Rough Fracture Research Articles

Tensile strength and failure behavior of rock-mortar interfaces: Direct and indirect measurements

The tensile strength at the rock-concrete interface is one of the crucial factors controlling the failure mechanisms of structures, such as concrete gravity dams. Despite the critical importance of the failure mechanism and tensile strength of rock-concrete interfaces, understanding of these factors remains very limited. This study investigated the tensile strength and fracturing processes at rock-mortar interfaces subjected to direct and indirect tensile loadings. Digital image correlation (DIC) and acoustic emission (AE) techniques were used to monitor the failure mechanisms of specimens subjected to direct tension and indirect loading (Brazilian tests). The results indicated that the direct tensile strength of the rock-mortar specimens was lower than their indirect tensile strength, with a direct/indirect tensile strength ratio of 65%. DIC strain field data and moment tensor inversions (MTI) of AE events indicated that a significant number of shear microcracks occurred in the specimens subjected to the Brazilian test. The presence of these shear microcracks, which require more energy to break, resulted in a higher tensile strength during the Brazilian tests. In contrast, microcracks were predominantly tensile in specimens subjected to direct tension, leading to a lower tensile strength. Spatiotemporal monitoring of the cracking processes in the rock-mortar interfaces revealed that they show AE precursors before failure under the Brazilian test, whereas they show a minimal number of AE events before failure under direct tension. Due to different microcracking mechanisms, specimens tested under Brazilian tests showed lower roughness with flatter fracture surfaces than those tested under direct tension with jagged and rough fracture surfaces. The results of this study shed light on better understanding the micromechanics of damage in the rock-concrete interfaces for a safer design of engineering structures.

Fourier-based generation method of rough discrete fracture network

Natural fractures have been often generated with rough morphologies as a result of complex geological processes. Joint surface undulation/roughness degree dominantly affects mechanical characteristics of jointed rock masses, hence should be considered in geometrical modeling of fracture networks. Considering the intrinsic geometric characteristic of natural fractures, this paper proposes a method to generate rough discrete fracture networks (RDFN) for jointed rock mass. Fourier transform is employed to obtain statistical spectrum information of natural rough fractures and fractures in the RDFN model are individually reconstructed in spatial frequency domain based on the information. Besides, three scale-independent shape descriptors, namely Elongation, Regularity and Smoothness, are selected to characterize the geometric characteristics of fractures in different scales and to verify the rationality of the proposed method. A case study is further employed to demonstrate the accuracy of the proposed method, and its applicability to numerical realization is discussed. The proposed method is important for a wide range of applications when considering the discrete modelling of rough fractures.

PRODUCTION QUALITY CONTROL ANALYSIS OF HARUM MANIS USING THE SIX SIGMA METHOD (CASE STUDY: MSME HARUM MANIS, LAMONGAN)

The Harum Manis was a popular traditional food in the 1990s made from sugar, flour, and food coloring. MSME Harum Manis is an MSME that produces harum manis snacks that have been in production since 2012. The author's observations found that the company had problems in its production process, namely, defective products. Types of harum manis product defects are stable fracture, rough fracture, and soft looseness. This research aims to identify the factors that cause product defects, calculate the sigma value in the production harum manis products, and provide suggestions for improving the quality control of harum manis production. The research uses the six sigma method with the concept of DMAIC (define, measure. analyze, improve, and control). The sample used in each data collection is 30 kg. The defect factors for the harum manis product are the slow gulali withdrawal process, the employees being less skilled, the lack of employee training, the addition of flour needs to be more stable, and the production room is now open. The sigma level obtained from MSME Harum Manis in October was 3.4, while in November, a sigma value of 3.28 was obtained. Proposed improvements include conducting training for new and old workers on an ongoing basis, making standard operating procedures (SOP) for workers, making SOP regarding the production process in detail, and closing the production room during production.

Size effect on hydraulic properties of rough-walled fractures upscaled from meter-scale granite fractures

