Differential Effective Medium Research Articles

Correlation between cementation exponent and pore geometry with varying pore pressure for the joint elastic-electrical modelling of porous sandstones

Summary Seismic and electrical surveys are the most employed geophysical exploration applications for understanding the subsurface earth. Differential effective medium (DEM) models are the models to interpret the seismic and electrical survey data with the greatest success. However, cementation exponent and pore aspect ratio as the indispensable geometric parameters in the electrical and elastic DEM models are independent, making the models not suitable for the joint elastic-electrical modelling, a key requirement for the joint interpretation of seismic and electrical exploration data to better understand the increasingly complex hydrocarbon reservoirs. We show how cementation exponent and pore aspect ratio are correlated in three Berea sandstone samples with changing porosity resulting from varying pore pressure. We find that cementation exponent inverted from the electrical DEM model shows a strong positive linear correlation with pore aspect ratio obtained from the elastic DEM model as an implicit function of porosity induced by increasing pore pressure. We also find that the established linear correlation can enable the DEM models to calculate one physical property (e.g., elastic or electrical) from the geometric parameter describing the other property (e.g., electrical or elastic). The results reveal how the elastic and electrical geometric parameters are linked, and provide a consistent microstructure that enables the existing elastic and electrical DEM models to be suitable for the joint elastic-electrical modelling of rocks undergoing varying pore pressure.

Constructions of multi-scale 3D digital rocks by associated image segmentation method

Digital rocks constructed from micro-CT image at a single-resolution face limitations in accurately identifying the entire pore space and mineral components of tight sandstones, due to their high content of nanoscale pores and clay. Consequently, the porosity values derived from such digital rocks are significantly lower compared to those obtained through laboratory measurements, resulting in discrepancies between the measured and calculated petrophysical properties. This study introduces a multi-scale digital rock modeling method by integrating three-dimensional micro-CT images acquired at two distinct resolutions and two-dimensional SEM images. Plunger-shaped core samples and their corresponding sub-samples were scanned at resolutions of 13.99 μm/voxel and 2.99 μm/voxel, respectively. The scale-invariant feature transform (SIFT) image registration technique was employed to accurately align the two sets of grayscale CT images. Correlation curves between the grayscale value in low-resolution CT images and various mineral contents were established based on the aligned regions, and utilized to construct multi-scale digital rock models. Intragranular pores, unresolvable by the micro-CT images, were identified using SEM imaging, enabling the incorporation of fine-scale features into the models. The resulting multi-scale digital rock models exhibited bulk porosity values that closely matched laboratory helium porosity measurements. Additionally, the elastic moduli calculated by the differential effective medium (DEM) model and the finite element method (FEM) demonstrated good correspondence with experimental results. These results validate the proposed multi-scale digital rock modeling method as an effective approach for accurately characterizing the porosity and mineral components of tight sandstone reservoirs.

Fluid effect on elastic properties of carbonate and implication for CO2 geologic sequestration monitoring

Laboratory measurement of the elastic properties of carbonates saturated with different fluids is crucial for characterizing reservoirs and monitoring CO2 sequestration. However, it is challenging to distinguish the effects of different fluids. We measure eight carbonate samples under varying pressure and fluid saturation conditions and conduct quantitative analysis. The measurements indicate that water saturation can increase P-wave velocity ([Formula: see text]), whereas oil and CO2 saturation may lead to an increase, decrease, or no change in [Formula: see text]. Meanwhile, all fluid saturation reduces the S-wave velocity ([Formula: see text]). The velocities of the dolomite samples are higher and less pressure sensitive than that of limestone samples. Four attributes are adopted to distinguish the fluid effect, including elastic moduli, impedance, [Formula: see text]/[Formula: see text] ratio, and a newly designed fluid discrimination factor F, which is obtained by multiplying P-wave modulus and square value of density change. Among the attributes, the F factor performs the best as it achieved evident and consistent results for all the samples. Rock-physics models are used to simulate elastic behaviors with the differential effective medium model predicting [Formula: see text] the best. The Gassmann’s equation correctly indicates positive or negative changes in rock velocity after fluid saturation even though its prediction does not exactly match the data. This study highlights the impact of various pore fluids on the carbonate elastic properties through laboratory measurement and theoretical modeling and introduces a novel fluid identification factor, providing insights for reservoir seismic characterization and CO2 sequestration monitoring.

