Pore Fractal Dimension Research Articles

Fractal Dimension of Digital 3D Rock Models with Different Pore Structures

The macroscopic physical properties of rocks are profoundly determined by their microstructure, and the research of accurately characterizing rock pore structure has been extensively carried out in the fields of petroleum engineering and geoscience. Fractal geometry is an effective means of quantitatively estimating the pore structure properties of porous media. In this study, the evolution law of the fractal dimension and the quantitative relationship between the fractal dimension and porosity were investigated based on the digital 3D rock models. First, three kinds of models with gradually changing pore structures, namely sedimentation, compaction, and cementation, were systematically reconstructed by the process-based approach. Then, the fractal dimensions of the skeleton, pore, and surface of the models were computed and analyzed. Finally, the relationships among the fractal dimension, porosity, and complexity were explored qualitatively. These works reveal the changing laws of three types of fractal dimensions for different pore structure models. The pore structure differences in sedimentation model can only be distinguished by the surface fractal dimension, while both pore and surface fractal dimensions are available parameters for characterizing different pore structures in compaction and cementation models. The quantitative relations between box-counting fractal dimension and porosity were established, which can be expressed by combining linear and logarithmic formulas. The comparison of fractal dimensions of compaction and cementation models proves that fractal dimensions can distinguish the subtle pore structure differences in digital 3D rock models. Understanding the evolution law between the fractal dimension and pore structure parameters provides more references for classifying and evaluating rock pore structure features using fractal dimensions.

Thermal and non-thermal mechanism of microwave irradiation on moisture content reduction of municipal sludge

Both huge volume and high moisture content of municipal sludge have brought great troubles and attracted extensive concerns in the world. The bound water of sludge and pore clogging in the process of pressure filtration dewatering are two key factors influencing the deep-dewatering effect of municipal sludge. The results of this study suggest that microwave irradiation (MI) can be used to synchronously evaporate water, reduce the bound water of sludge and solve the blockage of sludge pore channels during the process filtration dewatering, which can greatly reduce the moisture content of municipal sludge. Low-field nuclear magnetic resonance, carbon dioxide gas absorption and desorption, and scanning electron microscope were synthetically used to detect the pore structure of sludge cakes. Thermogravimetric differential scanning calorimetry was used to detect binding energy to calculate moisture distribution. Thermal mechanism was revealed by dielectric constant, thermal conductivity, fractal dimensions, water saturation and porosity in different layers of sludge cake. The results showed that the bound water in sludge samples after MI was reduced by 19.4%, the pore fractal dimension was reduced from 2.955 to 2.867, the surface fractal dimension increased from 2.099 to 2.362 with the conditions of microwave power (700 w) and treat time (5 min). When the water saturation was close to 1, the dielectric constant of middle and outer layers was the main factor of heating, while the water saturation was close to 0, the main factor became the difference of thermal conductivity in middle and outer layers. Moreover, after MI, moisture content of sludge was greatly reduced from 68.4% to 40.1% for its thermal effect, further reduced to 34.1% by the continuous mechanical dewatering for its non-thermal effect which change the pore structure and moisture distribution. These conclusions are helpful to understand microwave thermal and non-thermal mechanism and shed light on new dewatering-drying integrated techniques of municipal sludge.

Mechanism of a novel ultrasonic promoting fracturing technology in stimulating permeability and gas extraction

Coalbed methane exploitation can optimize the energy composition, help to achieve carbon neutrality and carbon peak. As a key factor affecting the effect of coalbed methane production, fracturing fluid can greatly improve the micropore structure of the coal seam and the effect of gas desorption, and improve the efficiency of gas extraction. Due to the ordinary physical and chemical reaction rate between fracturing fluid and coal and the short effective extraction time, it is difficult to achieve an effective extraction effect. A novel ultrasonic promoting fracturing technology is proposed in this paper to increase gas production, that is, applying an ultrasonic field to the coal seam during the fracturing and extraction stage to enhance the fracturing effect, the desorption effect, and the integrity of the seepage channel. This technology uses the mechanical, cavitation, thermal and chemical effects of ultrasonic waves to strengthen the interaction effect of fracturing fluid and coal and gas extraction rate. In the ultrasonic–temperature–pressure multiple fields experiments, it is found that after the application of ultrasonic, the effect of the fracturing fluid was greatly improved, the diameter of the macropores was significantly increased, and a large number of new micropores were generated. Compared with the effect of only fracturing fluid, the pore volume, fractal dimension, and permeability of coal were increased by 14.1 %, 15.9 %, and 26.9 %, respectively. The experimental results prove the feasibility and effectiveness of the ultrasonic promoting fracturing technology.

