Natural Fracture Surfaces Research Articles

Analysis of Critical Instability Conditions for Solid-Phase Plugging of Natural Fractures during Temporary Plugging and Fracturing.

Hydraulic fracturing has become a key technology for the development of unconventional oil and gas resources, such as deep shale. Due to the development of natural fractures in deep shale reservoirs, the opening of natural fractures during the fracturing process can cause a significant loss of fracturing fluid, resulting in a reduction in the width of the main fracture and construction risks, such as sand plugging. It is important to improve the fracturing effect of deep shale reservoirs by plugging natural fractures with solid phases, reducing filtration, and improving the efficiency of the fracturing fluid. Ensuring the effectiveness of solid plugging is key to optimizing the fracturing design and improving the stimulation effect after fracturing. In this study, solid plugging technology is introduced into the filtration control process of natural fractures. By setting a plugging zone with a certain length and permeability inside the natural fracture, a stability prediction model for the plugging zone of natural fractures is established, and the instability conditions of the plugging zone are analyzed. The simulation results indicate that the instability of the plugging zone is related to permeability and there is a critical permeability. When the permeability of the plugging zone is greater than this value, expansion instability will occur, and when it is less than or equal to this value, shear slip instability may occur. The strength of shear slip instability is mainly determined by the length of the plugging zone, the friction angle of the natural fracture surface, the friction angle between the plugging particles, and the porosity of the plugging zone. The friction angle of natural fracture surfaces affects only the strength of slip instability, while the friction angle of plugging particles and porosity mainly affect the strength of shear instability. The research results provide a theoretical basis for the optimization of fracturing construction parameters in deep shale reservoirs.

Distinct element modeling of hydraulic fracture propagation with discrete fracture network at Gonghe enhanced geothermal system site, northwest China

Accurate prediction of hydraulic fracture propagation is vital for Enhanced Geothermal System (EGS) design. We study the first hydraulic fracturing job at the GR1 well in the Gonghe Basin using field data, where the overall direction of hydraulic fractures does not show a delineated shape parallel to the maximum principal stress orientation. A field-scale numerical model based on the distinct element method is set up to carry out a fully coupled hydromechanical simulation, with the explicit representation of natural fractures via the discrete fracture network (DFN) approach. The effects of injection parameters and in situ stress on hydraulic fracture patterns are then quantitatively assessed. The study reveals that shear-induced deformation primarily governs the fracturing morphology in the GR1 well, driven by smaller injection rates and viscosities that promote massive activation of natural fractures, ultimately dominating the direction of hydraulic fracturing. Furthermore, the increase of in situ differential stress may promote shear damage of natural fracture surfaces, with the exact influence pattern depending on the combination of specific discontinuity properties and in situ stress state. Finally, we provide recommendations for EGS fracturing based on the influence characteristics of multiple parameters. This study can serve as an effective basis and reference for the design and optimization of EGS in the Gonghe basin and other sites.

Scale effects and spatial distribution characteristics of 3D roughness of natural rock fracture surfaces: statistical analysis

Scale effects and spatial distribution characteristics of 3D roughness of natural rock fracture surfaces: statistical analysis

Reverse calculation and quantitative estimation of JRC3D for rough rock fracture surfaces in various shear directions