Improving interfacial thermal transport in silicon-reinforced epoxy resin composites with self-assembled monolayers

Epoxy resin (EP) based composite materials, due to their advantages such as light weight, ease of processing, and mechanical properties, have been widely applied across thermal packaging field. However, the overall thermal conductivity is constrained by the interfacial thermal resistance between the filler and the substrate. Existing studies suggest that self-assembled monolayers (SAM) can enhance the interfacial thermal conductance (ITC) by forming covalent bonds. Nevertheless, limited research has focused on using SAM to form bilateral covalent bonds to regulate ITC. Therefore, SAM capable of forming bilateral covalent bonds at the EP/silicon (Si) interface were employed to enhance ITC. In this study, time-domain thermoreflectance (TDTR) experiments and molecular dynamics (MD) simulations were conducted to investigate the EP/SAM/Si system. The results demonstrate that SAM-NH2 modification, which forms bilateral covalent bonds at the EP/Si interface, increased the interfacial adhesion strength and enhanced ITC to 140%, thereby significantly promoting interfacial heat transfer. Conversely, ITC was reduced with SAM-CH3 due to the formation of single covalent bond. Subsequently, the differential effective medium (DEM) model was used to determine that the thermal conductivity of the composite modified with SAM-NH2 was improved by 11%. This study provides new insights into adjusting ITC using SAM.

Achieving excellent thermal transport in diamond/Cu composites by breaking bonding strength-heat transfer trade-off dilemma at the interface

The heat transport enhancement of diamond/Cu composites, a new generation of thermal management materials, is trapped in the bonding strength-heat transfer trade-off dilemma at the interface due to the noticeable difference in physical and chemical properties between Cu and diamond. Herein, we propose a new strategy combining ultrathin interface modification and low-temperature high-pressure (LTHP) sintering process to prepare the diamond/Cu composites. With a suitable coefficient of thermal expansion (CTE) of <10 ppm/K, the obtained diamond/Cu composites exhibit an outstanding thermal conductivity (k) value of 763 W/m K, over 90 % of the theoretical prediction of the differential effective medium (DEM) model. Meanwhile, using a lower diamond volume fraction (45 % vs. 50%–70 %), the k value is higher than those by conventional powder metallurgy, meaning a substantial reduction in the cost by reducing diamond filler content. For such a highly mismatched diamond/Cu interface, we maintain a high bonding strength by lowering the thermal stress damage while achieve a high thermal conductance (G) of 93.5 MW/m2 K by minimizing the heat transfer obstacles. The prepared interface structure is a diamond/TiC/CuTi2/Cu configuration, where the two possible heat transfer bottlenecks (the diamond/TiC interface and the TiC/CuTi2 interlayer) are no longer limiting factors on the overall interface. The successful resolution to the interfacial heat transfer problem is responsible for the superior thermal transport performance of the composites. This work deals with the critical challenge for the diamond/Cu composites and offers deep insight into the improvement mechanisms of thermal transfer. The proposed strategy can be generalized to the integration of highly mismatched interfaces widely present in other composites or thermal management systems.

Analytic solutions for effective elastic moduli of isotropic solids containing oblate spheroid pores with critical porosity

AbstractAccurate characterization for effective elastic moduli of porous solids is crucial for better understanding their mechanical behaviour and wave propagation, which has found many applications in the fields of engineering, rock physics and exploration geophysics. We choose the spheroids with different aspect ratios to describe the various pore geometries in porous solids. The approximate equations for compressibility and shear compliance of spheroid pores and differential effective medium theory constrained by critical porosity are used to derive the asymptotic solutions for effective elastic moduli of the solids containing randomly oriented spheroids. The critical porosity in the new asymptotic solutions can be flexibly adjusted according to the elastic moduli – porosity relation of a real solid, thus extending the application of classic David‐Zimmerman model because it simply assumes the critical porosity is one. The asymptotic solutions are valid for the solids containing crack‐like oblate spheroids with aspect ratio &lt; 0.3, nearly spherical pores (0.7 &lt; &lt; 1.3) and needle‐like prolate pores with &gt; 3, instead of just valid in the limiting cases, for example perfectly spherical pores (= 1) and infinite thin cracks (0). The modelling results also show that the accuracies of asymptotic solutions are weakly affected by the critical porosity and grain Poisson's ratio , although the elastic moduli have appreciable dependency of and . We then use the approximate equations for pore compressibility and shear compliance as inputs into the Mori–Tanaka and Kuster–Toksoz theories and compare their calculations to our results from differential effective medium theory. By comparing the published laboratory measurements with modelled results, we validate our asymptotic solutions for effective elastic moduli.