To better bridge the gap between lab-scale data and larger-scale applications. In this study, an integrated method was developed to investigate the size dependence of fluid flow through rough-walled fractures. Granite fracture surfaces of up to 1 m in size were first scanned to acquire data on their morphology and corresponding surface distribution, the asperity height of which was found to follow a normal distribution. Digital fracture surfaces were then created on the basis of the scanned data and upscaled to 20 m by a statistical method, and individual rough-walled fractures were constructed by superimposing two statistically generated surfaces. Fluid flow through the fractures was subsequently simulated by solving the Reynolds’ equation. The simulated results showed evident links between the hydraulic properties and sample sizes. Specifically, both hydraulic aperture and transmissivity of the fracture varied as sample sizes increased until a threshold ranging from 2 to 5 m, beyond which an invariant transmissivity was attained. Thus, the sample size corresponding to invariant transmissivity could be defined as the representative size, the value of which was found to depend on the fracture aperture and roughness. In particular, whereas the augmentation of the fracture aperture appeared to suppress the size dependence on hydraulic properties, increased roughness tended to increase size dependence. The data and modelling presented herein provide insights into the scale dependence of fluid flow through a single fracture. It is concluded that even samples as large as 1 m may not be sufficient to characterize the hydraulic properties of fractures according to the representative sizes obtained, which usually exceeded 2 m under the conditions specified in the present study.

Proppant transport in rough fractures of unconventional oil and gas reservoirs

A method to generate fractures with rough surfaces was proposed according to the fractal interpolation theory. Considering the particle-particle, particle-wall and particle-fluid interactions, a proppant-fracturing fluid two-phase flow model based on computational fluid dynamics (CFD)-discrete element method (DEM) coupling was established. The simulation results were verified with relevant experimental data. It was proved that the model can match transport and accumulation of proppants in rough fractures well. Several cases of numerical simulations were carried out. Compared with proppant transport in smooth flat fractures, bulge on the rough fracture wall affects transport and settlement of proppants significantly in proppant transportation in rough fractures. The higher the roughness of fracture, the faster the settlement of proppant particles near the fracture inlet, the shorter the horizontal transport distance, and the more likely to accumulate near the fracture inlet to form a sand plugging in a short time. Fracture wall roughness could control the migration path of fracturing fluid to a certain degree and change the path of proppant filling in the fracture. On the one hand, the rough wall bulge raises the proppant transport path and the proppants flow out of the fracture, reducing the proppant sweep area. On the other hand, the sand-carrying fluid is prone to change flow direction near the contact point of bulge, thus expanding the proppant sweep area.

An experimental study of the temporary plugging mechanisms of rough fractures in hot dry rocks under a high temperature

The temporary plugging and diverting fracturing (TPDF) technique is important for improving the production capacity of hot dry rock (HDR) reservoirs. The key to this technique is to form effective plugged layers in existing fractures. However, HDR reservoirs have a high temperature, high pressure, and tight rocks. Accordingly, temporary plugging agents (TPAs) deliver different plugging performances for HDR fractures and conventional tight reservoirs. To investigate the plugging mechanisms of TPAs for rough fractures in HDRs, this study first reconstructed the physical models of rough fractures in HDRs using the computed tomography (CT) and 3D printing techniques. Second, it proposed a computational method of fracture surface roughness based on the joint roughness coefficient (JRC) theory. Using this method, the surface roughness of the physical models was calculated and then compared with the rock roughness spectra recommended by the International Society for Rock Mechanics and Rock Engineering (ISRM). Third, with the aid of the temporary plugging characteristic experimental system, this study designed and conducted temporary plugging characteristic experiments on rough fractures in HDRs under a high temperature. Last, this study analyzed the influences of different factors, including fracture surface roughness and the particle concentration and type of TPAs, on the fracture plugging efficiency under a high temperature. The results of this study are as follows: Under the same conditions, the temporary plugging efficiency for fractures in HDRs increased by 67.6% when the fracture surface roughness increased by 10.44; the amount of the required TPA mixture increased by 82.5% when the temperature doubled in value, and the optimal particle concentration of TPAs was 1.5% in this experiment. These results can be used as a reference for the hydraulic fracturing of HDRs.

Inertia and diffusion effects on reactive transport with fluid-solid reactions in rough fracture flows

This study investigates the impacts of fluid inertia and solute diffusion on the reactive transport involving bimolecular fluid-solid reactions in rough channel flows. The critical role of flow fields on fluid-solid reactions is highlighted. Further, a parsimonious upscaled model that successfully captures the reactive transport process is developed.

Investigation on fatigue failure of split-sleeve cold expansion holes of 7075-T651 aluminum alloy

7075-T6 is widely used in the manufacture of aircraft structural components, the majority of which are joined and assembled through hole structures. However, the geometric discontinuity near the fastener holes facilitates stress concentration and makes the joints susceptible to crack nucleation and fatigue failure. It is essential to improve the fatigue resistance of the hole structure. In this paper, the factors affecting the split-sleeve cold expansion on the fatigue behavior of fastener holes of 7075-T651 are investigated based on the compressive residual stress, microstructure, surface roughness, and fatigue fracture. Results revealed that cold expansion causes sub-grain refinement near the hole wall, which increases the surface micro-hardness and favors inhibition of crack growth. Grain refinement, plastic deformation on the surface of the holes, and residual compressive stress produced by the cold expansion process all work together to extend the fatigue life of the hole structure. The constituent particles and microstructure after expansion are important factors affecting fatigue performance, higher level of Fe content could result in the formation of a large number of iron-bearing particles leading to the acceleration of the failure of the workpiece.

