Conductivity Model Research Articles

Model for fracture conductivity considering particle size redistribution caused by proppant crushing

Clarifying the dynamic evolution and control mechanisms of fracture conductivity is crucial for optimizing hydraulic fracturing design. Previous studies on fracture conductivity mechanisms in deep shale reservoirs have been insufficient, particularly when considering proppant crushing, rendering existing models inapplicable. Therefore, in this study, the coupled effects of particle size redistribution caused by proppant crushing were considered. A particle crushing model based on fractal theory was introduced. It was combined with the Kozeny–Carman equation, and equations were derived for the evolution of the equivalent diameter of the proppant pile gradation curve and permeability, establishing a new model for predicting the fracture conductivity considering the particle size redistribution caused by proppant crushing. Furthermore, it provides an optimized chart of conductivity that matches the supply conductivity of the reservoir. The results of the study reveal that the fracture conductivity decreases owing to proppant rearrangement, compaction, and crushing, with a more significant decline in the initial compression stage, where the rate of conductivity reduction is 2.5 times that of the compaction stage. Proppant crushing shifts the gradation curve leftward, reducing the equivalent particle diameter and, consequently, the fracture conductivity. By adjusting the crushing ratio, apparent Young's modulus, looseness factor, and proportion of large-particle components of the proppant, the fracture conductivity can be controlled. This provides a theoretical basis for the development of proppant properties and fracturing optimization in deep shale reservoirs.

Role of sodium sulfate in electrical conductivity and structure of lignin-derived carbons

Lignin is a promising renewable alternative to fossil fuels for producing carbon materials such as carbon fibers, activated carbons, or carbon black. Despite extensive research, lignin-derived carbon materials show limited graphitization relative to comparable petroleum-derived carbons. Further, lignin-derived carbons show high variation in graphitization and electrical conductivity depending on the source of the lignin. Herein, nine lignins, derived from various feedstocks and isolation procedures, are pyrolyzed to produce biochar at 1100∘C. These lignins have a range of chemical compositions, carbon structures, and particle sizes. As a result, the pyrolysis behavior of these lignins varies, with powdered, clumped powder, and “foam” biochar morphologies resulting from finely powdered lignin. The produced biochars vary widely in both electrical conductivity, from 0.19 to 19 S/cm, and in-plane graphitic crystallite size, from 3.4 to 41.2Å. A significant decrease in electrical conductivity is identified when Na2SO4 is removed from lignin, accompanied by an increase in graphitic crystallite size. Based on this finding, a quadratic relationship between biochar graphitic crystallite aspect ratio and electrical conductivity is proposed that builds on established quasi-percolation models for biochar electrical conductivity.

Ab initio modeling and experimental analysis of electronic conductivity in PEDOT:PSS-PEO films for extrusion-based manufacturing

In this study, a combination of ab initio modeling and experimental analysis is presented to investigate and elucidate the electronic conductivity of films composed of conducting polymer blend PEDOT:PSS-PEO. Detailed density functional theory (DFT) calculations, aligned with experimental data, aided at profound understanding of the chemical composition, band structure, and the mechanical behavior of these composite materials. Systematic evaluation across diverse ratios of PEDOT, PSS, and PEO revealed a pronounced transformation in electronic properties. Specifically, the addition of PEO into the polymer matrix remarkably changes the band gap, with a marked alteration observed near a PEO concentration of 52 wt-%. This adjustment led to a substantial enhancement in the electrical conductivity, exhibiting an increase by a factor of approximately 20, compared to the original PEDOT:PSS polymer. The present investigation determined the crucial role of the PEDOT to PSS ratio in band gap determination, emphasizing its significant impact on the material's electrical conductivity. Concurrently, the mechanical property analysis unveiled a consistent increase in Young's modulus, reaching up to 765.93 MPa with increased PEO content, signifying a notable mechanical stiffening of the blend. The obtained combined theoretical and experimental insights illustrate a detailed perspective on the conductivity anomalies observed in PEDOT:PSS-PEO systems, establishing a robust framework for designing highly conducting and mechanically stable polymer blends. This comprehensive approach elucidates the interplay between chemical composition and electronic behavior, offering a strategic pathway for extrusion-based manufacturing techniques such as Direct Ink Writing (DIW).

