A FRACTAL NETWORK MODEL FOR FRACTURED POROUS MEDIA

Fractals ◽  
2016 ◽  
Vol 24 (02) ◽  
pp. 1650018 ◽  
Author(s):  
PENG XU ◽  
CUIHONG LI ◽  
SHUXIA QIU ◽  
AGUS PULUNG SASMITO
Keyword(s):  
Porous Media ◽  
Chemical Engineering ◽  
Oil And Gas ◽  
Fractal Dimensions ◽  
Fractured Porous Media ◽  
Fracture System ◽  
Fracture Density ◽  
Fracture Length ◽  
Dual Porosity Model ◽  
Porosity Model

The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

scholarly journals EFFECTIVE PERMEABILITY OF FRACTURED POROUS MEDIA WITH FRACTAL DUAL-POROSITY MODEL

Fractals ◽  
2017 ◽  
Vol 25 (04) ◽  
pp. 1740014 ◽  
Author(s):  
PENG XU ◽  
HAICHENG LIU ◽  
AGUS PULUNG SASMITO ◽  
SHUXIA QIU ◽  
CUIHONG LI
Keyword(s):  
Porous Media ◽  
Hydraulic Properties ◽  
Effective Permeability ◽  
Scaling Laws ◽  
Fractured Porous Media ◽  
Dual Porosity ◽  
Statistical Characteristics ◽  
Fracture Aperture ◽  
Dual Porosity Model ◽  
Porosity Model

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.

A FRACTAL SCALING LAW BETWEEN TORTUOSITY AND POROSITY IN POROUS MEDIA

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050025
Author(s):  
PENG XU ◽  
LIPEI ZHANG ◽  
BINQI RAO ◽  
SHUXIA QIU ◽  
YUQING SHEN ◽  
...  
Keyword(s):  
Porous Media ◽  
Chemical Engineering ◽  
Oil And Gas ◽  
Scaling Law ◽  
Morphological Characteristics ◽  
Fractal Model ◽  
Statistical Characteristics ◽  
Scale Model ◽  
Reservoir Water ◽  
Flow Through

Hydraulic tortuosity is one of the key parameters for evaluating effective transport properties of natural and artificial porous media. A pore-scale model is developed for fluid flow through porous media based on fractal geometry, and a novel analytical tortuosity–porosity correlation is presented. Numerical simulations are also performed on two-dimensional Sierpinski carpet model. The proposed fractal model is validated by comparison with numerical results and available experimental data. Results show that hydraulic tortuosity depends on both statistical and morphological characteristics of porous media. The exponents for the scaling law between tortuosity and porosity depend on pore size distribution and tortuous fractal dimension. It has been found that hydraulic tortuosity indicates evident anisotropy for asymmetrical particle arrangements under the same statistical characteristics of porous media. The present work may be helpful to understand the transport mechanisms of porous materials and provide guidelines for the development of oil and gas reservoir, water resource and chemical engineering, etc.

scholarly journals A Computational Workflow for Flow and Transport in Fractured Porous Media Based on a Hierarchical Nonlinear Discrete Fracture Modeling Approach

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6667
Author(s):  
Wenjuan Zhang ◽  
Waleed Diab ◽  
Hadi Hajibeygi ◽  
Mohammed Al Kobaisi
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Boundary Conditions ◽  
Large Scale ◽  
Fractured Porous Media ◽  
Small Scale ◽  
Flow And Transport ◽  
Fracture Length ◽  
Discrete Fracture ◽  
Computational Workflow

Modeling flow and transport in fractured porous media has been a topic of intensive research for a number of energy- and environment-related industries. The presence of multiscale fractures makes it an extremely challenging task to resolve accurately and efficiently the flow dynamics at both the local and global scales. To tackle this challenge, we developed a computational workflow that adopts a two-level hierarchical strategy based on fracture length partitioning. This was achieved by specifying a partition length to split the discrete fracture network (DFN) into small-scale fractures and large-scale fractures. Flow-based numerical upscaling was then employed to homogenize the small-scale fractures and the porous matrix into an equivalent/effective single medium, whereas the large-scale fractures were modeled explicitly. As the effective medium properties can be fully tensorial, the developed hierarchical framework constructed the discrete systems for the explicit fracture–matrix sub-domains using the nonlinear two-point flux approximation (NTPFA) scheme. This led to a significant reduction of grid orientation effects, thus developing a robust, applicable, and field-relevant framework. To assess the efficacy of the proposed hierarchical workflow, several numerical simulations were carried out to systematically analyze the effects of the homogenized explicit cutoff length scale, as well as the fracture length and orientation distributions. The effect of different boundary conditions, namely, the constant pressure drop boundary condition and the linear pressure boundary condition, for the numerical upscaling on the accuracy of the workflow was investigated. The results show that when the partition length is much larger than the characteristic length of the grid block, and when the DFN has a predominant orientation that is often the case in practical simulations, the workflow employing linear pressure boundary conditions for numerical upscaling give closer results to the full-model reference solutions. Our findings shed new light on the development of meaningful computational frameworks for highly fractured, heterogeneous geological media where fractures are present at multiple scales.

A MULTI-LINEAR FRACTAL MODEL FOR PRESSURE TRANSIENT ANALYSIS OF MULTIPLE FRACTURED HORIZONTAL WELLS IN TIGHT OIL RESERVOIRS INCLUDING IMBIBITION

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940004 ◽  
Author(s):  
ZHIYUAN WANG ◽  
ZHENGMING YANG ◽  
YUNHONG DING ◽  
YING HE ◽  
WEI LIN ◽  
...  
Keyword(s):  
Fractal Theory ◽  
Horizontal Wells ◽  
Fractal Model ◽  
Oil Reservoirs ◽  
Dual Porosity ◽  
Tight Oil ◽  
Fracture System ◽  
Dual Porosity Model ◽  
Fractured Horizontal Wells ◽  
Porosity Model

Most models for multiple fractured horizontal wells (MFHWs) in tight oil reservoirs (TORs) are based on classical simplified dual-porosity model that ignores the influence of imbibition, while the distribution of fracture system is heterogeneous, multi-scale and self-similar, which can be described by fractal dual-porosity model on fractal theory, and imbibition production is the important part of fracture system production. In this paper, a multi-linear fractal model (MFM) considering imbibition for MFHWs in TORs was established based on fractal theory and semi-analytical method. In this model, fractal theory was used to describe the heterogeneous, complex fracture network, and imbibition was considered by analogy of fluid crossflow law in fractured-porous dual media. And the approximate analytic solution was given by using the Laplace transformation and iteration method. The pressure responses in the domain of real time were obtained with Stehfest numerical inversion algorithms. The pressure transient and production rate were used to analyze, and sensitivity analysis of some related parameters were discussed. The results show that the fluid flow in MFHWs can be divided into nine main flow periods by analysis of type curves, and the fractal parameters of fracture system have great effect on the middle and later periods and imbibition influences the period of crossflow.

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