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Numerical Analysis of Rock Mechanics and Crack Propagation

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A special issue of Sustainability (ISSN 2071-1050). This special issue belongs to the section "Sustainable Engineering and Science".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 20939

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Dr. Daobing Wang

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College of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing 102699, China
Interests: hydraulic fracturing; rock mechanics; reduced-order modeling
Special Issues, Collections and Topics in MDPI journals

Dr. Fujian Zhou

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Guest Editor

State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing 102249, China
Interests: hydraulic fracturing; carbonate acidizing and acid fracturing; sand control; degradable diverting agent

Dr. Bo Wang

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School of Petroleum, China University of Petroleum-Beijing at Karamay, Karamay 834000, China
Interests: hydraulic fracturing; fracture propagation simulation
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Dr. Jie Wang

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Guest Editor

School of Petroleum Engineering, Yangtze University, Wuhan 430100, China
Interests: enhanced oil recovery; reservoir stimulation; natural gas hydrate
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Within the context of the exploration and development of tight reservoirs, such as shale oil, coal bed methane, deep shale gas, deep and ultra-deep carbonate or sandstone rocks, and hot dry rocks, hydraulic fracturing has become a key technique for stimulating hydrocarbon production from these reservoirs. Crack propagation during hydraulic fracturing involves rock deformation, fluid flow in hydrofractures, heat transfer between fluid and rock, and fracture mechanics, among other phenomena, thus representing a very complex multi-physical problem. Moreover, large amounts of fracturing fluids, such as conventional slickwater fracturing fluid, variable-viscosity slick water, and nano-emulsion fluids, are injected into the formation, and there are strong fluid–rock interactions in the subsurface, which includes physical processes such as rock imbibition, fracturing fluid flowback, reservoir damage and protection, and fracturing fluid retention. Some microcrack initiation and propagation occurs due to the chemical and physical interaction in hydraulic fracturing. Numerical simulation is thus a very powerful tool to solve the complex hydraulic fracturing problems in tight reservoirs.

This Special Issue aims to present the most recent advances related to the numerical analysis of rock mechanics and crack propagation during the hydraulic fracturing of tight reservoirs.

Topics of interest for publication include but are not limited to:

(1) new hydraulic fracturing technology, such as for variable-viscosity slickwater, temporary plugging and diverting fracturing, refracturing, and variable rate fracturing

(2) evaluation of rock mechanical properties including frackability, fluid–rock interaction, and fracture toughness

(3) fluid flow and heat transfer in fractured reservoirs

(4) optimization method of hydraulic fracturing parameters

(5) water hammer diagnostic method for hydrofracture propagation

(6) diagnostic fracture injection test (DFIT) analysis

(7) fracturing fluid flowback

(8) reservoir damage and protection

(9) fracturing fluid retention

(10) rock imbibition in fractured reservoirs

Dr. Daobing Wang
Dr. Fujian Zhou
Dr. Bo Wang
Dr. Jie Wang
Guest Editors

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Keywords

hydraulic fracturing
rock mechanics
crack propagation
rock–fluid interaction
fracturing fluid flowback
reservoir damage and protection
fracturing fluid retention
rock imbibition

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Published Papers (11 papers)

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Research

14 pages, 3880 KiB

Open AccessArticle

Quantitative Investigation of Fracture Apertures during Temporary Plugging and Diverting Fracturing

by Yubin Wang, Baojiang Sun, Tianju Wang, Zhiwei Hao and Bo Wang

Sustainability 2023, 15(20), 14664; https://doi.org/10.3390/su152014664 - 10 Oct 2023

Viewed by 995

Abstract

Oil and gas resources are closely related to daily life and are an important support for the economy of a city or even a country. Hydraulic fracturing is an indispensable technique to economically develop oil and gas resources through creating complex fractures. Temporary plugging and diverting fracturing (TPDF) can generate diversion fractures perpendicular to the initial fractures and enhance the stimulated area. The aperture of the diversion fractures determines its conductivity and the oil/gas production. However, it is difficult to evaluate the aperture of the diversion fracture due to the complex physical process of hydraulic fracturing. This work established a fluid–solid fully coupled simulation model to investigate the fracture aperture influenced by various factors during TPDF. The model can simulate the propagation of the initial fracture and the diversion fracture. Various factors include the tight plug’s permeability, the tight plug’s length, Young’s modulus, rock tensile strength, in situ stress contrast, the leak-off coefficient of the fracture surface, and fluid injection rate. The results show that the aperture of the previous fracture can be enlarged, and the aperture of the diversion fracture can be decreased by the tight plug. The aperture at the diversion fracture mouth is much smaller than that along the diversion fracture. Reservoirs with low Young’s modulus values and high rock tensile strength can generate the diversion fracture with a wider aperture. Moreover, increasing the fluid injection rate can effectively increase the fracture mouth aperture. In this way, the risk of screenout can be lowered. This work is beneficial for the design of the TPDF and ensures safe construction. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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19 pages, 6118 KiB

