A computational model of a vertical well with waterflooding fracturing for pressure transient analysis
- Authors: Maykov D.N.1,2, Isupov S.V.1, Makarov S.S.2
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Affiliations:
- SIAM MASTER Ltd
- Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences
- Issue: Vol 29, No 1 (2025)
- Pages: 91-108
- Section: Mathematical Modeling, Numerical Methods and Software Complexes
- URL: https://journal-vniispk.ru/1991-8615/article/view/311040
- DOI: https://doi.org/10.14498/vsgtu2080
- EDN: https://elibrary.ru/AMYRIA
- ID: 311040
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Abstract
A new computational model for a vertical well with waterflooding fracturing is presented, which accounts for changes in the fracture half-length during the interpretation of pressure transient analysis (PTA) parameters. The model is based on a numerical algorithm derived from an analytical solution, utilizing a proposed relationship between the fracture half-length, process time, and its geometric dimensions. This functional dependence is developed using available PTA data.
The model employs the infinite-conductivity fracture equation and the superposition principle to describe changes in fracture geometry. The superposition principle is implemented through a series of activations and deactivations of fictitious wells with varying fracture half-lengths, where each well operates for a specific time interval before being shut down.
It is demonstrated that the change in fracture half-length during the closure stage follows a functional dependence on the initial and final fracture half-lengths, as well as the well operation time. The results obtained from the proposed model, incorporating the fracture half-length dependence function, show good agreement with experimental data when calculating pressure in a well with waterflooding fracturing.
A numerical analysis of the vertical well model with waterflooding fracturing is conducted using the developed algorithm. The influence of the final fracture half-length and the duration of fracture closure on pressure changes and the pressure derivative in the well is established. The use of the proposed fracture half-length dependence in calculating well operating conditions is shown to be justified. The application of this model allows for a more accurate description of parameter changes during PTA interpretation in wells with fractures of variable length.
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##article.viewOnOriginalSite##About the authors
Dmitriy N. Maykov
SIAM MASTER Ltd; Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences
Author for correspondence.
Email: dmaykov@integra.ru
ORCID iD: 0000-0002-6526-4870
https://www.mathnet.ru/person180418
Leading Specialist1, Junior Researcher2
Russian Federation, 634003, Tomsk, Belaya st., 3; 426067, Izhevsk, T. Baramzina st., 34Sergey V. Isupov
SIAM MASTER Ltd
Email: svisupov@integra.ru
ORCID iD: 0009-0006-5599-4366
https://www.mathnet.ru/person227480
Head of the Automation Dept1
Russian Federation, 634003, Tomsk, Belaya st., 3Sergey S. Makarov
Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences
Email: ssmak15@mail.ru
ORCID iD: 0000-0003-1500-6950
https://www.mathnet.ru/person54490
Doctor of Engineering Science; Senior Researcher2
Russian Federation, 426067, Izhevsk, T. Baramzina st., 34References
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