Percolation Theory Model Research Articles

Brauer diagram model of suppositional phantom network in double-network gel undergoing mechanochemical coupling

Complex coupling of brittle and stretchable networks in double-network (DN) gel has been a hot research topic to understand working principle of ultra-high mechanical toughness, in comparison with the conventional gels. In this study, both the percolation theory and phantom network model were employed to formulate a Brauer diagram model, which was used to describe the suppositional phantom double networks and explore their coupling effects in DN gel. The mechanochemical coupling was investigated using the proposed Brauer diagram model, in which three critical parameters of coupling fraction, surviving probability and phantom degree, were proposed to formulate a constitutive relationship among rubber elasticity, mechanochemical coupling and stress-elongation ratio. Finally, effectiveness of the Brauer diagram model was verified using analytical data from the finite element analysis and molecular dynamics, as well as experimental results of DN gels reported in the literature.

The novel oxy-sulfide glassy ionic conductors Na4P2S7-xOx 0 ≤ x ≤ 7: Understanding the features of static and dynamic cations

We present a 23Na nuclear spin dynamics model for interpreting nuclear magnetic resonance (NMR) spin-lattice relaxation and central linewidth data in the invert glass system Na4P2S7-xOx, 0 ≤ x ≤ 7. The glassy nature of this material results in variations in local Na+ cation environments that may be described by a Gaussian distribution of activation energies. A consistent difference between the mean activation energies determined by NMR and DC conductivity measurements was observed, and interpreted using a percolation theory model. From this, the NaNa coordination number in the sodium cation sublattice was obtained. These values were consistent with jumps through tetrahedral faces of the sodium cages for the sulfur rich glasses, x < 5, consistent with proposed models of their short range order (SRO) structures. From NMR spin-echo measurements, we determined the NaNa second moment M2 resulting from the NaNa magnetic dipole interaction of nearest neighbors. Values of M2 obtained as a function of sodium number density N were in agreement with models for uniform sodium distribution, indicating that these invert glass systems form so as to maximize the average NaNa distance. A simple Coulombic attraction model between Na+ cation and X (=S−, O−) anion was applied to calculate the activation energy. In the range 1.5 ≤ x ≤ 7, an increase in activation energy with increasing oxygen content x occurred, and was consistent with the decrease in average anionic radius, and the increase in Coulombic attraction. For small oxygen additions, 0 ≤ x ≤ 1.5, the suggested minimum at low oxygen concentration seen in the activation energies obtained from DC conductivity data is not evident in the model.

Conductive Filament Composites from Waste Battery Rod-Derived Exfoliated Graphite for Fused Deposition Modeling 3D Printing: A Two-Level Factorial Design Optimization Study

This study used carbon rods from spent zinc-carbon batteries as a source of exfoliated graphite (EG) to produce conductive filament composites for fused deposition modeling 3D printing. The EG filler was prepared through microwave irradiation, while the resulting 3D printable electroconductive EG composites were prepared using polylactic acid (PLA) and polyethylene glycol (PEG) as the polymer matrix and compatibilizer, respectively, via a sonication-assisted solution blending and melt extrusion process. A two-level full factorial design was employed to fully investigate the influence of filament production parameters such as EG loading, PEG:PLA ratio, and sonication time on the resistivity (i.e., conductivity-1) of the prepared composites. Analysis of variance showed that both EG loading and sonication time had significant effects on the resistivity of the composites. The optimum electrical resistivity of the new EG filament composites was found to be 916.418 Ω-cm (maximum conductivity = 1.091 x10-3 S/cm) at EG loading = 45 % w/w, PEG:PLA ratio = 1:10, and sonication time = 2 hours. The conductivity of the 3D printed composites was also correlated with EG amount by the power law model of percolation theory, resulting in an electrical percolation threshold at around 35 % w/w of EG. Our filament composites enable the fabrication of high-value conductive materials from waste resources for sustainable additive manufacturing in the electronics industry.