In situ SAXS study on the evolution of coal nanopore structures with uniaxial compressive stress

In this study, an in situ synchrotron radiation small-angle X-ray scattering (SAXS) experiment is used to characterize the evolution of coal nanopore structures under uniaxial compression. The variation in the coal nanopores is measured by analyzing the obtained scattering data. From the results, the coal scattering data show a positive Porod deviation in which the deviation slope decreases with increasing stress. Smaller nanopores are more sensitive to uniaxial compressive stress. There is a positive correlation between scattering intensity I and stress at less than 30 nm. The scattering intensity I of pores larger than 30 nm is negatively correlated with uniaxial compressive stress. The structure of smaller pores is more complex. The surface fractal dimension DS and pore fractal dimension DP increases and decreases with increasing uniaxial compressive stress, respectively. The specific surface area is positively correlated with DS. In the measuring range of 3–80 nm, the coal nanopores show a bimodal distribution. At the stage of below 0.6σp, the average diameter decreases by 1.98%, the porosity and specific surface area increases by 6.21% and 31.5%, respectively; At the stage of above 0.6σp, the average diameter decreases by 1.04%, the porosity and specific surface area increases by 1.18% and 5.57%, respectively. These results suggest that the variation of coal nanopores with stress have phased characteristics, and the evolution of the coal nanopores under uniaxial stress can be divided into two stages. In the nanopore fracture stage, the nanopores are deform, fracture and create new smaller pores with increasing stress, and the roughness of pore surface increase. In the nanopore closure stage, high stress intensifies the degree of pore fracture, and nanopores begin to close and disappear. This study reveals the evolution characteristics of the pore structures of coal under uniaxial compression at the nanoscale.

Insights into the Nanoscale Microstructure Diversity of Different Rank Coals

The gas flow pattern of the coal seam is closely related to the pore structure of the coal. In order to better understand the pore distribution in different coal samples, the pore distribution and fractal dimension characteristics of five coal samples with different degrees of metamorphism were investigated and analyzed by using the low-temperature nitrogen adsorption method and CO2 adsorption methods based on the fractal theory. The results showed that the higher the degree of metamorphism, the better the pore development, and the fractal dimension of micropores and mesopores varied with the degree of metamorphism. The pore variability between the outburst and non-outburst coals is mainly in the stage of micropores, with the outburst coal having a larger pore volume and specific surface area and a more complex microstructure. The pore formation and distribution patterns of different coal samples under the combined influence of geological and coalification effects are discussed.

Effect of Uniaxial Compression on Coal Nanostructure as Measured by Small Angle X-ray Scattering

Abstract To study the effect of uniaxial compression on coal nanostructure during uniaxial compression, in situ synchrotron radiation small angle X-ray scattering experiments were carried out on four coals with different ranks under uniaxial compression. According to the scattering data during the uniaxial compression process, the fractal characteristics and the variation feature of fractal dimension with stress were obtained. Four coals with different ranks all possess two fractal characteristics: pore fractal occur in the smaller pore range (7–17 nm) in the high q value range, and surface fractal occur in the larger pore range (17–52 nm) in the low q value range. For two low rank coals, with increasing stress, the pore fractal dimension DP decreased and the surface fractal dimension DS increased, respectively; the variation trends of DP and DS were obvious. This indicates that with increasing stress, the heterogeneity and complexity of the pores decrease, the surface roughness of the pores increases, and stress has a significant effect on the nanopore structure. The smaller pores are more susceptible to stress, and the influence range of stress on low rank coals is larger than that on high rank coals. The change rate of fractal dimension (RD) has a poor relationship with compressibility during uniaxial loading and is related to coal rank. The RD per unit stress for high rank coals is larger than that for low rank coals. Nanostructure response to uniaxial compressive stress is more significant in low rank coals than in high rank coals. Compared with low rank coals, high rank coals have strong aromatization and molecular structure, and the nanostructures are less susceptible to failure under uniaxial stress.

