The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

The effect of scale on the shear behaviour of joints is studied by performing direct shear tests on different sized replicas cast from various natural joint surfaces. The result show significant scale effects on both the shear strength and deformation characteristics. Scale effects are more pronounced in the case of rough, undulating joint types, whereas they are virtually absent for planar joints. The key factor is the involvement of different asperity sizes in controlling the peak behaviour of different lengths of joints. It is shown that as a results both the joint roughness coefficient (JRC) and the joint compression strength (JCS) reduce with increasing scale. The behaviour of multiple jointed masses with different joint spacing is also considered. It is found that despite unchanged roughness, jointed masses consisting of many small blocks have higher peak shear strength than jointed masses with larger joint spacing. These scale effects are related to the changing stiffness of a rock mass as the block size or joint spacing increases or decreases. Economic methods for obtaining scale-free estimates of shear strength are described.

Experimental studies of scale effects on the shear behaviour of rock joints

Characterizations of full-scale pore size distribution, porosity and permeability of coals: A novel methodology by nuclear magnetic resonance and fractal analysis theory

Shale gas transport model in 3D fractal porous media with variable pore sizes

Shale pore structure characteristics of the high and low productivity wells, Jiaoshiba shale gas field, Sichuan Basin, China: Dominated by lithofacies or preservation condition?

Fractal dimension, lacunarity and succolarity analyses on CT images of reservoir rocks for permeability prediction

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when...

A new method for calculating fractal dimensions of porous media based on pore size distribution

Creeping microstructure and fractal permeability model of natural gas hydrate reservoir

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. Cited as : Wei, W., Xia, Y. Geometrical, fractal and hydraulic properties of fractured reservoirs: A mini-review. Advances in Geo-Energy Research, 2017, 1(1): 31-38, doi: 10.26804/ager.2017.01.03

/pdf/geometrical-fractal-and-hydraulic-properties-of-fractured-1ueb2afbys.pdf

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

In this paper, a simple and efficient fractal-based approach is presented for capturing the effects of initial void ratio on the soil-water characteristic curve (SWCC) in a deformable unsaturated soil. In terms of testing results, the SWCCs (expressed by gravimetric water content) of the unsaturated soils at different initial void ratios were found to be mainly controlled by the air-entry value (Ψa), while the fractal dimension (D) could be assumed to be constant. As a result, in contrast to the complexity of existing models, a simple and efficient model with only two parameters (i.e., D and Ψa) was established for predicting the SWCC considering the effects of initial void ratio. The procedure for determining the model parameters with clear physical meaning were then elaborated. The applicability and accuracy of the proposed model were well demonstrated by comparing its predictions with four sets of independent experimental data from the tests conducted in current work, as well as the literature on a wide range of soils, including Wuhan Clay, Hefei and Guangxi expansive soil, Saskatchewan silt, and loess. Good agreements were obtained between the experimental data and the model predictions in all of the cases considered.

Yuxuan Xia

Papers

Fractal dimension, lacunarity and succolarity analyses on CT images of reservoir rocks for permeability prediction

A new method for calculating fractal dimensions of porous media based on pore size distribution

Creeping microstructure and fractal permeability model of natural gas hydrate reservoir

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

A Simple Fractal-Based Model for Soil-Water Characteristic Curves Incorporating Effects of Initial Void Ratios