Open AccessArticle

Research on the Fracture Propagation Law of Separate Layered Fracturing in Unconventional Sandstone Reservoirs

by Qiquan Ran, Xin Zhou, Mengya Xu, Jiaxin Dong, Dianxing Ren and Ruibo Li

Sustainability 2023, 15(13), 10444; https://doi.org/10.3390/su151310444 - 3 Jul 2023

Cited by 1 | Viewed by 973

Abstract

The unconsolidated sandstone is a type of rock that has poor cementation, a low strength, a high porosity, and permeability. It is highly compressible under high stress and exhibits non-linear plastic deformation during hydraulic fracturing construction in its reservoir. In this study, the mechanical properties of unconsolidated sandstone with a different permeability were studied, and a three-dimensional hydraulic fracture propagation numerical model was established based on the modified traditional Cambridge model. This model was used to simulate the fracture propagation law of unconsolidated sandstone in separate layer fracturing under different construction conditions. During hydraulic fracturing construction, the fracturing fluid slowly invades the reservoir when the displacement of the fracturing fluid is small. The unconsolidated sandstone undergoes compaction and hardening, followed by shear expansion, and then complete destruction. A larger displacement will cause the reservoir rock to directly enter the state of destruction from compaction and hardening. This study found that several critical parameters are obtained for fracturing construction. When the displacement is greater than 5 m³/min, the fracturing fluid exceeds 100 mPa·s, or when the filtration coefficient exceeds 1.2 × 10⁻³ m/

\sqrt{s}

, the second and third layers will be penetrated. This study provides valuable insights into the mechanical properties of unconsolidated sandstone and reveals the critical parameters for the successful hydraulic fracturing construction in this type of reservoir. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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19 pages, 5482 KiB

Open AccessArticle

Study on Secondary Brine Drainage and Sand Control Technology of Salt Cavern Gas Storage

by Yi Zhang, Kun Zhang, Jun Li, Yang Luo, Li-Na Ran, Lian-Qi Sheng and Er-Dong Yao

Sustainability 2023, 15(10), 7793; https://doi.org/10.3390/su15107793 - 10 May 2023

Cited by 3 | Viewed by 1545

Abstract

Geological conditions of salt cavern gas storage in China are characterized by dominantly layered salt layers with a high content of insoluble mudstone. After the water leaching of the salt layer, a large amount of sediment accumulates at the bottom of the gas storage cavity. During the gas injection process, only the clean brine above the sediment can be expelled, leaving a brine layer of 2–5 m and a large amount of brine in the pore space of the sediment. To increase storage capacity, it is urgent to explore the secondary gas injection and brine drainage technology to further expel residual brine in pores of the sediment at the cavern bottom. The sediment is relatively loosely packed and is composed of mudstone particles, which easily migrate and block the brine withdrawal pipe. In this paper, firstly, the mineral composition, particle size and distribution characteristics of the sediment at the bottom of the salt cavern are fully understood by XRD and sieve analysis methods. Then, a lab simulation device suitable for secondary gas injection and brine drainage of a high-salinity salt cavern with a diameter and height of 25 cm was designed and built. A screen sand control experiment, a gravel pack artificial wall sand control experiment and chemical cementing sand were simulated. The effects of gas injection, brine drainage pressure, brine layer height and insoluble particle size on sand production and liquid drainage were studied. The influence factors of brine withdrawal on the sand control in secondary brine drainage were intensively investigated, and finally, the gravel pack artificial wall sand control technology system was recommended. The optimal construction parameters for secondary brine discharge are recommended as follows: Under the condition of gravel packing with the same particle size, the trend of sand content with different artificial wall thicknesses is not obvious, and a 2 cm wall thickness is the best in the overall experiment, corresponding to 28 cm in the field. The larger the particle size of the gravel pack, the better the sand control, and the best gravel size is 10–20 mesh. The injection pressure should be as low as possible. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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13 pages, 4123 KiB