The quantitative evaluation of the three-dimensional roughness feature of natural rock fracture surface is essential for predicting shear strength. This article presents an effective approach to estimate the three-dimensional roughness of natural fracture surfaces from the two-dimensional roughness of fracture profile. Firstly, four types of rough fracture samples were created using rock-like materials, followed by conducting direct shear tests of the fracture surfaces under 4 different normal pressures and 4 shear directions. The results of the shear strength tests exhibited a distinct discrete pattern and consistently increased with higher normal pressures. Furthermore, the distribution of the damage area on the fracture surface after shear was significantly impacted by the distribution and size of asperities, as well as the shear direction. The three-dimensional roughness of four fracture surfaces in different directions was first reverse calculated using the shear strength model. Using the weighted positive angle, the estimation of the three-dimensional roughness in different directions of the fracture surface was then determined from the two-dimensional roughness of fracture profiles using both the arithmetic mean method and the weighted average method. The weighted average method effectively captures the contribution of the two-dimensional roughness of fracture profiles to the three-dimensional roughness of fracture surfaces, and exhibits a lower estimation error compared to the arithmetic mean method. Compared to other roughness indicators, the three-dimensional roughness evaluated through the weighted positive angle indicator are closest to the experimental result. Finally, the influence of transverse spacing on the estimated three-dimensional roughness was discussed.

Effects of fracture intersection on the hydraulic properties of 3D crossed rough-walled fractures

Characterization of hydraulic properties of crossed fractures is a key issue in understanding flow behavior of rock masses with complex fracture networks, which is of primary importance for many geoengineering practices. The effects of fracture intersection on fluid flow through 3D crossed rough-walled fractures in a linear flow regime were investigated by numerical simulations. A self-developed finite volume code was employed to solve the Navier–Stokes equation in 3D crossed fracture models. Different synthetic fractures were generated based on the data collected from three natural fracture surfaces. A series of numerical models were established by intersecting the different generations of the synthetic fractures to study the effect of surface roughness, intersection angle, intersection length, and scale on fluid flow through crossed rough-walled fractures. To evaluate the intersection effects, the effective transmissivity of the fracture segments, Teff, which is defined as the transmissivity affected by fracture intersection, was compared with the actual transmissivity of the fracture segments, Ta. The results showed that the ratio of Teff/Ta fluctuates more severely for the models with rougher fracture surfaces due to the formation of more complex geometry at fracture intersection. The ratio tends to reach a converged magnitude at large intersection lengths but with a wider ranges of variation for the models with rougher fracture surfaces. The results also showed that beside the complex geometry of intersection, the difference in the ratio of the mean aperture of the intersection facet to the actual hydraulic aperture of the corresponding fracture segment between different fracture segments may have an even more significant impact on the fluid flow in crossed fractures. The intersection angle affects the fluid flow through crossed fractures by altering the geometrical characteristics of the intersection in a heterogeneous manner, which stems from random nature of fracture surface roughness. The effects of intersection angle become negligible at large intersection lengths. The simulation results suggest one of the conditions to ignore the intersection effects on flow behavior of large-scale rough-walled fracture networks when flow is in a linear regime. Accordingly, all the fracture lengths in the fracture network should be larger than REV size of the fractures.

Influence of natural fractures on hydraulic fracture propagation behaviour

The propagation behaviour of hydraulic fractures is affected by natural fractures in unconventional reservoirs and determines the effect of reservoir reconstruction to a certain extent. Using the splitting mode of mesh nodes and zero-thickness cohesive elements, we established a hydraulic fracture random propagation method. The KGD model and Blanton’s experiment were used to verify the reliability of this method, and the cohesive element parameters of the natural shale core were obtained using three-point bending and digital image correlation methods. Finally, the model was used to simulate the propagation behaviour of hydraulic fractures in natural fracture–developed formations. The results show that even if the hydraulic fracture does not come into contact with the natural fracture, the natural fracture will open, accompanied by the shear slip of the natural fracture surface. The propagation of hydraulic fractures generates a stress shadow effect, causing an increase in the local formation pore pressure and minimum horizontal stress. When the horizontal stress difference was more than 2 MPa, the hydraulic fracture expanded along the direction of the maximum horizontal stress, and the fracture morphology was simple. A formation with a high elastic modulus and high injection rate can contribute to increasing the hydraulic fracture complexity. Hydraulic fracture propagation can be captured using natural fractures. Simultaneously, owing to the stress shadow effect, the stress state at the tip of the hydraulic fractures may change from tensile stress to compressive stress, eventually leading to the stop propagation of hydraulic fractures and the formation of asymmetric hydraulic fractures. The research results are helpful for improving the understanding of the geometric shape of the propagation behaviour of hydraulic fractures in natural fractures that develop formations.