A universal model for the permeability of sintered materials

Sintered materials are used as permeable filters and flow controllers, for which a validated and general model of porosity and permeability is required. Here, we prepare samples built from mono- and polydisperse glass bead populations sintered for known times at high temperature, and then measure the sample porosity and permeability. We supplement our new dataset with published permeability data for sintered systems including high-temperature in situ determinations of permeability during sintering. We test a range of mathematical models for the change in permeability with porosity as sintering progresses from a value for the initial granular particle packing geometry, down to the percolation threshold at low porosity. We find good agreement between our datasets and a preferred theoretical approach – a percolation theory model – with no explicit requirement for empirical adjustment. However, we propose semi-empirical steps that generalize this theory to a universal description across all porosities. Finally, we quantify the inertial component of fluid transport at high flow rates through these materials. Our model framework is made available via a user-friendly downloadable spreadsheet which takes particle size distribution as an input and provides permeability as an output.

Gas-to-nanotextile: high-performance materials from floating 1D nanoparticles.

Suspended in the gas phase, 1D inorganic nanoparticles (nanotubes and nanowires) grow to hundreds of microns in a second and can be thus directly assembled into freestanding network materials. The corresponding process continuously transforms gas precursors into aerosols into aerogels into macroscopic nanotextiles. By enabling the assembly of very high aspect ratio nanoparticles, this processing route has translated into high-performance structural materials, transparent conductors and battery anodes, amongst other embodiments. This paper reviews progress in the application of such manufacturing process to nanotubes and nanowires. It analyses 1D nanoparticle growth through floating catalyst chemical vapour deposition (FCCVD), in terms of reaction selectivity, scalability and its inherently ultra-fast growth rates (107-108 atoms per second) up to 1000 times faster than for substrate CVD. We summarise emerging descriptions of the formation of aerogels through percolation theory and multi-scale models for the collision and aggregation of 1D nanoparticles. The paper shows that macroscopic ensembles of 1D nanoparticles resemble textiles in their porous network structure, high flexibility and damage-tolerance. Their bulk properties depend strongly on inter-particle properties and are dominated by alignment and volume fraction. Selected examples of nanotextiles that surpass granular and monolithic materials include structural fibres with polymer-like toughness, transparent conductors, and slurry-free composite electrodes for energy storage.

Numerical simulation of pore structure and heat transfer behavior in aerated concrete

The pore structure of porous concrete is randomly formed, which brings thorny obstacle to accurately predict its thermal performance. In this study, a numerical approach was proposed for the simulation of pore structure and heat transfer behavior in aerated concrete. According to the porosity (ε) and log-normal pore size distribution parameters (μ, σ), an idea of “random distribution” was developed to reconstruct the pore structure via computer modeling, and also an overlap ratio (δ) was defined and adopted to generate a structure closer to reality. In parallel with this, a Finite Volume Model (FVM) was established to solve the energy control equation, and thus the effective thermal conductivities (ETCs) were numerically calculated. The calibrated and validated FVM model was also used to systematically study the effects of air-void content, air-void distribution and structural parameters, including pore size and porosity on the heat transfer behavior of aerated concrete. The numerical results show that the ETCs tend to slightly decrease with the increase of overlap ratio (δ), pore size (μ) and distribution (σ) due to an increased degree of consolidation between pores, which leads to the solid phase easily blocked by the connected pores so that the optimal heat transfer path through the solid phase conduction is blocked. Further, the comparisons of predictions of ETCs with the experimental data and other existing models indicate that the numerical predictions agree well with the experimental data, and the experimental and simulated values of the ETCs are intermediate between the Maxwell-Eucken 1 and Effective Medium Percolation Theory (EMPT) models.

