Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction
We consider the boundary value problem, where the motion of the object is described by the two-dimensional linear system of partial differential equations of hyperbolic type where a discontinuity is at a point within the interval that defines the phase coordinate x. Using the method of series and La...
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| Дата: | 2016 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2016
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/140549 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction / F.A. Aliev, N.A. Aliev, A.P. Guliev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 2. — С. 101-112. — Бібліогр.: 27 назв. — англ. |
Репозитарії
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irk-123456789-1405492018-07-11T01:23:06Z Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction Aliev, F.A. Aliev, N.A. Guliev, A.P. We consider the boundary value problem, where the motion of the object is described by the two-dimensional linear system of partial differential equations of hyperbolic type where a discontinuity is at a point within the interval that defines the phase coordinate x. Using the method of series and Laplace transformation in time t (time-frequency method), an analytical solution is found for the determination of debit Q(2l, t) and pressure P(2l, t), which can be effective in the calculation of the coefficient of hydraulic resistance in the lift at oil extraction by gas lift method where l is the well depth. For the case where the boundary functions are of exponential form, the formulas for P(2l, t) and Q(2l, t) depending only on t are obtained. It is shown that at constant boundary functions, these formulas allow us to determine the coefficient of hydraulic resistance in the lift of gas lift wells, which determines the change in the dynamics of pollution. 2016 Article Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction / F.A. Aliev, N.A. Aliev, A.P. Guliev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 2. — С. 101-112. — Бібліогр.: 27 назв. — англ. 1812-9471 DOI: doi.org/10.15407/mag12.02.101 Mathematics Subject Classification 2000: 65M38, 35L02, 35L40, 58J45, 58J90 http://dspace.nbuv.gov.ua/handle/123456789/140549 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider the boundary value problem, where the motion of the object is described by the two-dimensional linear system of partial differential equations of hyperbolic type where a discontinuity is at a point within the interval that defines the phase coordinate x. Using the method of series and Laplace transformation in time t (time-frequency method), an analytical solution is found for the determination of debit Q(2l, t) and pressure P(2l, t), which can be effective in the calculation of the coefficient of hydraulic resistance in the lift at oil extraction by gas lift method where l is the well depth. For the case where the boundary functions are of exponential form, the formulas for P(2l, t) and Q(2l, t) depending only on t are obtained. It is shown that at constant boundary functions, these formulas allow us to determine the coefficient of hydraulic resistance in the lift of gas lift wells, which determines the change in the dynamics of pollution. |
| format |
Article |
| author |
Aliev, F.A. Aliev, N.A. Guliev, A.P. |
| spellingShingle |
Aliev, F.A. Aliev, N.A. Guliev, A.P. Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction Журнал математической физики, анализа, геометрии |
| author_facet |
Aliev, F.A. Aliev, N.A. Guliev, A.P. |
| author_sort |
Aliev, F.A. |
| title |
Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction |
| title_short |
Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction |
| title_full |
Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction |
| title_fullStr |
Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction |
| title_full_unstemmed |
Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction |
| title_sort |
time frequency method of solving one boundary value problem for a hyperbolic system and its application to the oil extraction |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/140549 |
| citation_txt |
Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction / F.A. Aliev, N.A. Aliev, A.P. Guliev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 2. — С. 101-112. — Бібліогр.: 27 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
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2023-10-18T21:22:54Z |
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