Direct visualization of colloid transport over natural heterogeneous and artificial smooth rock surfaces

Colloid transport in fractured rock formations is an important process impacting the fate of pollutants in the subsurface. Despite intensive and outstanding research on their transport phenomena, the impact of small-scale surface heterogeneity on colloid behavior at the fracture scale remains difficult to assess. In particular, there is relatively little direct experimental evidence on the impact of natural fracture surface heterogeneity on colloid transport. To investigate this, we developed an experimental setup allowing the direct visualization of fluorescent colloid transport in a flow cell containing a natural chalk rock sample while simultaneously monitoring effluent colloid concentrations. We used samples containing both a natural fracture surface and an artificially made smooth surface from the same chalk core. We characterized the roughness and chemical composition of both surface types and numerically calculated each surface's velocity field. From the experiments, we obtained direct images of colloid transport over the surfaces, from which we calculated their dispersion coefficients and quantified the residual deposition of colloids on the rock surface. We also measured the colloid breakthrough curves by collecting eluent samples from the flow cell outlet. The natural fracture surface exhibited larger physical and chemical heterogeneity than the smooth, artificially generated surface. The aperture variability across the natural surface led to preferential flow and colloid transport which was qualitatively apparent in the fluorescent images. The colloid transport patterns matched the calculated velocity fields well, directly linking the surface topography and aperture variation to colloid transport. Compared to the artificially made surface, the natural surface also showed higher dispersion coefficients, which corresponded to the colloids' earlier breakthrough from the flow cell. While we found differences between the elemental composition of the natural and artificially smooth surfaces, we could not observe their impact on the colloids' surface attachment and retention. The main novelty in this work is the coupling of direct colloid transport imaging, breakthrough curve measurements, and colloid surface deposition analyses, in a flow cell containing a natural carbonate rock sample. Our experimental setup can be used to further investigate the link between surface heterogeneity, both chemical and physical, and colloid transport and deposition in natural rock fractures.

Fully 3D Simulation of Hydraulic Fracture Propagation in Naturally Fractured Reservoirs Using Displacement Discontinuity Method

Summary The shape, size, and orientation of natural fractures significantly impact the geometry of hydraulic fractures in unconventional reservoirs, such as shale gas/oil, tight gas, and enhanced geothermal system. The behaviors after the hydraulic fracture encounters natural fractures have been summarized as crossing, diverting, step over, and stopping based on a great number of numerical and experimental analysis with plain strain assumptions. However, under practical situations, the geometries of natural and hydraulic fractures are much more complex than the vertical and rectangular shape assumed by 2D models. The experimental studies on the role of height and inclination of natural fractures have revealed some other phenomena (e.g., bypassing process that the fluid-driven hydraulic fracture propagates up the back side of the natural fracture), which are unable to be captured in 2D. To better describe the intersection behaviors among different kind of fractures, a fully 3D model based on the displacement discontinuity method (DDM) is developed on top of our previous models, which only considered the propagation of hydraulic fractures. A novel crossing criterion to judge whether the hydraulic fracture will cross the cemented natural fracture in 3D is proposed. The successive node snapping scheme is adopted to construct conforming meshes for the evolving intersected curves between hydraulic and natural fracture surfaces, which only alters the location of a small fraction of nodes without changing the nodal connectivity. With this model, the evolution of fracture geometry after the hydraulic fracture intersects with the natural fractures of different toughness, size, orientation, and number is investigated. Because an extra dimension is considered, the fractures are allowed to propagate in more directions, resulting in a series of complex fracture geometries. The dynamic grid evolution method proposed in this work can promote the development of DDM in modeling fully 3D fracture networks in naturally fractured reservoirs.

