Decrease In Fractal Dimension Research Articles

A Fractal Permeability Model of Tight Oil Reservoirs Considering the Effects of Multiple Factors

The prediction of permeability and the evaluation of tight oil reservoirs are very important to extract tight oil resources. Tight oil reservoirs contain enormous micro/nanopores, in which the fluid flow exhibits micro/nanoscale flow and has a slip length. Furthermore, the porous size distribution (PSD), stress sensitivity, irreducible water, and pore wall effect must also be taken into consideration when conducting the prediction and evaluation of tight oil permeability. Currently, few studies on the permeability model of tight oil reservoirs have simultaneously taken the above factors into consideration, resulting in low reliability of the published models. To fill this gap, a fractal permeability model of tight oil reservoirs based on fractal geometry theory, the Hagen–Poiseuille equation (H–P equation), and Darcy’s formula is proposed. Many factors, including the slip length, PSD, stress sensitivity, irreducible water, and pore wall effect, were coupled into the proposed model, which was verified through comparison with published experiments and models, and a sensitivity analysis is presented. From the work, it can be concluded that a decrease in the porous fractal dimension indicates an increase in the number of small pores, thus decreasing the permeability. Similarly, a large tortuous fractal dimension represents a complex flow channel, which results in a decrease in permeability. A decrease in irreducible water or an increase in slip length results in an increase in flow space, which increases permeability. The permeability decreases with an increase in effective stress; moreover, when the mechanical properties of rock (elastic modulus and Poisson’s ratio) increase, the decreasing rate of permeability with effective stress is reduced.

Particle morphology of mineral filler and its effects on the asphalt binder-filler interfacial interaction

This paper focused on the particle morphology of mineral filler and its effects on asphalt binder-filler interfacial interaction. The limestone, basalt, and granite fillers with various particle sizes were selected to prepare asphalt mastics. The relationship between morphological characteristics of mineral filler and asphalt binder-filler interfacial interaction was established. The results show that the angularity index and fractal dimension decrease while the form factor increase with the decreasing particle size. The granite filler particles demonstrated the higher morphological index values than the limestone and basalt ones. The K-B-G* value based on Palierne emulsion model exhibits the least susceptibility but strongest stability to filler particle size among the evaluation parameters studied. Form factor is the determining influential factor for asphalt binder-filler interfacial interaction, regardless of filler lithology. Furthermore, the packing characteristics of filler particles and the associated mastic morphologies could provide insight to possible relationship between particle morphology and interfacial behavior. All the results contribute to the selection of appropriate mineral filler to improve the asphalt binder-filler interfacial interaction and then the performance of asphalt mix system.

An analytical solution on spontaneous imbibition coupled with fractal roughness, slippage and gravity effects in low permeability reservoir

Spontaneous imbibition (SI) refers to displacement of non-wetting phase by wetting phase fluids in porous media which driven by capillary force. Spontaneous imbibition plays an important role in terms of increasing hydrocarbon recovery in low-permeability and tight reservoirs. In this study, we derived a new analytical model of spontaneous imbibition height in low-permeability reservoir considering effective viscosity, surface roughness, slip and gravity effects in a single tortuous capillary tube. Firstly, analytical solutions of imbibition height are derived in a single tortuous rough capillary tube with and without gravity effects. Moreover, our analytical model shows satisfactory match with experimental results from literatures in typical low-permeability core samples. Finally, sensitivity studies are conducted to discuss the effect of surface fractal dimension, effective viscosity, contact angle, interfacial tension, pore sizes and slip length on imbibition height, respectively. The results show that imbibition height inversely proportional to surface fractal dimension, effective viscosity, and contact angle on rough surface. Higher surface fractal dimension, effective viscosity and contact angle decrease imbibition height significantly. On the contrary, the imbibition height is proportional to pore radius, IFT, and slip length. Neglecting the slip effect results in underestimation of imbibition height in nanopore sizes, and insignificant changes are observed for micro-pore sizes. The presented models have clear physical meaning in every parameter on the imbibition height performance.

