Differential Effective Medium Model Research Articles

Fluid effect on elastic properties of carbonate and implication for CO2 geological 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 measured eight carbonate samples under varying pressure and fluids saturation conditions, and conducted quantitative analysis. The measurements showed that water saturation can increase P-wave velocity (Vp), while oil and CO2 saturation may lead to an increase, decrease or no change in Vp. Meanwhile, all fluids saturation reduces the S-wave velocity (Vs). The velocities of dolomite samples are higher and less pressure-sensitive than that of limestone samples. Four attributes are adopted to distinguish the fluids effect, including elastic moduli, impedance, Vp/Vs ratio, and a newly designed fluid discrimination factor F, which is proposed by multiplying P-wave modulus and square value of density change. Among the attributes, the F factor performed the best as it achieved evident and consistent results for all the samples. Rock physics models were used to simulate the elastic behaviors with the differential effective medium model predicting Vs the best. The Gassmann’s equation correctly indicated the positive or negative changes of rock velocity after fluid saturation even though its prediction did 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.

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.

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.

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.

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.

Bayesian linearized rock-physics amplitude-variation-with-offset inversion for petrophysical and pore-geometry parameters in carbonate reservoirs

Rock-physics amplitude-variation-with-offset (AVO) inversion aims at directly predicting reservoir properties from prestack seismic data. However, carbonate reservoir rocks often develop complex pore structures, which limits the application of conventional inversion methods with fixed pore-geometry parameters. We derive a PP-wave reflectivity equation in terms of porosity, water saturation, and pore-aspect ratio and we develop a rock-physics AVO inversion method to jointly estimate the petrophysical and pore-geometry parameters in carbonates. The reflectivity equation is obtained by linearizing the rock-physics model based on the differential effective medium model and Gassmann’s equation using Taylor series approximation, and we combine the linearization with the Aki-Richards equation. Thanks to the linearized model, the analytical solution to the inverse problem is derived using Bayesian linear theory. Our solution combines simulated annealing to estimate the prior information of the pore geometry and the iterative Bayesian inversion to update the posterior model. The method is tested on a benchmark data set and compared with conventional methods with a fixed aspect ratio. The results show that our method improves the petrophysical results. The method is also compared with two-step and nonlinear inversion methods to demonstrate its advantages. The method is applied to a field seismic section from a carbonate reservoir with a complex pore structure to demonstrate its advantages in terms of prediction accuracy.

A simulation and data informed approach to porosity partitioning

Information about pore shape and geometry form one of the significant inputs in determining the effective elastic properties of porous rocks. The size and structure of the pores determine the amount of fluid contents which in turn determine their bulk response. Conventionally, effective medium models have been used to study the macroscopic properties of these rocks. These models often use a fixed set of microscopic variables (like the shape parameter) to describe their bulk behavior. Barring the specification of the elastic properties of the starting host material, their original formulations often lack the provision to integrate any experimental data, later. In the context of carbonates, the rocks exhibit a large variation in pore shapes and sizes, hindering the development of rock physics models. Therefore, they eventually require calibration. This is an important issue as the size of the pores here range from nanoscale to meter scale due the presence of primary and secondary porosity systems. In this paper we develop a method that can integrate the pore shape information into differential effective medium models using simple statistical and machine learning algorithms. Avoiding the use of conceptual values for the interparticle and vug type pores, our technique facilitates a data-based inference of the shape parameters from both the image data and forward model simulations. Micro-tomography images were used to extract the pore shape information for relatively larger pores such as the vugs. The information about the interparticle pores was deduced using a simulation-based approach from well-logs. Both of these were used to specify the properties of the new inclusions, hence aiding in data informed porosity partitioning. Finally, we outline a simple regression-based scheme using a first order polynomial model that can be used to calibrate any general rock physics model.

