Editorial

4 pages, 178 KiB

Open AccessEditorial

Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications

by Mehrdad Massoudi

Energies 2020, 13(6), 1344; https://doi.org/10.3390/en13061344 - 13 Mar 2020

Cited by 1 | Viewed by 2002

This Special Issue of Energies is dedicated to all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction, and convection in porous media [...] Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

Research

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17 pages, 3948 KiB

Open AccessArticle

A Novel Porous Media Permeability Model Based on Fractal Theory and Ideal Particle Pore-Space Geometry Assumption

by Yongquan Hu, Qiang Wang, Jinzhou Zhao, Shouchang Xie and Hong Jiang

Energies 2020, 13(3), 510; https://doi.org/10.3390/en13030510 - 21 Jan 2020

Cited by 10 | Viewed by 3519

Abstract

In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the model. Compared with previous models, the results of [...] Read more.

In this paper, a novel porous media permeability model is established by using particle model, capillary bundle model and fractal theory. The three-dimensional irregular spatial characteristics composed of two ideal particles are considered in the model. Compared with previous models, the results of our model are closer to the experimental data. The results show that the tortuosity fractal dimension is negatively correlated with porosity, while the pore area fractal dimension is positively correlated with porosity; The permeability is negatively correlated with the tortuosity fractal dimension and positively correlated with the integral fractal dimension of pore surface and particle radius. When the tortuosity fractal dimension is close to 1 and the pore area fractal dimension is close to 2, the faster the permeability changes, the greater the impact. Different particle arrangement has great influence on porous media permeability. When the porosity is close to 0 and close to 1, the greater the difference coefficient is, the more the permeability of different arrangement is affected. In addition, the larger the particle radius is, the greater the permeability difference coefficient will be, and the greater the permeability difference will be for different particle arrangements. With the increase of fractal dimension, the permeability difference coefficient first decreases and then increases. When the pore area fractal dimension approaches 2, the permeability difference coefficient changes faster and reaches the minimum value, and when the tortuosity fractal dimension approaches 1, the permeability difference coefficient changes faster and reaches the minimum value. Our research is helpful to further understand the connotation of medium transmission in porous media. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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26 pages, 6364 KiB

Open AccessArticle

Semi-Analytical Model for Two-Phase Flowback in Complex Fracture Networks in Shale Oil Reservoirs

by Yuzhe Cai and Arash Dahi Taleghani

Energies 2019, 12(24), 4746; https://doi.org/10.3390/en12244746 - 12 Dec 2019

Cited by 10 | Viewed by 2310

Abstract

Flowback data is the earliest available data for estimating fracture geometries and the assessment of different fracturing techniques. Considerable attention has been paid recently to analyze flowback data quantitively in order to obtain fracture properties such as effective half-length and effective conductivity by [...] Read more.

Flowback data is the earliest available data for estimating fracture geometries and the assessment of different fracturing techniques. Considerable attention has been paid recently to analyze flowback data quantitively in order to obtain fracture properties such as effective half-length and effective conductivity by simply assuming fractures having bi-wing planar geometries and constant fracture compressibility. However, this simplifying assumption ignores the complexity of fracture networks. To overcome this limitation, we proposed a semi-analytical method, which can be used as a direct model for fast inverse analysis to characterize complex fracture networks generated during hydraulic fracturing. A two-phase oil–water flowback model with a matrix oil influx for wells with bi-wing planar fractures is also presented to identify limitations of the former solution. Since most available flowback studies use constant fracture properties and the assumption of planar fractures, considering variable fracture properties and complex fracture geometries gives this model more robustness for modeling fracture flow during flowback, more realistically. The proposed models have been validated by numerical simulations. The presented procedure provides a simple way for modeling early flowback in complex fracture networks and it can be used for inverse analysis. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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14 pages, 8115 KiB

Open AccessArticle

Numerical Study of Highly Viscous Fluid Sloshing in the Real-Scale Membrane-Type Tank

by Shuo Mi, Zongliu Huang, Xin Jin, Mahdi Tabatabaei Malazi and Mingming Liu

Energies 2019, 12(22), 4244; https://doi.org/10.3390/en12224244 - 07 Nov 2019

Cited by 3 | Viewed by 3167

Abstract

The highly viscous liquid (glycerin) sloshing is investigated numerically in this study. The full-scale membrane-type tank is considered. The numerical investigation is performed by applying a two-phase numerical model based on the spatially averaged Navier-Stokes equations. Firstly, the numerical model is validated against [...] Read more.