Shear Slip of Fracture Surface: A New Mechanism for Increased Drilling Fluid Loss in Deep Formation

During drilling and completion of fractured reservoirs, drilling fluid loss is the most serious form of reservoir damage, and it is one of the complicated engineering problems that affect safe and efficient drilling in the long term. This paper aims at the problem of repeated leakage of deep fractured reservoir with more leakage after the failure of the initial plugging. In order to analyze the causes of the increased drilling fluid loss, simulation experiment of fracture sample sealing before and after shear slip of fracture surface was designed and carried out, combining with drilling fluid under the environment of rock plate and block sliding friction experiment, rock mechanics parameter test based on micro-indentation and surface 3D scanning. Then we analyze the induced effect of drilling fluid invasion into natural fracture on the friction sliding of fracture surface and discuss the influence of fracture surface friction on drilling fluid leakage in fractured reservoir. The experimental results show that drilling fluid intrudes into natural fractures, both oil-based drilling fluid and water-based drilling fluid can weaken the friction coefficient of rock blocks, and the weakening effect of oil-based drilling fluid is stronger, and it is easy to induce friction slip of the fracture surface to form dislocation fractures, which provides passage and space for intensified drilling fluid leakage. Friction slip of the fracture surface can strengthen the permeability of the fracture, leading to the decrease of drilling fluid plugging ability and the increase of drilling fluid leakage. After friction sliding, the fracture surface is smoother, which may further expand the dislocation degree, increase the fracture length and width greatly, and promote a larger lost circulation. The results show that shear slip of fracture surface in deep fractured reservoir is one of the reasons for drilling fluid leakage increase, strengthening the friction strength between the natural fracture surfaces and effectively controlling the friction slipping is one of the important ways to control the drilling fluid leakage in deep fractured oil and gas reservoirs.

Unconventional Well Test Analysis for Assessing Individual Fracture Stages through Post-Treatment Pressure Falloffs: Case Study

Researchers and operators have recently become interested in the individual stage optimization of unconventional reservoir hydraulic fracture. These professionals aim to maximize well performance during an unconventional well’s early-stage and potential Enhanced Oil Recovery (EOR) lifespan. Although there have been advances in hydraulic fracturing technology that allow for the creation of large stimulated reservoir volumes (SRVs), it may not be optimal to use the same treatment design for all stages of a well or many wells in an area. We present a comprehensive review of the main approaches used to discuss applicability, pros and cons, and a detailed comparison between different methodologies. Our research outlines a combination of the Diagnostic Fracture Injection Test (DFIT) and falloff pressure analysis, which can help to design intelligent production and improve well performance. Our field study presents an unconventional well to explain the objective optimization workflow. The analysis indicates that most of the fracturing fluid was leaked off through natural fracture surface area and resulted in the estimation of larger values compared to the hydraulic fracture calculated area. These phenomena might represent a secondary fracture set with a high fracture closure stress activated in neighbor stages that was not well-developed in other sections. The falloff pressure analysis provides significant and vital information, assisting operators in fully understanding models for fracture network characterization.

Numerical Investigation of the Fracturing Effect Induced by Disturbing Stress of Hydrofracturing