Deterioration characteristics of coal gangue concrete under the combined action of cyclic loading and freeze-thaw cycles

Coal gangue is a kind of solid waste. Adding coal gangue as aggregate into concrete can realize the resource utilization of solid waste. The deterioration law of coal gangue concrete under the combined action of cyclic loading and freeze-thaw was studied by macro and micro methods. The mass loss, relative dynamic elastic modulus loss, and compressive strength loss of specimens under the combined action were analyzed. The microscopic morphology and pore structure deterioration law of gangue concrete were investigated by scanning electron microscopy and mercury compression test. The quantitative relationship between the pore structure and compressive strength damage was established. The results show that with the increase of cyclic loading and freeze-thaw cycles, the mass of the specimen first increases and then decreases. The relative dynamic elastic modulus and compressive strength gradually decrease. The larger fractal dimension indicates the higher complexity of the pore structure. The fractal dimension decreases with the increase of cyclic loading times and freeze-thawing, implying that the pore structure gradually deteriorates under the combined action. The regression effect between compressive strength damage and composite pore structure parameters and fractal dimension is evident, describing the quantitative relationship between compressive strength damage and pore structure under the combined action of cyclic loading and freeze-thaw cycles.

Reaction kinetics, mechanical properties, and microstructure of nano-modified recycled concrete fine powder/slag based geopolymers

Nano-materials are increasingly being used as modified binder for improve the performance of cementitious materials. In this paper, nano-SiO2 and nano-Al2O3 were incorporated into the geopolymers formed by the mixture of construction solid waste (recycled concrete fine powder) and industrial solid waste (slag). The effects of the type and content of nanomaterials on the early reaction kinetics, physical and mechanical properties and microstructure of geopolymer composites were explored. Results show that the addition of nanomaterials mainly affected the dissolution stage of geopolymerization, played a nucleation effect and improved the reaction rate. The promotion effect of nano-Al2O3 was slightly greater than that of nano-SiO2. Based on the results of JMAK model, the formation of geopolymers composites was an one-dimensional heterogeneous nucleation control reaction, which followed a plate-like structure thickening mechanism. The addition of nanomaterials shortened the setting time. The incorporation of nano-Al2O3 was beneficial to improve the fluidity of geopolymer. Furthermore, the addition of the two nanomaterials could improve the compressive strength of geopolymers. The compressive strength tended to first increase and then decrease with increasing nano-SiO2 or nano-Al2O3 content. The optimal mixing ratio of nano-silica and nano-alumina were 1.2% and 1.6% respectively, and the 28-day compressive strengths were both 59.05 MPa, which were 23.35% higher than that without nano-materials. XRD and SEM-EDS analysis indicate that the incorporation of nanomaterials had no impact on the type of final products, but increased their number, particularly calcium-based gel products. The internal structure of geopolymer with nanomaterials was more dense and uniform than that without nanomaterials. The MIP observed that the addition of the two nano-materials reduced the porosity in the matrix, the number of macropores and the pore fractal dimension. The pore fractal dimension of geopolymer was negatively correlated with the compressive strength.

Study on the strength mechanism of red clay improved by waste tire rubber powder

The objective of this research is to improve the strength characteristics of red clay as a subgrade filler and increase the stability of subgrade engineering. During the laboratory tests, different amounts of waste tire rubber powder were added to the red clay. This study aims to identify the optimal amount of rubber powder required to improve the strength characteristics of red clay using a triaxial test and Duncan–Chang model. Using the depth of a field microscope, the apparent morphology of red clay and modified red clay was analyzed, and the pore variation of plain red clay and rubber powder modified red clay was described using a mercury intrusion test(MIP). The experimental results indicate that the asymptotic value of the main stress difference is significantly higher than the other four admixtures at 3%. The 3D surface comparison chart indicates that the addition of rubber powder significantly increases the relatively flat area range while reducing the overall area range. According to the comparison of porosity and contact area ratio, RPA1 is larger than RPA2, and RCA1 is smaller than RCA2. According to the characteristics of BJH pore size distribution, modified red clay has a higher pore fractal dimension than pure red clay.

