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.

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

Fracture stratigraphy and DFN modelling of tight carbonates, the case study of the Lower Cretaceous carbonates exposed at the Monte Alpi (Basilicata, Italy)

Fracture characterization and modeling of karsted carbonate reservoirs: A case study in Tahe oilfield, Tarim Basin (western China)

Heterogeneous fracture aperture distribution, dictated by surface roughness, mechanical rock and fracture properties, and effective stress, limits the predictive capabilities of many reservoir‐scale models that commonly assume smooth fracture walls. Numerous experimental studies have probed key hydromechanical responses in single fractures; however, many are constrained by difficulties associated with sample preparation and quantitative roughness characterisation. Here, we systematically examine the effect of roughness on fluid flow properties by 3D printing seven self‐affine fractures, each with controlled roughness distributions akin to those observed in nature. Photogrammetric microscopy was employed to validate the 3D topology of each printed fracture surface, enabling quantification using traditional roughness metrics, namely the Joint Roughness Coefficient (JRC). Core‐flooding experiments performed on each fracture across eight incremental confining pressure increases (11 to 25 bar), shows smoother fractures (JRC 7) show as much as a 219% permeability increase. Micro‐computed tomography imaging of the roughest fracture under varying effective stresses (5 to 13.8 bar), coupled with inspection into the degree of similarity between fracture closure behaviour in 3D‐printed and natural rock fractures, highlight the capabilities of 3D‐printed materials to act as useful analogues to natural rocks. Comparison of experimental data to existing empirical aperture‐permeability models demonstrates that fracture contact area is a better permeability predictor than roughness when the mechanical aperture is below ∼20 μm. Such findings are relevant for models incorporating the effects of heterogeneous aperture structures and applied stress to predict fracture flow in the deep subsurface.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2020WR028671

A Systematic Investigation into the Control of Roughness on the Flow Properties of 3D‐Printed Fractures

School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China GeoEnergy Research Centre (GERC), University of Nottingham, Nottingham NG7 2RD, UK The Fifth Project Co., Ltd. of China Railway Bureau 14 Group, Yanzhou, Shandong 272117, China Jiangsu Vocational Institute of Architectural Technology, Xuzhou Jiangsu 221116, China

/pdf/cement-grout-nonlinear-flow-behavior-through-the-rough-1w4pd0kl87.pdf

Cement Grout Nonlinear Flow Behavior through the Rough-Walled Fractures: An Experimental Study

Fluid flow through a single fracture is traditionally described by the cubic law, which is derived from the Navier-Stokes equation for the flow of an incompressible fluid between two smooth-parallel plates. Thus, the permeability of a single fracture depends only on the so-called hydraulic aperture which differs from the mechanical aperture (separation between the two fracture wall surfaces). This difference is mainly related to the roughness of the fracture walls, which has been evaluated in previous works by including a friction factor in the permeability equation or directly deriving the hydraulic aperture. However, these methodologies may lack adequate precision to provide valid results. This work presents a complete protocol for fracture surface mapping, roughness evaluation, fracture modeling, fluid flow simulation, and permeability estimation of individual fracture (open or sheared joint/pressure solution seam). The methodology includes laboratory-based high-resolution structure from motion (SfM) photogrammetry of fracture surfaces, power spectral density (PSD) surface evaluation, synthetic fracture modeling, and fluid flow simulation using the Lattice-Boltzmann method. This work evaluates the respective controls on permeability exerted by the fracture displacement (perpendicular and parallel to the fracture walls), surface roughness, and surface pair mismatch. The results may contribute to defining a more accurate equation of hydraulic aperture and permeability of single fractures, which represents a pillar for the modeling and upscaling of the hydraulic properties of a geofluid reservoir.

/pdf/analysis-of-fracture-roughness-control-on-permeability-using-186boi556r.pdf

Ali Ibrahim Mahmoud Abdelhamid Salama

Papers

Analysis of Fracture Roughness Control on Permeability Using SfM and Fluid Flow Simulations: Implications for Carbonate Reservoir Characterization