Fracturing induced by disturbing stress of hydraulic fracturing is the frontier common core scientific problem of reservoir stimulation of coal bed methane and shale gas. The finite-discrete element method, numerical calculation method, is used to analyze the basic law of shear failure and tension failure of natural fractures induced by the disturbing stress of the hydraulic fracture. The simulation results show that when natural fractures and other weak structures exist on the front or both sides of hydraulic fracture, the shear stress acting on the surface of natural fracture will increase until the natural fracture failure, which is caused by the disturbing stress of hydraulic fracturing. The seepage area on the front and both sides of the hydraulic fracture did not extend to the natural fracture while the natural fracture failure occurred. It indicates that the shear failure of natural fractures is induced by the disturbing stress of hydraulic fracturing. When the hydraulic fracture propagates to the natural fracture, the hydraulic tension fracture and disturbed shear fractures are connected and penetrated. As the fluid pressure within the natural fracture surface increases, the hydraulic fracture will continue to propagate through the natural fracture. Meanwhile, due to the action of fluid pressure, a tensile stress concentration will occur at the tip of the natural fracture, which will induce the airfoil tension failure of the natural fracture. With the increase of the principal stress difference, the range of the disturbing stress area and the peak value of the disturbing stress at the front of the hydraulic fracture tip increase, as well as the shear stress acting on the natural fracture surface. During the process of hydraulic fracture approaching natural fracture, the disturbing stress is easier to induce shear failure of natural fracture. With the increase of the cohesive force of natural fracture, the ability of natural fractures to resist shear failure increases. As the hydraulic fracture approaches natural fractures, the disturbing stress is more difficult to induce shear failure of natural fracture. This study will help to reveal the formation mechanism of the fracture network during hydraulic fracturing in the natural fractures developed reservoir.

Hydraulic fracturing network modeling based on peridynamics

A coupled hydromechanical model based on peridynamics is proposed to simulate the hydraulic fracturing in a complex fracture network. The proposed method is validated by comparing the numerical results with the analytical and experimental solution. Then, the influence of the crustal stress distribution, the friction force acting on the natural fracture (NF) surface and the NF network on hydraulic fracture (HF) propagation are investigated. The simulation results reveal that the crustal stress ratio mainly affects the HF propagation direction. When HFs and NFs are connected, the induced stress caused by the opening of NFs deflects the propagation direction of new fractures. The friction force on NF surface is an important factor affecting the interaction between HFs and NFs.

Numerical modeling of closure effect of natural fracture surfaces of rock on behavior of fluid flow

It is essential to understand the hydraulic behavior of rock apertures as the fluid flow path in the rock mass. The geometric parameters of fracture such as roughness of walls and fracture aperture have a significant effect on its hydromechanical behavior. In this paper, the laboratory tests are performed on the samples and then, the laboratory conditions are numerically simulated. The three-dimensional (3D) scanning of the walls of natural rock fractures is used to prepare the geometric model, and the ICEM CFD software is employed to prepare the geometry of fractures. Also, using the Ansys Fluent software and considering the Navier-Stokes equations in the model, the fluid flow in the rock fractures is simulated. Due to the fact that the two joint surfaces are in contact with each other, the model geometry is constructed in the case when the joints are mated and the contact is established in a certain percentage. In this way, the geometries are prepared for 15, 30, 45, 60, 75, and 90% contact between the upper and lower surfaces. The numerical modeling is also validated by the analytical Darcy formula, which indicates the accuracy of the modeling technique. The modeling results show that the macroscopic Forchheimer relation well describes the nonlinear fluid flow in the rock fracture. The values of linear and nonlinear coefficients of Forchheimer equation are estimated for each of the geometric models. The results show that the Forchheimer coefficients are directly related to the joint contact surface in an exponential manner, and the hydraulic aperture increases proportional to the reduced joint contact surface.

Fracture Reactivation Modeling in a Depleted Reservoir

Injection-induced fracture reactivation during hydraulic fracturing processes in shale gas development as well as coal bed methane (CBM) and other unconventional oil and gas recovery is widely investigated because of potential permeability enhancement impacts. Less attention is paid to induced fracture reactivation during oil and gas production and its impacts on reservoir permeability, despite its relatively common occurrence. During production, a reservoir tends to shrink as effective stresses increase, and the deviatoric effective stresses also increase. These changes in the principal effective stresses may cause Coulomb fracture slip in existing natural fractures, depending on their strength, orientation, and initial stress conditions. In this work, an extended finite element model with contact constraints is used to investigate different fracture slip scenarios induced by general reservoir pressure depletion. The numerical experiments assess the effect of Young’s modulus, the crack orientation, and the frictional coefficient of the crack surface on the distribution of stress and displacement after some reservoir depletion. Results show that the crack orientation significantly affects the state of stress and displacement, particularly in the vicinity of the crack. Slip can only occur in permitted directions, as determined by the magnitudes of the principal stresses and the frictional coefficient. Lastly, a larger frictional coefficient (i.e., a rougher natural fracture surface) makes the crack less prone to shear slip.