Multi-fractal structure features of corn stalks and their correlation with pretreatment homogeneity and efficacy

Lignocellulose biomass is a natural porous medium with fractal characteristics, which tend to be distinct after certain pretreatment and relational with processing effects. In this work, multi-scale fractal features of corn stalks after steam explosion pretreatment were systematically characterized employing digital image processing and mercury intrusion porosimetry methodologies. The macroscopic surface fractal features (Ds: 2.8278 ∼ 2.8523) and microscopic pore fractal features (Dp: 2.3003 ∼ 2.8867) presented same variation tendency with pretreatment severity, revealing the self-similarity of processing results of corn stalks with the scale. In association with pretreatment homogeneity and efficacy, the decrease in fractal dimensions corresponded to morphologically homogeneous and structurally complex samples with preferable auto-hydrolysis degree of structural components, which led to high reactivity with enzymes. Quantitatively, there were strongly linear correlation between fractal dimensions and enzymatic digestibility with r2 > 0.95. Fractal dimension was expected to theoretically guide the rational evaluation, prediction and promotion of the key pretreatment technique in biorefinery.

Influence of Soil Particle Size on the Engineering Properties and Microstructure of a Red Clay

Particle size exerts a significant influence on the mechanical behavior of soil. However, insufficient research has been carried out on red clay formations, which are widespread in some Chinese provinces. Here, using unconfined compressive strength (UCS) tests, wetting–drying (WD) tests, and low-temperature nitrogen adsorption tests, we examined the relationship between the particle size and a number of mechanical and microstructural characteristics of a red clay outcropping at a construction site in China. Our results suggest that, depending on the surface area, porosity, particle size, and dry density, the failure mechanism in UCS tests will be different. That is, as the particle size increases, the failure mode of soil changes from split failure into shear failure. In addition, as the dry density increases, the UCS of the soil sample is significantly improved, and its total porosity and fractal dimension decrease. We also evaluated a dependence on particle size and the number of WD cycles on the distribution and size of cracks in WD tests. We conclude by suggesting that particle size, dry density, and WD behavior should all be taken into account in roadbed designs in red clay formations.

Explosion wave and crack field of an eccentric decoupled charge.

To investigate the characteristics of the explosion damage from an eccentric decoupled charge, the rock-breaking mechanism of an eccentric decoupled charge is revealed from the perspectives of the explosion wave field and crack field through theoretical and experimental analyses. The ratio of the maximum to minimum pressure on an eccentric decoupled hole wall increases exponentially with an increase in the decoupling coefficient, but it does not change with a change in the explosive density or explosive detonation velocity. The explosive energy on the eccentric charge side has a certain accumulation effect, the velocity of the reflected shock wave at the blasthole wall is greater than that of the incident shock wave, and the incident velocity of the explosion wave on the eccentric side is greater than that on the non-eccentric side. The expansion range of the explosion gas is significantly better than that on the non-eccentric side, indicating that the eccentric decoupled charge can strengthen the action of the explosion gas product on the eccentric side. In addition, the overpressure of the explosion wave on the eccentric side is greater than that on the non-eccentric side. The fractal dimension and damage degree of the explosion crack on the eccentric side are larger than those on the non-eccentric side. The explosion cracks can be divided into intensive, transition, and sparse areas, and the fractal dimension and damage degree decrease successively in the three areas. The explosion cracks formed on the non-eccentric side outside the range of three times the blasthole diameter concentrate in the sparse area, and the destructive effect of the explosion on the non-eccentric side medium is effectively reduced.

Coupling Effect of Temperature, Gas, and Viscoelastic Surfactant Fracturing Fluid on the Microstructure and its Fractal Characteristics of Deep Coal

The study of the microstructure evolution law of coal in a natural reservoir environment for the extraction of coalbed methane mining (ECBM), especially deep ECBM, is of major significance. We treated coal samples from Qinshui Basin under combined temperature–gas–fracturing fluid conditions and analyzed the evolution of the microstructure and its fractal characteristics to study the microstructural evolution of coal under natural hydraulic fracturing conditions. In the temperature range of 303.15 to 343.15 K and the gas-pressure range of 0.5–4.5 MPa, our data demonstrate that the pore structure is more susceptible to the temperature influence, compared with microfracture. The treatment of viscoelastic surfactant fracturing fluid (VES-FF) can effectively increase the permeation pore and fracture ratio by more than 300% and reduce the adsorption pore by more than 200% through dissolution, gas wedge, and other effects, which is favorable to ECBM. At the same temperature, as the gas pressure increases, the pore decreases, whereas the fracture ratio increases. The pore fractal dimension ranges from 2.90 to 2.99, which is significantly higher than that of microfractures. The temperature has a minor effect on the fracture fractal dimension, but it causes a decrease in the pore fractal dimension. The treatment of VES-FF induces an increase in the fracture fractal dimension, implying an increase in the fractal complexity. In contrast, the pore fractal characteristics show a contrary trend. At a gas pressure of 4.5 MPa, the negative effect of VES-FF on the pore structure reaches its maximum, whereas the effect on the fracture drops to its minimum. The results document that high temperature and high gas pressure can severely limit the penetration enhancement effect of VES-FF.