Effect of proppant injection condition on fracture network structure and conductivity

AbstractThe hydraulic fracturing of shale reservoirs is an important topic, and adjusting the fracturing process can enhance fracturing efficiency. To analyze the effect of injection conditions on the fracture network structure and conductivity, numerical simulations and theoretical calculations are carried out based on the construction data, and the variation patterns of the fracture network parameters are determined. During the theory study, a fracture network conductivity model was obtained by combining the fracture network expansion model and the fracture diversion model. Then a numerical model was set up according to the analysis results of monitoring data. The numerical simulation results showed the fracture network structure and proppant distribution under different conditions. Throughout the simulation process, the structural parameters and conductivity of the fracture network can be determined by controlling the injection amount and adjusting the injection method, speed, and sand ratio. Results indicated that the proppant pulse frequency during the injection process was a major factor affecting the structure and conductivity of the fracture network. At the same time, a comparison of the distribution structure of the proppant revealed that although the intermittent injection of the proppant improved the flow channel, the efficiency of fracture utilization can still be improved.

A logging evaluation method for shale and calcium-bearing reservoirs based on the effective medium HB resistivity model—a case study on the Sartu Formation and Putaohua Formation West of the Daqing Placanticline

Abstract To solve the problems of low logging interpretation accuracy and fluid identification in shale and calcium-bearing formations in the study area, this paper uses the effective medium theory and electric double layer theory, combined with artificial core technology, to carry out the first quantitative study of the influence of calcareous on rock resistivity, and establishes a conductive model for the evaluation of the oil and gas properties of shale and calcium-bearing formations. First, considering the salt exclusion effect of clay pore water and its dispersion distribution, an improved Berg model was established. Compared with the original Berg model, the improved Berg model achieved a higher interpretation accuracy. Second, artificial cores with different calcium and clay content were designed and prepared using artificial core technology. A quantitative formula describing the relationship between the cementation exponent m and the calcium and clay content was established and combined with the improved Berg model to build an effective medium HB resistivity model suitable for shale and calcium-bearing formations. Finally, the hierarchical decomposition crossplot approach was used to identify the calcareous cemented rock layers, then the reservoir parameters were calculated. The new model is applied to the quantitative evaluation of reservoir logging, and the comparison with the oil test results indicates that the new model established in this paper can be applied to the quantitative evaluation of reservoir logging in this area, and the corresponding evaluation techniques provided a good reference for logging interpretation and evaluation in other corresponding areas.

Polaron-mediated transport and relaxation phenomena in the lead zinc niobate (PZN) modified bismuth ferrite solid solution

To investigate the dielectric and conductivity properties of PZN modified BF solid solution high temperature mixed oxide technique is employed. The material is subjected to analysis using XRD, SEM, and impedance spectroscopy. A polycrystalline PZN-BF sample with an average crystallite size of 63.3 nm has been formed. The scanning electron micrographs show that the grains and grain boundaries are distributed suitably. dielectric characteristics of the 0.1PZN-0.9BF compound are studied at frequencies ranging from 1 kHz to 1 MHz and temperatures ranging from ambient temperature to 400 °C. The confined mobility of charge carriers causes nearly continuous loss (NCL) behavior at low temperatures (<200 °C). High-temperature relaxation resulting from charge carrier hopping induces maximum loss and elevated conductivity. Rendering to the Overlapping Large Polaron Tunnelling (OLPT) model of conductivity, the transport mechanism in this modified BiFeO3 (BF) compound is facilitated by the short-range hopping of polarons. The NTCR behavior from Arrhenius plot of ac conductivity and temperature independent conductivity relaxation from loss modulus (M'') analysis are demonstrated. Sensors, actuators, and optoelectronic devices can benefit from the PZN-modified BF compound's electrical and dielectric characteristics, which have been studied in detail.

Electrical conductivity of the suboceanic upper mantle constrained by satellite-derived tidal magnetic fields: three-dimensional inversion, validation and interpretation

SUMMARY We present the first 3-D upper-mantle conductivity models obtained by an inversion of the satellite-derived tidally induced magnetic fields (TIMFs). We primarily use the M$_2$ period, but the potential benefit of the O$_1$ period is also inspected. The inverse-problem solution is found using the recently developed frequency-domain, spherical harmonic finite-element method based on the adjoint approach. We tested two different TIMF data sets derived from the satellite measurements of the Swarm mission and two different regularizations; the solution is either required to be sufficiently smooth or reasonably close to the a priori 3-D conductivity model WINTERC-e Wd-emax. The reconstructed conductivity models are locally compared with the 1-D conductivity profiles from other studies. If we use one of the available TIMF data sets, the smooth reconstructed model gravitates towards Wd-emax and the TIMF-adjusted Wd-emax model is closer to the reference conductivity profiles than the original Wd-emax model. Finally, we use the obtained 3-D conductivity distributions to calculate the corresponding 3-D water distribution in the upper mantle using thermodynamical and compositional models coupled to the electrical-conductivity laboratory measurement of individual mantle constituents.

