scholarly journals Analytical Treatment and Convergence of the Adomian Decomposition Method for Instability Phenomena Arising during Oil Recovery Process

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ramakanta Meher ◽  
Srikanta K. Meher
Keyword(s):  
Porous Medium ◽  
Oil Recovery ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Porous Medium Equation ◽  
Recovery Process ◽  
Analytical Treatment ◽  
Medium Equation ◽  
Double Phase ◽  
Adomian Decomposition

An abstract result is proved for the convergence of Adomian decomposition method for partial differential equations that model porous medium equation. Moreover, we prove that this decomposition scheme applied to a porous medium equation arising in instability phenomena in double phase flow through porous media is convergent in a suitable Hilbert space. Furthermore, this technique is utilized to find closed-form solutions for the problem under consideration.

scholarly journals Study on Approximate Analytical Method with Its Application Arising in Fluid Flow

2021 ◽  
Author(s):  
Twinkle R. Singh
Keyword(s):  
Differential Equation ◽  
Oil Recovery ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equation ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Recovery Process ◽  
Adomian Decomposition ◽  
Independent Variable ◽  
Counter Current

This chapter is about the, Variational iteration method (VIM); Adomian decomposition method and its modification has been applied to solve nonlinear partial differential equation of imbibition phenomenon in oil recovery process. The important condition of counter-current imbibition phenomenon as v i = − v n , has been considered here main aim, here is to determine the saturation of injected fluid S i x t during oil recovery process which is a function of distance ξ and time θ , therefore saturation S i is chosen as a dependent variable while x and t are chosen as independent variable. The solution of the phenomenon has been found by VIM, ADM and Laplace Adomian decomposition method (LADM). The effectiveness of our method is illustrated by different numerical.

Adomian decomposition method to magnetohydrodynamics natural convection heat generating/absorbing slip flow through a porous medium

2019 ◽  
Vol 15 (3) ◽  
pp. 673-684 ◽  
Author(s):  
Abiodun O. Ajibade ◽  
Jeremiah Jerry Gambo
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Decomposition Method ◽  
Slip Flow ◽  
Adomian Decomposition Method ◽  
Convection Heat ◽  
Content Type ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Effect Parameter

Purpose The purpose of this paper is to analyze magnetohydrodynamics fully developed natural convection heat-generating/absorbing slip flow through a porous medium. Adomian decomposition method was applied to find the solutions to the problem. Design/methodology/approach In this study, Adomian decomposition method was used. Findings Results show that heat generation parameter enhanced the temperature and velocity of the fluid in the annulus. Moreover, slip effect parameter increases the velocity of the fluid. Originality/value Originality is in the application of Adomian decomposition method which allowed the slip at interface.

scholarly journals Mathematical Analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Samuel O. Adesanya ◽  
J. A. Falade ◽  
J. C. Ukaegbu ◽  
K. S. Adekeye
Keyword(s):  
Porous Medium ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Temperature Fields ◽  
Bejan Number ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Velocity And Temperature Fields ◽  
Fluid Parameters

An investigation has been carried out to study entropy generation in a viscous, incompressible, and reactive fluid flowing steadily through a channel with porous materials. Approximate solutions for both velocity and temperature fields are obtained by using a rapidly convergent Adomian decomposition method (ADM). These solutions are then used to determine the heat irreversibility and Bejan number of the problem. Variations of other important fluid parameters are conducted, presented graphically, and discussed.

scholarly journals Influence of Soret, Hall and Joule heating effects on mixed convection flow saturated porous medium in a vertical channel by Adomian Decomposition Method

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Ch. Ram Reddy ◽  
K. Kaladhar ◽  
D. Srinivasacharya ◽  
T. Pradeepa
Keyword(s):  
Porous Medium ◽  
Joule Heating ◽  
Decomposition Method ◽  
Saturated Porous Medium ◽  
Adomian Decomposition Method ◽  
Vertical Channel ◽  
Convective Transport ◽  
Convection Flow ◽  
Similarity Transformations ◽  
Adomian Decomposition

Abstract This paper analyzes the laminar, incompressible mixed convective transport inside vertical channel in an electrically conducting fluid saturated porous medium. In addition, this model incorporates the combined effects of Soret, Hall current and Joule heating. The nonlinear governing equations and their related boundary conditions are initially cast into a dimensionless form using suitable similarity transformations and hence solved using Adomian Decomposition Method (ADM). In order to explore the influence of various parameters on fluid flow properties, quantitative analysis is exhibited graphically and shown in tabular form.

Modelling of Imbibition Phenomena in Fluid Flow through Heterogeneous Inclined Porous Media with different porous materials

2017 ◽  
Vol 6 (4) ◽  
Author(s):  
Hardik S. Patel ◽  
Ramakanta Meher
Keyword(s):  
Porous Media ◽  
Porous Materials ◽  
Oil Recovery ◽  
Recovery Rate ◽  
Adomian Decomposition Method ◽  
Recovery Process ◽  
Fine Sand ◽  
Heterogeneous Porous Media ◽  
Adomian Decomposition ◽  
Flow Through

AbstractIn this paper, the counter - current imbibition phenomenon is discussed in an inclined heterogeneous porous media with the consideration of two types of porous materials like volcanic sand and fine sand. Adomian decomposition method is applied to find the saturation of wetting phase and the recovery rate of the reservoir. Finally, a simulation result is developed to study the saturation of wetting phase and the optimum recovery rate of reservoir with the choices of some interesting parametric values. This problem has a great importance in the field of oil recovery process.

scholarly journals Spectral Adomian Decomposition Method for the MHD Three-Dimensional Flow due to a Stretching Sheet in a Porous Medium

2021 ◽  
pp. 87-96
Author(s):  
Yassir Daoud ◽  
Mohammed Abdalbagi ◽  
Ahmed A. Khidir
Keyword(s):  
Porous Medium ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Adomian Decomposition Method ◽  
Physical Parameters ◽  
Three Dimensional Flow ◽  
Adomian Decomposition ◽  
Steady Laminar

An approximate solution is obtained of the steady, laminar three-dimensional ow for an incompressible, viscous uid past a stretching sheet using the Spectral Adomian Decomposition Method (SADM). The governing partial dierential equations are transformed into ordinary dierential equations using suitable transformations. A comparison between the obtained results with solutions obtained early in the literature and the numerical solution has been made to testthe validity, accuracy and convergence of the SADM. The eects of physical parameters on the velocity are determined and discussed.

Modelling of imbibition phenomena in two-phase fluid flow through fractured porous media

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Hardik S. Patel ◽  
Ramakanta Meher
Keyword(s):  
Porous Media ◽  
Oil Recovery ◽  
Recovery Rate ◽  
Adomian Decomposition Method ◽  
Recovery Process ◽  
Porous Matrix ◽  
Dimensionless Time ◽  
Two Phase ◽  
Adomian Decomposition ◽  
Phase Fluid

AbstractIn this paper, the counter-current imbibition phenomenon in two phase fluid through fracture porous media is discussed and Adomian decomposition method is applied to find the saturation of wetting phase and the recovery rate of the reservoir. A simulation result is developed for the saturation of wetting phase in fracture matrix and in porous matrix for some interesting choices of parametric value to study the recovery rate of the oil reservoir with dimensionless time. This problem has a great importance in the oil recovery process.

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