A Novel Fractal Model for Two-Phase Relative Permeability in Porous Media

Lei, Gang; Dong, Pingchuan; Mo, Shaoyuan; Gai, Shaohua; Wu, Zhongwei

doi:10.1142/s0218348x15500176

Cited by 18 publications

(18 citation statements)

References 37 publications

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“…It has been shown that the relative permeability curve should be a function of saturation and viscosity. 43 Therefore, the trend of relative permeability versus fluid viscosity is of theoretical significance. Figure 14 shows the significant influences of fluid viscosity ratio on the relative permeability.…”

Section: Resultsmentioning

confidence: 99%

“…And the mobile fluid flow occurs in-between the boundary layer fluid. The boundary layer saturation is also known as the immobile phase saturation which can be written as 38,43…”

Section: Theoretical Modelmentioning

confidence: 99%

“…More details about the relative permeability for each phase can be found in the work. 43 According to the proposed model, the algorithm for determination of stress-dependent oil-water relative permeability can be summarized as follows:…”

Section: Theoretical Modelmentioning

confidence: 99%

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Theoretical and Experimental Study on Stress-Dependency of Oil–water Relative Permeability in Fractal Porous Media

Lei

Dong

et al. 2018

Fractals

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The coupled flow deformation behavior in the porous media has drawn tremendous attention in various scientific and engineering fields. It is reported that the porous media will be compressed and relative permeability in porous media will be changed as the effective stress increases. However, previous studies provided contradictory evidence for the stress-dependent irreducible water saturation and stress-dependent relative permeability. Until now, appropriate stress-dependent relative permeability curve for two-phase flow through porous media remains unclear. The goal of this work was to theoretically and experimentally study the stress-dependent relative permeability. Laboratory sample flooding tests were conducted to measure two-phase relative permeability in porous media under changing effective stress, and a corresponding theoretical model of stress-dependent relative permeability was derived to interpret the experimental results. The predictions from the proposed analytical model exhibited similar variation trends as the experimental data, which verified the theoretical model. Though the results for the stress-dependent relative permeability from previous studies are different, or even opposite, our proposed model with different conditions can provide explanations to these different results. This work provides a comprehensive experimental and theoretical study of stress-dependent relative permeability in porous media, which is beneficial to accurate performance forecasts for the coupled flow deformation behavior in porous media.

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Section: Resultsmentioning

confidence: 99%

“…And the mobile fluid flow occurs in-between the boundary layer fluid. The boundary layer saturation is also known as the immobile phase saturation which can be written as 38,43…”

Section: Theoretical Modelmentioning

confidence: 99%

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Theoretical and Experimental Study on Stress-Dependency of Oil–water Relative Permeability in Fractal Porous Media

Lei

Dong

et al. 2018

Fractals

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“…In this section, the derived models are validated by comparing the calculated results to different experimental data sets. Firstly, a former model by Lei et al (2015) are selected to validate our derived relative permeability model with hydrate saturation S h = 0. Additionally, experimental results of K rw in HBS are also utilized to validate the relative permeability model in HBS.…”

Section: Validationmentioning

confidence: 99%

Stress dependent gas-water relative permeability in gas hydrates: A theoretical model

Lei

Liao

Lin

et al. 2020

Adv. Geo-Energy Res.

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Research activities are currently being conducted to study multiphase flow in hydratebearing sediments (HBS). In this study, in view of the assumption that hydrates are evenly distributed in HBS with two major hydrate-growth patterns, i.e., pore filling hydrates (PF hydrates), wall coating hydrates (WC hydrates) and a combination of the two, a theoretical relative permeability model is proposed for gas-water flow through HBS. Besides, in this proposed model, the change in pore structure (e.g., pore radius) of HBS due to effective stress is taken into account. Then, model validation is performed by comparing the predicted results from the derived model with that from the existing model and test data. By setting the value of hydrate saturation to zero, our derived model can be reducible to the existing model, which demonstrates that the existing model is a special case of our model. The results reveal that, under the same saturation, relative permeability to water K rw (or gas K rg) in PF hydrates is smaller than that in WC hydrates. Moreover, the morphological characteristics of relative permeability curve (relative permeability versus gas saturation) for WC hydrate and PF hydrate are different.

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“…When the contact angle is higher than 90 • , the surface of hydrophobic material decreases the resistance of fluid flow, and the relative permeability correspondingly increases with the contact angle. Lei et al [26] proposed a fractal model for the prediction of gas-water relative permeability in fractures. They found that increasing the complexity of pore structure (fractal dimension) would result in a decrease of water relative permeability, while the gas relative permeability has a corresponding increase with the ratio of fluid viscosity.…”

Section: Introductionmentioning

confidence: 99%

An Improved Relative Permeability Model for Gas-Water Displacement in Fractal Porous Media

Wang

et al. 2019

Water

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Many researchers have revealed that relative permeability depends on the gas-water-rock interactions and ultimately affects the fluid flow regime. However, the way that relative permeability changes with fractal porous media has been unclear so far. In this paper, an improved gas-water relative permeability model was proposed to investigate the mechanism of gas-water displacement in fractal porous media. First, this model took the complexity of pore structure, geometric correction factor, water film, and the real gas effect into account. Then, this model was compared with two classical models and verified against available experimental data. Finally, the effects of structural parameters (pore-size distribution fractal dimension and tortuosity fractal dimension) on gas-water relative permeability were investigated. It was found that the sticking water film on the surface of fracture has a negative effect on water relative permeability. The increase of geometric correction factor and the ignorance of real gas effect cause a decrease of gas relative permeability.Water 2020, 12, 27 2 of 24 relative permeability is equal to 1, which does not agree with the actual fluid flow in porous media. Subsequently, this model was further modified by many scholars. Gates and Leitz [8] integrated the relative permeability from the capillary pressure. Burdine [9] thought that the assumption of capillary parallelism was not accurate and introduced the tortuosity factor into the Purcell model. Mualem [10] proposed an integration method based on the Purcell model. For simplicity, Romm [11] developed a relative permeability model which ignored the phase interference between the gas and water phases. This model is also called the X model. Brooks and Corey [12] introduced a pore-size distribution index to modify the capillary pressure function and proposed a more generalized gas-water relative permeability model. The Brooks-Corey model has been widely used in modeling two-phase flow in complex porous media. Fourar and Lenormand [13] derived a viscous coupling model after integrating Stokes' equation and the effect of viscosity. Combined with momentum balance, viscosity, and cubic law, Chima and Geiger [14] developed a new relative permeability model. After ignoring the capillary pressure, Chima's model became a unique form of the viscous coupling model. Li et al. [15] improved Chima's model through the consideration of the influences of capillary tortuosity and irreducible water saturation on relative permeability. The above relative permeability models have made significant contributions to the prediction of two-phase flow in porous media. They also found that the relative permeability of the gas phase is more susceptible to the geometry of flow channels. However, these relative permeability models did not thoroughly consider the effects of complex pore microstructures on fluid flow.

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A Novel Fractal Model for Two-Phase Relative Permeability in Porous Media

Cited by 18 publications

References 37 publications

Theoretical and Experimental Study on Stress-Dependency of Oil–water Relative Permeability in Fractal Porous Media

Theoretical and Experimental Study on Stress-Dependency of Oil–water Relative Permeability in Fractal Porous Media

Stress dependent gas-water relative permeability in gas hydrates: A theoretical model

An Improved Relative Permeability Model for Gas-Water Displacement in Fractal Porous Media

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