Evaluation of thermal conductivity models and dielectric properties in metal oxide-filled poly(butylene succinate-co-adipate) composites

This study examines how various nanofillers impact thermal conductivity, dielectric characteristics, and electromagnetic interference (EMI) shielding potential of bio-based and biodegradable poly(butylene succinate-co-adipate) (PBSA). TiO2, NiFe2O4, Fe2O3, and Fe3O4 were selected as fillers for nanocomposites at 4–50 vol.% (12–81 wt.%). The nanocomposites were analyzed in three domains: structural (scanning electron microscopy, energy dispersive X-ray spectroscopy mapping, density, tensile testing), thermal (light flash analysis, literature models), and dielectric (AC conductivity, permittivity, EM shielding effectiveness (SE)). The investigated fillers showed good dispersion and compatibility with the PBSA matrix. LFA was analyzed according to literature models, where Bruggeman and Agari models showed the best fit at high concentrations. The dielectric analysis revealed that most of the nanocomposites did not reach percolation; thus, producing thermally conductive plastics that are electrically insulating. EMI shielding was limited to frequencies below 10 Hz, with the notable exception of Fe3O4 (100 nm and loading of > 25 vol.%), which showed shielding at frequencies up to 105 Hz. The investigated composites based on a biodegradable polyester and abundant metal oxide nanofillers are suitable for the production of cheap, ecological, and electrically insulating heat dissipation solutions required for modern and lightweight applications.

Influences of defective interphase and contact region among nanosheets on the electrical conductivity of polymer graphene nanocomposites

In the current article, a defective interface is characterized by “Dc,” representing the smallest diameter of nanosheets crucial for effective conduction transfer from the conductive filler to the medium, and by “ψ” as interfacial conduction. These parameters define the effective aspect ratio and operational volume fraction of graphene in the samples. The resistances of the graphene and polymer layer in contact zones are also considered to determine the contact resistance between adjacent nanosheets. Subsequently, a model for the tunneling conductivity of composites is proposed based on these concepts. This innovative model is validated by experimental data. Additionally, the effects of various factors on the conductivity of the composites and contact resistance are analyzed. Certain parameters such as filler concentration, graphene conductivity, interfacial conduction, and “Dc” do not affect the contact resistance due to the superconductivity of the nanosheets. However, factors like thin and large nanosheets, short tunneling distance (d), high interfacial conduction (ψ), low “Dc,” and low tunnel resistivity (ρ) contribute to increased conductivity in nanocomposites. The maximum conductivity of 0.09 is obtained at d = 2 nm and ψ = 900 S/m, but d > 6 nm and ψ < 200 S/m produce an insulated sample. Additionally, the highest conductivity of 0.11 S/m is achieved with Dc = 100 nm and ρ = 100 Ω m, whereas the conductivity approaches 0 at Dc = 500 nm and ρ = 600 Ω m.

Analytical Model for the Molecular Ionization Energy in an External Electric Field.

A model for the molecular ionization energy in an applied electric field is presented on the basis of a perturbation expansion in the electric field. The leading term arises from the Frenkel approach, which is the same for all molecules normally used in the Poole-Frenkel model for conductivity in an electric field. For a set of test molecules, the quality of the results is comparable to that of previous results using constrained density functional theory. We conclude that the Frenkel term is dominant and sufficient at relatively low fields and that the dipole and polarizability terms, the leading terms dependent on the properties of the individual molecule, make a significant contribution only at high fields and for relatively large molecules. Because the presented model is analytical, quantum chemical calculations are avoided for a variety of electric field strengths and molecular orientations, and the model can therefore be applied directly in coarse-grained models for electronic processes in dielectric condensed phases.

Simulating induction heating of fabric based thermoplastic composites using measured electrical conductivities

A novel method for defining the measured electrical conductivity of CFRTP in induction heating simulations is presented. This method considers the electrical conductivity’s orientation dependence and accurately predicts electromagnetic and transient temperature fields. The study demonstrates that temperature predictions using the present electrical conductivity model are in good agreement with the experiments, and that it yields improved transient temperature field predictions compared to the other electrical conductivity models.

