A Mathematical Model of Co-current Imbibition Phenomenon in Inclined Homogeneous Porous Medium

Patel, M. A.; Desai, N. B.

doi:10.29007/jq63

Cited by 3 publications

(8 citation statements)

References 14 publications

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“…The solution contains the convergence control parameter c 0 and the proper value of the convergence control parameter c 0 gives us the convergent homotopy series solution. The proper value of c 0 is chosen from the c 0 -curve [6,8,9,10,11,12,17,21,24]. The line segment almost parallel to horizontal axis in c 0 -curve gives us the admissible range of c 0 .…”

Section: Resultsmentioning

confidence: 99%

Homotopy Analysis Approach of Boussinesq Equation for Infiltration Phenomenon in Unsaturated Porous Medium.

Patel

Desai

2018

Math. J. Interdiscip. Sci.

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Boussinesq’s equation is one-dimensional nonlinear partial differential equation which represents the infiltration phenomenon. This equation is frequently used to study the infiltration phenomenon in unsaturated porous medium. Infiltration is the process in which the groundwater of the water reservoir has entered in the unsaturated soil through vertical permeable wall. An approximate analytical solution of nonlinear partial differential equation is presented by homotopy analysis method. The convergence of homotopy analysis solution is discussed by choosing proper value of convergence control parameter. The solution represents the height of free surface of infiltrated water.

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Section: Resultsmentioning

confidence: 99%

Homotopy Analysis Approach of Boussinesq Equation for Infiltration Phenomenon in Unsaturated Porous Medium.

Patel

Desai

2018

Math. J. Interdiscip. Sci.

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“…Generalised separable solution was used by Parikh et al [9] to solve this phenomenon in horizontal direction and it was solved by Pathak and Singh [13] in inclined homogenous porous medium. A Homotopy Series Solution in a inclined homogenous Porous Medium was studied by Patel and Desai [10]. Hybrid Differential Transform Finite Difference Method (HDTFDM) is used to solve this problem (Süngü and Demir [16]).…”

Section: Introductionmentioning

confidence: 99%

Semi Analytic-Numerical Solution of Imbibition Phenomenon in Homogeneous Porous Medium Using Hybrid Differential Transform Finite Difference Method

Sharma,

Parikh

2023

Comm. Math. Appl.

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Analysis of the counter current imbibition phenomenon in a two-phase flow in a homogeneous porous media under specific conditions is the primary goal of the current work. Imbibition is said to occur when a wetting fluid in a porous medium displaces a non-wetting fluid. The phenomena of imbibition are significant in natural and man-made systems. When oil and water form the two immiscible liquid phases, it is assumed that water is the wetting phase. The partial differential equation that governs this imbibition phenomenon is highly non-linear It is solved using the Hybrid Differential Transform Finite Difference Method (HDTFDM) which gives the solution in the form of an infinite series emphasizing the semi analytic nature of this method. The solution to this equation enables the measurement of the saturation of the injected water in a double phase flow at different distances and time. HDTFDM is a combination of the Differential Transform Method (DTM) and Finite Difference Method (FDM). The flexibility of the DTM is integrated with the efficiency of the FDM which speeds up computation compared to the conventional DTM. This approach has been discovered to be reliable and effective. Further, to overcome the shortcomings of this method for large values of time, the Multistep Differential Transform Method (MDTM) and Finite Difference Method (FDM) have been used to achieve the solution for large values of time. Using MATLAB, the numerical solution and graphical representation were obtained. The results obtained were compared with the existing results and found to be in close agreement.

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“…as the initial approximation of S i (X, T ) which satisfies boundary conditions (20) and (21). Besides we choose the auxiliary linear operator as…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…We solve equation (19) together with boundary conditions (20) and (21) using optimal homotopy analysis method.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Besides this if a phase (oil) contained in a porous medium is displaced by another phase of lesser viscosity, then instead of regular displacement of the whole front, protuberances may occur which shoot through the porous medium at relatively very great speed giving rise to the fingering phenomenon. This simultaneous occurrence of both phenomena was termed as fingero-imbibition by Verma. Many researchers have discussed this problem from different viewpoints and solved by different methods: Mishra and Verma [14], Patel, Rabari and Bhathawala [19], Shah [26], Patel and Rabari [18],Shah and Verma [27], Parikh, Mehta and Pradhan [17], Verma and Rajput [31], Verma [30], Patel and Desai [20], Desai [4], Mehta [13] etc. In this paper, we have discussed the fingero-imbibition phenomenon through homogeneous porous medium with the involvement of a layer of magnetic fluid in the injected phase.…”

Section: Introductionmentioning

confidence: 99%

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Optimal homotopy analysis solution of fingero-imbibition phenomenon in homogeneous porous medium with magnetic fluid effect

Prajapati¹,

Desai²

Kalpa Publications in Computing

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The present paper discusses the fingero-imbibition phenomenon in a double phase displacement process through homogeneous porous medium with the involvement of a layer of magnetic fluid in the injected phase. This phenomenon has much importance in petroleum technology. The nonlinear partial differential equation governing this phenomenon with appropriate boundary conditions is solved by an optimal homotopy analysis method. The convergence of the solution is decided by minimizing discrete squared residual.

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A Mathematical Model of Co-current Imbibition Phenomenon in Inclined Homogeneous Porous Medium

Cited by 3 publications

References 14 publications

Homotopy Analysis Approach of Boussinesq Equation for Infiltration Phenomenon in Unsaturated Porous Medium.

Homotopy Analysis Approach of Boussinesq Equation for Infiltration Phenomenon in Unsaturated Porous Medium.

Semi Analytic-Numerical Solution of Imbibition Phenomenon in Homogeneous Porous Medium Using Hybrid Differential Transform Finite Difference Method

Optimal homotopy analysis solution of fingero-imbibition phenomenon in homogeneous porous medium with magnetic fluid effect

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