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Flow and Transport in Porous Media
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Flow and Transport in Porous Media

A topical collection in Energies (ISSN 1996-1073). This collection belongs to the section "H: Geo-Energy".

Viewed by 21497

Editor

Prof. Dr. Jianchao Cai

E-Mail Website
Collection Editor
College of Geosciences, China University of Petroleum, Beijing 102249, China
Interests: porous media; nanofluids; EOR; fractal; capillary pressure; imbibition; mutlphase flow in porous media
Special Issues, Collections and Topics in MDPI journals

Topical Collection Information

Dear Colleagues,

Flow and transport in porous media are of great significance for basic scientific research as well as cutting-edge technical applications, such as geological energy storage, hydrocarbon recovery, nano-fluidics, fuel cells, etc. Many fundamental and practical aspects of flow and transport processes, which are crucial in various energy and environmental applications, are not well understood. For instance, the existence of pore space morphology, different wetting conditions and interfacial forces of solid–fluid properties in porous media pose many scientific challenges to the fluid flow processes at different physical length scales. Moreover, the physics involved during the flow and transport in tight formations (e.g., shales, coal seam gas), nanomaterials, new emerging contaminants, and new remediation technologies require, probably, newer insight into the way we model porous media problems. Therefore, in-depth understanding for the physical principle and fluid transport mechanism in porous media is of great importance for the energy sector. Over the past few decades, research has made significant breakthroughs and contributions to the understanding the fundamentals/challenges of fluid flow in porous media.

This Collection of Energies focuses on the recent advances on all aspects of fluid flow in porous media with an emphasis on new physical insights, experimental investigations, numerical modelling, and theoretical developments in a diverse range of disciplines. Research and review papers regarding these specific topics above are welcome. Topics of interest include, but are not limited to: multiphase fluid transport mechanism in porous media, computational fluid mechanics, novel experimental analysis and numerical modelling of multiphase fluid flow, multiscale and multiphysical modelling of fluid flow, and related technical applications.

Prof. Dr. Jianchao Cai
Collection Editor

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Keywords

  • multiphase flow
  • transport mechanism
  • computational fluid mechanics
  • advanced experimental analysis
  • numerical modeling
  • multi-scale transport phenomenon
  • multi-physics flow process
  • machine learning and big data
  • underground energy storage
  • wetting, capillarity, and interfacial phenomenon

Published Papers (15 papers)