Experimental analysis of pore structure and fractal characteristics of soft and hard coals with same coalification

Accurate and quantitative investigation of the physical structure and fractal geometry of coal has important theoretical and practical significance for coal bed methane (CBM) development and the prevention of dynamic disasters such as coal and gas outbursts. This study investigates the pore structure and fractal characteristics of soft and hard coals using nitrogen and carbon dioxide (N2/CO2) adsorption. Coal samples from Pingdingshan Mine in Henan province of China were collected and pulverized to the required size (0.20–0.25 mm). N2/CO2 adsorption tests were performed to evaluate the specific surface area (SSA), pore size distribution (PSD), and pore volume (PV) using Braunuer-Emmett-Teller (BET), Barrett-Joyner-Halenda (BJH), and Density Functional Theory (DFT). The pore structure was characterized based on the theory of fractal dimensions. The results unveiled that the strength of coal has a significant influence on pore structure and fractal dimensions. There are significant differences in SSA and PV between both coals. The BJH-PV and BET-SSA obtained by N2-adsorption for soft coal are 0.029–0.032 cm3/g and 3.523–4.783 m2/g. While the values of PV and SSA obtained by CO2-adsorption are 0.037–0.039 cm3/g and 106.016–111.870 m2/g. Soft coal shows greater SSA and PV than hard coal, which is consistent with the adsorption capacity ({V}_{mathrm{L}}). The fractal dimensions of soft and hard coal are respectively different. The Ding coal exhibits larger D1 and smaller D2, and the reverse for the Wu coal seam is observed. The greater the value of D1 (complexity of pore surface) of soft coal is, the larger the pore surface roughness and gas adsorption capacity is. The results enable us to conclude that the characterization of pores and fractal dimensions of soft and hard coals is different, tending to different adsorption/desorption characteristics. In this regard, the results provide a reference for formulating corresponding coal and gas outburst prevention and control measures.

Semi-homogeneous model of coal based on 3D reconstruction of CT images and its seepage-deformation characteristics

To study the effect of isolated pores on gas seepage and coal deformation, computed tomography (CT) scanning was used to analyse the porosity and fractal characteristics of isolated pores. A geometric model of coal was then established using 3D reconstruction. Finally, a seepage-stress semi-homogeneous coupling model was established by considering the adsorption and desorption of gas. The significant difference between this model and the existing models is that the non-homogeneity of isolated pores is considered. The results show that the porosity of the isolated pores is 5.73%, accounting for 58.41% of the total pores, and the diameter is concentrated in the range of 0–10 μm. The average fractal dimension of the connected pores (1.25) is smaller than that of the isolated pores (1.35), indicating that isolated pores have a more complex structure. The gas seepage velocity is negatively correlated with the isolated pore porosity, and it varies strongly at each point of the model, with a maximum and minimum of 5.08 m/s and 1.45 × 10−4 m/s, respectively. The inhomogeneous distribution of isolated pores led to a differential deformation of the model. The total displacement of the slices varies from 13,550 μm to 14,300 μm and decreases with increasing isolated pore porosity and fractal dimension. Both low fractal dimension and low isolated pore porosity increase the deformation.

Study on the Mechanics and Pore Characteristics of Coal Seam Drilling Sealing Materials Based on Nanomaterial Optimization.

In order to modify and optimize the performance of cement-based sealing materials and improve the gas drainage rate of boreholes. In this paper, nanosilica (NS), multiwalled carbon nanotubes (MWCNT), and graphene oxide (GO) were used to modify cement and optimize the pore structure. Uniaxial compression tests, X-ray diffraction (XRD), nuclear magnetic resonance (NMR), and combined fractal theory were used to analyze the mechanics and pore characteristics. The results show that the synergy of the three nanomaterials promotes the generation of hydration products such as calcium silicate hydrate (C–S–H) and ettringite (AFt), improves the total pore fractal dimension (Dw) and seepage pore fractal dimension (Ds), and optimizes the microscopic pore structure. However, when the content of NS increases from 2 to 4 wt %, the improvement in the mechanical properties is obviously weakened. The best ratio is where the SiO2 content is 2 wt %, the MWCNT content is 0.1 wt %, and the GO content is 0.03 wt %. Compared with pure cement, the fractal dimension increases significantly, the mechanical properties are increased by 24.7%, and the total porosity is reduced by 23.9%. This paper is of great significance for improving the efficiency of gas mining.