Evaluation of Porous Media Gas Diffusion Models for PEMFC Applications

. Polymer electrolyte membrane fuel cells (PEMFCs) are considered as zero emission power sources for transportation and stationary power purposes. The membrane electrode assembly (MEA) is the core of PEMFC and is composed of a gas diffusion layer (GDL), catalyst layer (CL) and proton exchange membrane (PEM). GDL is a carbon-based, fibrous porous medium that simultaneously provides a path for heat, mass and electron transport, as well as providing a mechanically robust support for the CL. The gas diffusion in the GDL can be estimated by Fick’s law where the effective diffusion coefficient of gaseous species is used.There are many models in the literature based on correlations defining the effective diffusion coefficients through GDLs. Some of these models were originally derived to estimate the transport properties of a porous media composed of spherical particles, e.g. Bruggeman approximation and effective medium approximation. Inherently, such models tend to result to more inaccurate outcomes compared to the models which assume the GDL structure as cylindrical carbon fibers, i.e. the diffusion model based on percolation theory. The percolation theory model considers GDL as a medium composed of freely overlapping fibers oriented in different directions. However, there are several models available in the literature with less simplifying assumptions in GDL structure. The pore network model (PNM) reconstruct the porous media using topology and size information extracted from high resolution tomographic patterns. Also CFD based models can even investigate the actual GDL structure and reconstruct the 3D stochastic porous medium microstructure. These models combine pore-scale model with CFD approaches, e.g. lattice Boltzmann method (LBM) or direct numerical simulation (DNS). This study compares the available models for dry gas diffusion in GDL with experimental data acquired from symmetrical modified Loschmidt cell (SMLC). The SMLC is employed to measure the effective diffusion coefficient of oxygen passing through GDL samples, i.e. SGL SIGRACET 24BA, 24 BC, 25BA, 25BC and TGP-H-060. The SMLC result for effective diffusion coefficient in TGP-H-060 has less than 2% difference with the available data in the literature for this type of GDL. In order to evaluate the accuracy of effective medium models and percolation theory model, the experimental data for the above-mentioned GDLs is compared with the predictions of these models. The porosity of GDL samples are in the valid range of diffusion models. The diffusion models based on the effective medium approximation have the greater difference with SMLC data in compare with the percolation theory model. The model’s predictions are the worst for the GDLs with microporous layer (MPL), i.e. SIGRACET 24 BC and 25BC. Since the MPL imposes an extra resistance to gas diffusion which is not considered in any GDL diffusion models. The least error in model’s outcome is 30% which associates to the effective diffusion coefficient predicted by percolation theory model for SIGRACET 25BA.

Silver nanoparticles–deposited sub-micro sized BaTiO3/PVDF composites: greatly increased enhanced constant and effectively suppressed dielectric loss

Silver (Ag) nanoparticles deposited sub–micro sized BaTiO3 particles (µBT) were fabricated as hybrid particles (Ag@µBT) to promote the dielectric response in a poly(vinylidene fluoride) (PVDF). The dielectric constant (ε′) of the Ag@µBT/PVDF composites continuously increased as the volume fraction (f Ag@ µ BT) increased, while the loss tangent (tanδ) was effectively suppressed. The ε′∼173.49 was obtained in the composite with f Ag@ µ BT=0.49, while a low tanδ was achieved (0.024), which was close to 0.021 for the PVDF. The Ag@µBT hybrid particles played essential roles in increased ε′ and inhibited conductive pathways, resulting in a low tanδ. The ε′ increased slightly, whereas tanδ changed significantly over the measured temperature range. Furthermore, ε′ was fitted with the effective medium percolation theory model. Therefore, the significantly improved dielectric properties were attributed to the high ε′ value of the µBT phase and interfacial polarization between the conductive Ag and insulating phases (i.e. µBT and PVDF).

Novel polymer composites of RuO2@nBaTiO3/PVDF with a high dielectric constant

The dielectric properties of a novel polymer dielectric material were investigated. The conductive phase of RuO2 was synthesized for deposition on the surface of a nanosized BaTiO3 (nBT). The RuO2@nBT hybrid particles were incorporated into a poly (vinylidene fluoride) (PVDF) as a three-phase composite (RuO2@nBT/PVDF). The obtained dielectric constant (ε′) was significantly high (3837.16) for the composite with a volume fraction of fRuO2@nBT = 0.50. The large interfacial polarization between the RuO2−nBT and RuO2−PVDF interfaces considerably increased the value of ε′. Therefore, interfacial polarization is a critical factor in improving the dielectric properties. The dielectric behavior of the RuO2@nBT/PVDF composites can be described using the effective medium percolation theory model, which indicates the significant contributions of the conductive RuO2 phase and high-permittivity nBT phase.