Evaluation of Cashew Nut Shell Liquid Borate Ester as Pour Point Depressant for Flow Assurance of Waxy Crude Oil

The development of chemical solutions to wax problems by modifying renewable natural products is an innovative response to the need for cheaper, eco-friendly pour point depressants for waxy crude oil flow improvement. Natural cashew-nut shell liquid (CNSL) was extracted from shells of Anacardium occidentale and derivatized into the borate ester. Pour point of oil doped with 500ppm CNSL borate ester was reduced by -24oC. The effect of borate ester addition on wax morphology was studied by cross-polarized microscopy. Analysis of micrographs using ImageJ software showed a decrease in Feret diameter, aspect ratio, and boundary fractal dimension of wax crystals in doped oil and increased crystal circularity and solidity, indicating the evolution of smaller, rounder, regular structures with smoother, even surfaces. At 10oC, oil shear stress and dynamic viscosity were reduced by 27.6% and 24.6%, respectively. Pour point depressant and flow improvement effects of additive were related to changes in crystal morphology.

Surface properties of oxidized lignite and its application in congo red dye adsorption

ABSTRACT Lignite is easily oxidized, and spontaneous combustion occurs during its storage, which greatly reduces its calorific value and affects its quality and economic benefits. The surface properties of the oxidized lignite including pore structure and oxygen-containing functional groups were investigated by N2 adsorption/desorption isotherms and Fourier transform infrared spectroscopy. The adsorption of Congo red dye in aqueous solution by oxidized lignite was carried out. It was observed that due to oxidation, the specific surface area and total pore volume of the Huolinhe lignite samples decreased, and the average pore size increased. As oxidation temperature increased, the number of microporous and mesoporous structures decreased, resulting in the decrease of fractal dimension. The hydroxyl content was negatively correlated with the oxidation temperature, but the carbonyl content showed an opposite trend. At the initial stage of oxidation, the rate of hydroxyl consumption is higher than that of formation. The reaction to generate carbonyl, such as the oxidation of aliphatic hydrocarbons, alcohol hydroxyl groups and ethers, requires a higher reaction temperature, so the carbonyl content increased when the temperature was higher than 70 °C. Oxidized lignite was used to adsorb Congo red dye in aqueous solution, and the removal increased significantly with increasing oxidation temperature. Therefore, oxidized lignite can effectively remove Congo red dye from aqueous solution, so as to improve the economic benefit of oxidized lignite.

Development of Novel Fractal Method for Characterizing the Distribution of Blood Flow in Multi-Scale Vascular Tree.

Blood perfusion is an important index for the function of the cardiovascular system and it can be indicated by the blood flow distribution in the vascular tree. As the blood flow in a vascular tree varies in a large range of scales and fractal analysis owns the ability to describe multi-scale properties, it is reasonable to apply fractal analysis to depict the blood flow distribution. The objective of this study is to establish fractal methods for analyzing the blood flow distribution which can be applied to real vascular trees. For this purpose, the modified methods in fractal geometry were applied and a special strategy was raised to make sure that these methods are applicable to an arbitrary vascular tree. The validation of the proposed methods on real arterial trees verified the ability of the produced parameters (fractal dimension and multifractal spectrum) in distinguishing the blood flow distribution under different physiological states. Furthermore, the physiological significance of the fractal parameters was investigated in two situations. For the first situation, the vascular tree was set as a perfect binary tree and the blood flow distribution was adjusted by the split ratio. As the split ratio of the vascular tree decreases, the fractal dimension decreases and the multifractal spectrum expands. The results indicate that both fractal parameters can quantify the degree of blood flow heterogeneity. While for the second situation, artificial vascular trees with different structures were constructed and the hemodynamics in these vascular trees was simulated. The results suggest that both the vascular structure and the blood flow distribution affect the fractal parameters for blood flow. The fractal dimension declares the integrated information about the heterogeneity of vascular structure and blood flow distribution. In contrast, the multifractal spectrum identifies the heterogeneity features in blood flow distribution or vascular structure by its width and height. The results verified that the proposed methods are capable of depicting the multi-scale features of the blood flow distribution in the vascular tree and further are potential for investigating vascular physiology.

