A Fractal Analysis of Permeability for Power-Law Fluids in Porous Media

Zhang, Bin; Yu, Bo; Wang, Haixia; Yun, Meijuan

doi:10.1142/s0218348x06003167

Cited by 39 publications

(14 citation statements)

References 21 publications

(29 reference statements)

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“…Mandelbrot pointed out that fractal dimensions D l and D d vary between 1 and 3. The flow rate through single capillary/channel for power-law fluids is given by (Zhang et al 2006;Yun et al 2008b)…”

Section: The Absolute Permeability Of Power-law Fluids In the Fractalmentioning

confidence: 99%

“…Furthermore, the structural characteristic of cracks in natural rocks directly relates the ground oil production, the rational development and utilization of soil/gas layer and groundwater resources. The seepage for non-Newtonian fluids in network of fractures and porous media have thus been received more and more attention (Zhang et al 2006;Yun et al 2008a;Yu and Xu 2007) in crude oil production, the low permeability oil reservoir production and the application of polymer water flooding and tertiary recovery technologies.…”

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confidence: 99%

“…Hunt and Ewing (2009) used percolation theory and critical path analysis to find a consistent and accurate description of the saturation dependence of basic flow properties such as hydraulic conductivity and permeability, the electrical conductivity, solute and gas diffusion, as well as the pressure-saturation relationships, including hysteresis and non-equilibrium effect. Zhang et al (2006) developed a fractal permeability model for power-law fluids in porous media based on the assumptions that porous media consist of a bundle of tortuous capillaries, whose size distribution and tortuosity follow the fractal scaling laws. Pearson and Tardy (2002) made a comprehensive review on non-Newtonian fluid flow in porous media and on the several models for transport in porous media such as variable-bundle model, equal-bundle model, and network of capillaries.…”

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confidence: 99%

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Analysis of Seepage for Power-Law Fluids in the Fractal-Like Tree Network

Wang¹,

Yu²

2010

Transp Porous Med

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This work studies the flow characteristics of power-law fluids in the fractal-like tree network. A fractal model is developed for the permeability of power-law fluid flow in fractal-like tree network based on straight capillary model, generalized Darcy's law and constitutive equation for power-law fluids. Analytical expression for permeability of power-law fluids in the network is presented and found to be a function of network microstructural parameters such as the branching diameter ratio, the branching length ratio, the total number of branching levels, the bifurcation angle, the branching number, the diameter of the zeroth branching level and the power exponent of power-law fluids. Both the phase permeabilities and the relative permeabilities are also derived and found to be a function of power exponent for the wetting phase and non-wetting phase, the saturation and other microstructural parameters and independent of the bifurcation angle.

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Section: The Absolute Permeability Of Power-law Fluids In the Fractalmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Analysis of Seepage for Power-Law Fluids in the Fractal-Like Tree Network

Wang¹,

Yu²

2010

Transp Porous Med

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“…permeability) for porous media. [10][11][12][13][14] Additionally, many fractal models developed for permeability have been presented in recent decades. [15][16][17] Many fractal permeability models were developed based on the classic Kozeny-Carman (KC) equation because of its longstanding application in permeability prediction.…”

Section: Introductionmentioning

confidence: 99%

A Novel Fractal Model for Estimating Permeability in Low-Permeable Sandstone Reservoirs

Dong

Dai

et al. 2020

Fractals

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Permeability is one of the most important parameters for accurately predicting water flow in reservoirs and quantifying underground water inrush into coal mines. This study developed a predictive permeability model by considering the microstructural parameters and tortuosity effects of low-permeability sandstone. The model incorporates the fractal geometry theory, Darcy’s law, and Poiseuille equation into a multistep inversion framework for systematic interpretation of sandstone scanning electron microscopy (SEM) images. A threshold segmentation algorithm is applied to transform SEM images into binary images. Then, we used an improved statistical algorithm with binary image data to estimate the geometric parameters of each pore, such as the perimeter and area. The fractal parameters of pore microstructure were determined by fitting the data of pore perimeters and areas. Finally, the effects of tortuosity on microscopic percolation were considered, and a conventional model was modified for quantifying the relationship between microscopic pore structures parameters and macroscopic permeability. Eight groups of sandstone samples from the Xingdong coal mine in North China were collected for estimating permeability by the developed inversion framework. A direct permeability measurement was also conducted on each sample with an AP-608 automatic measuring instrument. The measured permeability values were compared with results from theoretical models, and we found that the accuracy of the newly developed predictive model is better than that of a conventional permeability model. The predictive model developed in this study provides a useful tool for estimating permeability in low-permeable sandstone reservoirs.

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“…The Herschel-Bulkley model represents the Bingham plastic fluid with n ¼ 1, and becomes the power-law fluid model with τ 0 ¼ 0. Based on the fractal geometry of porous media (Cai et al, 2010), the flow behavior of power-low fluids was quantified by fractal dimensions from single tortuous tubes (Yun et al, 2008) to generous porous Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces systems with wide pore size distribution (Zhang et al, 2006). Eq.…”

Section: Introductionmentioning

confidence: 99%