Fracture Critical Length Estimative Using Percolation Theory and Well Logging Data

Groundwater transport in crystalline rocks follows pathways along fractured zones because of low primary porosity and permeability in such formations. Fractured systems encompass an imbricated set of joints and fractures with different lengths, apertures and orientations resulting in complex permeable systems with heterogeneous groundwater transport properties. Geophysical well logging has proved effectiveness in detecting depth levels with denser fracture distributions as well as the apparent aperture of fractures contributing to groundwater flow. In many cases, the extension spanned by a fracture network cannot be directly inferred because it may extend beyond the radius of investigation of common well logging probes, thus preventing quantitative estimation of critical length for lateral extension a connected fractured system may have. Here we apply a percolation theory model to estimate the critical length as inferred from the linear density of fracture distribution observed at the borehole wall with an optical imaging probe. Our results are analyzed with electrical well logging data (normal resistivity and single-point resistance) cross borehole slug tests using a set of three boreholes. A critical length of 3.9 m was inferred with a percolation model which revealed consistency with the cross borehole slug tests from two wells situated 10 m and 30 m in the vicinity of the monitored borehole. Our results suggest the utility of inferring critical percolation lengths from fracture parameters obtained using standard well logging imaging techniques with potential applications to evaluate groundwater resources, characterize contaminated sites and provide geotechnical information for works in fractured formations.

Permeability estimation of tight sandstone from pore structure characterization

Permeability, a crucial parameter in the subsurface geological and industrial activities, is highly heterogeneous in tight sandstone. Great difficulties and accuracy losses present in the permeability estimation of tight sandstone owing to its intricate pore structures. In this paper, to obtain reliable permeability estimation models for tight gas sandstone, the popular Coates, Schlumberger Doll Research, and Pittman models are improved from a systematic pore structure characterization. The characterization, integrating multiple techniques and incorporating percolation theory and fractal model, identifies the presences of three pore structure types, involving the mixed pore type, single-pore dominant type, and dual porous type. Attribute differences are discovered in the pore constitute, size distribution, microscopic heterogeneity, and connectivity of different structure types, in which disparate structural variation rules are identified in the pore-controlled and dual porous structures. These differences are responsible for the distinctions in the continuous fluid percolation pathways. The pore-controlled sandstone shares similar reticular networks with variations in extension degrees, while the dual porous sandstone exhibits a completely different tubular network, indicating different permeability variation mechanisms. Differed correlation trends between pore attributes and permeability in pore-controlled and dual porous tight sandstone suggest that permeability is primarily affected by pore structure type, followed by connectivity. The permeability of pore-controlled tight sandstone is determined by the pore geometrical features and influenced by connectivity and heterogeneity, while that of dual porous one is controlled by the attributes of micro cracks. Modification is performed on the Coates, SDR, and Pittman models by taking pore structures, particularly the structure types and connectivity, into account. Evident performance enhancements occur in these calibrated models. The excellent applicability of the improved models in pore-controlled tight sandstone confirms that pore structural types should be addressed in priority, followed by pore connectivity, in the permeability estimation of tight sandstone.

Gold-Nanoparticle-Deposited TiO2 Nanorod/Poly(Vinylidene Fluoride) Composites with Enhanced Dielectric Performance.

Flexible dielectric polymer composites have been of great interest as embedded capacitor materials in the electronic industry. However, a polymer composite has a low relative dielectric permittivity (ε′ < 100), while its dielectric loss tangent is generally large (tanδ > 0.1). In this study, we fabricate a novel, high-permittivity polymer nanocomposite system with a low tanδ. The nanocomposite system comprises poly(vinylidene fluoride) (PVDF) co-filled with Au nanoparticles and semiconducting TiO2 nanorods (TNRs) that contain Ti3+ ions. To homogeneously disperse the conductive Au phase, the TNR surface was decorated with Au-NPs ~10–20 nm in size (Au-TNRs) using a modified Turkevich method. The polar β-PVDF phase was enhanced by the incorporation of the Au nanoparticles, partially contributing to the enhanced ε′ value. The introduction of the Au-TNRs in the PVDF matrix provided three-phase Au-TNR/PVDF nanocomposites with excellent dielectric properties (i.e., high ε′ ≈ 157 and low tanδ ≈ 0.05 at 1.8 vol% of Au and 47.4 vol% of TNRs). The ε′ of the three-phase Au-TNR/PVDF composite is ~2.4-times higher than that of the two-phase TNR/PVDF composite, clearly highlighting the primary contribution of the Au nanoparticles at similar filler loadings. The volume fraction dependence of ε′ is in close agreement with the effective medium percolation theory model. The significant enhancement in ε′ was primarily caused by interfacial polarization at the PVDF–conducting Au nanoparticle and PVDF–semiconducting TNR interfaces, as well as by the induced β-PVDF phase. A low tanδ was achieved due to the inhibited conducting pathway formed by direct Au nanoparticle contact.

