIM, with the maximum error of 40%. Therefore, the improvement was more significant in the case of organic-rich mudrocks with complex pore structure. In the case of synthetic digital organic-rich mudrock samples, our simulation results confirm that not only the pore structure but also spatial distribution and tortuosity of water, kerogen, and pyrite networks affect the measurements of dielectric permittivity and electrical resistivity. Taking into account these parameters through the joint interpretation of dielectric-permittivity and electrical-resistivity measurements significantly improves assessment of hydrocarbon saturation.

To prevent CO2 leakage and ensure the safety of long-term CO2 storage, it is essential to investigate the flow mechanism of CO2 in complex pore structures at the pore scale. This study focused on reviewing the experimental, theoretical, and numerical simulation studies on the microscopic flow of CO2 in complex pore structures during the last decade. For example, advanced imaging techniques, such as X-ray computed tomography (CT) and nuclear magnetic resonance (NMR), have been used to reconstruct the complex pore structures of rocks. Mathematical methods, such as Darcy’s law, the Young–Laplace law, and the Navier-Stokes equation, have been used to describe the microscopic flow of CO2. Numerical methods, such as the lattice Boltzmann method (LBM) and pore network (PN) model, have been used for numerical simulations. The application of these experimental and theoretical models and numerical simulation studies is discussed, considering the effect of complex pore structures. Finally, future research is suggested to focus on the following. (1) Conducting real-time CT scanning experiments of CO2 displacement combined with the developed real-time CT scanning clamping device to achieve real-time visualization and provide a quantitative description of the flow behavior of CO2 in complex pore structures. (2) The effect of pore structures changes on the CO2 flow mechanism caused by the chemical reaction between CO2 and the pore surface, i.e., the flow theory of CO2 considering wettability and damage theory in a complex pore structures. (3) The flow mechanism of multi-phase CO2 in complex pore structures. (4) The flow mechanism of CO2 in pore structures at multiscale and the scale upgrade from microscopic to mesoscopic to macroscopic. Generally, this study focused on reviewing the research progress of CO2 flow mechanisms in complex pore structures at the pore scale and provides an overview of the potential advanced developments for enhancing the current understanding of CO2 microscopic flow mechanisms.

Grain-size-insensitive dielectric properties of Sr0.6Ba0.4Nb2O6 relaxor ferroelectric ceramics with tetragonal tungsten bronze structure

Study by hysteresis measurements of the influence of grain size on the dielectric properties of ceramics of the Sr0.4Ba0.60TiO3 type prepared under different sintering conditions