Open AccessArticle

Mechanism Study and Performance Evaluation of Nano-Materials Used to Improve Wellbore Stability

by Yan Ye, Hanxuan Song, Jinzhi Zhu, Weiru Zheng, Fujian Zhou, Guangxu Zhou and Qingwen Zhang

Sustainability 2023, 15(6), 5530; https://doi.org/10.3390/su15065530 - 21 Mar 2023

Cited by 3 | Viewed by 1643

Abstract

In the drilling process of Tarim Oilfield, a representative of ultra-deep oil and gas reservoirs, there are many problems of wellbore stability/instability caused by the development of a large number of micro-fractures. According to the nano-plugging mechanism, rigid nano-SiO₂ and deformable nano-paraffin emulsion are added to the drilling fluid to improve the plugging rate. The effect of nanomaterials on the mechanical properties of limestone in the Karatal Formation was evaluated through a triaxial mechanical experiment, and it was found that rigid nano-SiO₂ can have a better plugging effect under high formation pressure. It can increase the compressive strength of the limestone core by 10.32% and the cohesion of the core by 12.19%, and the internal friction angle of the core was increased from 25.67° to 26.39°. The internal structure of the core after nano-blocking was observed using CT scanning, and the fracture distribution state of the core before and after plugging and the fracture characteristics of the core under the pressure gradient were obtained, which confirmed that nano-SiO₂ can effectively solve the fracture problem of deep limestone caused by micro-fractures. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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14 pages, 7739 KiB

Open AccessArticle

An Experimental Study on the Determination of Shale K_IC by Semi-Disk Three-Point Bending

by Hongjian Wang, Wenchang Zhang, Zijiang Zhao, Zhendong Cui, Jian Li and Hao Zeng

Sustainability 2023, 15(3), 1863; https://doi.org/10.3390/su15031863 - 18 Jan 2023

Viewed by 1507

Abstract

In order to accurately test the K_IC of the vertical stratification direction of shale, a semi-circular bending specimen with a linear chevron notch ligament (LCNSCB) was designed. The minimum dimensionless stress intensity factor (Y^*_min) of the LCNSCB specimen was calculated by the finite element method and the slice synthesis method, respectively. Two sets of prefabricated samples of the LCNSCB specimen under arrester and divider mode were used to conduct three-point bending loading experiments. The dispersion of the measured K_IC value of the specimens was analyzed by standard deviation and coefficient of variation, and the reason that the K_IC dispersion of specimens in divider mode was larger than in arrester mode was discussed. Compared with the experimental data of the existing literature, the data of this experiment shows that the LCNSCB specimen can avoid the disadvantage of lower measured K_IC values due to a larger fracture processing zone featured in the CSTSCB and CCNBD specimens, combined with the merits of a shorter fracture processing zone of the SR or CR specimens, and the render measured the K_IC value to be closer to the material’s true fracture toughness value. The narrow ligament of the LCNSCB specimen has a favorable crack propagation guiding effect, can generate consistent K_IC values, and could be used to accurately test the fracture toughness of rock material in vertical bedding direction. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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12 pages, 2736 KiB

Open AccessArticle

Optimization of the Well Start-Up Procedure and Operating Parameters for ESP Gas Well Dewatering

by Xiaolei Wang, Xuezhang Feng, Jinbo Liu, Jiangling Hong, Jinsong Yao, Honglei Liu, Zelin Liu and Guoqing Han

Sustainability 2023, 15(2), 1498; https://doi.org/10.3390/su15021498 - 12 Jan 2023

Viewed by 3053

Abstract

The Electrical Submersible Pump (ESP) systems were deployed in two gas wells for the dewatering of the gas reservoir. However, problems, such as the failure to start up the ESP, and changes in reservoir parameters occurred during the production. For the first problem, the well start-up operation records indicate that the ESP’s gas locking happened. To avoid this, an optimization method of the well start-up procedure for the ESP well with a check valve was correspondingly proposed, which can solve the problem without any workovers. Secondly, based on the working characteristics of the ESP and the nodal analysis method, a set of optimization methods for the operating parameters of ESPs were introduced to achieve the inflow and outflow balance. For one well, the original ESP system was planned to be installed after hydraulic fracturing. Traditionally, the ESP operating parameters were designed based on the production rate. However, in this case, the production rate and the ESP operating frequency were designed simultaneously to maximize the pump efficiency. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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15 pages, 7046 KiB