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2023

Jump to: 2022

17 pages, 4036 KiB  
Article
Seepage Model and Pressure Response Characteristics of Non-Orthogonal Multi-Fracture Vertical Wells with Superimposed Sand Body in Tight Gas Reservoirs
by Ziwu Zhou, Ao Xia, Rui Guo, Lin Chen, Fengshuo Kong and Xiaoliang Zhao
Energies 2023, 16(21), 7275; https://doi.org/10.3390/en16217275 - 26 Oct 2023
Viewed by 548
Abstract
Faced with difficulties stemming from the complex interactions between tight gas sand bodies and fractures, when describing and identifying reservoirs, a composite reservoir model was established. By setting the supply boundary to characterize the superposition characteristics of sand bodies, a mathematical model of [...] Read more.
Faced with difficulties stemming from the complex interactions between tight gas sand bodies and fractures, when describing and identifying reservoirs, a composite reservoir model was established. By setting the supply boundary to characterize the superposition characteristics of sand bodies, a mathematical model of unstable seepage in fractured vertical wells in tight sandstone gas reservoirs was developed, considering factors such as stress sensitivity, fracture density and fracture symmetry. The seepage law and pressure response characteristics of gas wells in tight sandstone discontinuous reservoirs with stress sensitivity, semi-permeable supply boundary and complex fracture topology were determined, and the reliability of the model was verified. The research results more accurately display the pressure characteristic of a vertical well in the superimposed sand body with complex fractures and provide a more comprehensive model for tight gas production dynamic analysis and well test data analysis, which can more accurately guide the dynamic inversion of reservoir and fracture parameters. Full article
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15 pages, 3445 KiB  
Article
A Study on the Permeability and Damage Characteristics of Limestone under Stress–Seepage Coupling Conditions
by Lu Wang, Jianfeng Liu, Yilin Liao, Shuyu Yang, An He and Huining Xu
Energies 2023, 16(19), 6899; https://doi.org/10.3390/en16196899 - 30 Sep 2023
Viewed by 666
Abstract
With the increase in energy demand, energy engineering has gradually developed to go deeper, accompanied by a complex geological environment, such as the coupling of stress and seepage. Limestone is widely found in underground rock engineering, and its stress–seepage coupling characteristics have a [...] Read more.
With the increase in energy demand, energy engineering has gradually developed to go deeper, accompanied by a complex geological environment, such as the coupling of stress and seepage. Limestone is widely found in underground rock engineering, and its stress–seepage coupling characteristics have a great influence on the safety and stability of related engineering projects. In order to study the permeability characteristics and damage evolution of limestone during the deformation and failure process under stress–seepage coupling conditions, permeability and acoustic emission tests on limestone were performed in this paper. The results showed that: the stress–strain curve demonstrated periodicity, as did the permeability change. The change in permeability in different deformation stages of axial strain and lateral strain was similar, but it was more appropriate to reflect the permeability evolution in terms of lateral strain. The permeability of the limestone slightly decreased in the volumetric compression stage, and tended to saturate after a sudden increase in the expansion stage. The presence of the confining pressure reduced the permeability of the rock. In the process of limestone deformation and failure, the level of acoustic emission activity can reflect the degree of fracture development. The permeability characteristics and acoustic emission characteristics had a good corresponding relationship. The greater the confining pressure, the higher the acoustic emission activity. The deformation and damage process of limestone experienced three stages: damage stable growth, damage acceleration development, and damage saturation. Full article
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13 pages, 4226 KiB  
Article
Improve Oil Recovery Mechanism of Multi-Layer Cyclic Alternate Injection and Production for Mature Oilfield at Extra-High Water Cut Stage Using Visual Physical Simulation Experiment
by Lun Zhao, Jincai Wang, Libing Fu, Li Chen and Zhihao Jia
Energies 2023, 16(3), 1546; https://doi.org/10.3390/en16031546 - 03 Feb 2023
Viewed by 1051
Abstract
In order to achieve sustainable development of mature oilfield, a series of adjustment measures should be implemented to improve production performance at the extra-high water cut stage. South Kumkol reservoir is a typical multi-layer low viscosity oil reservoir, which has the characteristics of [...] Read more.
In order to achieve sustainable development of mature oilfield, a series of adjustment measures should be implemented to improve production performance at the extra-high water cut stage. South Kumkol reservoir is a typical multi-layer low viscosity oil reservoir, which has the characteristics of small sandstone body, high shale volume, and strong heterogeneity. At present, the water cut of the South Kumkol reservoir is about 90%, which is on the verge of being abandoned. Multi-layer cyclic alternate injection and production (MCA-IP) is an ideal adjustment measure for multi-layer oil reservoir to improve oil recovery (IOR) at the extra-high water cut stage. In this paper, we designed the double-plate visual physical device and the MCA-IP experimental program and then calculated the sweep coefficient using image recognition method. Furthermore, the sweep coefficient was quantitatively calculated by image recognition method. The results show that the sweep area extends to both sides of the main streamline and the sweep efficiency is gradually improved after the completion of MCA-IP. In addition, the IOR mechanism of MCA-IP mainly includes reperforation, well-pattern encryption, and asynchronous injection-production. The reperforation and well-pattern encryption increased the sweep coefficient by about 19.52%, while asynchronous injection-production increased the sweep coefficient by about 1.2%, and the overall sweep coefficient increased by about 20.7%. According to the experimental data statistics, the MCA-IP method can increase oil recovery by about 11% and reduce water cut by about 6%. Full article
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2022