The highly viscous liquid (glycerin) sloshing is investigated numerically in this study. The full-scale membrane-type tank is considered. The numerical investigation is performed by applying a two-phase numerical model based on the spatially averaged Navier-Stokes equations. Firstly, the numerical model is validated against the available numerical model and a self-conducted experiment then is applied to systematically investigate the full-scale sloshing. In this study, two filling levels (50% and 70% of the tank height) are considered. The fluid kinematic viscosity is fixed at a value being 6.0 × 10⁻⁵ m²/s with comparative value to that of the crude oil. A wide range of forcing periods varying from 8.0 s to 12.0 s are used to identify the response process of pressures as well as free surface displacements. The pressures are analyzed along with breaking free surface snapshots and corresponding pressure distributions. The slamming effects are also demonstrated. Finally, the frequency response is further identified by the fast Fourier transformation technology. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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16 pages, 5790 KiB

Open AccessArticle

Three-Dimensional Numerical Simulation of Geothermal Field of Buried Pipe Group Coupled with Heat and Permeable Groundwater

by Xinbo Lei, Xiuhua Zheng, Chenyang Duan, Jianhong Ye and Kang Liu

Energies 2019, 12(19), 3698; https://doi.org/10.3390/en12193698 - 27 Sep 2019

Cited by 16 | Viewed by 3091

Abstract

The flow of groundwater and the interaction of buried pipe groups will affect the heat transfer efficiency and the distribution of the ground temperature field, thus affecting the design and operation of ground source heat pumps. Three-dimensional numerical simulation is an effective method [...] Read more.

The flow of groundwater and the interaction of buried pipe groups will affect the heat transfer efficiency and the distribution of the ground temperature field, thus affecting the design and operation of ground source heat pumps. Three-dimensional numerical simulation is an effective method to study the buried pipe heat exchanger and ground temperature distribution. According to the heat transfer control equation of non-isothermal pipe flow and porous media, combined with the influence of permeable groundwater and tube group, a heat-transfer coupled heat transfer model of the buried pipe group was established, and the accuracy of the model was verified by the sandbox test and on-site thermal response test. By processing the layout of the buried pipe in the borehole to reduce the number of meshes and improve the meshing quality, a three-dimensional numerical model of the buried pipe cluster at the site scale was established. Additionally, the ground temperature field under the thermal-osmotic coupling of the buried pipe group during groundwater flow was simulated and the influence of the head difference and hydraulic conductivity on the temperature field around the buried pipe group was calculated and analyzed. The results showed that the research on the influence of the tube group and permeable groundwater on the heat transfer and ground temperature field of a buried pipe simulated by COMSOL software is an advanced method. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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27 pages, 7800 KiB

Open AccessArticle

Analysis of Coupled Wellbore Temperature and Pressure Calculation Model and Influence Factors under Multi-Pressure System in Deep-Water Drilling

by Ruiyao Zhang, Jun Li, Gonghui Liu, Hongwei Yang and Hailong Jiang

Energies 2019, 12(18), 3533; https://doi.org/10.3390/en12183533 - 14 Sep 2019

Cited by 10 | Viewed by 3202

Abstract

The purpose of this paper is to discuss the variation of wellbore temperature and bottom-hole pressure with key factors in the case of coupled temperature and pressure under multi-pressure system during deep-water drilling circulation. According to the law of energy conservation and momentum [...] Read more.

The purpose of this paper is to discuss the variation of wellbore temperature and bottom-hole pressure with key factors in the case of coupled temperature and pressure under multi-pressure system during deep-water drilling circulation. According to the law of energy conservation and momentum equation, the coupled temperature and pressure calculation model under multi-pressure system is developed by using the comprehensive convective heat transfer coefficient. The model is discretized and solved by finite difference method and Gauss Seidel iteration respectively. Then the calculation results of this paper are compared and verified with previous research models and field measured data. The results show that when the multi-pressure system is located in the middle formation, the temperature of the annulus corresponding to location of the system is the most affected, and the temperature of the other areas in annulus is hardly affected. However, when the multi-pressure system is located at the bottom hole, the annulus temperature is greatly affected from bottom hole to mudline. In addition, the thermo-physical parameters of the drilling fluid can be changed by overflow and leakage. When only overflow occurs, the annulus temperature increases the most, but the viscosity decreases the most. When only leakage occurs, the annulus temperature decreases the most and the viscosity increases the most. However, when the overflow rate is greater than the leakage rate, the mud density and bottom-hole pressure increase the most, and both increase the least when only leakage occurs. Meanwhile, bottom-hole pressure increases with the increase of pump rate but decreases with the increase of inlet temperature. The research results can provide theoretical guidance for safe drilling in complex formations such as multi-pressure systems. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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18 pages, 2324 KiB

Open AccessArticle

Multiscale Apparent Permeability Model of Shale Nanopores Based on Fractal Theory

by Qiang Wang, Yongquan Hu, Jinzhou Zhao, Lan Ren, Chaoneng Zhao and Jin Zhao

Energies 2019, 12(17), 3381; https://doi.org/10.3390/en12173381 - 02 Sep 2019

Cited by 19 | Viewed by 3389

Abstract

Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size [...] Read more.