Highly enhanced frequency- and temperature-stability permittivity of three-phase poly(vinylidene-fluoride) nanocomposites with retaining low loss tangent and high permittivity

Although ceramic/polymer composites have been of great interest as embedded capacitor materials, the composites have a low dielectric permittivity (ε′ ≪ 100) and very large dissipation factor (tanδ ≫ 0.1). In this work, the hybrid particles of silver nanoparticles deposited on BaTiO3 nanoparticles (nAg-nBT) have been used as a filler to enhance the ε′ response in a poly(vinylidene-fluoride) (PVDF) polymer with retaining low tanδ. Residual isolated particles of nAg (i-nAg) and nBT (i-nBT) are the key factors for enhancing the dielectric properties. Significantly increased ε′ ~ 247 (at 103 Hz) with tanδ ~ 0.038 is obtained. The ε′ value is slightly dependent on frequency and temperature over wide ranges. A linear increase in ε′ of the composites at low volume fractions of filler (fAg+nBT < 0.29) is caused by a high ε′ value of nBT particles. An abrupt change in ε′ is observed in the composites at fnAg+nBT > 0.29, which is attributed to a shorten interparticle distance between filler particles, giving rise to strong interfacial polarization. The dielectric behavior can be well described by the effective medium percolation theory (EMPT) model. The discrete deposition of nAg observed in the nAg-nBT and uniform distribution of i-nAg in the PVDF matrix, which is dispersed by nAg-nBT and i-nBT particles, can effectively prevent the formation of the conduction pathways. The obtained low tanδ over the temperature range of 30-140 °C is explained by these two reasons. This research provides a new important concept for the material development of dielectric polymer matrix composites..

Significantly Enhanced Dielectric Properties of Ag-Deposited (In1/2Nb1/2)0.1Ti0.9O2/PVDF Polymer Composites.

The enhanced dielectric permittivity (ε′) while retaining a low loss tangent (tanδ) in silver nanoparticle−(In1/2Nb1/2)0.1Ti0.9O2/poly(vinylidene fluoride) (Ag-INTO/PVDF) composites with different volume fractions of a filler (fAg-INTO) was investigated. The hybrid particles were fabricated by coating Ag nanoparticles onto the surface of INTO particles, as confirmed by X-ray diffraction. The ε′ of the Ag−INTO/PVDF composites could be significantly enhanced to ~86 at 1 kHz with a low tanδ of ~0.044. The enhanced ε′ value was approximately >8-fold higher than that of the pure PVDF polymer for the composite with fAg-INTO = 0.5. Furthermore, ε′ was nearly independent of frequency in the range of 102–106 Hz. Therefore, filling Ag−INTO hybrid particles into a PVDF matrix is an effective way to increase ε′ while retaining a low tanδ of polymer composites. The effective medium percolation theory model can be used to fit the experimental ε′ values with various fAg-INTO values. The greatly increased ε′ primarily originated from interfacial polarization at the conducting Ag nanoparticle–PVDF and Ag–INTO interfaces, and it was partially contributed by the high ε′ of INTO particles. A low tanδ was obtained because the formation of the conducting network in the polymer was inhibited by preventing the direct contact of Ag nanoparticles.

Effect of Different Carbon Materials on the Conductivity of Epoxy Resin Conductive Coatings

In this work, the conductive coating was prepared by electrostatic spraying with graphene and Multi-walled carbon nanotube (MWCNTs) as conductive medium and epoxy resin powder as film-forming material, in order to solve the pro·blem of high content and uneven dispersity of conductive particles in conductive coatings prepared by brushing method. The resistance of the coating was measured by four probe method, the dispersity of conductive particles in the coating was analyzed by scanning electron microscope (SEM), and the conductive mechanism of the coating was analyzed by percolation theory model. The results show that the conductive particles can be dispersed evenly in the whole coating by electrostatic force. Meanwhile, the electrostatic force can also stretch the conductive particles in the coating along the direction of the thickness of that. The flake graphene is vertically arranged in the coating, and the curled MWCNTs forms the conductive network of "island-bridge" structure. The conductive particles laped each other to form a conductive path, which greatly reduced the content of conductive particles. The seepage threshold of graphene conductive coating was only 1.5 wt.%, which lower than that of the MWCNTs conductive coating, which is 3 wt.%. The resistance of epoxy coating containing with 0.5 wt.% graphene is 3397 Ω·m, and that of epoxy coating containing with 0.5 wt.% MWCNTs is 1049 Ω·m.