Achieving high thermal conductivity and strong bending strength diamond/aluminum composite via nanoscale multi-interface phase structure engineering

Diamond/aluminum composites, as a new generation of thermal management materials, are caught in the dilemma between inhibiting the formation of Al4C3 and improving the performance. Herein, we proposed a strategy for nanoscale multi-interface phase structure engineering, utilizing a combination of magnetron sputtering and vacuum heat treatment to obtain diamond particles with nanoscale TiC-Ti layers. Prolonging the vacuum heating time increases the content of TiC, but results in significant differences in the morphology and coverage of TiC formed on the diamond(100) and (111) facets. First-principles calculations reveal that the work of adhesion and C-Ti reaction tendency of diamond(100)/Ti are stronger than those of diamond(111)/Ti, clarifying the difference in interfacial properties between diamond/Ti and diamond/TiC. Diamond-TiC-Ti configuration obtained in advance contributes to fabricating the composite with diamond-TiC-Al(Al3Ti) structure, and the multi-interface phase structure is beneficial to improve the interface bonding, adjust the acoustic mismatch, and inhibit the formation of Al4C3. (800 °C 0.5 h)@Ti-coated diamond(100 μm)/aluminum composite with the multi-interface phase exhibits excellent thermal conductivity(646 W m−1 K−1) and outstanding bending strength(358 MPa), exceeding 90 % of the theoretical prediction of the differential effective medium model. The performance of (800 °C 0.5 h)@Ti-coated diamond/aluminum composite is about 30 % higher than that of traditional Ti-coated diamond/aluminum composite. The TiC layer formed by increasing the heat treatment time is thicker and discontinuous, leading to a decrease in the thermal conductivity of the composite and a weakening effect of Al4C3 inhibition. We clarified the formation mechanism of interface structure related to diamond orientation by multi-scale characterization. Based on the thermal conductivity prediction models, the interface structures corresponding to different diamond orientations were considered, and the predicted values showed good consistency with the experimental results. By interface modification engineering, we overcome the dilemma of introducing modified layer to inhibit Al-C reaction while leading to additional interface thermal resistance, providing insights into the interfacial thermal transport mechanism.

Effective medium approximation for the electromagnetic properties of rocks with surface conductivity

We present an approach to calculate the complex dielectric permittivity of a microheterogeneous rock composed of non-conductive solid grains with surface conductivity and a conductive liquid.We have calculated the effective electrical properties of a rock using the model that consider the complex structure of the conducting double layer between a solid grain and the electrolyte in the pores. The influence of two parts of double layer: the Stern (inner) layer on the solid surface and the diffuse (outer) layer was considered.Previously, the Differential Effective Medium (DEM) scheme was used to calculate the effective conductivity and dielectric permittivity. In contrast, we have adopted the Effective Medium Approximation (EMA) method for calculation of the effective electromagnetic properties of a rock with high inclusion concentration. This method allows one to describe both elastic and electromagnetic properties of the rock based on the unified model of the pore space.The calculations were performed both for the rock model with a fixed grain size and for the model with a fractal distribution of grain sizes.Our calculations have shown that the value of the dielectric permittivity in the low frequency range depends on the concentration and dimension of solid grains. However, the frequency-dispersion behavior is a function of the inclusion size only and it does not relate to the inclusion concentration in the porosity range typical for sedimentary rocks. This effect confirms the feasibility of the determination of the inclusion concentration and dimension by using the dielectric permeability and electrical conductivity dispersion curves.