Based on fractal geometry theory, the Hagen–Poiseuille law, and the Langmuir adsorption law, this paper established a mathematical model of gas flow in nano-pores of shale, and deduced a new shale apparent permeability model. This model considers such flow mechanisms as pore size distribution, tortuosity, slippage effect, Knudsen diffusion, and surface extension of shale matrix. This model is closely related to the pore structure and size parameters of shale, and can better reflect the distribution characteristics of nano-pores in shale. The correctness of the model is verified by comparison with the classical experimental data. Finally, the influences of pressure, temperature, integral shape dimension of pore surface and tortuous fractal dimension on apparent permeability, slip flow, Knudsen diffusion and surface diffusion of shale gas transport mechanism on shale gas transport capacity are analyzed, and gas transport behaviors and rules in multi-scale shale pores are revealed. The proposed model is conducive to a more profound and clear understanding of the flow mechanism of shale gas nanopores. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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28 pages, 2817 KiB

Open AccessArticle

Techno-Economic Comparison of Onshore and Offshore Underground Coal Gasification End-Product Competitiveness

by Natalie Nakaten and Thomas Kempka

Energies 2019, 12(17), 3252; https://doi.org/10.3390/en12173252 - 23 Aug 2019

Cited by 7 | Viewed by 3136

Abstract

Underground coal gasification (UCG) enables utilization of coal reserves, currently not economically exploitable due to complex geological boundary conditions. Hereby, UCG produces a high-calorific synthesis gas that can be used for generation of electricity, fuels, and chemical feedstock. The present study aims to [...] Read more.

Underground coal gasification (UCG) enables utilization of coal reserves, currently not economically exploitable due to complex geological boundary conditions. Hereby, UCG produces a high-calorific synthesis gas that can be used for generation of electricity, fuels, and chemical feedstock. The present study aims to identify economically-competitive, site-specific end-use options for onshore- and offshore-produced UCG synthesis gas, taking into account the capture and storage (CCS) and/or utilization (CCU) of produced CO

_{2}

. Modeling results show that boundary conditions favoring electricity, methanol, and ammonia production expose low costs for air separation, low compression power requirements, and appropriate shares of H

_{2}

/N

_{2}

. Hereby, a gasification agent ratio of more than 30% oxygen by volume is not favorable from the economic and CO

_{2}

mitigation viewpoints. Compared to the costs of an offshore platform with its technical equipment, offshore drilling costs are marginal. Thus, uncertainties related to parameters influenced by drilling costs are negligible. In summary, techno-economic process modeling results reveal that air-blown gasification scenarios are the most cost-effective ones, while offshore UCG-CCS/CCU scenarios are up to 1.7 times more expensive than the related onshore processes. Hereby, all investigated onshore scenarios except from ammonia production under the assumed worst-case conditions are competitive on the European market. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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25 pages, 11980 KiB

Open AccessArticle

Steady Flow of a Cement Slurry

by Chengcheng Tao, Barbara G. Kutchko, Eilis Rosenbaum, Wei-Tao Wu and Mehrdad Massoudi

Energies 2019, 12(13), 2604; https://doi.org/10.3390/en12132604 - 06 Jul 2019

Cited by 23 | Viewed by 4744

Abstract

Understanding the rheological behavior of cement slurries is important in cement and petroleum industries. In this paper, we study the fully developed flow of a cement slurry inside a wellbore. The slurry is modeled as a non-linear fluid, where a constitutive relation for [...] Read more.

Understanding the rheological behavior of cement slurries is important in cement and petroleum industries. In this paper, we study the fully developed flow of a cement slurry inside a wellbore. The slurry is modeled as a non-linear fluid, where a constitutive relation for the viscous stress tensor based on a modified form of the second grade (Rivlin–Ericksen) fluid is used;we also propose a diffusion flux vector for the concentration of particles. The one-dimensional forms of the governing equations and the boundary conditions are made dimensionless and solved numerically. A parametric study is performed to present the effect of various dimensionless numbers on the velocity and the volume fraction profiles. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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15 pages, 4169 KiB

Open AccessArticle

Correlational Analytical Characterization of Energy Dissipation-Liberation and Acoustic Emission during Coal and Rock Fracture Inducing by Underground Coal Excavation

by Pengfei Shan, Xingping Lai and Xiaoming Liu

Energies 2019, 12(12), 2382; https://doi.org/10.3390/en12122382 - 20 Jun 2019

Cited by 40 | Viewed by 2515

Abstract

This paper uses an acoustic emission (AE) test to examine the energy dissipation and liberation of coal and rock fracture due to underground coal excavation. Many dynamic failure events are frequently observed due to underground coal excavation. To establish the quantitative relationship between [...] Read more.