Numerical Simulation of the Influence of Natural Fractures on Hydraulic Fracture Propagation

According to the theory of plane mechanics involving the interaction of hydraulic and natural fractures, the law of hydraulic fracture propagation under the influence of natural fractures is verified using theoretical analysis and RFPA2D-Flow numerical simulation approaches. The shear and tensile failure mechanisms of rock are simultaneously considered. Furthermore, the effects of the approach angle, principal stress difference, tensile strength and length of the natural fracture, and elastic modulus and Poisson’s ratio of the reservoir on the propagation law of a hydraulic fracture are investigated. The following results are obtained: (1) The numerical results agree with the experimental data, indicating that the RFPA2D-Flow software can be used to examine the hydraulic fracture propagation process under the action of natural fractures. (2) In the case of a low principal stress difference and low approach angle, the hydraulic fracture likely causes shear failure along the tip of the natural fracture. However, under a high stress difference and high approach angle, the hydraulic fracture spreads directly through the natural fracture along the original direction. (3) When natural fractures with a low tensile strength encounter hydraulic fractures, the hydraulic fractures likely deviate and expand along the natural fractures. However, in the case of natural fractures with a high tensile strength, the natural fracture surface is closed, and the hydraulic fracture directly passes through the natural fracture, propagating along the direction of the maximum principal stress. (4) Under the same principal stress difference, a longer natural fracture corresponds to the easier initiation and expansion of a hydraulic fracture from the tip of the natural fracture. However, when the size of the natural fracture is small, the hydraulic fracture tends to propagate directly through the natural fracture. (5) A smaller elastic modulus and larger Poisson’s ratio of the reservoir result in a larger fracture initiation pressure. The presented findings can provide theoretical guidance regarding the hydraulic fracturing of reservoirs with natural fractures.

Numerical simulation of mixed-mode hydraulic fracture propagation and interaction with different types of natural fractures in shale gas reservoirs

Shale gas reservoirs have an extremely low permeability and porosity; hence, it is necessary to perform hydraulic fracturing to improve production. To design effective stimulation measures, it is necessary to fully understand the propagation of hydraulic fractures and their interactions with natural fractures. In this study, a two-dimensional fully coupled mixed-mode model based on the extended finite-element method (XFEM) is established, which includes rock deformation, fracturing fluid flow and leak-off and mixed-mode fracture propagation. We focused on different factors (Young’s modulus, Poisson’s ratio, in situ stress and fracturing fluid rate) to investigate hydraulic fracture initiation, propagation and interaction with two kinds of natural fractures. The results reveal that all the factors have great influences on the fracture geometry, among which in situ stress has the greatest influence. A smaller frictional coefficient of the natural fracture surface enables the hydraulic fracture to divert into the natural fracture. A smaller interaction angle and lower natural cemented fracture strength allow hydraulic fracture propagation along the cemented natural fracture. In the field, hydraulic fracturing parameters should be adapted to the specific conditions to achieve the desired fracturing effect and better economic exploitation.