Pore Structure evolution and fractal analysis of Shenhua non-caking coal during low-temperature oxidation

ABSTRACT Revealing the evolution of pore structure during low-temperature oxidation is important for the deep-going understanding of coal spontaneous combustion disasters. For this purpose, the pore structure parameters and fractal dimension of Shenhua bituminous coal during low-temperature oxidation were examined by low-temperature nitrogen adsorption and mercury intrusion porosimetry. With the enhancement of oxidation degree, the pore connectivity increased, but the pore volume decreased, especially micropores, which decrease by 79.08%. In the two fractal dimensions, D1 increases from 2.684 to 2.924 while D2 decreases from 2.686 to 2.481, indicating that the pores have a rougher surface and a less heterogenous structure after low-temperature oxidation. An exponential characteristic is observed between the comprehensive fractal dimension and the gas yield. At last, a pore structure evolution mechanism was proposed, dividing the evolution into two stages: collapse of micropores and merging of micropores and transition pores. The research findings in this paper will lay the foundation for understanding the mass transfer in the low-temperature oxidation process.

Pore Characteristics and Fractal Dimension Analysis of Tectonic Coal and Primary-Structure Coal: A Case Study of Sanjia Coal Mine in Northern Guizhou.

Understanding the pore heterogeneity of tectonic coal and primary-structure coal is of great significance for predicting and preventing tectonic coal. This study adopts the low-temperature nitrogen adsorption method, mercury injection experiment, and other methods, combined with fractal theory, to quantitatively analyze the pore distribution of coal samples inside and outside the outburst cavities of the Sanjia coal mine. The experiments have shown that the contents of aliphatic functional groups and hydrogen in tectonic coal are higher than those of aromatic structural functional groups. Raw coal has more straight chains than side chains, whereas aliphatic hydrocarbon mostly has short chains, and the branching degree is high. Soft and primary-structure coals have similar elemental content and tectonic effects endow the coal with better connectivity. The pores are filled with particles and flakes, and the surfaces of tectonic coal have more pores and fissures on them. According to the experimental curve, the pores are divided into five types. The pore size of primary-structure coal is mainly type II pores, and the pore size distribution of tectonic coal is relatively wide, with the majority being class I and class II pores. The specific surface area of tectonic coal is 60.7% more than that of primary-structure coal. The box fractal dimension of coal decreases with the increase in scanning electron microscopy (SEM) magnification. The minimum fractal dimension of tectonic coal is 2.49, which is 7.8% lower than the peak of 2.70. It can be seen from the fractal dimension that the fractal dimensions of pore types II, III, and IV are rougher.

Characterization and Control of Pore Structural Heterogeneity for Low-Thermal-Maturity Shale: A Case Study of the Shanxi Formation in the Northeast Zhoukou Depression, Southern North China Basin

The Shanxi Formation layers in the northeast of the Zhoukou Depression, Southern North China Basin, mainly consist of dark mudstone interbed with tight stone and widely developed coal seam, which is a promising target for unconventional oil and gas exploration. A series of geochemical and geological methods were used to analyze the characterization and controls of the pores structural heterogeneity in low-thermal-maturity shale. These methods include the Rock-Eval analysis, total organic carbon (TOC) analysis, scanning electron microscope observation with an energy-dispersive spectrometer (SEM-EDS), X-ray diffraction, and low-pressure N2 adsorption. Based on these measurements, the pore diameter, specific surface area (SSA), and fractal dimension (D) were calculated, and then, the pore structure heterogeneity was analyzed. The result shows the pores of Shanxi Formation shale are mainly interparticle pores with low porosity and low permeability, and the pore structure is highly complex. The average fractal dimension of the micropore and the macropore are both 2.77, but that of the mesopore is 2.65, indicating a less-complex mesopore structure than the micropore and macropore. The S2, S1, and TOC exhibit no clear correlation with SSA and fractal dimension of pores, which proved the little impact of organic matter on the heterogeneity of pore structure in the low-maturity shale of the research area. The illite has a strong effect on the pore structural heterogeneity of Shanxi Formation shale. The samples with high content of illite show higher SSA, better physical properties, and low fractal dimension, reflecting low pore structural heterogeneity. However, the quartz and clay minerals show a slight correlation with SSA and no obvious relationship with the fractal dimension, indicating a little effect of them on the pore structure heterogeneity. The pore structural heterogeneity decreases along with the increase in porosity, while the permeability influenced by a variety of reasons under the compaction shows a poor relationship with SSA and fractal dimension. On the whole, the pore structural heterogeneity decreases for low-thermal-maturity shale with high content of illite and high porosity, which should be considered to be the better unconventional oil and gas reservoir in the research area.