This paper uses an acoustic emission (AE) test to examine the energy dissipation and liberation of coal and rock fracture due to underground coal excavation. Many dynamic failure events are frequently observed due to underground coal excavation. To establish the quantitative relationship between the dissipated energy and AE energy parameters, the coal and rock fracturing characteristics were clearly observed. A testing method to analyze the stage traits and energy release mechanism from damage to fracture of the unloading coal and rock under uniaxial compressive loading is presented. The research results showed that the relevant mechanical parameter discreteness was too large because the internal structures of the coal and rock were divided into multiple structural units (MSU) by a few main cracks. The AE test was categorized into four stages based on both the axial stress and AE event parameters: initial loading stage, elastic stage, micro-fracturing stage, and post-peak fracturing stage. The coal and rock samples exhibited minimum (maximum) U values of 60.44 J (106.41 J) and 321.19 J (820.87 J), respectively. A theoretical model of the dissipation energy during sample fracturing based on the AE event energy parameters was offered. The U decreased following an increase in ΣE_AE-II/ΣE_AE. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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16 pages, 6934 KiB

Open AccessArticle

Influence of Permeability and Injection Orientation Variations on Dispersion Coefficient during Enhanced Gas Recovery by CO₂ Injection

by Muhammad Kabir Abba, Athari Al-Otaibi, Abubakar Jibrin Abbas, Ghasem Ghavami Nasr and Martin Burby

Energies 2019, 12(12), 2328; https://doi.org/10.3390/en12122328 - 18 Jun 2019

Cited by 12 | Viewed by 2528

Abstract

This investigation was carried out to highlight the influence of the variation of permeability of the porous media with respect to the injection orientations during enhanced gas recovery (EGR) by CO₂ injection using different core samples of different petrophysical properties. The laboratory [...] Read more.

This investigation was carried out to highlight the influence of the variation of permeability of the porous media with respect to the injection orientations during enhanced gas recovery (EGR) by CO₂ injection using different core samples of different petrophysical properties. The laboratory investigation was performed using core flooding technique at 1300 psig and 50 °C. The injection rates were expressed in terms of the interstitial velocities to give an indication of its magnitude and variation based on the petrophysical properties of each core sample tested. Bandera Grey, Grey Berea, and Buff Berea sandstone core samples were used with measured permeabilities of 16.08, 217.04, and 560.63 md, respectively. The dispersion coefficient was observed to increase with a decrease in permeability, with Bandera Grey having the highest dispersion coefficient and invariably higher mixing between the injected CO₂ and the nascent CH₄. Furthermore, this dispersion was more pronounced in the horizontal injection orientation compared to the vertical orientation with, again, the lowest permeability having a higher dispersion coefficient in the horizontal orientation by about 50%. This study highlights the importance of the permeability variation in the design of the injection strategy of EGR and provides a revision of the CO₂ plume propagation at reservoir conditions during injection. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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28 pages, 9039 KiB

Open AccessArticle

An Efficiently Decoupled Implicit Method for Complex Natural Gas Pipeline Network Simulation

by Peng Wang, Shangmin Ao, Bo Yu, Dongxu Han and Yue Xiang

Energies 2019, 12(8), 1516; https://doi.org/10.3390/en12081516 - 22 Apr 2019

Cited by 10 | Viewed by 2947

Abstract

The simulation of a natural gas pipeline network allows us to predict the behavior of a gas network system under different conditions. Such predictions can be effectively used to guide decisions regarding the design and operation of the real system. The simulation is [...] Read more.

The simulation of a natural gas pipeline network allows us to predict the behavior of a gas network system under different conditions. Such predictions can be effectively used to guide decisions regarding the design and operation of the real system. The simulation is generally associated with a high computational cost since the pipeline network is becoming more and more complex, as well as large-scale. In our previous study, the Decoupled Implicit Method for Efficient Network Simulation (DIMENS) method was proposed based on the ‘Divide-and-Conquer Approach’ ideal, and its computational speed was obviously high. However, only continuity/momentum Equations of the simple pipeline network composed of pipelines were studied in our previous work. In this paper, the DIMENS method is extended to the continuity/momentum and energy Equations coupled with the complex pipeline network, which includes pipelines and non-pipeline components. The extended DIMENS method can be used to solve more complex engineering problems than before. To extend the DIMENS method, two key issues are addressed in this paper. One is that the non-pipeline components are appropriately solved as the multi-component interconnection nodes; the other is that the procedures of solving the energy Equation are designed based on the gas flow direction in the pipeline. To validate the accuracy and efficiency of the present method, an example of a complex pipeline network is provided. From the result, it can be concluded that the accuracy of the proposed method is equivalent to that of the Stoner Pipeline Simulator (SPS), which includes commercially available simulation core codes, while the efficiency of the present method is over two times higher than that of the SPS. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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15 pages, 2772 KiB