Dynamic flexural failure of rocks under hydrostatic pressure: Laboratory test and theoretical modeling

Dynamic flexural failure of rocks is commonly encountered near deep underground openings due to the bending load derived from earthquakes or production blasts in rock engineering. Meanwhile, deep underground rock is also generally subjected to static hydrostatic pressure. Thus, it is desirable to investigate dynamic flexural failure characteristics and mechanisms of rocks under static hydrostatic pressure. In this study, the dynamic flexural tensile strengths of Laurentian granite (LG) under five hydrostatic pressures (i.e., 0 MPa, 5 MPa, 10 MPa, 15 MPa and 20 MPa) were measured by using a triaxial split Hopkinson pressure bar (SHPB) system in combination with the semi-circular bend (SCB) method. The experimental results indicate that dynamic flexural tensile strength under a certain hydrostatic pressure rises with the loading rate, and dynamic flexural tensile strength at a certain loading rate increases with the hydrostatic pressure due to the closure of microcracks in rocks. In addition, an empirical formula is proposed to successfully predict both the rate dependence and the hydrostatic pressure effect on the dynamic flexural tensile strength. Moreover, the parameter in terms of the hydrostatic pressure is first introduced in the two-parameter tensile strength model, which is improved in this study to quantitatively rationalize the discrepancy between the dynamic intrinsic tensile strength and the dynamic flexural tensile strength for rocks under hydrostatic pressures, and to further establish the relationship between the hydrostatic pressure and the characteristic material length δ for rocks. Meanwhile, the characteristic material length is optimized by the particle swarm optimization method and the value of δ decreases with the hydrostatic pressure due to the closure of microcracks and pores. Besides, an equation is established to describe the relation between the hydrostatic pressure and the characteristic material length. In addition, the morphology of the main fracture in the tested SCB specimens is digitized and the fractal dimension is applied to quantitively describe the fracture surfaces roughness. There is no clear trend to indicate the influence of hydrostatic pressure on the surface roughness, whereas there is generally a decrease of fractal dimension with increasing loading rate for LG under each hydrostatic pressure.

Normal fault growth in continental rifting: Insights from changes in displacement and length fault populations due to increasing extension in the Central Kenya Rift

This study examines the scaling relationship between fault length and displacement for the purpose of gaining a better understanding of the evolution of normal faults within the central Kenya Rift. 620 normal faults were manually mapped from a digital elevation model (DEM), with 30 m2 resolution and an estimated maximum displacement of ~40–~6030 m and fault lengths of 1270 ‐ 60,600 m. To assess the contribution of fault populations to the strain accommodation from south to north, the study area has been divided into three zones of fault populations based upon their average fault orientations; zone 1 in the north is dominated by NNE striking faults, zone 2 in the centre of the rift is characterised by NNW to NNE fault trends, whereas zone 3 in the south is characterised by NNW striking fault systems. Extensional strain was estimated by summing fault heaves across six transects along the rift, which showed a progressive increase of strain from south to north. The fault length and displacement data in the three zones fit to a power law distribution. The cumulative distributions of fault length populations showed similar fractal dimension (D) in the three zones. The cumulative displacement distributions for the three zones showed a decrease in the Power-law fractal dimension with increasing strain, which implies that the strain is increasingly localized onto larger faults as the fault system becomes more evolved from south to north. Increasing displacement with increasing strain while the fault length remains almost constant may indicate that the fault system could be evolving in accordance with a constant length fault growth model, where faults lengthen quickly and then accrue displacement. Results of this study suggest that the process of progressively increasing fault system maturity and strain localization onto large faults can be observed even over a relatively small area (240 × 150 km) within the rift system. It is also suggested that patterns of fault growth can be deduced from the fractal dimension of cumulative distribution of fault size populations.