A Thermal Conductivity Model for Lamellar and Compacted Graphite Irons

A Thermal Conductivity Model for Lamellar and Compacted Graphite Irons

Prediction model of hydraulic conductivity for sedimentary residual soil mixed bentonite as compacted clay liner

Prediction model of hydraulic conductivity for sedimentary residual soil mixed bentonite as compacted clay liner

Computational model for the thermal conductivity of soil-rock mixture

Soil-rock mixture (S-RM) consists of a mixture of soil and crushed rocks, and their thermal conductivity is highly important in underground engineering. Currently, research on thermal conductivity is primarily focused on soil and rock individually, with minimal attention given to S-RM thermal conductivity. This paper aims to develop a model capable of accurately calculating the thermal conductivity of S-RM by conducting an in-depth analysis of the macrostructure of soil and crushed rocks. First, a series-parallel model of S-RM was developed based on the series-parallel concept of resistors. Second, considering that the intermixing of fine-grained soil and coarse-grained crushed rocks during the fabrication of S-RM results in reduced porosity and elevated saturation - factors that influence thermal conductivity - a refinement has been applied to the generalized thermal conductivity model proposed by Côté and Konrad. The proposed modified model of thermal conductivity is applicable to the S-RM. Finally, the modified model was proven to have high accuracy in predicting the thermal conductivity of S-RM through testing.

Study on electrical conductive mechanism of mayenite derivative C12A7:C

Abstract This study explains the conductive mechanism of C12A7:C from the perspective of crystal structure. C12A7:C is a carbon derivative of C12A7 and prepared by CaCO3 and Al2O3 in sealed graphite crucible through high-temperature sintering experiments. The main component was confirmed to be C12A7:C through X-ray diffraction inversion analysis. The four-probe method revealed that it is a semiconductor with conductivity of 4,339 S/m. A conductive model of C12A7:C crystal was established to study its conductive mechanism. Through theoretical calculations of the conductive structure model, the density of states and transfer function are important factors determining the conductivity of C12A7:C crystals. Based on the analysis of these two factors, C is the key to electron transfer in the C12A7:C crystal. Further research indicates that the C–C bond is the main form of C in C12A7:C crystals. These C–C bonds satisfy the formation conditions of conjugated systems and are key to the conductivity of C12A7:C crystals. Through simulation calculations, the volt ampere characteristic curve of C12A7:C exhibits Ohmic conductor characteristics. The conductivity of C12A7:C obtained through theoretical calculation is consistent with the experimental results. In conclusion, the conductivity of C12A7:C crystal is mainly due to the C–C conjugated system formed by carbon atoms in the crystal.

Research on the thermal conductivity and mechanical properties of carbon fiber reinforced thermoplastic composites doped with different sizes carbon nanotubes: A combination of experiments, numerical simulations and multi‐objective optimization

AbstractWhile improving the thermal conductivity of composites, single‐size carbon nanotubes (CNT) often degrade their mechanical properties due to the agglomerates. To overcome this limitation, this study reported thermoplastic resin matrix composites synergistically reinforced with small, medium, and large‐size carbon nanotubes (S‐CNT, M‐CNT, and L‐CNT). Using the thermal conductivity (λ) and mechanical properties (flexural strength [F], compressive strength [C] and tensile strength [T]) as the response values, we conducted 21 sets of mixing design experiments and developed the associated quadratic term models. Further multi‐objective optimization was carried out for the above response values. Optimized multiscale CNT synergistically modified composites (S‐CNT, M‐CNT, and L‐CNT contents of 1.25, 7.02, and 2.56 wt%) exhibited a λ value of 1.168 W/mK, which was 121% higher than that of pure composite and also superior to the same content of S‐CNT‐ (1.031 W/mK), M‐CNT‐ (1.016 W/mK), and L‐CNT‐modified composites (0.983 W/mK). Additionally, the optimized composite demonstrated excellent mechanical properties (F = 1482 MPa, C = 848 MPa, and T = 1759 MPa), which were 13%, 11%, and 13% higher than those of the pure composites, respectively, and also surpassed those of the S‐CNT‐, M‐CNT‐and L‐CNT‐modified composites.Highlights Using three different scales of carbon nanotubes modified CF/PPBESK composites. Polynomial modeling of composite's thermal conductivity and mechanical properties. Synergistic interactions between carbon nanotubes to improve the composite's thermal conductivity and mechanical properties.