Jump to: 2023

16 pages, 4111 KiB  
Article
Characterization of a Non-Darcy Flow and Development of New Correlation of NON-Darcy Coefficient
by Abadelhalim Elsanoose, Ekhwaiter Abobaker, Faisal Khan, Mohammad Azizur Rahman, Amer Aborig and Stephen D. Butt
Energies 2022, 15(20), 7616; https://doi.org/10.3390/en15207616 - 15 Oct 2022
Cited by 2 | Viewed by 1432
Abstract
Darcy’s law has long been used to describe the flow in porous media. Despite the progress that took place in oil production industry research, it became clear that there is a loss of pressure, especially in the area near the wellbore region, where [...] Read more.
Darcy’s law has long been used to describe the flow in porous media. Despite the progress that took place in oil production industry research, it became clear that there is a loss of pressure, especially in the area near the wellbore region, where Darcy’s law is not applicable. For this reason, Forchheimer presented his equation in 1910, where he added a new term to Darcy’s law dealing with pressure loss due to inertial forces by introducing a new term, the β coefficient, into the equation. This paper presents a study of fluid flow through porous media, where water was used as a working fluid. Furthermore, the characteristics of the non-Darcy flow were analyzed by presenting the corresponding pressure and velocity gradient curves for each pressure. Extensive analysis indicates that many of the correlations available in the literature either have defective units or are the product of a small number of experiments. In this study, we benefit from relatively large samples, the radial flow, and the perforation in the middle of the samples. The properties of the samples were measured using mercury intrusion porosimetry. It was found that there is a direct relationship between the porosity and the grain’s size; the greater the size of the grains, the greater the porosity, and vice versa. The non-Darcy coefficient term, β, is found to be inversely proportional to the porosity and permeability. In a previous study, the β was investigated for compressible flow scenarios; however, this study calculated it for an incompressible flow. Finally, by analyzing the β values of both studies, we could deduce new novelty correlations for the β coefficient term, where the permeability, porosity, and tortuosity are included. Full article
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16 pages, 5038 KiB  
Article
Fractal Dimension of Digital 3D Rock Models with Different Pore Structures
by Xiaobin Li, Wei Wei, Lei Wang and Jianchao Cai
Energies 2022, 15(20), 7461; https://doi.org/10.3390/en15207461 - 11 Oct 2022
Cited by 7 | Viewed by 1608
Abstract
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 [...] Read more.
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. Full article
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15 pages, 4337 KiB  
Article
A Technique to Determine the Breakthrough Pressure of Shale Gas Reservoir by Low-Field Nuclear Magnetic Resonance
by Juanjuan Xiao, Yufeng Xiao, Xinmin Ge and Tianqi Zhou
Energies 2022, 15(19), 7223; https://doi.org/10.3390/en15197223 - 01 Oct 2022
Viewed by 1231
Abstract
The porous and low-permeability characteristics of a shale gas reservoir determine its high gas storage efficiency, which is manifested in the extremely high breakthrough pressure of shale. Therefore, the accurate calculation of breakthrough pressure is of great significance to the study of shale [...] Read more.
The porous and low-permeability characteristics of a shale gas reservoir determine its high gas storage efficiency, which is manifested in the extremely high breakthrough pressure of shale. Therefore, the accurate calculation of breakthrough pressure is of great significance to the study of shale gas preservation conditions. Based on a systematic analysis of a low-field NMR experiment on marine shales of the Longmaxi Formation in the Sichuan Basin, a shale gas breakthrough pressure determination technique different from conventional methods is proposed. The conventional methods have low calculation accuracy and are a tedious and time-consuming process, while low-field NMR technique is less time-consuming and of high accuracy. Firstly, the NMR T2 spectrum of shale core sample in different states is measured through low-field NMR experiment. The NMR T2 spectra of sample in water-saturated state and dry state are combined to model the mathematical relationship between shale gas breakthrough pressure and NMR T2 spectrum. It is found that the gas breakthrough pressure is power-exponentially related to the geometric mean of NMR T2 spectrum and positively related to the proportion of micropores. Accordingly, the shale gas breakthrough pressure is quickly and accurately calculated using continuous NMR logging data and then the sealing capacity of the shale caprocks is evaluated, providing basic parameters for analyzing unconventional hydrocarbon accumulation, preservation and migration. This technique has been successfully applied with actual data to evaluate the sealing capacity of shale caprock in a shale gas well in the Sichuan Basin. It can provide a good basis for the evaluation and characterization of shale oil and gas reservoirs. Full article