Open AccessArticle

Fractal and Multifractal Analysis of Pore Size Distribution in Low Permeability Reservoirs Based on Mercury Intrusion Porosimetry

by Penghui Su, Zhaohui Xia, Ping Wang, Wei Ding, Yunpeng Hu, Wenqi Zhang and Yujie Peng

Energies 2019, 12(7), 1337; https://doi.org/10.3390/en12071337 - 08 Apr 2019

Cited by 13 | Viewed by 3159

Abstract

To quantitatively evaluate the complexities and heterogeneities of pore structures in sandstone reservoirs, we apply single fractal theory and multifractal theory to explore the fractal characteristics of pore size distributions based on mercury intrusion porosimetry. The fractal parameters were calculated and the relationships [...] Read more.

To quantitatively evaluate the complexities and heterogeneities of pore structures in sandstone reservoirs, we apply single fractal theory and multifractal theory to explore the fractal characteristics of pore size distributions based on mercury intrusion porosimetry. The fractal parameters were calculated and the relationships between the petrophysical parameters (permeability and entry pressure) and the fractal parameters were investigated. The results show that the single fractal curves exhibit two-stage characteristics and the corresponding fractal dimensions D₁ and D₂ can characterize the complexity of pore structure in different sizes. Favorable linear relationships between log(ε) and log(μ,(ε)) indicate that the samples satisfy multifractal characteristics and ε is the sub-intervals with size ε = J × 2^−k. The multifractal singularity curves used in this study exhibit a right shape, indicating that the heterogeneity of the reservoir is mainly affected by pore size distributions in sparse regions. Multifractal parameters, D(0), D(1), and Δf, are positively correlated with permeability and entry pressure, while D(0), D(1), and Δf are negatively correlated with permeability and entry pressure. The ratio of larger pores volumes to total pore volumes acts as a control on the fractal dimension over a specific pore size range, while the range of the pore size distribution has a definite impact on the multifractal parameters. Results indicate that fractal analysis and multifractal analysis are feasible methods for characterizing the heterogeneity of pore structures in a reservoir. However, the single fractal models ignore the influence of microfractures, which could result in abnormal values for calculated fractal dimension. Compared to single fractal analysis, multifractal theory can better quantitatively characterize the heterogeneity of pore structure and establish favorable relationships with reservoir physical property parameters. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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14 pages, 2790 KiB

Open AccessArticle

Mathematical Modeling of Unsteady Gas Transmission System Operating Conditions under Insufficient Loading

by Vasyl Zapukhliak, Lyubomyr Poberezhny, Pavlo Maruschak, Volodymyr Grudz Jr., Roman Stasiuk, Janette Brezinová and Anna Guzanová

Energies 2019, 12(7), 1325; https://doi.org/10.3390/en12071325 - 06 Apr 2019

Cited by 21 | Viewed by 2661

Abstract

Under insufficient loading of a main gas transmission system, high-amplitude fluctuations of pressure may occur in it. A mathematical model is proposed to estimate the amplitude of pressure fluctuations in a gas pipeline along its length. It has been revealed that the shutdown [...] Read more.

Under insufficient loading of a main gas transmission system, high-amplitude fluctuations of pressure may occur in it. A mathematical model is proposed to estimate the amplitude of pressure fluctuations in a gas pipeline along its length. It has been revealed that the shutdown of compressor stations along the gas pipeline route has a significant impact on the parameters of the unsteady transient operating conditions. The possibility of minimizing oscillation processes by disconnecting compressor stations is substantiated for the “Soyuz” main gas pipeline. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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11 pages, 1866 KiB

Open AccessArticle

A Semi-Analytical Method for Three-Dimensional Heat Transfer in Multi-Fracture Enhanced Geothermal Systems

by Dongdong Liu and Yanyong Xiang

Energies 2019, 12(7), 1211; https://doi.org/10.3390/en12071211 - 28 Mar 2019

Cited by 3 | Viewed by 2282

Abstract

Multiple fractures have been proposed for improving the heat extracted from an enhanced geothermal system (EGS). For calculating the production temperature of a multi-fracture EGS, previous analytical or semi-analytical methods have all been based on an infinite scale of fractures and one-dimensional conduction [...] Read more.