Low-frequency conductivity of low wear high-entropy alloys

High-entropy alloys (HEAs) provide new research avenues for alloy combinations in the periodic table, opening numerous possibilities in novel-alloy applications. However, their electrical characteristics have been relatively underexplored. The challenge in establishing an HEA electrical conductivity model lies in the changes in electronic characteristics caused by lattice distortion and complexity of nanostructures. Here we show a low-frequency electrical conductivity model for the Nb-Mo-Ta-W HEA system. The cocktail effect is found to explain trends in electrical-conductivity changes in HEAs, while the magnitude of the reduction is understood by the calculated plasma frequency, free electron density, and measured relaxation time by terahertz spectroscopy. As a result, the refractory HEA Nb15Mo35Ta15W35 thin film exhibits both high hardness and excellent conductivity. This combination of Nb15Mo35Ta15W35 makes it suitable for applications in atomic force microscopy probe coating, significantly improving their wear resistance and atomic-scale image resolution.

Discrete element model for effective electrical conductivity of spark plasma sintered porous materials

AbstractThis paper aims to analyse electrical conduction in partially sintered porous materials using an original resistor network model within discrete element framework. The model is based on sintering geometry, where two particles are connected via neck. Particle-to-particle conductance depends on neck size in sintered materials. Therefore, accurate evaluation of neck size is essential to determine conductance. The neck size was determined using volume preservation criterion. Additionally, grain boundary correction factor was introduced to compensate for any non-physical overlaps between particles, particularly at higher densification. Furthermore, grain boundary resistance was added to account for the porosity within necks. For numerical analysis, the DEM sample was generated using real particle size distribution, ensuring a heterogeneous and realistic microstructure characterized by a maximum-to-minimum particle diameter ratio of 15. The DEM sample was subjected to hot press simulation to obtain geometries with different porosity levels. These representative geometries were used to simulate current flow and determine effective electrical conductivity as a function of porosity. The discrete element model (DEM) was validated using experimentally measured electrical conductivities of porous NiAl samples manufactured using spark plasma sintering (SPS). The numerical results were in close agreement with the experimental results, hence proving the accuracy of the model. The model can be used for microscopic analysis and can also be coupled with sintering models to evaluate effective properties during the sintering process.

From density functional theory to machine learning predictive models for electrical properties of spinel oxides.

This work focuses on predicting and characterizing the electronic conductivity of spinel oxides, which are promising materials for energy storage devices and for the oxygen evolution and oxygen reduction reactions due to their attractive properties and abundance of transition metals that can act as active sites for catalysis. To this end, a new database was developed from first principles, including band structure and conductivity properties of spinel oxides, and machine learning algorithms were trained on this database to predict electronic conductivity and band gaps based solely on the compositions. The models developed in this study are scaled from the quantum level up to a continuum conductivity model. The relatively small database used in this study allowed for accurate predictions of band gap and conductivity. By altering the composition of spinel oxides, the model was able to predict high conductivity for spinels with high nickel content and to match experimental trends for manganese cobalt spinels. The ability to predict material properties is especially important in energy conversion devices such as batteries and supercapacitors where redox reactions take place.

Equivalent Thermal Conductivity of Topology-Optimized Composite Structure for Three Typical Conductive Heat Transfer Models

Composite materials and structural optimization are important research topics in heat transfer enhancement. The current evaluation parameter for the conductive heat transfer capability of composites is effective thermal conductivity (ETC); however, this parameter has not been studied or analyzed for its applicability to different heat transfer models and composite structures. In addition, the optimized composite structures of a specific object will vary when different optimization methods and criteria are employed. Therefore, it is necessary to investigate a suitable method and parameter for evaluating the heat transfer capability of optimized composites under different heat transfer models. Therefore, this study analyzes and summarizes three typical conductive heat transfer models: surface-to-surface (S-to-S), volume-to-surface (V-to-S), and volume-to-volume (V-to-V) models. The equivalent thermal conductivity (keq) is proposed to evaluate the conductive heat transfer capability of topology-optimized composite structures under the three models. A validated simulation method is used to obtain the key parameters for calculating keq. The influences of the interfacial thermal resistance and size effect on keq are considered. The results show that the composite structure optimized for the V-to-S and V-to-V models has a keq value of only 79.4 W m−1 K−1 under the S-to-S model. However, the keq values are 233.4 W m−1 K−1 and 240.3 W m−1 K−1 under the V-to-S and V-to-V models, respectively, which are approximately 41% greater than those of the in-parallel structure. It can be demonstrated that keq is more suitable than the ETC for evaluating the V-to-S and V-to-V heat transfer capabilities of composite structures. The proposed keq can serve as a characteristic parameter that is beneficial for heat transfer analysis and composite structural optimization.