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17 pages, 9417 KiB  
Article
Research and Application of Waterflooding Mechanism at the Bottom of Ultra-Low Permeability Shallow Reservoir with Horizontal Fractures
by Lihua Shi, Shiqing Cheng, Yuwen Chang, Haiyang Yu and Binchi Hou
Energies 2022, 15(19), 6973; https://doi.org/10.3390/en15196973 - 23 Sep 2022
Cited by 1 | Viewed by 1458
Abstract
The Yanchang Eastern Oilfield of Ordos Basin is a typical ultra-low permeability shallow reservoir. Because of the relatively low vertical pressure, horizontal artificial fractures are prone to take place in the case of oil well fracturing. Given the bigger contact surface between the [...] Read more.
The Yanchang Eastern Oilfield of Ordos Basin is a typical ultra-low permeability shallow reservoir. Because of the relatively low vertical pressure, horizontal artificial fractures are prone to take place in the case of oil well fracturing. Given the bigger contact surface between the horizontal fracture and the waterflood front of the water injection well, the oil well may be flooded fast in a short time, leading to a low mobilization degree of the reservoir. According to the characteristics of waterflooding of horizontal fractures, the development mode of waterflooding at the bottom of oil reservoirs was proposed. Through core sample displacement experiments and nuclear magnetic resonance online tests, combined with numerical simulation of reservoirs, field tracer test, and other comprehensive methods, the heterogeneity of reservoirs and the limit of waterflooding parameters were optimized. The research results show that the waterflooding effect is the best when the variation coefficient of permeability is less than 0.5, the permeability rush coefficient is less than 1.5, the permeability contrast is less than 5, the waterflooding rate is 0.06 mL/min, and the waterflooding pressure is 7 MPa. Through field practice, the daily oil production of a single well in the test well group increased from 0.054 t/d before the test to 0.179 t/d, the water cut decreased from 15% before the test to 10%, the formation pressure increased by 0.18 MPa, and it is predicted that the final recovery would increase by 2%. This study provides an experimental and theoretical basis for water injection development of ultra-low permeability shallow reservoirs with horizontal fracture, and also plays a good demonstration role for high-efficiency water injection development of shallow reservoirs. Full article
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16 pages, 4260 KiB  
Article
Dual-Zone Gas Flow Characteristics for Gas Drainage Considering Anomalous Diffusion
by Xiangyu Wang, Hongwei Zhou, Lei Zhang, Wei Hou and Jianchao Cheng
Energies 2022, 15(18), 6757; https://doi.org/10.3390/en15186757 - 15 Sep 2022
Viewed by 958
Abstract
Gas drainage in deep coal seam is a critical issue ensuring the safety of mining and an important measure to obtain gas as a kind of clean available energy. In order to get a better understanding of gas flow and diffusion for gas [...] Read more.
Gas drainage in deep coal seam is a critical issue ensuring the safety of mining and an important measure to obtain gas as a kind of clean available energy. In order to get a better understanding of gas flow and diffusion for gas drainage in deep coal seams, a dual-zone gas flow model, including the drainage damage zone (DDZ) and the non-damaged zone (NDZ), are characterized by different permeability models and anomalous diffusion models to analyze the influence of damage induced by drilling boreholes on gas flow. The permeability model and anomalous diffusion model are verified with experiment and field data. A series of finite-element numerical simulations based on developed models are carried out, indicating that, compared with normal diffusion model, the anomalous diffusion is more accurate and appropriate to field test data. The coal fracture permeability increases rapidly with the distance decreasing from the borehole, and the area of DDZ is increasing significantly with the extraction time. Moreover, with the increasing of fractional derivative order, the diffusion model transforms the anomalous diffusion to the normal gradually, and the decay of gas pressure is aggravated. The higher value of non-uniform coefficient results in the larger increment of fracture permeability. The permeability–damage coefficient increase makes the increment of fracture permeability bigger. Full article
