Time Frequency Method of Solving One Boundary Value Problem for a Hyperbolic System and Its Application to the Oil Extraction
DOI:
https://doi.org/10.15407/mag12.02.101Анотація
Розглянуто граничну задачу, коли рух об'єкта описується двовимiрною лiнiйною системою диференцiальних рiвнянь в частинних похiдних гiперболiчного типу, де всерединi iнтервалу, що визначає фазову координату x, є розрив в однiй точцi. За допомогою методу рядiв i перетворення Лапласа за часом t (частотно-часовий метод) надано аналiтичний розв'язок для визначення дебiту Q(2l, t) i тиску P(2l, t), який може бути ефективним при обчисленнi коефiцiєнта гiдравлiчного опору в пiдйомнику при видобутку нафти газлiфтним способом, де l є глибина свердловини. Для випадку, коли граничнi функцiї є експоненцiального виду, отримано формули для P(2l, t) i Q(2l, t) виду, що залежить тiльки вiд t. Показано, що при постiйних граничних функцiях цi формули дозволяють визначити коефiцiєнт гiдравлiчного опору в пiдйомнику газлiфтної свердловини, який визначає змiну динамiки забруднення.
Mathematics Subject Classification: 65M38, 35L02, 35L40, 58J45, 58J90.
Ключові слова:
гіперболічне рівняння, крайові задачі, метод рядів, перетворення Лапласа, частотно-часовий метод, газліфт, коефіцієнт гідравлічного опоруПосилання
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