The combined approach to obtain approximate analytical solution of instability phenomenon arising in secondary oil recovery process

• Published in: Computational & applied mathematics Vol. 37; no. 3; pp. 3593 - 3607
• Main Authors: Shah, Kunjan, Singh, Twinkle
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.07.2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Integral transforms; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Nonlinear differential equations; Oil recovery; Partial differential equations; Recovering; Stability; Stability analysis; 65R10; 58B05; Secondary oil recovery process; Instability phenomenon; 76XX; 35Q35; Homotopy perturbation method; New integral transform
• ISSN: 0101-8205; 2238-3603; 1807-0302
• DOI: 10.1007/s40314-017-0534-x

Instability phenomenon mainly occurs in secondary oil recovery process due to viscosity difference of water and oil. Mathematical modeling of this phenomenon yields the non-linear partial differential equation. The homotopy perturbation new integral transform method has been proposed to solve this non-linear partial differential equation subject to appropriate initial and boundary conditions. It is concluded that the saturation of injected water S w ( X , T ) is increasing during instability phenomenon, when length of fingers(perturbance) and time increases.