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13 pages, 9676 KiB  
Article
Characterizing the Microscopic Anisotropic Permeabilities of Tight Oil Reservoirs Impacted by Heterogeneous Minerals
by Ziqiang Wang, Hongkui Ge, Yun Wei, Yi Wang, Kerui Jia, Ning Xu, Yuankai Zhang and Shuheng Du
Energies 2022, 15(18), 6552; https://doi.org/10.3390/en15186552 - 07 Sep 2022
Cited by 2 | Viewed by 1045
Abstract
This study aimed to reveal the anisotropic permeabilities of tight oil reservoirs impacted by heterogeneous minerals. SEM imaging, image processing, fractal calculation, microscopic reservoir modeling, and visual flow simulation were carried out to investigate the above problems. Results show that the variation coefficient [...] Read more.
This study aimed to reveal the anisotropic permeabilities of tight oil reservoirs impacted by heterogeneous minerals. SEM imaging, image processing, fractal calculation, microscopic reservoir modeling, and visual flow simulation were carried out to investigate the above problems. Results show that the variation coefficient of two-dimensional permeability for the studied tight reservoir samples ranges from 0.09 to 0.95, with an average value of 0.68. The penetration coefficient ranges from 1.16 to 2.64, with an average value of 2.13. The ratio of maximum to minimum permeability is between 1.25 and 7.67, with an average value of 5.62. The fluid flow in tight reservoirs has significant anisotropy comprising dominant flow through conductive channels. Flow in tight oil reservoirs tends to involve minor hydraulic fracturing with no proppant. Full article
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15 pages, 2616 KiB  
Article
Experimental and Numerical Simulation of Water Adsorption and Diffusion in Coals with Inorganic Minerals
by Yong Xu, Xuexi Chen, Wei Zhao and Peng Chen
Energies 2022, 15(12), 4321; https://doi.org/10.3390/en15124321 - 13 Jun 2022
Cited by 1 | Viewed by 1263
Abstract
The study on the adsorption and micropore filling of water vapor in coal is significant for predicting coalbed methane content in coal seams. The primary purpose of this study is to explain the effects of coal pore structure and its surface chemistry on [...] Read more.
The study on the adsorption and micropore filling of water vapor in coal is significant for predicting coalbed methane content in coal seams. The primary purpose of this study is to explain the effects of coal pore structure and its surface chemistry on water vapor monolayer adsorption, micropore filling, and diffusion coefficient. First, X-ray diffraction (XRD) and mercury intrusion porosimetry (MIP) analyzed inorganic mineral components of two kinds of coal samples and pore fissures structures. Then, we divide pores and fissures according to the theory of fractal dimensions. Furthermore, we carried out the water vapor adsorption and desorption experiments on two kinds of coal; in particular, we set 14 points of relative pressure between 0 and 0.2. Guggenheim–Anderson–de Boer (GAB), Frenkel–Halsey–Hill (FHH), and Freundlich models were used to analyze the data of water vapor adsorption to obtain the boundary pressure points of the monolayer, multilayer adsorption, and capillary condensation. Finally, the parameters of the models were obtained by fitting the adsorption data of water vapor according to the combined GAB, Freundlich, DA, and bidisperse adsorption (BDA) models to analyze the interaction mechanism between coal and water. We explain why the strongly adsorbed water minerals, such as pyrite, illite, and nacrite coal, can improve water vapor’s adsorption and diffusion capacity in coal pore fissures. Full article
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15 pages, 4400 KiB  
Article
Experimental Study on the Microstructure of Coal with Different Particle Sizes
by Jianbao Liu, Zhimin Song, Bing Li, Jiangang Ren, Feng Chen and Ming Xiao
Energies 2022, 15(11), 4043; https://doi.org/10.3390/en15114043 - 31 May 2022
Cited by 4 | Viewed by 1466
Abstract
In the study of coal pore structure, the traditional test method does not consider the influence of coal particle size. During the crushing process, coal samples are affected by crushing stress. While the particle size changes, the change characteristics of pore structure and [...] Read more.