Multiple fractures have been proposed for improving the heat extracted from an enhanced geothermal system (EGS). For calculating the production temperature of a multi-fracture EGS, previous analytical or semi-analytical methods have all been based on an infinite scale of fractures and one-dimensional conduction in the rock matrix. Here, a temporal semi-analytical method is presented in which finite-scale fractures and three-dimensional conduction in the rock matrix are both considered. Firstly, the developed model was validated by comparing it with the analytical solution, which only considers one-dimensional conduction in the rock matrix. Then, the temporal semi-analytical method was used to predict the production temperature in order to investigate the effects of fracture spacing and fracture number on the response of an EGS with a constant total injection rate. The results demonstrate that enlarging the spacing between fractures and increasing the number of fractures can both improve the heat extraction; however, the latter approach is much more effective than the former. In addition, the temporal semi-analytical method is applicable for optimizing the design of an EGS with multiple fractures located equidistantly or non-equidistantly. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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20 pages, 6025 KiB

Open AccessArticle

Numerical Investigation of Fracture Compressibility and Uncertainty on Water-Loss and Production Performance in Tight Oil Reservoirs

by Kai Liao, Shicheng Zhang, Xinfang Ma and Yushi Zou

Energies 2019, 12(7), 1189; https://doi.org/10.3390/en12071189 - 27 Mar 2019

Cited by 12 | Viewed by 3757

Abstract

Multi-stage hydraulic fracturing along with horizontal wells are widely used to create complex fracture networks in tight oil reservoirs. Analysis of field flowback data shows that most of the fracturing fluids are contained in a complex fracture network, and fracture-closure is the main [...] Read more.

Multi-stage hydraulic fracturing along with horizontal wells are widely used to create complex fracture networks in tight oil reservoirs. Analysis of field flowback data shows that most of the fracturing fluids are contained in a complex fracture network, and fracture-closure is the main driving mechanism during early clean up. At present, the related fracture parameters cannot be accurately obtained, so it is necessary to study the impacts of fracture compressibility and uncertainty on water-loss and the subsequent production performance. A series of mechanistic models are established by considering stress-dependent porosity and permeability. The impacts of fracture uncertainties, such as natural fracture density, proppant distribution, and natural fracture heterogeneity on flowback and productivity are quantitatively assessed. Results indicate that considering fracture closure during flowback can promote water imbibition into the matrix and delay the oil breakthrough time compared with ignoring fracture closure. With the increase of natural fracture density, oil breakthrough time is advanced, and more water is retained underground. When natural fractures connected with hydraulic fractures are propped, well productivity will be enhanced, but proppant embedment can cause a loss of oil production. Additionally, the fracture network with more heterogeneity will lead to the lower flowback rate, which presents an insight in the role of fractures in water-loss. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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15 pages, 4724 KiB

Open AccessArticle

The Percolation Properties of Electrical Conductivity and Permeability for Fractal Porous Media

by He Meng, Qiang Shi, Tangyan Liu, FengXin Liu and Peng Chen

Energies 2019, 12(6), 1085; https://doi.org/10.3390/en12061085 - 21 Mar 2019

Cited by 13 | Viewed by 3649

Abstract

Many cases have indicated that the conductivity and permeability of porous media may decrease to zero at a nonzero percolation porosity instead of zero porosity. However, there is still a lack of a theoretical basis for the percolation mechanisms of the conductivity and [...] Read more.

Many cases have indicated that the conductivity and permeability of porous media may decrease to zero at a nonzero percolation porosity instead of zero porosity. However, there is still a lack of a theoretical basis for the percolation mechanisms of the conductivity and permeability. In this paper, the analytical percolation expressions of both conductivity and permeability are derived based on fractal theory by introducing the critical porosity. The percolation models of the conductivity and permeability were found to be closely related to the critical porosity and microstructural parameters. The simulation results demonstrated that the existence of the critical could lead to the non-Archie phenomenon. Meanwhile, the increasing critical porosity could significantly decrease the permeability and the conductivity at low porosity. Besides, the complex microstructure could result in more stagnant pores and a higher critical porosity. This study proves the importance of the critical porosity in accurately evaluating the conductivity and permeability, and reveals the percolation mechanisms of the conductivity and permeability in complex reservoirs. By comparing the predicted conductivity and permeability with the available experimental data, the validity of the proposed percolation models is verified. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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31 pages, 13322 KiB

Open AccessArticle

CO₂, Water and N₂ Injection for Enhanced Oil Recovery with Spatial Arrangement of Fractures in Tight-Oil Reservoirs Using Huff-‘n-puff

by Jie Bai, Huiqing Liu, Jing Wang, Genbao Qian, Yongcan Peng, Yang Gao, Lin Yan and Fulin Chen

Energies 2019, 12(5), 823; https://doi.org/10.3390/en12050823 - 01 Mar 2019

Cited by 25 | Viewed by 3589

Abstract

Tight oil has been effectively developed thanks to artificial fracture technology. The basic mechanism of effective production through fractures lies in the contact between the fractures (both natural and artificial) and the matrix. In this paper, the natural tight cores from J field [...] Read more.

