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TRAVELING WAVE ANALYSIS OF COCURRENT IMBIBITION IN POROUS MEDIA

Volume 17, Issue 3, 2014, pp. 185-195
DOI: 10.1615/JPorMedia.v17.i3.10
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ABSTRACT

Spontaneous imbibition plays a very significant role in oil recovery during water flooding, steam injection, water-alternating-gas, and production from petroleum reservoirs with natural active aquifer. This phenomenon may involve cocurrent and countercurrent flow of oil and water, jointly or separately, depending on the imposed boundary condition of the matrix block. These modes of imbibition are completely different in the rate and extent of oil recovery and manner of saturation distribution within the porous matrix block. Unfortunately, the majority of numerical, theoretical, and experimental imbibition studies have concentrated on the countercurrent mode of the imbibition process. So, the main focus of this work is on cocurrent imbibitions, which has not received much attention in the previous studies. An analytical solution is presented in this article for linear, one-dimensional, cocurrent imbibition of a wetting phase (water) into a porous medium (reservoir rock) to expel a nonwetting phase (oil) in the same direction. The robust approach of traveling wave solution is employed to solve a generalized unsteady saturation diffusion equation and analytical solution is provided in a closed form. Although the analytical solution is developed for water imbibition into petroleum reservoirs, it is applicable to every liquid−liquid and gas−liquid system with broad application to analysis of flow in geothermal reservoirs, hydrology, soil science, etc. The newly proposed solution has several advantages over the existing ones. The main advantage is that it does not require any simplifying assumptions, discretization, linearization, transformation, self-similarity or perturbation assumption, etc. Fortunately, this solution has the advantage of describing the entire imbibition time including unsteady, late-transient, and pseudo-steady-state periods. Additionally, despite the previous works, the outcome of this paper is not restricted to special forms of saturation functions and capillary diffusion coefficient (e.g., linear). Eventually, the benefit of knowing water saturation profile in the matrix block is utilized to calculate average water saturation and matrix-fracture transfer function.

CITED BY
  1. Hamidpour Esmaeil, Mirzaei-Paiaman Abouzar, Masihi Mohsen, Harimi Behrouz, Experimental study of some important factors on nonwetting phase recovery by cocurrent spontaneous imbibition, Journal of Natural Gas Science and Engineering, 27, 2015. Crossref

  2. Saboorian-Jooybari Hadi, Analytical Estimation of Water-Oil Relative Permeabilities through Fractures, Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, 71, 3, 2016. Crossref

  3. Saboorian-Jooybari Hadi, Pourafshary Peyman, Significance of non-Darcy flow effect in fractured tight reservoirs, Journal of Natural Gas Science and Engineering, 24, 2015. Crossref

  4. Saboorian-Jooybari Hadi , Abeyat Ehsan , Derivation of New Analytical Expressions for Calculation of Gas-Liquid Relative Permeabilities through Fractures-Part I: Incompressible Flow, All Days, 2015. Crossref

  5. Saboorian-Jooybari Hadi, New analytical formulas for prediction of gas–liquid relative permeabilities through fractures – Part I: Incompressible flow, Journal of Natural Gas Science and Engineering, 30, 2016. Crossref

  6. Mirzaei-Paiaman Abouzar, Saboorian-Jooybari Hadi, Masihi Mohsen, Incorporation of viscosity scaling group into analysis of MPMS index for laboratory characterization of wettability of reservoir rocks, Journal of Petroleum Exploration and Production Technology, 7, 1, 2017. Crossref

  7. Mirzaei-Paiaman A., Kord S., Hamidpour E., Mohammadzadeh O., Scaling one- and multi-dimensional co-current spontaneous imbibition processes in fractured reservoirs, Fuel, 196, 2017. Crossref

  8. Aghashahi Ardestani Erfan, Davarpanah Afshin, Zargar Ghasem, Mirshekari Behnam, Mathematical modeling of formation damage effect during underbalanced drilling operations, Modeling Earth Systems and Environment, 5, 4, 2019. Crossref

  9. Aghashahi Ardestani E., Davarpanah A., Mirshekari B., An analytical approach to investigate formation damage caused by underbalanced drilling performances, International Journal of Energy and Water Resources, 3, 4, 2019. Crossref

  10. Liu Qiang, Song Rui, Liu Jianjun, Pei Guihong, Lei Yun, Mass transfer model of fracture-controlled matrix unit: Model derivation and experimental verification based on fractal theory and micro-CT scanning technology, Energy Reports, 6, 2020. Crossref

  11. Wang Yuejie, Liu Huiqing, Li Yu, Wang Qing, Numerical Simulation of Spontaneous Imbibition under Different Boundary Conditions in Tight Reservoirs, ACS Omega, 6, 33, 2021. Crossref

  12. Saboorian-Jooybari H.. , Dejam M.. , Chen Z.. , Pourafshary P.. , Fracture Identification and Comprehensive Evaluation of the Parameters by Dual Laterolog Data, Day 2 Tue, January 27, 2015, 2015. Crossref

  13. Saboorian-Jooybari Hadi , Pourafshary Peyman , Non-Darcy Flow Effect in Fractured Tight Reservoirs: How Significant Is It at Low Flow Rates and Away from Wellbores?, Day 2 Tue, January 27, 2015, 2015. Crossref

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