Study on Anisotropic Petrophysical Modeling of Shale: A Case Study of Shale Oil in Qingshankou Formation in Sanzhao Sag, Songliao Basin, China

Seismic petrophysics is an important link between seismic elastic properties and reservoir physical properties. Based on the petrological and microstructure characteristics of shale in the Qingshankou formation of Sanzhao sag in the north of Songliao Basin, this paper presents an anisotropy petrophysical model with complex pore structure suitable for organic shale constructed with the use of the Voigt-Reuss-Hill average model, an anisotropy self-consistent approximation+differential effective medium model, and the layering of clay and kerogen is simulated by using the Voigt-Reuss-Hill average and bond transform to achieve the simulation of shale anisotropy. Based on the proposed model, the effects of the organic volume fraction, porosity, and pore aspect ratio on rock elastic properties are discussed. The result shows that with the increase of matrix porosity, all elastic parameters show a decreasing trend; with the increase of the organic volume fraction, except shear modulus, other elastic parameters show an increasing trend. Through comparative analysis, the elastic parameters (Lamé impedance and Shear impedance) sensitive to the organic volume fraction and porosity are optimized; the seismic petrophysical cross-plot template with core calibration is constructed. The application shows that the predicted S-wave velocity based on the proposed model is in good agreement with the S-wave velocity derived from dipole source logging. Combined with the high-precision prestack elastic parameter inversion, the “sweet spot” characteristics can be well described, and the research could contribute to a better “sweet spot” description and provide a better support for shale exploration in Sanzhao sag.

Rock physics based velocity-porosity correlations developed for estimation of the elastic properties of the Bakken formations of the Williston Basin, North Dakota

Rock physics models are predictive tools used to estimate the velocity, or elastic properties of formations, based on strong theoretical foundations, as opposed to some of the simple empirical correlations that have been developed for specific regional formations. While the basic rock physics models use simplified assumptions and involve less input, more complex models, such as inclusion-based models, estimate velocity-porosity relation as function of different parameters including pore's fluid saturation and type, cementation, confining pressure and diagenesis. The downside is that these models require performing tedious calculations and in some cases solving complex differential equations. These models may also differ depending on the type of formation, for example, separate models may be used for shales compared to the siliciclastic or carbonate formations.In this paper, we present newly developed correlations that can substitute the rock physics modeling. The developed velocity-porosity correlationsare based on the mineralogical data from the Bakken formation in the Williston Basin, North Dakota, however, they can be used with good accuracy for other formations too. These models were developed based on large volumes of data from simulation of many cases using the differential effective medium (DEM) theory, a commonly used rock physics model. DEM models were developed for composite rock, but assuming single mineral type constituting the rock. The inclusion phase was incrementally added to the matrix phase. The pores were then modeled with three phase fluid (water, oil, and gas) at different saturation levels and finally, different pore's aspects ratios (AR) were assumed to simulate pores heterogeneity (i.e., crack, intraparticle, intergranular and moldic type pore geometries). The correlations constants were extracted for different key minerals in the Bakken, including quartz, calcite, dolomite, anhydrite, illite and kerogen. Having the volume fraction of minerals from lab-based XRD or Elemental Capture Spectroscopy (ECS) logs, linear averaging was applied to estimate the equivalent velocity and elastic properties of the formations.The correlations were applied to several case studies in the Bakken and also compared with the existing lab data, which showed a good agreement with the DEM model. The simplicity of using the correlations consists of simply entering the input values in an excel template that accounts for the constant parameters, using a single approach for different type of formations. This offers a great advantage for their applications. The workflow of developing the correlations and its applications in one case stduy using data from a Well in the Mountrail County will be presented.

Seismic rock-physics linearized inversion for reservoir-property and pore-type parameters with application to carbonate reservoirs