A new rock physics model for fractured oil shale reservoirs in Mahu oil field

The exploration of unconventional reservoirs such as oil shale has become a focus of research in the oil/gas industry, but due to the diversity of lithology and structural complexity of shale reservoirs, the study of their rock physics laws is a challenge. By analyzing the physical, lithologic, and fluid characteristics of oil shale reservoirs in the Mahu area of Xinjiang, China, we adopted a variety of effective-medium theories to carry out rock physics modeling. We analyzed the differences in the calculation results of various theoretical models, and finally constructed a set of rock physics modeling processes suitable for oil shale reservoirs. The analysis shows that the calculation results of Voigt-Reuss-Hill (VRH) and Hashin-Shtrikman (HS) average for mixed mineral matrix are very similar, but there are certain differences between the upper and lower bounds calculated by them. The upper and lower bounds of HS average are closer than VRH average. We used the Kuster-Toksoz effective-medium, differential effective-medium (DEM), and self-consistent approximation models to construct the rock skeleton and analyzed the differences of the models. The results of the three models are almost identical, but their assumptions and limitations differ. We used DEM in the final shale model, considering the large porosity and the order of inclusion filling. According to the fracture distribution characteristics of oil shale reservoirs, we used an inclined fracture model to describe the fractures with different structural characteristics. Finally, the established shale rock physics model was used to calculate the actual logging data, and the results of elastic parameters are consistent with the measured data. Through the inversion of the fracture parameters, the inversion results are consistent with the measured results as a whole, indicating that the model has certain applicability to the simulation of oil shale reservoirs.

Joint inversion of crack properties of tight carbonates from electrical conductivity and ultrasonic velocity

Understanding the effects of cracks on the elastic and electrical properties of tight carbonates is crucial for the exploration and development of deep and ultra-deep carbonate reservoirs. In this work, the porosity, electrical conductivity and ultrasonic velocities of two brine-saturated carbonate samples (where the pore space is dominated by cracks) are measured jointly at different effective pressures (5–90 MPa), as well as the velocities with saturating nitrogen at the same pressure conditions. The results show non-linear changes in the measured values, indicating a correlation with the presence of cracks. To analyze the pressure-dependent elastic and electrical properties, an approach combining a multiphase Kachanov model with a multiphase reformulated electrical differential effective medium (REDEM) model is proposed. This approach agrees well with the pressure-dependent experimental results of brine-saturated carbonate samples. The crack aspect ratio spectra are estimated using the experimental porosity as a constraint to improve the accuracy of the inverted crack geometry. The spectra from the elastic (electrical) inversion are input into the multiphase REDEM (Kachanov) model to predict the electrical conductivity (wave velocities). Comparisons with laboratory measurements show the ability of the proposed approach to estimate elastic wave velocities from the electrical conductivity using the inverted crack geometry, and vice versa.

Improved Bending Strength and Thermal Conductivity of Diamond/Al Composites with Ti Coating Fabricated by Liquid-Solid Separation Method.

In response to the rapid development of high-performance electronic devices, diamond/Al composites with high thermal conductivity (TC) have been considered as the latest generation of thermal management materials. This study involved the fabrication of diamond/Al composites reinforced with Ti-coated diamond particles using a liquid-solid separation (LSS) method. The interfacial characteristics of composites both without and with Ti coatings were evaluated using SEM, XRD, and EMPA. The results show that the LSS technology can fabricate diamond/Al composites without Al4C3, hence guaranteeing excellent mechanical and thermophysical properties. The higher TC of the diamond/Al composite with a Ti coating was attributed to the favorable metallurgical bonding interface compounds. Due to the non-wettability between diamond and Al, the TC of uncoated diamond particle-reinforced composites was only 149 W/m·K. The TC of Ti-coated composites increased by 85.9% to 277 W/m·K. A simultaneous comparison and analysis were performed on the features of composites reinforced by Ti and Cr coatings. The results suggest that the application of the Ti coating increases the bending strength of the composite, while the Cr coating enhances the TC of the composite. We calculate the theoretical TC of the diamond/Al composite by using the differential effective medium (DEM) and Maxwell prediction model and analyze the effect of Ti coating on the TC of the composite.

