Mathematical modeling and analysis of Fingero-Imbibition phenomenon in vertical downward cylindrical homogeneous porous matrix

Parikh, A. K.; Mehta, M. N.; Pradhan, V. H.

doi:10.1109/nuicone.2013.6780207

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…Each side of the cylinder is bounded by impermeable surfaces expect at one end of the cylinder, which is labeled as imbibition surface (x = 0). This end is exposed to an adjacent formation of the injected fluid (I) as water [45]. Since water preferentially wets the medium, so such arrangements give rise to the linear counter-current imbibition, which is spontaneous and linear flow of wetting phase of fluid (water) into the medium and counter flow of the resident fluid (oil) from the medium.…”

Section: Statement Of the Problemmentioning

confidence: 99%

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Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

et al. 2020

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The flow of fluids in multi-phase porous media results due to many interesting natural phenomena. The counter-current water imbibition phenomena, that occur during oil extraction through a cylindrical well is an interesting problem in petroleum engineering. During the secondary oil recovery process, water is injected into a porous media having heterogenous and homogenous characteristics. Due to the difference in viscosities of fluids in oil wells, the counter-current imbibition phenomenon occurs. At that moment, the imbibition equation V i = −V n is satisfied by the viscosities of oil and water. In this paper, we have analyzed the governing mathematical model of the imbibition phenomenon occurring during the secondary oil recovery process. A new soft computing algorithm is designed and adapted to analyze the mathematical model of dual-phase flow in detail. Weighted Legendre polynomials based artificial neural networks are hybridized with an efficient global optimizer the Whale Optimization Algorithm (WOA) and a local optimizer the Nelder-Mead algorithm. It is established, that our algorithm LeNN-WOA-NM is efficient and reliable in calculating high-quality solutions in less time. We have compared our experimental outcome with state-of-the-art results. The quality of our solutions is judged based on values of absolute errors, MAD, TIC, and ENSE. It is obvious that LeNN-WOA-NM algorithm can solve real application problems efficiently and accurately. INDEX TERMS Counter-current imbibition phenomena, homogeneous porous media, heterogeneous porous media, capillary pressure, soft computing algorithm, weighted Legendre neural networks, Nelder-Mead algorithm, whale optimization algorithm. I. INTRODUCTION T HIS paper models the phenomena of counter-current imbibition in the multi-phase flow of two immiscible fluids through heterogeneous and homogenous porous mediums that occurs during the secondary oil recovery process or water flooding [1]. In applied sciences, various changes occur in porous mediums having multi-phase flows of different fluids. In the past few decades, researchers are focused on studying the flows in underground petroleum reservoirs [2]. The primary recovery process includes the production of oil by simple natural decompression with no effect of external forces at wells [3]. In secondary oil recovery or water flooding process, fluids like water, polymer, steam are injected into a reservoir through injection wells located in rocks that have fluid communication with production wells. This process is called the immiscible displacement process [3].

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Section: Statement Of the Problemmentioning

confidence: 99%

“…plugging Eq (44)(45)(46) in governing ordinary differential equations. Eq (29) and Eq (36) will be converted into an equivalent algebraic system of equations that can be solved for unknown parameters ζ n , ψ n and θ n using LeNN-WOA-NM algorithm.…”

Section: Approximate Solutions and Weighted Legendre Polynomialsmentioning

confidence: 99%

Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

et al. 2020

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“…This phenomenon for homogenous porous media was studied by Alazmi and Vafai [1], Scheidegger and Johnson [15], and Scheidegger [14]. 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].…”

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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An Approximate Solution of Fingering Phenomenon Arising in Porous Media by Successive Linearisation Method

Choksi

Singh

2018

Numerical Heat Transfer and Fluid Flow

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Mathematical modeling and analysis of Fingero-Imbibition phenomenon in vertical downward cylindrical homogeneous porous matrix

Cited by 3 publications

References 6 publications

Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

Analysis of Multi-Phase Flow Through Porous Media for Imbibition Phenomena by Using the LeNN-WOA-NM Algorithm

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

An Approximate Solution of Fingering Phenomenon Arising in Porous Media by Successive Linearisation Method

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