Carbonate reservoirs hold promising potential for hydrocarbon exploration, but they usually exhibit complex pore structures, which lead to difficulties in the seismic/elastic prediction via conventional rock physics modeling, and in turn, hinder an accurate estimation of reservoir properties from seismic observations. This work presents a seismic rock-physics inversion method to jointly estimating reservoir-property (porosity and fluid saturation) and pore-type (pore aspect ratio) parameters in carbonates from seismic/elastic data. The method considers the aspect ratio as a pending parameter, which favors the pore-type variation so as to describe the structure complexity. To achieve the joint estimation, we derive a linearized rock physics model based on the differential effective medium model and the Biot-Gassmann equation that relate porosity, water saturation, and aspect ratio to elastic parameters. Moreover, to realize the estimation with computational efficiency, we derive the analytical solution to the inversion with the linearized model based on the Bayesian inverse theory. We estimate the pore aspect ratio at a well location to provide prior information for the inversion and employ an iterative inversion strategy with piecewise linearization to improve the result. The proposed method is applied to two carbonate reservoirs including 2D and 3D field data sets. Compared with the conventional rock physics inversion scheme with a constant aspect ratio, the application demonstrates that the method achieves better accuracy for reservoir property estimation, which can be a good indicator for the potential target areas of complex reservoirs.

Interfacial Characterization and Thermal Conductivity of Diamond/Cu Composites Prepared by Liquid-Solid Separation Technique.

Diamond/Cu composites are widely studied as a new generation of thermal management materials in the field of electronic packaging and heat sink materials. The surface modification of diamond can improve interfacial bonding between the diamond and Cu matrix. The Ti-coated diamond/Cu composites are prepared via an independently developed liquid-solid separation (LSS) technology. It is worth noting that there are obvious differences for the surface roughness between the diamond-{100} and -{111} face by AFM analysis, which may be related to the surface energy of different facets. In this work, the formation of titanium carbide (TiC) phase makes up the chemical incompatibility between the diamond and copper, and the thermal conductivities of 40 vol.% Ti-coated diamond/Cu composites can be improved to reach 457.22 W·m-1·K-1. The results estimated by the differential effective medium (DEM) model illustrate that the thermal conductivity for 40 vol.% Ti-coated diamond/Cu composites show a dramatic decline with increasing TiC layer thickness, giving a critical value of ~260 nm.

Study the Elastic Parameters of Sandy Conglomerate under Different Burial History and Petrophysical Modeling

Over the past few years, significant exploration breakthroughs have been made in the sandy conglomerates reservoir of the Triassic Baikouquan Formation in the Mahu Sag, Junggar Basin, China. However, the elasticity and pore characteristics of the tight sandy conglomerates reservoir in this area are still unclear. Through a systematic sonic testing program of the sandy conglomerates sample collected from the Mahu Sag, the regularity behind the variation of the elasticity and pore characteristics of the sample has been analyzed and captured. The Triassic Baikouquan Formation of the slope of Mahu Sag has been through complex burial and diagenetic history. The compaction, cementation, and dissolution are the three types of diagenesis that have the greatest impact on pore characteristics in the study area. In order to quantitatively describe the influence of this complex burial and diagenetic history, we present a rock-physics modeling approach to describe the elastic properties of sandy conglomerate sample. The overall strategy of the modeling is to combine the contact cement theory (CCT), differential effective medium (DEM) and the upper Hashin-Shtrikman bound. The CCT model can well describe the history of cementation, DEM model is suitable for the history of dissolution, and HS upper bound is used to describe the history of compaction. Then, the model is used to describe well log data from sandy conglomerates reservoirs in Mahu Sag and successfully explain the rock porosity, pore shape trends, and the elasticity in the sandy conglomerate reservoirs.

Research on Rock Physics Modeling Methods for Fractured Shale Reservoirs

The Sichuan Basin is a significant region for exploration and development of shale gas in China, and it is essential to clarify the impact of deep shale gas reservoir parameters on cost-effective development at scale to ensure national energy security. Rock physics modeling is a significant means of communicating the physical and elastic parameters of rocks. A rock physics modeling method applicable to fractured shale gas reservoirs is proposed for the current situation of complex fluid relationships in shale gas reservoirs and unclear characteristics of gas identification seismic response. In this paper, based on the Self Consistent Approximation (SCA) model and the differential effective medium (DEM) model, the anisotropic source of shale is used as a starting point to add bound water, kerogen, clay, and brittle minerals, the Schoenberg linear slip theory is used to add fracture disturbance effects, and then the Brown–Korringa model is used to perform fluid replacement under anisotropic conditions. Finally a rock physics model applicable to fractured shale gas reservoirs is obtained, and the established rock physics model is used for analysis of elastic parameters, Thomsen parameters, and fracture weakness parameters. Rock physics tests were performed on shale in southern Sichuan as an example. The experimental results show that the model established by the process can accurately invert the longitudinal and transverse wave velocities of the shale, which can provide a conceptual basis for the study of fractured shale gas reservoirs.