Tight oil has been effectively developed thanks to artificial fracture technology. The basic mechanism of effective production through fractures lies in the contact between the fractures (both natural and artificial) and the matrix. In this paper, the natural tight cores from J field in China are used to conduct experimental studies on the different fluid huff-‘n-puff process. A new core-scale fracture lab-simulation method is proposed. Woven metallic wires were attached to the outer surface of the core to create a space between the core holder and core as a high permeable zone, an equivalent fracture. Three different injecting fluids are used, including CO₂, N₂ and water. The equivalent core scale reservoir numerical models in depletion and huff-n-puff mode are then restored by numerical simulation with the Computer Modeling Group—Compositional & Unconventional Reservoir Simulator (CMG GEM). Simulation cases with eight different fracture patterns are used in the study to understand how fracture mechanistically impact Enhanced Oil Recovery (EOR) in huff n puff mode for the different injected fluids. The results showed: Firstly, regardless of the arrangement of fractures, CO₂ has mostly obvious advantages over water and N₂ in tight reservoir development in huff-‘n-puff mode. Through EOR mechanism analysis, CO₂ is the only fluid that is miscible with oil (even 90% mole fraction CO₂ is dissolved in the oil phase), which results in the lowest oil phase viscosity. The CO₂ diffusion mechanism is also pronounced in the huff-‘n-puff process. Water may impact on the oil recovery through gravity and the capillary force imbibition effect. N₂, cannot recover more crude oil only by elasticity and swelling effects. Secondly, the fracture arrangement in space has the most impact on CO₂ huff-‘n-puff, followed by water and finally N₂. The fractures primarily supply more efficient and convenient channels and contact relationships. The spatial arrangement of fractures mainly impacts the performance of CO₂ through viscosity reduction in the contact between CO₂ and crude oil. Similarly, the contact between water in fractures and crude oil in the matrix is also the key to imbibition. In the process of N₂ huff-‘n-puff, the elasticity energy is dominant and fracture arrangement in space hardly to improve oil recovery. In addition, when considering anisotropy, water huff-‘n-puff is more sensitive to it, while N₂ and CO₂ are not. Finally, comparing the relationship between fracture contact area and oil recovery, oil production is insensitive to contact area between fracture and matrix for water and N₂ cases. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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15 pages, 2293 KiB

Open AccessArticle

Improved CRM Model for Inter-Well Connectivity Estimation and Production Optimization: Case Study for Karst Reservoirs

by Daigang Wang, Yong Li, Jing Zhang, Chenji Wei, Yuwei Jiao and Qi Wang

Energies 2019, 12(5), 816; https://doi.org/10.3390/en12050816 - 01 Mar 2019

Cited by 10 | Viewed by 3818

Abstract

Due to the coexistence of multiple types of reservoir bodies and widely distributed aquifer support in karst carbonate reservoirs, it remains a great challenge to understand the reservoir flow dynamics based on traditional capacitance–resistance (CRM) models and Darcy’s percolation theory. To solve this [...] Read more.

Due to the coexistence of multiple types of reservoir bodies and widely distributed aquifer support in karst carbonate reservoirs, it remains a great challenge to understand the reservoir flow dynamics based on traditional capacitance–resistance (CRM) models and Darcy’s percolation theory. To solve this issue, an improved injector–producer-pair-based CRM model coupling the effect of active aquifer support was first developed and combined with the newly-developed Stochastic Simplex Approximate Gradient (StoSAG) optimization algorithm for accurate inter-well connectivity estimation in a waterflood operation. The improved CRM–StoSAG workflow was further applied for real-time production optimization to find the optimal water injection rate at each control step by maximizing the net present value of production. The case study conducted for a typical karst reservoir indicated that the proposed workflow can provide good insight into complex multi-phase flow behaviors in karst carbonate reservoirs. Low connectivity coefficient and time delay constant most likely refer to active aquifer support through a high-permeable flow channel. Moreover, the injector–producer pair may be interconnected by complex fissure zones when both the connectivity coefficient and time delay constant are relatively large. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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16 pages, 7640 KiB

Open AccessFeature PaperArticle

A Case Study of an Optimized Intermittent Ventilation Strategy Based on CFD Modeling and the Concept of FCT

by Hui Liu, Shanjun Mao and Mei Li

Energies 2019, 12(4), 721; https://doi.org/10.3390/en12040721 - 22 Feb 2019

Cited by 9 | Viewed by 2823

Abstract

With the increasing operation costs and implementation of carbon tax in the underground coal mining systems, a cost-effective ventilation system with well methane removal efficiency becomes highly required. Since the intermittent ventilation provides a novel approach in energy saving, there still exists some [...] Read more.

