Fluid Flow through Rough Rock Fractures: Parametric Study

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

Abstract: 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.

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

Abstract: Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of two-dimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracture-length distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.

Chemically- and mechanically-mediated influences on the transport and mechanical characteristics of rock fractures - eScholarship

Abstract: A model is presented to represent changes in the mechanical and transport characteristics of fractured rock that result from coupled mechanical and chemical effects. The specific influence is the elevation of dissolution rates on contacting asperities, which results in a stress- and temperature-dependent permanent closure. A model representing this pressure-dissolution-like behavior is adapted to define the threshold and resulting response in terms of fundamental thermodynamic properties of a contacting fracture. These relations are incorporated in a stress-stiffening model of fracture closure to define the stress- and temperature-dependency of aperture loss and behavior during stress and temperature cycling. These models compare well with laboratory and field experiments, representing both decoupled isobaric and isothermal responses. The model was applied to explore the impact of these responses on heated structures in rock. The result showed a reduction in ultimate induced stresses over the case where chemical effects were not incorporated, with permanent reduction in final stresses after cooling to ambient conditions. Similarly, permeabilities may be lower than they were in the case where chemical effects were not considered, with a net reduction apparent even after cooling to ambient temperature. These heretofore-neglected effects may have a correspondingly significant impact on the performance of heated structures in rock, such as repositories for the containment of radioactive wastes.

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

Abstract: 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

Geometrical heterogeneity of the joint roughness coefficient revealed by 3D laser scanning

Abstract: The joint roughness coefficient (JRC) is an important indicator that characterizes the physical and mechanical behaviors of a jointed rock mass. To investigate the distribution characteristics of the JRC, 31 joint samples belonging to the same joint group with dominant attitude of 209°∠71° were collected from the Guanshan railway tunnel, and the morphologies of the joint samples were digitized using 3D laser scanning. The JRC values in different directions were obtained based on the fractal theory, and the effects of sampling interval on JRC were assessed during the JRC calculation process. The results show that the sampling intervals of profile line and digital point both affect the calculated JRC values. With sampling interval increasing, there exists an obvious threshold above which the JRC value changes from constant to variable. It is found that, the JRC value keeps constant if the profile line sampling interval is smaller than the threshold value (4 mm), which is independent of the roughness degree of the joint. However, the threshold of digital point sampling interval is influenced by joint roughness and has a negative exponential relationship with the JRC value. According to the calculated results of JRC in different directions of the 31 joint samples, it is clear that the JRC values present significant anisotropy and large variation in certain directions. Meanwhile, it is verified that the JRC values in the same direction follow a log-normal distribution. The expected JRC values calculated depending on the probability density function are generally larger than the arithmetic mean values, with a maximum difference up to 23.1%. In consideration of natural distribution, the expected JRC values calculated from probability density function should be more reliable than the arithmetic mean values. Therefore, accurate understanding on the geometrical heterogeneity of JRC will significantly affect the evaluation of mechanical effects of rock mass structure.

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

Abstract: 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.

Validity of Cubic Law for fluid flow in a deformable rock fracture

Abstract: 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.

Strength, deformation and conductivity coupling of rock joints

Abstract: Construction of dams, tunnels and slopes in jointed, water-bearing rock causes complex interactions between joint deformation and effective stress. Joint deformation can take the form of normal closure, opening, shear and dilation. The resulting changes of aperture can cause as much as three orders of magnitude change in conductivity at moderate compressive stress levels. Even the heavily stressed joints found in oil and gas reservoirs may also exhibit significant stress-dependent conductivity during depletion, and during waterflood treatments. The magnitudes of the above processes are often strongly dependent on both the character and frequency of jointing. In this paper the results of many years of research on joint properties are synthesized in a coupled joint behaviour model. Methods of joint characterization are described for obtaining the necessary input data. The model simulates stress- and size-dependent coupling of shear stress, diplacement, dilation and conductivity, and of normal stress, closure and conductivity. These processes are the fundamental building blocks of rock mass behaviour. Model simulations are compared with experimental behaviour and numerous examples are given.

Fluid flow through rock joints: The effect of surface roughness

Abstract: Fluid flow through rock joints is commonly described by the parallel plate model where the volume flow rate varies as the cube of the joint aperture. However, deviations from this model are expected because real joint surfaces are rough and contact each other at discrete points. To examine this problem further, a computer simulation of flow between rough surfaces was done. Realistic rough surfaces were generated numerically using a fractal model of surface topography. Pairs of these surfaces were placed together to form a “joint” with a random aperture distribution. Reynolds equation, which describes laminar flow between slightly nonplanar and nonparallel surfaces, was solved on the two-dimensional aperture mesh by the finite-difference method. The solution is the local volume flow rate through the joint. This solution was used directly in the cubic law to get the so-called “hydraulic aperture.” For various surface roughnesses (fractal dimensions) the hydraulic aperture was compared to the mean separation of the surfaces. At large separations the surface topography has little effect. At small separations the flow is tortuous, tending to be channeled through high-aperture regions. The parameter most affecting fluid flow through rough joints is the ratio of the mean separation between the surfaces to the root-mean-square surface height. This parameter describes the distance the surface asperities protrude into the fluid and accounts for most of the disagreement with the parallel plate model. Variations in the fractal dimension produce only a second-order effect on the fluid flow. For the range of joint closures expected during elastic deformation these results show that the actual flow rate between rough surfaces is about 70–90% of that predicted by the parallel plate model.

A Criterion for Non-Darcy Flow in Porous Media

Abstract: Non-Darcy behavior is important for describing fluid flow in porous media in situations where high velocity occurs. A criterion to identify the beginning of non-Darcy flow is needed. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the beginning of non-Darcy flow. Because each of these criteria has different versions of definitions, consistent results cannot be achieved. Based on a review of previous work, the Forchheimer number is revised and recommended here as a criterion for identifying non-Darcy flow in porous media. Physically, this revised Forchheimer number has the advantage of clear meaning and wide applicability. It equals the ratio of pressure drop caused by liquid–solid interactions to that by viscous resistance. It is directly related to the non-Darcy effect. Forchheimer numbers are experimentally determined for nitrogen flow in Dakota sandstone, Indiana limestone and Berea sandstone at flowrates varying four orders of magnitude. These results indicate that superficial velocity in the rocks increases non-linearly with the Forchheimer number. The critical Forchheimer number for non-Darcy flow is expressed in terms of the critical non-Darcy effect. Considering a 10% non-Darcy effect, the critical Forchheimer number would be 0.11.