Open AccessArticle

Study on the Optimal Volume Fracturing Design for Horizontal Wells in Tight Oil Reservoirs

by Yenan Jie, Jing Yang, Desheng Zhou, Haiyang Wang, Yi Zou, Yafei Liu and Yanjun Zhang

Sustainability 2022, 14(23), 15531; https://doi.org/10.3390/su142315531 - 22 Nov 2022

Cited by 7 | Viewed by 1909

Abstract

The application of horizontal well volume fracturing technology is an important method for enhancing oil recovery in tight oil reservoirs. However, the influence mechanism of the fracture placement scheme (FPC) on postfracturing productivity is still unclear. Based on the theory of the black oil model, combined with the reservoir stimulation characteristics of horizontal well volume fracturing in tight oil reservoirs, this paper established a postfracturing reservoir production simulation model. History fitting was used to verify the accuracy of the production model simulations. A series of numerical simulations was carried out to study the influence mechanisms of the fracture parameters and FPC on productivity. The simulation results show that compared with the fracture conductivity, the fracture length and number are the main parameters affecting tight oil reservoir productivity. Selecting a reasonable fracture length and number can realize the economical and efficient production of tight oil reservoir volume fracturing. Compared with the traditional fracture equal-length scheme, an FPC with an uneven fracture length can increase the cumulative oil production of oil wells. Under the condition of the same total fracture length, the scheme with a staggered distribution of long fractures and short fractures has the largest cumulative oil production over five years. A reasonable well spacing can greatly reduce the impact of interwell interference on postfracturing dual branch horizontal well productivity. When dual branch horizontal well fractures are alternately distributed, the postfracturing productivity is higher. The production simulation model established in this paper provides a method to accurately evaluate the productivity of horizontal wells after volume fracturing, which can provide guidance for the optimization of hydraulic fracturing operation parameters. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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23 pages, 7497 KiB

Open AccessArticle

Investigation of the Dynamic Pure-Mode-II Fracture Initiation and Propagation of Rock during Four-Point Bending Test Using Hybrid Finite–Discrete Element Method

by Yushan Song, Yuqing Fan, Huaming An, Hongyuan Liu and Shunchuan Wu

Sustainability 2022, 14(16), 10200; https://doi.org/10.3390/su141610200 - 17 Aug 2022

Cited by 1 | Viewed by 1746

Abstract

A hybrid finite–discrete element method (FDEM) is proposed to investigate dynamic pure-mode-II fracture behaviors. The transition of continuum to discontinuum was applied to the FDEM through the use of three fracture modes, so that the whole fracture process could be modeled naturally. The FDEM was then employed to model the dynamic pure-mode-II fracture behavior of rock during a four-point bending test with a prefabricated notch. The results showed that the fracture initiated from the tip of the prefabricated notch under a relatively lower loading rate, i.e., 1 m/s and 5 m/s. However, when the loading rate reached higher levels, i.e., 10 m/s and 50 m/s, the prefabricated notch played a small role in the fracture patterns. Under these conditions, the fracture initiated from the center of the beam bottom or the stress concentration vicinity, instead of the tip of the prefabricated notch. Regardless of the loading rate, the obtained force-loading displacement curves showed a typical brittle material failure process. Additionally, by incorporating the empirical correlation between the static and dynamic strengths obtained from the dynamic rock fracture tests, the hybrid finite–discrete element method could effectively reflect the impact of the loading rate on the strength of the rock. To conclude, the hybrid finite–discrete element method is an effective instrument to investigate the fracture initiation and propagation of rock, since it can both naturally simulate the process of rock fracture and capture the effect of the loading rate on the rock behaviors. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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17 pages, 7997 KiB

Open AccessArticle

Numerical Simulation of Fracture Propagation during Refracturing

by Daobing Wang, Arash Dahi Taleghani, Bo Yu, Meng Wang and Chunming He

Sustainability 2022, 14(15), 9422; https://doi.org/10.3390/su14159422 - 1 Aug 2022

