Analysis of permeability for the fractal-like tree network by parallel and series models

Xu, Peng; Yu, Bo; Feng, Yongjin; Liu, Yanjun

doi:10.1016/j.physa.2006.03.023

Cited by 102 publications

(50 citation statements)

References 8 publications

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“…Figure 3 shows a schematic plot of the fracture representative element volume (FREV), in which connected natural fractures and induced fractures are the main flow paths in the SRV, where permeability is much higher than the matrix. Given the process and relevant characteristics of the multi-stage hydraulic fracturing in unconventional reservoirs, the fractal fracture pattern is generated by construction theory [27] in According to the fractal self-similar construction theory [27], the fractal dimension and the scaling factor of fractures can be determined. In terms of the symmetrically-distributed fracture network on each side of the main fracture, the branching fracture in the same level has the same length, while the branching fractures grow further following certain ratio factors.…”

Section: Physical Modelmentioning

confidence: 99%

Numerical Simulation of Fluid Flow through Fractal-Based Discrete Fractured Network

Wang

et al. 2018

Energies

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Abstract:In recent years, multi-stage hydraulic fracturing technologies have greatly facilitated the development of unconventional oil and gas resources. However, a quantitative description of the "complexity" of the fracture network created by the hydraulic fracturing is confronted with many unsolved challenges. Given the multiple scales and heterogeneity of the fracture system, this study proposes a "bifurcated fractal" model to quantitatively describe the distribution of induced hydraulic fracture networks. The construction theory is employed to generate hierarchical fracture patterns as a scaled numerical model. With the implementation of discrete fractal-fracture network modeling (DFFN), fluid flow characteristics in bifurcated fractal fracture networks are characterized. The effects of bifurcated fracture length, bifurcated tendency, and number of bifurcation stages are examined. A field example of the fractured horizontal well is introduced to calibrate the accuracy of the flow model. The proposed model can provide a more realistic representation of complex fracture networks around a fractured horizontal well, and offer the way to quantify the "complexity" of the fracture network in shale reservoirs. The simulation results indicate that the geometry of the bifurcated fractal fracture network model has a significant impact on production performance in the tight reservoir, and enhancing connectivity of each bifurcate fracture is the key to improve the stimulation performance. In practice, this work provides a novel and efficient workflow for complex fracture characterization and production prediction in naturally-fractured reservoirs of multi-stage fractured horizontal wells.

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Section: Physical Modelmentioning

confidence: 99%

Numerical Simulation of Fluid Flow through Fractal-Based Discrete Fractured Network

Wang

et al. 2018

Energies

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“…Tree-like branched network models and assumptions are used to analyze their transport and flow properties of fractured reservoirs and porous media embedded with tree networks (Li et al, 2016a;Fan and Ettehadtavakkol, 2017). Xu et al (2006) analyzed the hydraulic conductivity and developed a permeability models of fractal-like tree networks between one point and a straight line, and also derive an analytical expression for the effective permeability for the network based on the parallel and series models. The effective permeability of a fractal-like tree network is expressed as:…”

Section: Relationships Between Fractal Dimension and Permeabilitymentioning

confidence: 99%

Geometrical, fractal and hydraulic properties of fractured reservoirs: A mini-review

Wei

Xia

2017

Adv. Geo-Energ. Res.

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Fractures and fracture networks play an important role in fluid flow and transport properties of oil and gas reservoirs. Accurate estimation of geometrical characteristics of fracture networks and their hydraulic properties are two key research directions in the fields of fluids flow in fractured porous media. Recent works focusing on the geometrical, fractal and hydraulic properties of fractured reservoirs are reviewed and summarized in this mini-review. The effects of several important parameters that significantly influences hydraulic properties are specifically discussed and analyzed, including fracture length distribution, aperture distribution, boundary stress and anisotropy. The methods for predicting fractal dimension of fractures and models for fracture networks and fractured porous media based on fractal-based approaches are addressed. Some comments and suggestions are also given on the future research directions and fractal fracture networks as well as fractured porous media.

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“…[13][14][15] Chang and Yortsos 16 proposed a fractal model for the radial permeability of fractured reservoirs, in which the relation between transport exponent and fractal dimension is unknown. Xu et al 17,18 employed the fractal tree-like networks to model the fracture system and developed a fractal dual-domain model for fractured porous media, and the effective planar linear and radial permeabilities have been proposed. They also carried out MonteCarlo simulation on the radial flow in fractured porous media based on the fractal capillary bundle model and indicated that the effective radial permeability relates to the geometrical parameters of well and size distribution of fractures.…”

Section: Introductionmentioning

confidence: 99%

Effective Permeability of Fractured Porous Media With Fractal Dual-Porosity Model

Liu

Sasmito

et al. 2017

Fractals

Self Cite

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As natural fractures show statistically fractal scaling laws, fractal geometry has been proposed and applied to model the fracture geometry and to study the hydraulic properties of fractured porous media. In this paper, a fractal dual-porosity model is developed to study the single-phase fluid flow through fractured porous media. An analytical expression for effective permeability of fractured porous media is derived, which depends on the fractal dimension and fracture aperture. The effect of fractal dimensions for fracture aperture distribution and tortuosity, the ratio of minimum to maximum fracture apertures and fracture fraction on the effective permeability have been discussed. In addition, a power law relationship between the effective permeability and fracture fraction is proposed to predict the equivalent hydraulic properties of fractured porous media. Compared with empirical formulas for effective permeability, the present fractal dual-porosity model can capture the statistical characteristics of fractures and shed light on the transport mechanism of fractured porous media.

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Analysis of permeability for the fractal-like tree network by parallel and series models

Cited by 102 publications

References 8 publications

Numerical Simulation of Fluid Flow through Fractal-Based Discrete Fractured Network

Numerical Simulation of Fluid Flow through Fractal-Based Discrete Fractured Network

Geometrical, fractal and hydraulic properties of fractured reservoirs: A mini-review

Effective Permeability of Fractured Porous Media With Fractal Dual-Porosity Model

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