Enhanced thermal conductivity of epoxy/alumina composite through multiscale-disperse packing

Inspired by the size of the voids in closest packing structures, we propose to use the combination of spherical particles with different size scales to increase the loading fraction of the fillers in epoxy-based composites. In this study, high loading up to 79 vol% has been achieved with multiscale particle sizes of spherical Al2O3 particles. The highest thermal conductivity of Al2O3-filled liquid epoxy measured by steady-state method is 6.7 W m−1 K−1 at 25°C, which is approximately 23 times higher than the neat epoxy (0.28 W m−1 K−1). Three models based on Maxwell mean-field scheme (MMF), differential effective medium (DEM) and percolation theory model (PTM) were utilized to assess our measured thermal conductivity data. We found that both DEM and PTM models could give good results at high volume fraction regime. We have also observed a considerable reduction (10–15%) of thermal conductivity in our Al2O3-filled cured epoxy samples. We attribute this reduction to the increasing of thermal interfacial resistance between Al2O3 particles and cured epoxy matrix, induced by cure shrinkage during the reaction. Our experiments have demonstrated that systems with multiscale particle sizes exhibit lower viscosity and can be filled with much higher fraction of fillers. We thus expect that higher thermal conductivity (probably &gt;12 W m−1 K−1 based on DEM) can be achieved in future via filling higher thermal conductivity spherical fillers (e.g., AlN, SiC), increasing loading fraction by multiscale-disperse packing and reducing the effect from cure shrinkage.

A Universal Model of Unsaturated Hydraulic Conductivity With Complementary Adsorptive and Diffusive Process Components

AbstractAccurate estimation of unsaturated hydraulic conductivity (HC) is one of the most challenging problems in soil science. Here, we propose a novel approach to model HC using percolation theory. Transient behavior of water transport phenomena at low moisture contents requires additional physical process representation, beside capillary conductivity, to ensure accurate prediction of unsaturated HC. We augment the capillary model from percolation theory with two additional components, namely, (1) film flow, which is the product of volumetric flow rate per perimeter by specific perimeter of solid particles, and (2) isothermal vapor HC, derived from the Fick's law of vapor diffusion and relative humidity. The fractal characteristics of last fractal regime are used to model tortuosity and ultimately HC of vapor flow. Since the typical pressure head range of universal scaling from percolation theory is analogous to the range of vapor flow, we demonstrate that the universal scaling presented in previous studies is not sufficient to model HC for water contents below a crossover point. We also, by analyzing the scaled water retention properties, demonstrate that most studied soils exhibit three fractal regimes. Therefore, a piecewise HC function of capillary flow is developed to account for three fractal regimes, providing more flexibility for soils with multimodal characteristics. The proposed joint HC function is more accurate compared to the model of Peters‐Durner‐Iden and predecessor percolation theory models.

The effect of electromigration on the lifetime and performance of flexible interconnections fabricated by laser printing and sintering

Laser Induced Forward Transfer (LIFT) combined with laser sintering of nanoinks, has been proven a key enabling technology for flexible electronics. In this paper we demonstrate how this technology can also be applied for achieving high-resolution flexible interconnections, with form factors tailored for high current density stress tests. To this end, we have employed different flexible substrates, such as Polyethylene Naphthalate (PEN) and SU-8, for the validation of the performance of these interconnections: an all-laser fabricated flexible platform comprising Ag nanoparticle microelectrodes has been developed for running stress tests for the investigation of electromigration (EM) of Ag, a phenomenon responsible for short lifetime of flexible circuits. In particular, we have studied the effect of grain size and substrate (joule heating) on the EM induced failure. Data extracted from these tests were fitted to the percolation theory model and a custom model suggested by the authors that achieved optimal fitting results and provided porosity factors of the printed patterns. On top of the porosity factor extraction, Scanning Electron Microscope (SEM) micrographs have confirmed that the porous morphology, the presence of voids and their evolution to cracks influence the rate and the intensity of failure mechanism.

