Analytical Treatment and Convergence of Adomian decomposition Method for Fingero-Imbibition Phenomena Arising during Oil Recovery Process

2016 ◽  
Vol 5 (3) ◽  
pp. 303-308
Author(s):  
Ramakanta Meher ◽  
S. K. Meher
Keyword(s):  
Oil Recovery ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Recovery Process ◽  
Analytical Treatment ◽  
Adomian Decomposition

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.

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.

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.

Nonlinear singular one dimensional thermo-elasticity coupled system and double Laplace decomposition methods

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain
Keyword(s):  
Laplace Transform ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
One Dimensional ◽  
Convergence Proof ◽  
Double Laplace Transform ◽  
Adomian Decomposition

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 182-188
Author(s):  
O. González-Gaxiola ◽  
Anjan Biswas ◽  
Abdullah Kamis Alzahrani
Keyword(s):  
Numerical Simulations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Decomposition Scheme ◽  
Error Analyses ◽  
Adomian Decomposition ◽  
Log Law

AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

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