Deep Dive into the factors influencing acoustic velocity in the Dalan-Kangan formations, the central Persian Gulf

The propagation of acoustic waves in rocks is directly influenced by the rocks’ elastic properties. To evaluate petrophysical properties from acoustic data, it is essential to understand the factors that influence the variations in acoustic velocity of sedimentary rocks. Carbonate reservoirs are heterogeneous, and their evaluation is complicated. A closer look at the factors affecting the elastic properties of these rocks is essential because they reveal important information about the reservoir properties and their formation evaluation. Rock physics modeling relies on laboratory-measured acoustic data. This study, however, employs acoustic logs to elucidate the key factors influencing sonic velocity, offering a more comprehensive and field-applicable perspective. Samples were prepared from the Permian–Triassic Upper Dalan and Kangan formations. Porosity, permeability, sedimentary textures, mineralogy, and pore types were investigated. Furthermore, compressional, shear, and Stoneley well-logs data were recorded and converted to acoustic velocity in the sampled interval. Porosity-velocity modeling based on the differential effective medium (DEM) theory was performed for different values of equivalent pore aspect ratio (EPAR). The results show that there is a strong inverse relationship between acoustic velocities and porosity. Acoustic velocities also exhibit an inverse correlation with permeability, but the strength of these relationships is relatively weak. Acoustic velocities are not affected by carbonate textures. A specific texture may exhibit different velocities due to the influence of diagenetic processes. Mineralogy has only a minor influence on acoustic velocities. Dolostones have a slightly higher velocity than limestones, but the difference is insignificant. Stoneley log values are slightly different in limestone and dolostone, because this wave propagates along the mud-borehole interface. The velocities were affected by the variations in pore types within the studied formations. Therefore, in carbonate rocks, porosity, and the pore types play a significant role in controlling acoustic velocities. The value of EPAR = 0.15 can be considered as the boundary between stiff pores (moldic and vuggy) and soft pores (interparticle, intercrystalline, micro-intercrystalline, and microporosity). The lower EPAR value of interparticle pores in limestones compared to dolostones can be attributed to diagenetic processes such as dolomitization and compaction. The findings of this study can help to better understand what factors affect acoustic velocity in carbonate rocks. This study also shows that acoustic logs data can be effectively used in rock physics modeling and pore type identification. By identifying the pore types, it is possible to recognize diagenetic processes and determine the rock types to control the heterogeneity and estimate reservoir quality.

Effect of temperature and fluid on rock microstructure based on an effective-medium theory

Abstract Temperature and pressure variations during the geologic diagenesis process can lead to complex pore structures in tight rocks. The effective-medium theory, based on the stress–strain relationship in combination with pore structure parameters, can be used to describe the elastic-wave responses of rocks. In this work, the differential effective medium (DEM) and self-consistent approximation (SCA) models are combined to invert the pore-crack spectrum. The Voigt–Reuss–Hill average is used to estimate the elastic moduli of the minerals. Then, based on SCA, the pore structures are incorporated into the rock matrix to create a new host phase. Subsequently, the DEM theory is used to add cracks with different volume fractions and aspect ratios to the host phase. To predict the structure of pores and cracks (crack density and aspect ratio), an objective function is defined as the sum of variances between experimentally measured and predicted wave velocities. The results show that the modeling predictions of P- and S-wave velocities at different temperatures and pressure ratios agree well with the experimental measurements. Variations in pore structure are determined at a zero effective pressure and different temperatures. We analyze the characteristics of how cracks change with variations in temperature and confining pressure, providing a theoretical basis for characterizing the structure of tight rocks.

Investigating the analytical relationship between pore geometry and other pore space properties in carbonate rocks

Although pore geometry plays an important role in carbonate rock physics modelling, few studies have been carried out on its analytic relationship with other pore space properties such as pore space stiffness. We propose an analytical workflow based on the differential effective medium (DEM) to estimate the elastic properties of carbonate rocks. The validity of our results is then cross-checked with the Xu and Payne model on a real carbonate dataset. This workflow establishes a direct and quantitative link between the pore geometry of carbonate rock and its other pore space properties such as the Biot coefficient and pore space stiffness. This relationship can, furthermore, be utilized in defining rock physics templates (RPTs) to investigate the role of pore geometry on the rock elastic properties. Furthermore, we extended the Biot–Gassmann–Krief (BGK) model through our proposed workflow by establishing a theoretical framework to relate the main components of the BGK model to the pore geometry usually estimated in the laboratory or empirically. This can help to investigate the impact of fluid substitution on each of these main components. Our investigation suggests that the higher the Biot and Gassmann coefficients, the more sensitive the rock is to fluid substitution. Moreover, this analytical workflow has been employed to examine the role of selecting different rotational spheroids (i.e. oblate and prolate) on the modelled velocities. Our results show that the modelled velocities depend on this selection in such a way that prolate pores are less sensitive to the variations in their pore aspect ratio compared with oblate pores.