Correlations of inclusion-based rock-physics model inputs from Bayesian analysis

AbstractFor any given rock-physics model, knowledge of correlations among its inputs helps to define geologically and physically meaningful and informed models for a given problem. These informed models can, in turn, reduce the uncertainty in forward and inverse problems. We use a Bayesian framework to identify such correlations among inputs of two rock-physics models. That framework makes use of velocity and porosity measurements on both dry and brine-saturated carbonate samples. Two inclusion-based rock-physics models, the self-consistent approximation and the differential effective medium model, are analyzed along with these data to identify the underlying correlations. To do so, the posterior distribution must be evaluated, which is based on a prior model and the calculated likelihood function. Exhaustive sampling of the posterior is convenient in this case because relatively few input parameters to consider. Results are multi-variate histograms that indicate maximum a posteriori values of the inputs. Correlations among the inputs become evident when the Bayesian analysis is repeated many times with different prior models. These correlated values provide the inputs to optimized maximum a posteriori models. The correlations identified for the two rock-physics models under study should be used in relevant applications. Finally, all rock-physics models, along with an appropriate data set, should be examined in a similar Bayesian framework.

Quantitative prediction of porosity and gas saturation based on a new dual-porosity rock-physics model and Shuey’s Poisson ratio for tight sandstone reservoirs

The prediction accuracy of physical parameters from seismic data has strong dependence on the quality of the used elastic parameters and rock-physics models especially for tight sandstone reservoirs. In this study, a new dual-porosity model with stiff and compliant porosities is firstly deduced from classical differential effective medium model according to the characteristics of both pores and fractures development in tight sandstones, it is the product of power function of both compliant and stiff porosities, and is independent of the addition order of pores. Then, the Shuey's AVO (Amplitude Variation with Offset) approximation is expanded, and a new Shuey Poisson's ratio which is the reciprocal of the difference between 1 and Poisson's ratio is defined and inverted from Shuey Poisson's ratio reflection seismogram to ensure the inversion accuracy of both P-wave impedance and ShueyPR. Next, a new two-dimension rock-physics template on P-wave impedance versus Shuey Poisson's ratio is built by the new dual-porosity model and Gassmann equations to characterize the quantitative relationship between P-wave impedance, Shuey Poisson's ratio and physical properties and is used to invert the porosity and saturation through global optimization algorithm. The new method has been applied to quantitative reservoir prediction of tight sandstone of Shaximiao Formation of QL gas field in Northwest Sichuan, China. Real application indicates that the distribution of high-porosity reservoirs with porosity more than 8% and their gas saturation can be accurately predicted.

Applicability of cross‐property differential effective medium model to the joint elastic–electrical properties of reservoir sandstones

ABSTRACTJoint seismic and controlled‐source electromagnetic surveys can reduce uncertainty and improve hydrocarbon quantification. However, the successful interpretation of joint seismic and controlled‐source electromagnetic survey data requires a valid rock physics model to link the elastic and electrical rock properties. A cross‐property differential effective medium is recently proposed with pores embedded in the mineral matrix. We have presented a technique to test the applicability of the cross‐property differential effective medium model to the joint elastic‐electrical properties of reservoir sandstones. The method is based on the common employment of measured sample porosity and inverted equivalent pore aspect ratio from cementation exponent for the modelling. Application of the modelling approach to a laboratory joint elastic‐electrical dataset shows that there is a systematic discrepancy in the modelled and measured joint elastic–electrical properties. It is also found that an equivalent pore aspect ratio is existing to reasonably predict the trend of the joint elastic–electrical data; however, the porosity used in the modelling is far from their measured values. Conversely, if the measured sample porosity is employed, the mentioned equivalent pore aspect ratio fails to fit either of the measured elastic and electrical rock properties. The results indicate the incapability of the cross‐property differential effective medium model for the joint elastic–electrical modelling of reservoir rocks and suggest the requirement of a new model to link the elastic and electrical properties.