Experimental investigation on the anisotropic fractal characteristics of the rock fracture surface and its application on the fluid flow description

Based on the anisotropic fractal characteristics of natural fracture surfaces, a fractal fluid flow model was developed. Three-dimensional printed fracture models were built using the morphological information of an actual tensile and shear fracture surface of a rock. The impacts of the fractal dimension on the fluid flow characteristics were investigated. The results demonstrated that the concentration distribution of the undulating height of tensile fracture was larger than that of shear fracture. The fractal dimension of fracture lines with different directional sections ranges from 1.01 to 1.03, which results in the fluid flow anisotropy of fracture surfaces. As predicted by the theoretical model, the fluid flows along the tensile fracture surface and the shear fracture surface in different directions are 0.7–1.2 times and 0.9–1.1 times the average flow rates, respectively. With increasing pressure head, the Reynolds number linearly increased, and the Euler number first rapidly decreased and then slowly decreased.

Effect of Clay and Organic Matter Content on the Shear Slip Properties of Shale

AbstractShale gas reservoirs contain a large number of natural fractures. When shear slip occurs during hydraulic fracturing, it will increase reservoir permeability and improve the reservoir stimulation performance. Because shale contains a large amount of clay and organic matter, its shear slip behavior differs from that of other rocks. In this study, the shear behavior of different shale blocks is experimentally studied, and the proportion of clay and organic matter in the shale dominates the shear slip behavior. Specifically, the friction coefficient and shear strength decrease with the increasing content of clay and organic matter. A microscopic support model was developed to describe the different shear slip behaviors for different contents of clay and organic matter. When the clay and organic matter content is lower than a critical threshold (~35%), shale is microscopically grain supported and brittle shear occurs and the material is prone to shear dilation. When this content is greater than a critical content (~43%), the microscopic structure is a matrix‐supported fabric and plastic shear occurs, which is prone to shear contraction. Shale with contents between these two critical thresholds has a mixed‐support fabric, which is a transition type between brittle and plastic shear. If the proportion of clay and organic matter is less than ~35%, the natural fracture tends to dilate and retain a certain degree of opening after shearing, improving stimulation performance. When the proportion is more than ~43%, shear contraction occurs on the natural fracture surface, which is not conductive and cannot increase reservoir permeability.

Focus stacking photogrammetry for micro‐scale roughness reconstruction: a methodological study

AbstractIn close‐range applications, it is unclear whether optical photogrammetry is capable of accurately reconstructing submillimetre‐scale roughness. This paper presents a study of fine‐scale rock fracture roughness measurements with a careful assessment of the error. The workflow combines the techniques of structure from motion with focus stacking, using consumer‐grade equipment and free or affordable software. The approach is tested firstly with synthetic data to check the influence of the number and position of cameras, object texture and image processing using focus stacking. Secondly, the optimised workflow is used to measure a natural shale rock fracture surface. To estimate the accuracy, the results were compared with a high‐precision reference dataset provided by white‐light interferometry. The standard deviation of error in the method is 6·5 μm, and is related with morphological structures with wavelengths below 150 μm and amplitudes smaller than 10 μm.

Three-dimensional flow characterization in a joint with plumose pattern

This work numerically simulates fracture flow in natural fractures, specifically in a joint with plumose pattern. A natural fracture surface, previously measured in the field using LiDAR scanning, was used to rebuild an open fracture geometry, assuming mode 1 fracture opening. Three-dimensional fracture flow was modeled by solving Stokes equation in a stationary regime using the finite element method. Three different pressure gradients and apertures were numerically investigated to better understand the impact of plumose patterns with different degrees of roughness. Resulting fracture flow fields were characterized by hydraulic aperture and by statistics on the directional components of the three-dimensional velocity vector. The results show that the hydraulic aperture and the longitudinal component of the velocity vector decrease with increasing roughness. Beyond this classical finding, the study shows that the variance of the longitudinal component of the flow velocity vector also decreases with increasing roughness. This behavior can be predicted based on variance estimates connected to the parabolic profile. The results further revealed that the variances of the transverse components of the velocity vector increase with fracture surface roughness. These findings suggest that the roughness-induced reduction in the mean and the variance of the longitudinal component of the velocity vector in joints with rough surfaces is accompanied with a simultaneous increase of the transverse components of the three-dimensional velocity vector.