In the study of coal pore structure, the traditional test method does not consider the influence of coal particle size. During the crushing process, coal samples are affected by crushing stress. While the particle size changes, the change characteristics of pore structure and macromolecular structure are a matter for which systematic research is still lacking. In this paper, mercury injection and liquid nitrogen were used to characterize the pore structure of coal. It was found that the porosity, total pore volume and total specific surface area of the coal increased with the decrease of particle size. However, during this process, the pore volume of macropores and mesopores decreases, while the micropores and transition pores increase significantly, indicating that while the particle size decreases, macropores and mesopores are broken into micropores and transition pores. In addition, the pore structure of samples with a particle size less than 200 mesh changes significantly. With the decrease of coal particle size, the areas of the D peak and G peak of the Raman spectrum increase, indicating that the ordering degree of coal increases. Finally, the statistical results of the peak area of the Fourier infrared spectrum show that alcohol, phenol, ammonia hydroxyl and fatty hydrocarbon CH2 and CH3 are greatly reduced, while the out-of-plane deformation vibration of alkyl ether and aromatic structure C–H are significantly increased, which also indicates the transformation of the coal macromolecular structure to an aromatic structure with strong stability. Full article
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13 pages, 1507 KiB  
Article
Experimental Study of Influence of Core Wettability on Imbibition Properties
by Xuegang Feng, Xiang’an Yue, Weiqing An and Jirui Zou
Energies 2022, 15(11), 3984; https://doi.org/10.3390/en15113984 - 28 May 2022
Cited by 1 | Viewed by 1398
Abstract
Through new core wettability simulation technology and the single-sided unidirectional imbibition experimental method, the influence of core wettability on oil imbibition characteristics was studied by using artificial cores with wettability index in the range of −0.9~0.95. Results show that for the cores with [...] Read more.
Through new core wettability simulation technology and the single-sided unidirectional imbibition experimental method, the influence of core wettability on oil imbibition characteristics was studied by using artificial cores with wettability index in the range of −0.9~0.95. Results show that for the cores with permeability from ultra-low to medium–high, the imbibition time shows a monotonically decreasing law with the increase in the wettability index. In the weak water-wet range, the imbibition time increases significantly with the weakening of water-wet. Oil imbibition rate goes up with the increase in wettability index. In the strong water-wet range, the imbibition rate will change significantly with wettability. In the water-wet zone, there is a positive correlation between imbibition oil limit recovery and wettability index, according to which a power exponent model of them is established. The imbibition–displacement ratio, which characterizes the contribution rate of oil recovery by imbibition to that by waterflooding, is also positively correlated with the wettability index. In addition, imbibition–displacement ratios of extra-low permeability cores are very close to that of medium–high permeability cores. According to the analysis of the research results, compared with the strongly water-wet oil layer, the weakly water-wet oil layer with a wettability index of 0–0.5 has a greater contribution to oil recovery by using the enhanced imbibition method. Full article
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16 pages, 2758 KiB  
Article
A Multi-Scale Fractal Approach for Coal Permeability Estimation via MIP and NMR Methods
by Weiguang Ren, Hongwei Zhou, Jiangcheng Zhong, Dongjie Xue, Chaosheng Wang and Zelin Liu
Energies 2022, 15(8), 2807; https://doi.org/10.3390/en15082807 - 12 Apr 2022
Cited by 4 | Viewed by 1381
Abstract
Permeability in porous media has an important role in many engineering applications, which depends mainly on the pore size, distribution, and connectivity of porous media. As the pore structure distribution of coal has a multi-scale fractal dimension characteristic, this study aimed to propose [...] Read more.
Permeability in porous media has an important role in many engineering applications, which depends mainly on the pore size, distribution, and connectivity of porous media. As the pore structure distribution of coal has a multi-scale fractal dimension characteristic, this study aimed to propose a multi-scale fractal dimension characteristics units model (MFU) to describe the pore structure distribution by analyzing the multi-scale fractal dimension characteristics of coal pore media. Then, a multi-scale fractal permeability model was established based on MFU. The pore structure distribution was obtained by mercury injection porosimetry (MIP) and nuclear magnetic resonance (NMR) experiments. Based on MIP and NMR experimental data, the permeability contribution of different pore diameters were calculated. The results show that the permeability contribution of the micropore was minimal and can be ignored. The permeability contribution of mesopores was about 1–5%, and the permeability contribution of macropores was about 95–99%, which plays a decisive role in the seepage process. The calculated results, based on multi-scale fractal permeability model and the experimental permeability data, are in the same order of magnitude. The permeability prediction based on proposed model is better than classical single fractal permeability model. Full article