Nonlinear petrophysical amplitude variation with offset inversion with spatially variable pore aspect ratio

Petrophysical amplitude variation with offset (AVO) inversion, which combines a rock-physics model and prestack inversion, aims at effectively quantifying reservoir-property parameters from prestack seismic data. However, for a reservoir with complex pore structures, this approach may suffer from difficulties in rock-physics modeling, which hinders solving the relevant inverse problem. We have proposed a petrophysical AVO inversion method that considers the complex pore structures within reservoir rocks. The method integrates a differential effective medium model, the Gassmann equation, and the exact Zoeppritz equation as the forward operator. In particular, the pore complexity is addressed by favoring the spatial variation of pore type. Differing from conventional sequential inversion methods, the pore-type variation is introduced by updating the aspect ratio together with the reservoir parameters during the inversion process. To enhance the stability of the results, the estimation of aspect ratio and reservoir parameters is jointly conditioned to seismic and elastic data under a Bayesian framework, which leads to the objective function with joint data misfit terms. The objective function is optimized with a simulated annealing algorithm that includes the full nonlinearity of the forward operator. The proposed method is demonstrated by testing and applying on a carbonate reservoir. It generally outperforms methods that are either purely conditioned on the seismic data or based on a constant aspect ratio.

Construction and validation of the upscaling model of organic-rich shale by considering water-sensitivity effects

Due to the complexity of its microscopic composition, the mechanical changes produced by the hydration process of organic-rich shale are more complicated than those of pure clay minerals. Although predecessors have researched the upscaling model of shale, the construction and evaluation of the water-saturated model remain a long-standing challenge. In this work, the combination of the differential effective medium (DEM) model and the self-consistent (SC) model (DEM-SC) was used to obtain a universal stiffness tensor of the clay matrix based on reverse modeling of ultrasonic pulse velocity (UPV) test results. Subsequently, a new water-sensitivity -based upscaling model was constructed that simultaneously considers: (1) the interlayer swelling, confining, and substitution effects of clay matrix under water-saturated conditions; and (2) the influence of depositional environment on the pore morphology of organic matter and the influence of maturity on its elastic properties. The upscaling model showed that the interlayer swelling effect is the most critical water-sensitivity effect, and the confining and the substitution effect can only compensate for part of the modulus reduction caused by interlayer swelling. In addition, the model behaved better when dealing with problems with a large volume ratio of inclusions (such as marine shale) and achieved good prediction results by controlling the relative errors compared with the microindentation experiments at less than 15%. Finally, the model was further applied to the well scale with better prediction results by considering the water-sensitivity effect, proving that the model has a wide range of application potential in formation evaluation and construction operations in shale gas production.

Theoretical modeling and optimization of interface design to improve thermal conductivity in Mg-Dia composites

This study aimed to theoretically optimize the Mg-Dia interface with components of different types and thicknesses to increase the thermal conductivity of diamond-doped magnesium matrix composites. Acoustic mismatch (AMM), diffusion mismatch model (DMM) and differential effective medium (DEM) models were used for TC calculations of the designed composites. According to the results, TiC, SiC, ZrC, and B 4 C carbides are the components that can increase the TC value up to 529 W/mK; however, most of them, except SiC, negatively affected the TC value with the increase in thickness. B and Cr elements also provided higher TC values compared to other elements. Except for the Cr-CrC 3 C 2 conversion, all other carbide conversions had a positive effect on TC. MgO, Al 2 O 3 and ZrO oxides alone or together with MgO increased the TC value up to 525 W/mK. Apart from this, MgO had a negative effect on all components except B or B 4 C. As a result, Mg-MgO-B-Dia was observed as the component providing the most stable TC value even if the thickness increased. This is thought to be due to less scattering during heat transfer between components with close Debye temperatures. It has also been understood that these results can deviate 29% from the experimental one even with the best method.