Nilesh Sonara, Dilip Joshi, Narendrasinh Desai

Modified B-Spline Collocation Solution of Countercurrent Imbibition Phenomenon with Inclined and Without Inclined in Homogeneous Porous Medium

Introduction

Modified b-spline collocation solution of countercurrent imbibition phenomenon with inclined and without inclined in homogeneous porous medium. Explore a modified B-spline collocation solution for countercurrent imbibition in homogeneous porous media during secondary oil recovery, analyzing both inclined and non-inclined conditions.

Abstract

During the process of secondary oil recovery, water is injected into the reservoir formation to displace the remaining oil. When water enters such a porous medium, countercurrent imbibition emerges along the fluid interface because of the distinct and contrasting wetting properties between water and oil. In this paper, a comprehensive and detailed numerical solution was developed and presented to accurately model and simulate the countercurrent imbibition phenomenon that takes place in homogeneous porous media. The study specifically investigates this process under both horizontal conditions and with various degrees of inclination, focusing particularly on its role and implications during the secondary oil recovery stage. The counter-current imbibition phenomenon has been extensively studied by numerous researchers from a variety of perspectives, contributing to a deeper understanding of its underlying mechanisms. To address this complex problem, we have employed the modified B-spline collocation method, which offers high accuracy and computational efficiency in solving the governing equations. All numerical results and graphical representations have been generated using MATLAB, a powerful tool for scientific computation and visualization. The findings clearly demonstrate that, for a given time, the saturation of injected water consistently increases with distance from the injection point. This trend holds true in both scenarios—porous media without inclination and those with inclination—highlighting the robustness of the observed behavior under different geometric conditions.

Review

The paper, "Modified B-Spline Collocation Solution of Countercurrent Imbibition Phenomenon with Inclined and Without Inclined in Homogeneous Porous Medium," tackles a crucial aspect of secondary oil recovery: countercurrent imbibition. The authors propose a comprehensive numerical solution using the modified B-spline collocation method to accurately model this phenomenon in homogeneous porous media, investigating its behavior under both horizontal and various inclined conditions. This work is highly relevant to petroleum engineering, as understanding and optimizing fluid displacement mechanisms in reservoir formations is paramount for maximizing oil recovery. The choice of a high-accuracy, computationally efficient numerical method suggests a rigorous approach to a complex multiphase flow problem. A significant strength of this study is its focused application of the modified B-spline collocation method to analyze countercurrent imbibition. This methodological choice offers a robust and precise tool for solving the governing equations, which is vital for accurately capturing the intricate fluid interactions driven by distinct wetting properties. The paper's novelty lies in its detailed comparison of imbibition under both horizontal and inclined conditions, thereby providing a more complete understanding of how gravitational and geometric factors influence the displacement front. The reported finding—that injected water saturation consistently increases with distance from the injection point, regardless of inclination—provides a clear and valuable insight into the progression of the imbibition front, demonstrating the robustness of the observed behavior. While the abstract provides a strong foundation, a more detailed review would benefit from the full manuscript clarifying specific aspects. For instance, the abstract could hint at the particular forms of the governing equations (e.g., Richards' equation or multiphase flow equations), the types of boundary and initial conditions employed, and the range of physical parameters (e.g., permeability, porosity, capillary pressure curves, fluid viscosities, specific inclination angles) investigated. Furthermore, comparing the modified B-spline collocation method's performance—in terms of accuracy, convergence, and computational cost—against other established numerical techniques or, ideally, experimental data, would solidify the claims of high accuracy and efficiency. Despite these points for potential elaboration, the paper presents a valuable numerical investigation into a critical reservoir phenomenon, offering promising insights for enhanced oil recovery strategies.

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