Counter-current Imbibition Phenomenon Research Articles

Study of imbibition phenomenon in homogeneous porous medium model for oil recovery with temporal-fractional approach

In this article, the phenomenon of countercurrent imbibition in a specific displacement method occurs within a dipping homogeneous porous medium. This phenomenon plays a vital role in the process of oil recovery, which motivates our analysis. To overcome the difficulties associated with the nonlinear partial differential equation governing the countercurrent imbibition phenomenon, we have been using two distinct methods: the natural transform decomposition method and the variational iteration transform method with their convergence analysis for solutions. These techniques give different perspectives and enable us to obtain approximate solutions. Notably, both the proposed methods demonstrate the potential for substantial production of oil during the secondary oil recovery process in the petroleum industry. The obtained results by the proposed methods show the efficiency in optimizing the oil recovery rate.

SOLUTION OF COUNTER-CURRENT IMBIBITION PHENOMENON IN FLUID FLOW THROUGH INCLINED POROUS MEDIA BY REDUCED DIFFERENTIAL TRANSFORM METHOD

This study presents the mathematical model of the counter-current imbibition phenomenon that occurs through inclined homogeneous and heterogeneous porous media. The effect of relative permeability, capillarity, and heterogeneity of porous materials such as glass beads, touchet silt loam, and fragmented mixture on the saturation rate of a reservoir is investigated and discussed. A variety of different types of sand have been considered for various lengths of time and distances in the current model in order to compare saturation levels between homogeneous and heterogeneous porous media. The reduced differential transform method (RDTM) is used to obtain an approximate analytical solution to the proposed model. The findings, illustrated both numerically and graphically, are presented for the distance and time variables.

Modelling of counter current imbibition phenomenon in two-phase fluid flows through fractured heterogeneous porous media under the effect of magnetic field

In this paper, the counter-current imbibition phenomenon is discussed in a fractured heterogeneous porous medium under the effect of magnetic field due to the presence of magnetic fluid particles in injected fluids as well as the effects of inclination, capillarity, relative permeability and the viscosity variation of native fluids on saturation rate and on the recovery rate are considered. The homotopy analysis method is used to derive an expression for finding the saturation profiles and to study the recovery rate of the reservoir with some interesting choices of parameters.

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

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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> =-V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> is satisfied by the viscosities of oil and water. In this article, 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.

Approximate solution of imbibition phenomenon arising in heterogeneous porous media by optimal homotopy analysis method

This paper deals with approximate homotopy series solution of imbibition phenomenon occurring in multiphase flow during the secondary oil recovery process. In heterogeneous porous media, the geometry of pores is irregular while in homogeneous porous media, the geometry of pores is uniformly same. The comparative study of counter-current imbibition phenomenon in heterogeneous and homogeneous porous medium has been also discussed. The governing partial differential equation obtained by mathematical formation of imbibition phenomenon has been solved by the optimal homotopy analysis method. The numerical as well as graphical interpretation of the solution have been given.

Effect of magnetic field on imbibition phenomenon in fluid flow through fractured porous media with different porous material

Abstract In this paper, the counter-current Imbibition phenomenon is considered in a fractured heterogeneous porous medium with the consideration of different porous materials like fine sand, volcanic sand and glass beads and magnetic field effect. The Homotopy analysis method is used here to derive an expression for finding the saturation profiles in a fractured heterogeneous porous medium with and without considering the magnetic field effect. Simulation results are developed for the saturation profiles to study the effect of inclination and the viscosity variation of native fluids on the saturation rate and the recovery rate of the reservoir with some interesting choices of parameters.

Effect of Viscous Fluid on the Counter-Current Imbibition Phenomenon in Two-Phase Fluid Flow Through Heterogeneous Porous Media with Magnetic Field

In this paper, the counter-current imbibition phenomenon is discussed in a heterogeneous porous medium with the consideration of magnetic field effects due to the presence of magnetic fluid particles in injected fluids. An advanced analytical approximation method, i.e., homotopy analysis method is used to derive an expression for finding the saturation profiles with and without considering the magnetic field effect with the choices of different parameters. Simulation results are developed to study the effects of different parameters on saturation rate and on recovery rate of the reservoir.

Simulation of counter-current imbibition phenomenon in a double phase flow through fracture porous medium with capillary pressure

Abstract In this paper, the counter-current imbibition phenomenon in a fracture porous media is studied 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.

Simulation of Counter-Current Imbibition Phenomenon with Corey’s Model in Double Phase Flow Through Heterogeneous Porous Medium with Capillary Pressure

In this paper, the counter-current imbibition phenomena with gravity, inclination effect and with Corey’s model in heterogeneous porous media is discussed and Adomian decomposition method is applied to find the saturation rate of wetting phase and the recovery rate for both medium. Finally a simulation result is developed to study the saturation and recovery rate of the oil reservoir with dimensionless time for some interesting choices of parametric data with gravity and inclination effect. This problem has a great importance in oil recovery process.

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

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.

A homotopy series solution to a nonlinear partial differential equation arising from a mathematical model of the counter-current imbibition phenomenon in a heterogeneous porous medium

The mathematical model describing the counter-current imbibition phenomenon in a heterogeneous porous medium gives rise to a non-linear partial differential equation. This equation has been solved using ​homotopy analysis methods together with appropriate boundary and initial conditions. The solution represents the saturation of injected water during counter-current imbibition in a secondary oil recovery process, when water is injected. This saturation of injected ​water increases as the distance, X, from the imbibition phase ​increases, for a given time T>0. It is also deduced that the saturation of injected water in a homogeneous porous matrix is higher than the saturation of injected water in a heterogeneous porous matrix for the same distance X and time T>0. The numerical and graphical presentation of the saturation of injected water in heterogeneous as well as homogeneous porous ​matrices for distance X and time T>0 are obtained ​in Maple.

Approximate analytical study of counter-current imbibition phenomenon in a heterogeneous porous media

Approximate analytical study of counter-current imbibition phenomenon in a heterogeneous porous media