Influence of fibers on desiccation cracks in sodic soil

Drying shrinkage of soil contaminated by alkaline solutions in ecologically fragile areas is a key issue that affects the strength, stability, and permeability of contaminated soil. Reinforcement with polypropylene fibers is a common physical treatment method. This paper presents experimental investigations of the shear strength, permeability, formation, and development of desiccation cracks in sodic soil with four different contents of polypropylene fibers: 0%, 2%, 4%, and 8%. The shear strength and permeability coefficient were tested by the SLB-1 triaxial shear permeability tester. Meanwhile, a series of crack images and water content evolution were obtained during free desiccation tests with self-designed monitoring equipment. The dynamic changes in the cracks are then quantitatively analyzed by using digital image processing and geographic information system (GIS) analysis. The experimental results show that shear strength increases and permeability coefficient decreases with the increase of fiber content. The evaporation process with different polypropylene fiber contents has three stages, namely, Stages I, II, and III that are in accordance with the slope of the evaporation curve. However, the polypropylene fiber content has little effect on the total duration of crack development. The crack development process has three stages. The crack ratio, fractal dimension, and average width decrease as the polypropylene fiber content increases. The fractal dimension gradually and linearly increases with time. The fractal dimensions of the cracks are reduced with increased polypropylene fiber content, which indicates that polypropylene fibers can inhibit the development of soil cracking. Because the elastic modulus of the fibers is very high, it is difficult for the fibers to be pulled out from the soil during cracking. Therefore, friction is produced at the interface between the fibers and soil particles, which can inevitably inhibit the relative sliding of the fibers and share the tensile stress caused by the structural shrinkage in the soil. Therefore, polypropylene fibers can dramatically improve the stability and integrity of soil, similar to a “bridge.” In conclusion, these research results provide an important explanation for dealing with alkali-contaminated foundations and soils.

Study of Macro‐ and Mesodamage of Remolded Loess under Alternating Dry and Wet Conditions in an Acid Rain Environment

As a national development plan, ecological protection of the Yellow River Basin has attracted extensive social attention in recent years. Considering the influence of acid rain on the engineering characteristics of loess in this area, we investigated changes in the physical and mechanical characteristics of remolded loess under the combined action of acid rain and dry‐wet cycles by means of triaxial tests, nuclear magnetic resonance spectroscopy, and scanning electron microscopy. The results are as follows: in the acidic environment, the stress‐strain relationship of remolded loess undergoes stress hardening after dry‐wet cycling. The cohesion and internal friction angle of remolded loess are negatively correlated with the number of cycles. From the multiscale analysis of the dry‐wet cycle process under acid rain condition, the T2 spectrum of the test soil has three peaks at the micropore level. With the increasing number of cycles, the spectral area increases gradually, and the sample transitions from small pores to large‐ and medium‐size pores. At the microscopic level, the clay mineral particles among soil particles decrease in size, the contact mode between soil particles develops from stable to unstable, the particles are gradually rounded, and the fractal dimension decreases. Chemical erosion and physical erosion are special features of this experiment. Physical erosion causes particle erosion and pore growth, while chemical erosion includes reactions by feldspar. Together, physical and chemical reactions aggravate the soil deterioration process. These research results have laid a good experimental foundation for the ecological protection of the Yellow River Basin.

Glycerol-modified cashew nut shell liquid as eco-friendly flow improvers for waxy crude oil

Use of pour point depressants/flow improvers is an effective strategy for alleviation of flow problems associated with wax formation in paraffinic crude oil. Biobased oilfield chemicals derived from renewables are appealing as low-cost, eco-friendly alternatives to conventional pour point depressants. Cashew nut shell liquid (CNSL) extracted from Anacardium occidentale shells was modified by esterification with glycerol. The CNSL derivatives were evaluated as pour point depressants and low-temperature flow improver for waxy crude oil. Pour point and viscosity of doped crude oil were reduced by a maximum of 15 °C and 86%, respectively. Cross-polarized micrographs of doped oil were analyzed with Image J software and showed decrease in wax crystal aspect ratio and boundary fractal dimension indicating modifications to wax morphology and microstructure.

Quantitative assessment of offshore wind speed variability using fractal analysis

Proper understanding of offshore wind speed variability is of essential importance in practice, which provides useful information to a wide range of coastal and marine activities. In this paper, long-term wind speed data recorded at various offshore stations are analyzed in the framework of fractal dimension analysis. Fractal analysis is a well-established data analysis tool, which is particularly suitable to determine the complexity in time series from a quantitative point of view. The fractal dimension is estimated using the conventional box-counting method. The results suggest that the wind speed data are generally fractals, which are likely to exhibit a persistent nature. The mean fractal dimension varies from 1.31 at an offshore weather station to 1.43 at an urban station, which is mainly associated with surface roughness condition. Monthly variability of fractal dimension at offshore stations is well-defined, which often possess larger values during hotter months and lower values during winter. This is partly attributed to the effect of thermal instability. In addition, with an increase in measurement interval, the mean and minimum fractal dimension decrease, whereas the maximum and coefficient of variation increase in parallel.