Cited by 6 | Viewed by 2003

Abstract

Hydraulic fracturing is repeated in some unconventional wells after production since the initial fracturing treatment. Due to prior production, the stress field around the existing fractures possibly rotates, and this impacts the refracturing operation. In this study, an extended finite element model (XFEM) including junction enrichments of intersecting fractures was proposed to simulate fracture propagation during refracturing in the cemented fractured reservoirs. In the XFEM model, a lubrication equation coupling both tangential and normal flow in hydraulic fractures (HFs) was used to describe the fluid flow behavior within the fractured elements, and the Newton-Raphson method was used to solve the nonlinear fluid–solid coupling system of the refracturing model. The effects of approaching angle, stress anisotropy, and production time were discussed. The results showed that the effects of these factors on improvement of fracture complexity during refracturing depend on the reservoir parameters and the stress field. The characteristics of the injection pressure curves during refracturing were analyzed. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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18 pages, 8558 KiB

Open AccessArticle

Multi-Fracture Synchronous Propagation Mechanism of Multi-Clustered Fracturing in Interlayered Tight Sandstone Reservoir

by Fuchun Tian, Yan Jin, Fengming Jin, Xiaonan Ma, Lin Shi, Jun Zhang, Dezhi Qiu and Zhuo Zhang

Sustainability 2022, 14(14), 8768; https://doi.org/10.3390/su14148768 - 18 Jul 2022

Cited by 6 | Viewed by 1897

Abstract

A numerical model was established by using the 3D lattice method to investigate the synchronous propagation mechanism of multiple clusters of hydraulic fractures in interlayered tight sandstone reservoirs in the Songliao Basin in China. The multi-fracture synchronous propagation model under different geological factors and fracturing engineering factors was simulated. The results show that the vertical stress difference, interlayer Young’s modulus, and lithologic interface strength are positively correlated with the longitudinal propagation ability of multiple hydraulic fractures. The three clusters of hydraulic fractures can have adequate longitudinal extension capacity and transverse propagation range with 15 m cluster spacing and a 12 m³/min pumping rate. The viscosity of the fracturing fluid is positively correlated with the ability of hydraulic fracture to penetrate the interlayer longitudinally but negatively correlated with the transverse propagation length. It is recommended that high viscosity fracturing fluid is used in the early stage of multi-clustered fracturing in interlayered tight sandstone reservoirs to promote hydraulic fractures to penetrate more interlayers and communicate more pay layers in the longitudinal direction, and low viscosity fracturing fluid in the later stage to make multiple clusters of fractures propagate to the far end where possible and obtain a more ideal SRV. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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22 pages, 9762 KiB

Open AccessArticle

Impacts of Fracture Roughness and Near-Wellbore Tortuosity on Proppant Transport within Hydraulic Fractures

by Di Wang, Bingyang Bai, Bin Wang, Dongya Wei and Tianbo Liang

Sustainability 2022, 14(14), 8589; https://doi.org/10.3390/su14148589 - 13 Jul 2022

Cited by 5 | Viewed by 1676

Abstract

For unconventional reservoir hydraulic fracturing design, a greater fracture length is a prime factor to optimize. However, the core observation results from the Hydraulic Fracturing Test Site (HFTS) show that the propped fractures are far less or shorter than expected, which suggests that the roughness and tortuosity of hydraulic fractures are crucial to sand transport. In this study, a transport model of sands is first built based on experimental measurements on the height and transport velocity of the sand bank in fractures with predetermined width and roughness. The fracture roughness is quantified by using the surface height integral. Then, three-dimensional simulations are conducted with this modified model to further investigate the impact of tortuous fractures on sand transport, from which a regression model is established to estimate the propped length of hydraulic fractures at a certain pumping condition. The experiment results show that the height of the sand bank in rough fractures is 20–50% higher than that in smooth fractures. The height of the sand bank decreases with the reduction in slurry velocity and increases with the increase in sand diameter. Sand sizes do little effect on the transport velocity of the sand bank, but the increase in slurry velocity and sand volume fraction can dramatically enhance the migration velocity of the sand bank. The appearance of tortuous fractures decreases the horizontal velocity of suspended particles and results in a higher sand bank compared with that in straight fractures. When the sand bank reaches equilibrium at the tortuous position, it is easy to produce vortices. So, there is a significant height of sand bank change at the tortuous position. Moreover, sand plugging can occur at the entrance of the fractures, making it difficult for the sand to transport deep into fractures. This study explains why the propped length of fractures in HFTS is short and provides a regression model that can be easily embedded in the fracturing simulation to quickly calculate dimensions of the propped fractures network to predict the length and height of propped fractures during fracturing. Full article

(This article belongs to the Special Issue Numerical Analysis of Rock Mechanics and Crack Propagation)

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