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Fracture Interference and Propagation Geometry of Hydraulic Fractures Based on XFEM in an Unconventional Oil Reservoir

Shuang Liang Di Wang Dan Liu Yang Tian Haibo Wang Fengxia Li Gang Dong Chengfeng Yin Yi Yang
Archives of Mining Sciences | 2023 | vol. 68 | No 2 | 301-318 | DOI: 10.24425/ams.2023.146181
Keywords hydraulic fracturing fracture interference XFEM fracture propagation geometry unconventional oil reservoir
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Abstract

Unconventional oil and gas reservoirs are characterised by low porosity, low permeability and low natural deliverability. At present, horizontal wells staged fracturing is an effective development method. However, in the case of staged hydraulic fracturing in horizontal wells, stress interference occurs between multiple fractures, leading to fracture deformation and even inhibiting the formation of fractures, thereby affecting reservoir production. In this paper, based on the extended finite element method (XFEM), considering the fluid flow in the fracture and fracturing fluid filtration, we analyse the effects of fracturing fluid pumping rate, fracture spacing and elastic modulus on horizontal in-situ stress, fracture parameters and fracture extension pattern during different fracturing initiation processes. The results show that the induced stress generated by the action of fracturing fluid changes the direction of horizontal in-situ stress in the elliptical region around the fracture. In the mode of simultaneous fracture initiation (TFIS), the extension of two symmetrical fractures is “repulsive”; in the mode of two fractures initiated at different times (TFIDT), the extension direction is “mutual attraction”. A large pumping rate and small elastic modulus are conducive to fracture propagation. In the TFIS mode, two fractures alternately expand, while in the TFIDT mode, the impact of rock mechanical properties and construction parameters on fracture propagation will be amplified. The extension of subsequent fractures will be restrained, especially when the fracture spacing is less than 10 m. The width of the previously created fracture will be severely affected, even causing a partial closure and becoming elongated fractures.
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Authors and Affiliations

Shuang Liang
1 2 3
ORCID: ORCID
Di Wang
1 2
ORCID: ORCID
Dan Liu
4
Yang Tian
3
ORCID: ORCID
Haibo Wang
1 2
ORCID: ORCID
Fengxia Li
1 2
ORCID: ORCID
Gang Dong
5
ORCID: ORCID
Chengfeng Yin
6
ORCID: ORCID
Yi Yang
7
ORCID: ORCID
  1. State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Beijing, China
  2. State Energy Center for Shale Oil Research and Development, Beijing, China
  3. Department of Petroleum Engineering, Northeast Petroleum University, Daqing, China
  4. PipeChina Oil & Gas Pipeline Control Center, Beijing, 122000, China
  5. The Eighth Oil Production Plant of Daqing Oilfield Limited Company, Daqing, China
  6. The Fourth Oil Production Plant of Daqing Oilfield Limited Company, Daqing, China
  7. The Tenth Oil Production Plant of Daqing Oilfield Limited Company, Daqing, China

Meshless local Petrov-Galerkin method for rotating Rayleigh beam using Chebyshev and Legendre polynomials

Vijay Panchore
Archive of Mechanical Engineering | 2022 | vol. 69 | No 2 | 301-318 | DOI: 10.24425/ame.2022.140416
Keywords meshless local Petrov-Galerkin method mechanical vibrations orthogonal polynomials Finite Element Method (FEM) rotating beams
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Abstract

The numerical solutions are obtained for rotating beams; the inclusion of centrifugal force term makes it difficult to get the analytical solutions. In this paper, we solve the free vibration problem of rotating Rayleigh beam using Chebyshev and Legendre polynomials where weak form of meshless local Petrov-Galerkin method is used. The equations which are derived for rotating beams result in stiffness matrices and the mass matrix. The orthogonal polynomials are used and results obtained with Chebyshev polynomials and Legendre polynomials are exactly the same. The results are compared with the literature and the conventional finite element method where only first seven terms of both the polynomials are considered. The first five natural frequencies and respective mode shapes are calculated. The results are accurate when compared to literature.
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Bibliography

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[9] V. Panchore, R. Ganguli, and S.N. Omkar. Meshless local Petrov-Galerkin method for rotating Timoshenko beam: a locking-free shape function formulation. Computer Modeling in Engineering and Sciences, 108(4):215–237, 2015. doi: 10.3970/cmes.2015.108.215.
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[19] V. Panchore and R. Ganguli. Quadratic B-spline finite element method for a rotating non-uniform Euler-Bernoulli beam. International Journal for Computational Methods in Engineering Science and Mechanics, 19(5):340–350, 2018. doi: 10.1080/15502287.2018.1520757.
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Authors and Affiliations

Vijay Panchore
1
  1. Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal, India

Radiation conditions in the Hornsund area (Spitsbergen)

Bronisław Głowicki
Polish Polar Research | 1985 | vol. 6 | No 3 | 301-318
Keywords Arctic Spitsbergen meteorology tundra radiation balance
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Abstract

On the basis of a year-long series of actinometric measurements performed in the vicinity of Polish Polar Station at Hornsund, this paper presents the characteristic of the value of solar radiation incoming at the active surface, of absorbed and net radiation. The maximum intensity of the direct solar radiation was 822 Wm-2, the annual sum total of total radiation was 2611 MJm-2, whereas the mean yearly albedo was 59%. The zero-crossing of the 24-hour sums of the net radiation towards negative values occurred at the turn of September and October.

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Authors and Affiliations

Bronisław Głowicki

The cognition of other minds according to Roman Ingarden. Critical analysis

Andrzej Stępnik
Przegląd Filozoficzny. Nowa Seria | 2020 | No 4 | 301-318 | DOI: 10.24425/pfns.2020.135076
Keywords cognition of other people’s mental states epistemology R. Ingarden other minds theory of mind
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Abstract

The article is a critical analysis of Ingarden’s theory of how we learn about other people’s mental states. The author discusses arguments that have been offered by Ingarden against competing theories and highlights their shortcomings. Next, he presents Ingarden’s original theory, underlining its strengths and weaknesses. He shows that Ingarden’s theory, apart from giving an insight into the mechanisms underlying the cognition of other people’s mental states, has a limited explanatory power even if treated as a phenomenological description of a select class of cognitive situations.
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Authors and Affiliations

Andrzej Stępnik
1
ORCID: ORCID
  1. Warszawska Szkoła Reklamy, ul. S. Szolc-Rogozińskiego 3, 02-777 Warszawa

On the “Common Ruthenian” Language of "A Remedy for the Idle Human Mind" of 1607

Michael Moser
Slavia Orientalis | 2020 | vol. LXIX | No 2 | 301-318 | DOI: 10.24425/slo.2020.133663
Keywords Lěkarstvo na ospalyj oumyslъ čolověcїј Demian Nalyvajko Middle Ruthenian (Ukrainian) language Prosta mova (Middle) Ukrainian (Ruthenian) orthography phonetics morphology
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Abstract

The study analyzes the Ruthenian language of a remarkable bilingual print that appeared in the important Orthodox cultural center Ostrih in Church Slavonic and in Ruthenian “prosta mova” (“common language”) in 1607. It offers a critical evaluation of earlier studies and adds several new observations and theses.

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Authors and Affiliations

Michael Moser
ORCID: ORCID

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