Quantitative assessment of offshore wind speed variability using fractal analysis

Proper understanding of offshore wind speed variability is of essential importance in practice, which provides useful information to a wide range of coastal and marine activities. In this paper, long-term wind speed data recorded at various offshore stations are analyzed in the framework of fractal dimension analysis. Fractal analysis is a well-established data analysis tool, which is particularly suitable to determine the complexity in time series from a quantitative point of view. The fractal dimension is estimated using the conventional box-counting method. The results suggest that the wind speed data are generally fractals, which are likely to exhibit a persistent nature. The mean fractal dimension varies from 1.31 at an offshore weather station to 1.43 at an urban station, which is mainly associated with surface roughness condition. Monthly variability of fractal dimension at offshore stations is well-defined, which often possess larger values during hotter months and lower values during winter. This is partly attributed to the effect of thermal instability. In addition, with an increase in measurement interval, the mean and minimum fractal dimension decrease, whereas the maximum and coefficient of variation increase in parallel.

3D digital rock modeling of the fractal properties of pore structures

Fractal parameters of porous media have been a focus of study in petroleum engineering and hydrogeology for several decades because they provide an effective way to describe the complexity of pore structure across a wide range of scales. This paper combines 3D process-driven digital rock modeling with fractal analysis in order to understand the effect of varying sorting, compaction, cementation, and the fine grain fraction of binary models on the fractal parameters and specific surface area of porous media. Digital rock models (DRMs) were constructed to simulate sandstone using a process-driven modeling technique which simulates sedimentation. The fractal parameters of the resulting pore geometry were calculated using the box-counting method on 2D and 3D representations of the DRMs. Our simulations indicate that increasing compaction or cementation lead to significant decreases in fractal dimension, specific surface area (SSp) and porosity, showing that these two diagenetic processes can affect the pore microstructure of the rock significantly. While interface fractal dimension (Di) and SSp both increase slightly with decreases in sorting (grain size variety), and porosity decreases slightly. Examining the behavior of binary models, the porosity of our digital models shows a V-shaped curve as fine grain fraction increases from 0 to 1, consistent with, but higher than the theoretical values, which we attribute to incomplete packing of the grains arising from the simplified packing algorithm and finite boundary of models. The value of both SSp and Di increase as the fine grain fraction increases. However, we must notice that the porosity may be underestimated, and the fractal dimension may be overestimated when we use models consisting of very fine spherical grains due to the effect of image resolution.

Effect of particle size distribution on flocculation and its growth in cement-ground limestone suspensions

The impact of particle size distribution on flocculation and its growth in cement-ground limestone suspensions was investigated by observing the flocculation states with a microscopic image analyzer and calculating the microscopic interparticle forces based on the multifractal methods and extended DLVO theory. The results showed that the particle size distribution exhibits a clear fractal feature and the flocculation and its growth have multifractal characteristics in cement-ground limestone suspensions. The spectral width, spectral difference and minimum fractal dimension of multifractal spectrum are used to depict the spatial arrangement, size distribution and average state of flocs, respectively. The multifractal spectrum of flocculation growth can be used to describe the growth of flocs. Compare with it, the multifractal spectrum of flocculation formation process has the advantages of integrity and simplification. When the fractal dimension of particle size distribution increases, the spectral width and spectral difference increase and the minimum fractal dimension decreases, which means that it is not beneficial to flocculation and flocculation growth. However, when it continues to increase, the opposite result appears because of the increase of effective distance ratio and interparticle force between particles.

A Numerical Study on Gas Flow through Anisotropic Sierpinski Carpet with Slippage Effect

A pore-scale model has been developed to study the gas flow through multiscale porous media based on a two-dimensional self-similar Sierpinski carpet. The permeability tensor with slippage effect is proposed, and the effects of complex configurations on gas permeability have been discussed. The present fractal model has been validated by comparison with theoretical models and available experimental data. The numerical results show that the flow field and permeability of the anisotropic Sierpinski model are different from that of the isotropic model, and the anisotropy of porous media can enhance gas permeability. The gas permeability of porous media increases with the increment of porosity, while it decreases with increased pore fractal dimension under fixed porosity. Furthermore, the gas slippage effect strengthens as the pore fractal dimension decreases. However, the relationship between the gas slippage effect and porosity is a nonmonotonic decreasing function because reduced pore size and enhanced flow resistance may be simultaneously involved with decreasing porosity. The proposed pore-scale fractal model can present insights on characterizing complex and multiscale structures of porous media and understanding gas flow mechanisms. The numerical results may provide useful guidelines for the applications of porous materials in oil and gas engineering, hydraulic engineering, chemical engineering, thermal power engineering, food engineering, etc.