«Equipment and technologies for oil and gas complex»

Application of interacting nonlinear wave processes in the oil industry

UDC: 622.276
DOI: 10.33285/1999-6934-2023-2(134)-7-11

Authors:

¹ Azerbaijan State University of Oil and Industry, Baku, Azerbaijan

Keywords: stability, soliton systems, wave equation, stability of soliton systems, Korteweg – de Vries equation (kdv), nonlinear Schrödinger equation (NLS), entropy

Annotation:

The article, in the analytical-numerical aspect, considers the problem of stability of interacting wave processes in the oil industry. In terms of the Tsallis – Lesche theory, a method of stability estimation is demonstrated on the example of Korteweg – de Vries (kdv) – nonlinear Schrödinger aquation (NLS) nonlinear systems; transformation of wave and oscillatory movements in oil reservoirs into the movements of liquid (oil or water) and solid inclusions. A recognition method is also considered, which can be considered in the context of a soliton signal recognition in the optical systems of an oil and gas information transmission complex (analysis of pulses and their spectrum at the output of the fiber with a periodic change of dispersion). A mathematical model of the interacting systems stability in conditions of natural mutual evolution of the wave functions of the system individual elements is presented. The union of two equations is applied, in the context of modeling the interaction of long and short waves. For the first time, in terms of Tsallisa – Lesche, an assessment of stability is given for the case of independent nonlinear wave heterogeneous systems in the oil industry.

Bibliography:

1. Volnovoe uravnenie. – URL: https://ru.wikipedia.org/wiki/Волновое_уравнение
2. Uravnenie Kortevega – de Vriza. – URL: https://ru.wikipedia.org/wiki/Уравнение_Кортевега_—_де_Вриза
3. Nelineynoe uravnenie Shredingera. – URL: https://ru.wikipedia.org/wiki/Нелинейное_уравнение_Шрёдингера
4. Chuangye Liu, Nghhiem V. Nguyen. On the (in) validity of the NLS-KdV system in the study of water waves. – 2016. – URL: https://arxiv.org/pdf/1604.08559.pdf
5. Abe S. Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: A basis for q-exponential distributions // Physical Review E. – Vol. 66, Issue 4. – DOI: 10.1103/PhysRevE.66.046134
6. Mamedov R.K., Aliev T.Ch., Mustafaeva N.P. Kontrol' polozheniya 3D-ob"ekta v gibkikh avtomatizirovannykh proizvodstvakh // Pribory i sistemy. Upravlenie, kontrol', diagnostika. – 2016. – № 6. – S. 8–10.
7. Blinkov O.G., Anisimova S.E., Serikov D.Yu. Osobennosti razvitiya innovatsionnoy deyatel'nosti na predpriyatiyakh neftegazovogo mashinostroeniya // Oborudovanie i tekhnologii dlya neftegazovogo kompleksa. – 2019. – № 6(114). – S. 5–8. – DOI: 10.33285/1999-6934-2019-6(114)-5-8
8. Nazarova L.N., Pyatibratov P.V. Sovershenstvovanie tekhnologii zavodneniya kak metod upravleniya razrabotkoy i uvelicheniya nefteotdachi // Oborudovanie i tekhnologii dlya neftegazovogo kompleksa. – 2021. – № 1(121). – S. 46–54. – DOI: 10.33285/1999-6934-2021-1(121)-46-54
9. Martynov A.I., Khalikov R.R., Zav'yalov A.P. Metody i tekhnologii povysheniya effektivnosti diagnosticheskogo obsluzhivaniya ob"ektov dobychi gaza // Oborudovanie i tekhnologii dlya neftegazovogo kompleksa. – 2019. – № 2(110). – S. 49–53. – DOI: 10.33285/1999-6934-2019-2(110)-49-53