A difference-fractal model for the permeability of fibrous porous media

Shou, Dahua; Fan, Jintu; Ding, Feng

doi:10.1016/j.physleta.2010.01.002

Cited by 70 publications

(32 citation statements)

References 34 publications

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“…Balankin et al (2006) thought that this phenomenon of wetting fluid advance in paper could be attributed to the complex time dependent due to swelling structure of paper. Fortunately, the randomness of pore sizes and the heterogeneity of natural porous media have been successfully characterized by fractal geometry such as sandstone rock (Katz and Thompson 1985), soil (Perfect and Kay 1991), artifact porous media (paper (Kopelman et al 1986;Balankin et al 2003), porous glasses (Kopelman et al 1986), porous membranes (Kopelman et al 1986), porous fabrics Shou et al 2010), and nanparticles (Xiao et al 2010a,b)). The behavior not obeying the LW equation may be explained based on the fractal nature of porous media.…”

Section: Introductionmentioning

confidence: 99%

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

2011

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In the past decades, there was considerable controversy over the LucasWashburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the L s (t) ∼ t 1/2D T law is obtained (here D T is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (D T = 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.

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Section: Introductionmentioning

confidence: 99%

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

2011

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“…1,2,4,7,8,11,13,[18][19][20] This means that the fractal theory can be used to predict the capillary pressure and water relative permeability of porous media. Besides, the pore size distribution and tortuosity of capillaries have also been proven to follow the fractal scaling laws, 2,4,8,18 i.e.…”

Section: Fractal Characteristics Of Unsaturated Porous Rocksmentioning

confidence: 99%

“…The capillary pressure (P c ) and relative permeability (k rw ) to water fluid flow in porous rocks are two key parameters to be considered in many fields including soil science, 1-3 reservoir engineering, 4-6 subsurface environmental engineering [7][8][9][10] and chemical engineering. [11][12][13][14][15] Past studies [15][16][17][18][19] have shown that the water flow processes in unsaturated porous rocks is complex and dependent on the complexity of the microstructure of rocks.…”

Section: Introductionmentioning

confidence: 99%

A Fractal Model for Water Flow Through Unsaturated Porous Rocks

et al. 2018

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In this work, considering the effect of porosity, pore size, saturation of water and tortuosity fractal dimension, an analytical model for the capillary pressure and water relative permeability is derived in unsaturated porous rocks. Besides, the formulas of calculating the capillary pressure and water relative permeability are given by taking into account the fractal distribution of pore size and tortuosity of capillaries. It can be seen that the capillary pressure for water phase decreases with the increase of saturation in unsaturated porous rocks. It is found that the capillary pressure for water phase decreases as the tortuosity fractal dimension decreases. It is further seen that the capillary pressure for water phase increases with the decrease of porosity, and at low porosity, the capillary pressure increases sharply with the decrease of porosity. Besides, it can be observed that the water relative permeability increases with the increase of saturation in unsaturated porous rocks. This predicted the capillary pressure and water relative permeability of unsaturated porous rocks based on the proposed models which are in good agreement with the experimental data and model predictions reported in the literature. § Corresponding author. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. 1840015-1 B. Xiao et al.The proposed model improved the understanding of the physical mechanisms of water flow through unsaturated porous rocks.

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“…Convert the unit system of Eq. (20) into SI field unit system to facilitate example calculation and substitute the standard pressure, standard temperature and circular constant into the obtained equation, Eq. (20) will be simplified as:…”

Section: The Productivity Equation Ofmentioning

confidence: 99%

“…Fractal theory has been used to describe kinds of physical phenomenon in porous media, [16][17][18][19][20][21][22][23][24][25] such as the seepage characters of transient flow, [26][27][28] capillary imbibition, 29,30 non-Darcy flow, 31-33 thermal conductivity. 34 and multiphase flow.…”

Section: Introductionmentioning

confidence: 99%

A Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

Zhang

Tan

et al. 2017

Fractals

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Because of the low permeability, multi-stage hydraulic fractured horizontal wells (MHFHWs) occupy a dominant position among production wells in tight gas reservoir. However, net present value (NPV) estimation method for MHFHW in tight gas reservoirs often ignores the effect of heterogeneity in microscopic pore structure. Apart from that, a new fractal model is presented for NPV of MHFHW, based on the fractal expressions of formation parameters. First, with the aid of apparent permeability model, a pseudo pressure expression considering both reservoir fractal features and slippage effect is derived, contributing to establish the productivity model. Secondly, economic assessment method is built based on the fractal productivity model, in order to obtain the NPV of MHFHW. Thirdly, the type curves are illustrated and the influences of different fractal parameters are discussed. The pore fractal dimensions D f and the capillary tortuosity fractal dimensions D T have significant effects on the NPV of an MHFHW. Finally, the proposed model in this paper provides a new methodology for analyzing and predicting the NPV of an MHFHW and may be conducive to a better understanding of the optimal design of MHFHW.

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A difference-fractal model for the permeability of fibrous porous media

Cited by 70 publications

References 34 publications

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

A Fractal Model for Water Flow Through Unsaturated Porous Rocks

A Fractal Analysis for Net Present Value of Multi-Stage Hydraulic Fractured Horizontal Well

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