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

## Authors

• Aruna Sharma Department of Mathematics, Mehsana Urban Institute of Sciences, Ganpat University, Kherva 384012, Mehsana, Gujarat, India
• Amit K. Parikh Mehsana Urban Institute of Sciences, Ganpat University, Kherva 384012, Mehsana, Gujarat, India

## Keywords:

Imbibition phenomenon, Hybrid Differential Transform Finite Difference Method (HDTFDM), Multistep differential transform method, Counter-current

## Abstract

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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18-10-2023
CITATION

## How to Cite

Sharma, A., & Parikh, A. K. (2023). Semi Analytic-Numerical Solution of Imbibition Phenomenon in Homogeneous Porous Medium Using Hybrid Differential Transform Finite Difference Method. Communications in Mathematics and Applications, 14(3), 1199–1213. https://doi.org/10.26713/cma.v14i3.2394

Research Article