With the increasing operation costs and implementation of carbon tax in the underground coal mining systems, a cost-effective ventilation system with well methane removal efficiency becomes highly required. Since the intermittent ventilation provides a novel approach in energy saving, there still exists some scientific issues. This paper adopts the design concept of frequency conversion technology (FCT) to the ventilation pattern design for the first time, and an optimized intermittent ventilation strategy is proposed. Specifically, a real excavation laneway of a coal mine in China is established as the physical model, and computational fluid dynamic (CFD) approaches are utilized to investigate the spatiotemporal characteristics of airflow behavior and methane distribution. Plus, the period of intermittency and appropriate air velocity are scientifically defined based on the conception of FCT by conducting the parametric studies. Therefore, an optimized case is brought out with well methane removal efficiency and remarkable energy reduction of 39.2% in a ventilation period. Furthermore, the simulation result is verified to be reliable by comparing with field measurements. The result demonstrates that a balance of significant energy saving and the methane removal requirement based on the concept of FTC is possible, which could in turn provide good operational support for FTC. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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22 pages, 5235 KiB

Open AccessFeature PaperArticle

Experimental and Theoretical Study on Dynamic Hydraulic Fracture

by Jingnan Dong, Mian Chen, Yuwei Li, Shiyong Wang, Chao Zeng and Musharraf Zaman

Energies 2019, 12(3), 397; https://doi.org/10.3390/en12030397 - 27 Jan 2019

Cited by 23 | Viewed by 3863

Abstract

Hydraulic fracturing is vital in the stimulation of oil and gas reservoirs, whereas the dynamic process during hydraulic fracturing is still unclear due to the difficulty in capturing the behavior of both fluid and fracture in the transient process. For the first time, [...] Read more.

Hydraulic fracturing is vital in the stimulation of oil and gas reservoirs, whereas the dynamic process during hydraulic fracturing is still unclear due to the difficulty in capturing the behavior of both fluid and fracture in the transient process. For the first time, the direct observations and theoretical analyses of the relationship between the crack tip and the fluid front in a dynamic hydraulic fracture are presented. A laboratory-scale hydraulic fracturing device is built. The momentum-balance equation of the fracturing fluid is established and numerically solved. The theoretical predictions conform well to the directly observed relationship between the crack tip and the fluid front. The kinetic energy of the fluid occupies over half of the total input energy. Using dimensionless analyses, the existence of equilibrium state of the driving fluid in this dynamic system is theoretically established and experimentally verified. The dimensionless separation criterion of the crack tip and the fluid front in the dynamic situation is established and conforms well to the experimental data. The dynamic analyses show that the separation of crack tip and fluid front is dominated by the crack profile and the equilibrium fluid velocity. This study provides a better understanding of the dynamic hydraulic fracture. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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Review

Jump to: Editorial, Research

55 pages, 10279 KiB

Open AccessReview

A Review of Rheological Modeling of Cement Slurry in Oil Well Applications

by Chengcheng Tao, Barbara G. Kutchko, Eilis Rosenbaum and Mehrdad Massoudi

Energies 2020, 13(3), 570; https://doi.org/10.3390/en13030570 - 24 Jan 2020

Cited by 54 | Viewed by 10689

Abstract

The rheological behavior of cement slurries is important in trying to prevent and eliminate gas-migration related problems in oil well applications. In this paper, we review the constitutive modeling of cement slurries/pastes. Cement slurries, in general, behave as complex non-linear fluids with the [...] Read more.

The rheological behavior of cement slurries is important in trying to prevent and eliminate gas-migration related problems in oil well applications. In this paper, we review the constitutive modeling of cement slurries/pastes. Cement slurries, in general, behave as complex non-linear fluids with the possibility of exhibiting viscoelasticity, thixotropy, yield stress, shear-thinning effects, etc. The shear viscosity and the yield stress are two of the most important rheological characteristics of cement; these have been studied extensively and a review of these studies is provided in this paper. We discuss the importance of changing the concentration of cement particles, water-to-cement ratio, additives/admixtures, shear rate, temperature and pressure, mixing methods, and the thixotropic behavior of cement on the stress tensor. In the concluding remarks, we propose a new constitutive model for cement slurry, considering the basic non-Newtonian nature of the different models. Full article

(This article belongs to the Special Issue Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications)

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