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17 pages, 3823 KiB  
Article
Characterization of Two-Phase Flow from Pore-Scale Imaging Using Fractal Geometry under Water-Wet and Mixed-Wet Conditions
by Shuangmei Zou, Peixing Xu, Congjiao Xie, Xuan Deng and Haodong Tang
Energies 2022, 15(6), 2036; https://doi.org/10.3390/en15062036 - 10 Mar 2022
Cited by 1 | Viewed by 1878
Abstract
High resolution micro-computed tomography images for multiphase flow provide us an effective tool to understand the mechanism of fluid flow in porous media, which is not only fundamental to the understanding of macroscopic measurements but also for providing benchmark datasets to validate pore-scale [...] Read more.
High resolution micro-computed tomography images for multiphase flow provide us an effective tool to understand the mechanism of fluid flow in porous media, which is not only fundamental to the understanding of macroscopic measurements but also for providing benchmark datasets to validate pore-scale modeling. In this study, we start from two datasets of pore scale imaging of two-phase flow obtained experimentally under in situ imaging conditions at different water fractional flows under water-wet and mixed-wet conditions. Then, fractal dimension, lacunarity and succolarity are used to quantify the complexity, clustering and flow capacity of water and oil phases. The results show that with the wettability of rock surface altered from water-wet to mixed-wet, the fractal dimension for the water phase increases while for the oil phase, it decreases obviously at low water saturation. Lacunarity largely depends on the degree of wettability alteration. The more uniform wetting surfaces are distributed, the more homogeneous the fluid configuration is, which indicates smaller values for lacunarity. Moreover, succolarity is shown to well characterize the wettability effect on flow capacity. The succolarity of the oil phase in the water-wet case is larger than that in the mixed-wet case while for the water phase, the succolarity value in the water-wet is small compared with that in the mixed-wet, which show a similar trend with relative permeability curves for water-wet and mixed-wet. Our study provides a perspective into the influence that phase geometry has on relative permeability under controlled wettability and the resulting phase fractal changes under different saturations that occur during multiphase flow, which allows a means to understand phase geometric changes that occur during fluid flow. Full article
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14 pages, 3010 KiB  
Article
Estimating of Non-Darcy Flow Coefficient in Artificial Porous Media
by Abadelhalim Elsanoose, Ekhwaiter Abobaker, Faisal Khan, Mohammad Azizur Rahman, Amer Aborig and Stephen D. Butt
Energies 2022, 15(3), 1197; https://doi.org/10.3390/en15031197 - 07 Feb 2022
Cited by 9 | Viewed by 2642
Abstract
This study conducted a radial flow experiment to investigate the existence of non-Darcy flow and calculate the non-Darcy “inertia” coefficient; the experiment was performed on seven cylindrical perforated artificial porous media samples. Two hundred thirty-one runs were performed, and the pressure drop was [...] Read more.
This study conducted a radial flow experiment to investigate the existence of non-Darcy flow and calculate the non-Darcy “inertia” coefficient; the experiment was performed on seven cylindrical perforated artificial porous media samples. Two hundred thirty-one runs were performed, and the pressure drop was reported. The non-Darcy coefficient β was calculated and compared with available in the literature. The results showed that the non-Darcy coefficient decreased nonlinearly and converged on a value within a specific range as the permeability increased. Nonetheless, it was found that the non-Darcy flow exists even in the very low flow rate deployed in this study. In addition, it has been found that the non-Darcy effect is not due to turbulence but also the inertial effect. The existence of a non-Darcy flow was confirmed for all the investigated samples. The Forchheimer numbers for airflow at varied flow rates are determined using experimentally measured superficial velocity, permeability, and non-Darcy coefficient. Full article
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