A Discussion on Fractal Models for Transport Physics of Porous Media

Xu, Peng

doi:10.1142/s0218348x15300019

Cited by 106 publications

(47 citation statements)

References 89 publications

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“…20 It was first born in the natural geometry, and shows a broad application prospects in many areas after nearly decades of development. [21][22][23][24][25][26] In 1996, A. M. Vidales obtained the fractal expression for porosity and permeability of fractal porous media.…”

Section: The Improved Porosity Methods Considering Fractal Characterismentioning

confidence: 99%

A New Improved Threshold Segmentation Method for Scanning Images of Reservoir Rocks Considering Pore Fractal Characteristics

Lin

Yang

et al. 2018

Fractals

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Based on the basic principle of the porosity method in image segmentation, considering the relationship between the porosity of the rocks and the fractal characteristics of the pore structures, a new improved image segmentation method was proposed, which uses the calculated porosity of the core images as a constraint to obtain the best threshold. The results of comparative analysis show that the porosity method can best segment images theoretically, but the actual segmentation effect is deviated from the real situation. Due to the existence of heterogeneity and isolated pores of cores, the porosity method that takes the experimental porosity of the whole core as the criterion cannot achieve the desired segmentation effect. On the contrary, the new improved method overcomes the shortcomings of the porosity method, and makes a more reasonable binary segmentation for the core grayscale images, which segments images based on the actual porosity of each image by calculated. Moreover, the image segmentation method based on the calculated porosity rather than the measured porosity also greatly saves manpower and material resources, especially for tight rocks.

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Section: The Improved Porosity Methods Considering Fractal Characterismentioning

confidence: 99%

A New Improved Threshold Segmentation Method for Scanning Images of Reservoir Rocks Considering Pore Fractal Characteristics

Lin

Yang

et al. 2018

Fractals

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“…Anomalous diffusion is frequently observed in transport in porous media and was subject of intense theoretical research in recent decades [1][2][3][4][5]. In such media, the mean-square displacement R of a tracer particle scales in time t as…”

Section: Introductionmentioning

confidence: 99%

Scaling relations in the diffusive infiltration in fractals

Reis

2016

Phys. Rev. E

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In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F ∼ t n , with n < 1/2, thus providing a macroscopic realization of anomalous diffusion [Filipovitch et al, Water Resour. Res. 52 5167 (2016)]. The results agree with simulations of a diffusion equation with constant pressure at one of the borders of those fractals, but the exponent n is very different from the anomalous exponent ν = 1/D W of single particle diffusion in the same fractals (D W is the random walk dimension). Here we use a scaling approach to show that those exponents are related as n = ν (D F − D B ), where D F and D B are the fractal dimensions of the bulk and of the border from which diffusing particles come, respectively. This relation is supported by accurate numerical estimates in two SCs and in two generalized Menger sponges (MSs), in which we performed simulations of single particle random walks (RWs) with a rigid impermeable border and of a diffusive infiltration model in which that border is permanently filled with diffusing particles. This study includes one MS whose external border is also fractal. The exponent relation is also consistent with the recent simulational and experimental results on fluid infiltration in SCs, and explains the approximate quadratic dependence of n on D F in these fractals. We also show that the mean-square displacement of single particle RWs has log-periodic oscillations, whose periods are similar for fractals with the same scaling factor in the generator (even with different embedding dimensions), which is consistent with the discrete scale invariance scenario. The roughness of a diffusion front defined in the infiltration problem also shows this type of oscillation, which is enhanced in fractals with narrow channels between large lacunas.

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“…Researches has shown that the fracture network surrounding the HFs is not irregular, but can be regressed using different types of fractal theoretical models. [31][32][33][34][35][36] Zhou et al 37,38 proposed a method based on the L-system (Lindenmayer system), in which The fracture geometry is calibrated by the matching of microseismic data with an Lsystem based on fractal-geometry theory. However, the density of induced fractures generated by Zhou's method increases the farther away they are from the well, which is not reasonable for horizontal wells.…”

Section: Figmentioning

confidence: 99%

Application of Fractal Geometry in Evaluation of Effective Stimulated Reservoir Volume in Shale Gas Reservoirs

Sheng

Javadpour

et al. 2017

Fractals

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According to hydraulic-fracturing practices conducted in shale reservoirs, effective stimulated reservoir volume (ESRV) significantly affects the production of hydraulic fractured well. Therefore, estimating ESRV is an important prerequisite for confirming the success of hydraulic fracturing and predicting the production of hydraulic fracturing wells in shale reservoirs. However, ESRV calculation remains a longstanding challenge in hydraulic-fracturing operation. In considering fractal characteristics of the fracture network in stimulated reservoir volume (SRV), § 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. 1740007-1Fractals 2017.25. Downloaded from www.worldscientific.com by 13.66.222.141 on 04/09/19. Re-use and distribution is strictly not permitted, except for Open Access articles.G. Sheng et al. this paper introduces a fractal random-fracture-network algorithm for converting the microseismic data into fractal geometry. Five key parameters, including bifurcation direction, generating length (d), deviation angle (α), iteration times (N ) and generating rules, are proposed to quantitatively characterize fracture geometry. Furthermore, we introduce an orthogonal-fractures coupled dual-porosity-media representation elementary volume (REV) flow model to predict the volumetric flux of gas in shale reservoirs. On the basis of the migration of adsorbed gas in porous kerogen of REV with different fracture spaces, an ESRV criterion for shale reservoirs with SRV is proposed. Eventually, combining the ESRV criterion and fractal characteristic of a fracture network, we propose a new approach for evaluating ESRV in shale reservoirs. The approach has been used in the Eagle Ford shale gas reservoir, and results show that the fracture space has a measurable influence on migration of adsorbed gas. The fracture network can contribute to enhancement of the absorbed gas recovery ratio when the fracture space is less than 0.2 m. ESRV is evaluated in this paper, and results indicate that the ESRV accounts for 27.87% of the total SRV in shale gas reservoirs. This work is important and timely for evaluating fracturing effect and predicting production of hydraulic fracturing wells in shale reservoirs.

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A Discussion on Fractal Models for Transport Physics of Porous Media

Cited by 106 publications

References 89 publications

A New Improved Threshold Segmentation Method for Scanning Images of Reservoir Rocks Considering Pore Fractal Characteristics

A New Improved Threshold Segmentation Method for Scanning Images of Reservoir Rocks Considering Pore Fractal Characteristics

Scaling relations in the diffusive infiltration in fractals

Application of Fractal Geometry in Evaluation of Effective Stimulated Reservoir Volume in Shale Gas Reservoirs

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