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AN APPROXIMATE ANALYTICAL SOLUTION FOR ONE-DIMENSIONAL IMBIBITION PROBLEM IN LOW-PERMEABILITY POROUS MEDIA

Volume 23, Issue 7, 2020, pp. 683-694
DOI: 10.1615/JPorMedia.2020033427
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ABSTRACT

Much attention has been given to the simulation of naturally fractured reservoirs in the recent literature. The most prevalent approach is a dual-porosity formulation, in which theoretical or empirical transfer functions are employed to account for the fracture/matrix flow. The accuracy of the transfer function is important for predicting the oil or gas production in naturally fractured reservoirs. For incompressible fluids, the transfer process is mainly dominated by imbibition due to the capillary pressure difference. For the oil-water two-phase imbibition process, the profiles of the saturation distributions before and after the water flooding frontier reaches the matrix inner boundary are different. This paper aims to estimate the transfer flux during the whole imbibition process via an analytical method. In the early time stage of imbibition process, the self-similar analytic solution of the corresponding one-dimensional dimensionless equation is employed. In the late time stage, an advanced approximate analytical solution is proposed, where the effect of the two-phase generalized viscosity ratio M is considered and described by an additional parameter g with its recommended value being 1 + [M (M + 1)]-1. Numerical tests show that the proposed solution is more accurate than the other existing ones. In practice, it can be used to calculate the matrix-fracture transfer flux in a dual-porosity model.

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CITED BY
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  2. Li Binglin, Su Yuliang, Lu Mingjing, Li Lei, Study of Imbibition Effect Using Temporal-Scale Analysis of Two-Phase Flow in a Tight Reservoir, Energy & Fuels, 36, 4, 2022. Crossref

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