Застосування перколяційних алгоритмів для оцінки надійності гетерогенних мереж військового призначення

In recent years, especially with the onset of aggression by the Russian Federation against Ukraine, the requirements for the reliability of existing heterogeneous networks as the technological basis of the command and control system of formations, unions and military control bodies of all levels of the Armed Forces of Ukraine have significantly increased. Indeed, the failure of only one element of the existing control system (due to deliberate (cyber-attacks) or unintentional interference) can lead to the loss of the control system as a whole. Therefore, the creation of a reliable heterogeneous network (GM) to ensure the functioning of the control system is an important and important task. As a result, the authors propose, in order to assess the reliability of the GM, to improve the existing method, in which information transfer within the network is viewed as passing data packets from one GM segment to another through the providers infrastructure (Internet), using percolations algorithms (algorithms build on percolation theory models). In 1956, in the article Percolation processes I. Crystals and mazes (flow process. Crystals and labyrinths) authors S.R. BROADBENT and J.M. HAMMERSLEY proposed to simulate the flow of matter in a porous material using the Monte Carlo method Further research in this area showed that the use of this approach is used in various fields of science, such as physics (statistical), materials science, economics, chemistry, geology, sociology, medicine, to describe the occurrence of related structures in random environments (clusters) of random environments. (clusters), consisting of individual elements.

Relative Permeability and Production-Performance Estimations for Bakken, Wolfcamp, Eagle Ford, and Woodford Shale Formations

Summary Relative permeability and residual water/gas saturations of organic-rich samples were determined from low-pressure nitrogen-adsorption/desorption measurements on shale samples. Adsorption/desorption isotherm measurements were performed on 100 organic-rich shale samples from the Bakken, Wolfcamp, Eagle Ford, and Woodford Formations, and were then interpreted to obtain pore-size distribution (PSD) using a modified Barrett-Joyner-Halenda (BJH) method (Barrett et al. 1951). A bimodal-fractal model was then applied to the PSD estimates to compute percolation and fractal parameters, which were incorporated in percolation theory (PT), effective-medium theory (EMT), and critical-path analysis (CPA) models to generate the relative permeability curves and residual saturations of the 100 samples. Robustness of this relatively new estimation technique for shale-reservoir samples is evaluated in this study. Petrophysical correlations of relative permeability and residual saturations with kerogen maturity, kerogen content, and kerogen removal through sample cleaning are developed for improved understanding of the saturation-dependent transport behavior of shale reservoirs. These correlations enable comparative predictions of intrawell- and interwell-production performance. Kerogen maturity was found to be the dominant factor affecting the relative permeability and residual-saturation estimates. Irreducible-water-saturation and residual-hydrocarbon-saturation estimates increased from 30 to 60% and 20 to 40%, respectively, with an increase in maturity from oil window to late-condensate window. Estimates of relative permeability of hydrocarbon and aqueous phases at 80% saturation of the corresponding phases increased from 0.7 to 0.75 and 0.05 to 0.2, respectively, with the decrease in kerogen maturity. When the samples were cleaned with a toluene/methanol mixture to remove soluble, dead hydrocarbons and bitumen from the samples, the hydrocarbon-phase residual-saturation estimates decreased by 20%, whereas the aqueous-phase irreducible-saturation estimates increased by 9%. The estimated relative permeability curves allow us to predict the production performance using a numerical simulator. Lower Bakken and Wolfcamp oil formations have the best hydrocarbon-transport characteristics because of lower thermal maturity. These formations show slower decline in hydrocarbon-production rates and more-uniform increase in water production. Hydrocarbon-phase production of the Lower Bakken oil formation is better than that of the Wolfcamp oil formation, but the water-production trend is significantly reversed. On the contrary, Wolfcamp and Woodford late-condensate formations exhibit the poorest transport characteristics and lower cumulative hydrocarbon and water production because of higher thermal maturity. Wells in these higher-maturity formations should show steeper decline in hydrocarbon-production rates and faster and sudden increase in water production after longer periods of sustained lower water production.