Effect of Interfacial Coatings on Thermal Conductivity of Diamond/Al Composites

In this paper, the acoustic mismatch model and the differential effective medium scheme were applied to predict the influence of different interfacial coatings (Si and SiC) on the interfacial thermal conductivity and thermal conductivity of the Diamond/Al composites, respectively. With the increase of the thickness of interfacial coatings, the interfacial thermal conductivity and of the thermal conductivity of Diamond/Al composites decreased. In order to obtain ideal thermal conductivity of Diamond/Al composites, the thickness of the coating should be controlled below 1 μm. When the volume fraction of diamond was 60% and the average particle size was 100 μm, the interfacial thermal conductivity of Si and SiC coated Diamond/Al composites were in the range of 1.77×107∼1.1×108 W/(m2 · K) and 2.44×107∼1.29×108 W/(m2 · K), respectively; the thermal conductivity of Si and SiC coated Diamond/Al composites were in the range of 541.58∼764.15 W/(m· K) and 594.45∼777.3 W/(m· K), respectively. The thermal conductivity of Si and SiC coated Diamond/Al composites increased with the volume fraction and average particle size of Diamond, and the thermal conductivity of SiC coated Diamond/Al composites was higher than that of Si coated composites. SiC interface coating was proposed to be the most promising candidates to improve the thermal performance of Diamond/Al composites.

Investigation of mechanical properties of garnet structured Li7La3Zr2O12 under Al3+ and Ta5+ co-substitutions

The influence of co-substitutions on the structural and mechanical properties of garnet structured Li7La3Zr2O12 (LLZO) is investigated. Ab initio simulations of the cubic phase under Al and Ta substitutions are performed for an analysis of substitution dependencies on lattice constants, elastic moduli and hardness. The use of the differential effective medium theory methods enables a scale bridging description towards porous LLZO, with a 27% decay of Young's modulus for a porosity of 10%, compared to dense LLZO.

Excluding quartz content from the estimation of saturated soil thermal conductivity: Combined use of differential effective medium theory and geometric mean method

Saturated soil thermal conductivity (λsat) is the maximum soil thermal conductivity value of a given soil. Although it can be determined accurately with a heat pulse sensor, there are challenges to prepare fully saturated soil samples. Numerous models have been developed to estimate λsat, and among these, the geometric mean method (GMM) generally performs well. The GMM requires soil mineral composition or quartz content information, which is unavailable for most soils. Earlier studies commonly used assumed that quartz content (fquartz) was equal to sand content (fsand) or to 0.5 × fsand, which led to significant λsat estimation errors especially on coarse-textured soils. We derived a novel method to estimate λsat from soil porosity (ϕ) based on a combination of the GMM and differential effective medium theory (DEM). The new DEM-GMM approach has a single parameter, cementation exponent (m). Using a calibration dataset of 43 soils, we determined best fit m values for soils in three groups: 1.66 for Group I (fsand < 0.4), 1.62 for Group II (0.4 <= fsand < 1) and m = -1.34ϕ+1.70 for Group III (fsand = 1). Using best fit m values for different groups, the new model can estimate λsat values from ϕ. Independent validation results on another 46 soils showed that the new model outperformed the GMM method with the assumption that fquartz = fsand or fquartz = 0.5 × fsand. The mean RMSE, Bias and R2 values of the DEM-GMM approach were 0.202 W m−1 K−1, 0.013 W m−1 K−1 and 0.89, respectively, and corresponding values of the GMM with the two assumptions were 0.295 and 0.476 W m−1 K−1, 0.056 and -0.28 W m−1 K−1, 0.80 and 0.82, respectively. The robust performance of the DEM-GMM approach suggests that it can be incorporated into thermal conductivity models to accurately estimate the thermal conductivity of unsaturated soils.