Relationship between Permeability Coefficient and Fractal Dimension of Pore in Ionic Rare Earth Magnesium Salt Leaching Ore

The change of permeability coefficient of ionic rare earth ore is one of the most important factors causing the uncontrollable flow of leaching solution, and the variation of pore structure of the ore body has a great influence on the permeability coefficient. The research on the evolution of the relationship between pore structure and permeability coefficient of ionic rare earths is of great significance for controlling water and soil pollution and improving the leaching rate of rare earths. In this paper, the column leaching test of ionic rare earth was carried out to study the evolution of the relationship between pore structure and permeability coefficient. In the process of MgSO4 solution and deionized water leaching, the T 2 spectrum and inversion image at each time were obtained by nuclear magnetic resonance (NMR). Based on the fractal theory, the pore structure change of the inversion image was quantitatively analysed, and the permeability coefficient of samples at each time of different leaching agents was calculated by using supercritical Dubinin-Redushckevich (SDR) model to analyse the nuclear magnetic resonance T 2 spectrum. The results show that in MgSO4 solution, the permeability coefficient of the sample changes significantly, and the growth rate of pore fractal dimension remains large. By discussing the evolution law of pore fractal dimension and seepage characteristics of ionic rare earth, the mathematical relationship between permeability coefficient and pore fractal dimension of mineral soil samples at different depths is fitted by polynomial function.

Effects of Fly Ash Dosage on Shrinkage, Crack Resistance and Fractal Characteristics of Face Slab Concrete

The crack resistance of face slab concretes to various shrinkages is crucial for the structural integrity and the normal operation of concrete-faced rockfill dams (CFRDs). In this work, the effects of fly ash with four dosages (i.e., 10%, 20%, 30% and 40%) on the drying shrinkage, autogenous shrinkage and the cracking resistance of face slab concrete were studied. Besides, the difference in shrinkage behavior due to fly ash addition was revealed from the viewpoint of the pore structure and fractal dimension of the pore surface (Ds). The findings demonstrate that (1) the incorporation of 10–40% fly ash could slightly reduce the drying shrinkage by about 2.2–13.5% before 14 days of hydration, and it could reduce the drying shrinkage at 180 days by about 5.1–23.2%. By contrast, the fly ash addition could markedly reduce the autogenous shrinkage at early, middle and long-term ages. (2) Increasing fly ash dosage from 0 to 40% considerably improves the crack resistance of concrete to plastic shrinkage. Nevertheless, the increase in fly ash dosage increases the drying-induced cracking risk under restrained conditions. (3) The pore structures of face slab concrete at 3 and 28 days become coarser with the increase in fly ash dosage up to 40%. At 180 days, the pore structures become more refined as the fly ash dosage increases to 30%; however, this refinement effect is not as appreciable as the fly ash dosage increases from 30% to 40%. (4) The Ds of face slab concrete is closely related with the concrete pore structures. The Ds of face slab concrete at a. late age increases from 2.902 to 2.946 with increasing of the fly ash dosage. The pore structure and Ds are closely correlated with the shrinkage of face slab concrete. (5) The fly ash dosage around 30% is optimal for face slab concretes in terms of lowering shrinkage and refining the pore structures, without compromising much mechanical property. However, the face slab concretes with a large fly ash dosage should be well cured under restrained and evaporation conditions at an initial hydration age.

