MATHEMATICAL SOLUTION OF FINGERING PHENOMENON IN VERTICAL DOWNWARD DIRECTION THROUGH HETEROGENEOUS POROUS MEDIUM

2021 ◽  
Vol 10 (1) ◽  
pp. 483-496
Author(s):  
D.A. Shah ◽  
A.K. Parikh
Keyword(s):  
Porous Medium ◽  
Oil Recovery ◽  
Analytic Solution ◽  
Variational Iteration Method ◽  
Approximate Analytic Solution ◽  
Order Partial Differential Equation ◽  
Heterogeneous Porous Medium ◽  
Fingering Instability ◽  
Oil Flow ◽  
Secondary Oil Recovery

Present study explores the Fingering (Instability) phenomenon's mathematical model that ensues during the process of secondary oil recovery where two not miscible fluids (water and oil) flow within a heterogeneous porous medium as water is injected vertically downwards. Variational iteration method with proper initial and boundary conditions is being used to determine approximate analytic solution for governing nonlinear second order partial differential equation. Whereas MATLAB is applied to acquire the solution's numerical findings and graphical representations.

scholarly journals Constant Accelerated Flow for a Third-Grade Fluid in a Porous Medium and a Rotating Frame with the Homotopy Analysis Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Zainal Abdul Aziz ◽  
Mojtaba Nazari ◽  
Faisal Salah ◽  
Dennis Ling Chuan Ching
Keyword(s):  
Porous Medium ◽  
Analytic Solution ◽  
Third Grade ◽  
Approximate Analytic Solution ◽  
Rotating Frame ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Accelerated Flow

The homotopy analysis method (HAM) is applied to obtain the approximate analytic solution of a constant accelerated flow for a third-grade fluid in a porous medium and a rotating frame. HAM is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. The approximate analytic solution for constant accelerated flow is obtained by using HAM. HAM contains the auxiliary parameterℏ, which provides us with a straightforward way to obtain the convergence region of the series solution. Graphical results are plotted and the consequences discussed. The obtained solutions clearly satisfy the governing equations and all the imposed initial and boundary conditions. Many interesting results can be obtained as the special cases of the presented analysis. The influence of the material parameters of a third-grade fluid and rotation upon the velocity field is finally deliberated.

Analysis of two-dimensional solute transport through heterogeneous porous medium

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Atul Kumar ◽  
◽  
Lav Kush Kumar ◽  
Shireen Shireen ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Two Dimensional ◽  
Heterogeneous Porous Medium

scholarly journals Computational study of enhanced oil recovery from a porous medium using nanosuspension

2021 ◽  
Vol 1867 (1) ◽  
pp. 012025
Author(s):  
D V Guzei ◽  
S V Ivanova ◽  
D V Platonov ◽  
A I Pryazhnikov
Keyword(s):  
Porous Medium ◽  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Computational Study
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