Rock-physics modeling of elastic properties of multiscale fractured rocks

Fractures, often existing across various scales, control the mechanical and fluid flow properties of upper crustal rocks. Inferring fracture properties at different scales from multiband geophysical measurements is essential for many fields of earth and energy sciences. Under the framework of multiscale homogenization, we develop a rock-physics model to characterize the elastic and anisotropic properties of multiscale fractured rocks following a certain statistical law. The isotropic differential effective medium theory is used to model the elasticity of randomly oriented microcracks, and the linear slip theory is used to model the elasticity of oriented or randomly oriented macroscale fractures. For a multiscale fractured rock covered by six orders of fracture length (10−4 m to 102 m), it is found that velocity exhibits a decreasing trend with the increment of scale. Nevertheless, the different statistical distribution of multiscale fractures significantly affects the velocity and anisotropy variation pattern with scale. The velocity for the fractal distribution decreases significantly at the seismic scale, whereas, for the log-Gaussian distribution, the dramatic change in velocity occurs more at the ultrasonic and logging scales, depending on the length of the dominant fractures. We apply our methodology to interpret a set of multiscale geophysical data of P-wave velocity in a fractured carbonate formation and estimate that the multiscale fracture is possibly distributed in a log-Gaussian manner. Our elastic and anisotropic modeling strategy has the potential to predict the distribution pattern of fractures, especially by reconciling the multifrequency geophysical measurements (e.g., ultrasonic, logging, and seismic data).

Design and development of polymer composite heat exchanger tubes using an integrated thermal-hydraulic and material design framework

In the current study, thermal-hydraulic design of the heat exchanger and composite material design are integrated to develop polymer composite tube materials for heat exchanger applications. For preliminary analysis, the scheme utilizes basic thermal resistance equations, Kern and Bell-Delaware methods for the design of baffled shell and tube heat exchangers, and differential effective medium theory for the design of composite materials. The preliminary analysis clarifies that the thermal conductivity of tubes is a performance-limiting parameter in the case of liquid-liquid applications. The heat exchanger's design imposes that the tubes' thermal conductivity must be enhanced to ≥8.5 W/m.K for achieving heat transfer comparable to those of metal counterparts. To attain the threshold thermal conductivity, the design of polymer composites employing differential effective medium theory requires that high volume fractions (> 0.3) of high effective aspect ratio (> 10 or 0.1) thermally conductive fillers be incorporated in a polymer matrix. Finally, the samples are fabricated of polypropylene matrix and expandable graphite filler with variable volume fractions (0.1–0.4). The highest thermal conductivity of 8.3 W/m.K was achieved in a 40 vol% sample. The comparison of measured and computed thermal conductivity values shows an acceptable agreement supported by electron microscopy and thermal images.

Chemo-hydro-mechanical effects of CO2 injection into a permeable limestone

CO2 storage in carbonate aquifers is a way to mitigate atmospheric CO2 emissions, but it leads to acid-producing reactions that may induce alterations in the rock pore structure and hydromechanical properties. To gain a better understanding of these changes in rock properties, percolation experiments under constant flow-rate conditions with (i) CO2-saturated water (PCO2 = 100 bar and T = 60 °C) and (ii) HCl solutions (P = 1 bar and T = 60 °C) were performed on centimetric cores of the grain-supported Pont du Gard Limestone (permeability about 10−14–10−13 m2). Effluent chemistry analyses, X-ray imaging, and measurements of the hydromechanical properties of intact and altered specimens were used to quantify acid-induced changes in the two acid-rock systems. Experimental results show that the rock dissolution patterns highly depend on the acid type and pore space heterogeneity. Under the flow conditions of these experiments, complete HCl dissociation (strong acid) and rapid HCl-rock reaction result in a compact dissolution pattern that only affects the hydromechanical properties of the core inlet. Conversely, partial dissociation of H2CO3 (weak acid) produces chemical reactions all along the core. Initial structural heterogeneities localize chemical reactions along preferential flow pathways, causing instabilities in the reaction front and wormhole formation, which markedly enhances permeability. A powerlaw relationship with a very large exponent (as high as 24) accounts for the variation in permeability as a function of porosity. Altered cores render both a significant attenuation in mechanical rock properties and ultrasonic velocities, which is reproduced using a Differential Effective Medium (DEM) homogenization approach. The high-pressure percolation experiments of this study using CO2-saturated water represent an extreme scenario of CO2-brine-rock interactions in carbonate reservoirs, which needs to be considered to improve the prediction and monitoring of the storage performance.