Porosity and crystallinity dynamics of carbon black during internal and surface oxidation

The structure of carbon black (CB) is investigated during its oxidation by O2 at 550 and 800 °C by thermogravimetric analysis, microscopy, N2 adsorption and X-ray diffraction (XRD). That way, the dynamics of its porosity and crystallinity during surface and internal oxidation are elucidated, for the first time to the best of our knowledge. At 800 °C, oxidation takes place largely on the CB surface. This increases the CB specific surface area, SSA, from 240 to about 453 m2/g, closely following the classic shrinking particle model and hardly affects the porosity and crystallinity of CB. At 550 °C, O2 diffuses and reacts with the bulk of CB particles forming pores with radius smaller than 2 nm after 25 and 50% conversion. At higher conversions, these small pores fuse together resulting in hollow CB particles with high SSA, up to 939 m2/g. Fractal and XRD analyses of the resulting pore network reveals that internal oxidation at 550 °C reduces the interlayer distance of the crystallites constituting the CB, compacting its pore network. This increases the pore fractal dimension, Dfp, from 2.43 up to about 2.7, in good agreement with the Dfp measured during diesel soot oxidation. The dynamics of CB porosity and crystallinity quantified in detail here can assist the design of new highly porous CB grades and activated carbons as well as battery materials.

The Influence of Pore Structure of the Core-Scale Fracture-Controlled Matrix Unit on Imbibition: Model Construction and Definition of the Fractal Coefficient

Abstract Imbibition oil recovery plays an important role in the development of low-permeability fractured reservoirs. However, the effects of the complex pore structure of the matrix on imbibition have not been considered comprehensively at different scales in the scientific literature. This paper reports a study of the mechanisms of influence of different matrix pores on imbibition recovery ratio and defines the concept of a fractal coefficient using the method of combining numerical simulation at the core scale with mathematical methods at a pore scale. A matrix model with different pore fractal dimensions and tortuosity of the capillary was established using Python language programming. Y-type and S-type were used to characterize the fractures, and a two-dimensional fracture-controlled matrix unit core-scale numerical model with complex pore structures was established. Based on phase field theory, an oil-water two-phase imbibition numerical simulation was conducted. Comparisons of numerical simulation results and microscopic analysis indicated that imbibition recovery ratio was 39.28% and 50.94%, respectively. The imbibition law revealed by the numerical simulation results is consistent with the results of the microscopic imbibition experiment, and the imbibition effect of bifurcated fractures was better than that of simple curved fractures. As the pore fractal dimension and tortuosity of the capillary increased, the imbibition recovery ratio decreased. A comparison of results of the mathematical model demonstrated that there was a difference between the pore scale and core scale because the pore fractal dimension and capillary tortuosity changed dynamically with pore structure at the core scale. Thus, a parameter that characterizes the relative change of pore fractal dimension and tortuosity was defined and called the fractal coefficient. When the skeleton particles are 200, 400, and 500, the fractal coefficient were calculated to be 0.625 and 0.6, respectively, indicating that when the pore structure changes, the imbibition recovery ratio should be dominated by capillary tortuosity.

THE CORRELATION BETWEEN FLUID FLOW AND HEAT TRANSFER OF UNSATURATED SHALE RESERVOIR BASED ON FRACTAL GEOMETRY

The dissimilar multi-scale structures of shale to conventional reservoirs make it a challenge to understand the fluid flow and heat transfer through unsaturated shale formations. In this paper, the pore structure and moisture content of shale samples are measured by low-field nuclear magnetic resonance technique and thermogravimetric differential scanning calorimetry test, respectively. A pore-scale model is accordingly developed for the immiscible two-phase fluid flow and heat conduction through unsaturated shale based on the statistically self-similar fractal scaling law of pore size distribution. The analytical expressions of effective and relative permeability, as well as effective thermal conductivity (ETC), are proposed, which indicate good agreement with experimental results. It has been shown that the capillary pressure and gas slippage play important role in multiphase flow through unsaturated shale. Both pore and tortuosity fractal dimensions show significant influence on the relative permeability for nonwetting phase (RPNW), while they indicate the marginal effect on the relative permeability for the wetting phase (RPW). The ETC decreases with the increase of pore and tortuosity fractal dimensions, and it is positively and negatively correlated with RPW and RPNW, respectively. The correlation between ETC and relative permeability is found to follow a logistic function. The present fractal model can characterize the multiscale structures of shale reservoirs and may help understand transport mechanisms of immiscible multiphase flow and heat transfer through unsaturated shale.