Wetting transition and fluid trapping in a microfluidic fracture

Immiscible fluid-fluid displacement in confined geometries is a fundamental process occurring in many natural phenomena and technological applications, from geological CO2 sequestration to microfluidics. Due to the interactions between the fluids and the solid walls, fluid invasion undergoes a wetting transition from complete displacement at low displacement rates to leaving a film of the defending fluid on the confining surfaces at high displacement rates. While most real surfaces are rough, fundamental questions remain about the type of fluid-fluid displacement that can emerge in a confined, rough geometry. Here, we study immiscible displacement in a microfluidic device with a precisely controlled structured surface as an analogue for a rough fracture. We analyze the influence of the degree of surface roughness on the wetting transition and the formation of thin films of the defending liquid. We show experimentally, and rationalize theoretically, that roughness affects both the stability and dewetting dynamics of thin films, leading to distinct late-time morphologies of the undisplaced (trapped) fluid. Finally, we discuss the implications of our observations for geologic and technological applications.

Experimental investigation of the seepage characteristics of a single fracture in limestone with different roughness and seepage fluids

To investigate the effects of roughness and seepage fluids on the seepage characteristics of limestone with rough fractures, five sets of limestone fracture specimens are obtained using 3D scanning and sculpting techniques, in which each set has the same fracture surface morphology. Both distilled water and sodium sulfate solutions were employed to implement seepage dissolution tests on the five sets of limestone specimens with different joint roughness coefficients (JRC). A novel method for characterizing the fracture surface morphology has been proposed, and the seepage characteristics of individual fractures have been investigated. Also, we analyzed the effects of different JRC and seepage solutions on the seepage parameters including seepage flow, equivalent hydraulic aperture, and permeability. Moreover, we presented a quantitative relationship between JRC and permeability. The results reveal that the seepage flow, equivalent hydraulic aperture, and permeability of each rough specimen under different seepage fluids decrease rapidly in the early stages and stabilize later. The dissolution can enhance the erosion of surface particles in the fracture and promote the seepage flow. The permeability and JRC follow a quadratic function in which the empirical parameters can be expressed as a quadratic function and an exponential function of time. This study can provide a theoretical basis for estimating the permeability of fracture with different roughness under different water environments.

Size Effects of Rough Fracture Seepage in Rocks of Different Scales

Percolation experiments were conducted on coal samples with various fracture lengths and inclination angles under different stress conditions using a gravity-loaded rock percolation test device. The goals of these experiments are (1) to improve the technology for protecting water resources while mining coal and (2) to enhance the research on how the size effects of fracture affect seepage. A three-dimensional seepage model was constructed using COMSOL numerical simulation software for larger fracture lengths ranging from 1 to 30 m to investigate the seepage pattern under the coupling of fracture roughness, fracture width, and other factors. Multiple regression analysis was used to investigate the effects of different factors on seepage from large and small fractures independently. The results show that, under laboratory conditions, for fracture lengths 10–70 mm (small length), permeability increases non-linearly with an increase in fracture length, and the overall increase is approximately 1.8 times. Whereas, for fracture lengths of 1–30 m (large length) in the simulation, permeability decreases and then increases with an increase in fracture length, and the overall change is approximately 0.03 times. The permeability varies in three stages (1–8 m obvious change, 8–23 m stabilization, 23–30 m stability) under different fracture lengths, widths, and roughness conditions. Acritical size was found to exist. The effect of fracture length on large length fracture seepage and small length fracture seepage was further verified by parameter sensitivity. The results of this study further reveal the mechanism of fracture seepage under coupling of fracture geometry size stress.

A new approach for predicting direct shear tests on rock fractures

The shear process can significantly affect the hydro-mechanical properties of rock fractures. In the present study, a new approach is developed to predict the direct shear process of rock fractures under the constant normal load condition. This approach is validated by three sets of laboratory direct shear test data and it is then used to study the impact of rock mechanical properties on the shear process. The results show that the presented shear modelling approach can reliably predict the entire shear process of direct shear tests on rough rock fractures under the constant normal load condition. The shear strengths and the normal displacement are sensitive to different physical parameters, which are demonstrated through a comprehensive sensitivity analysis of the physical parameters (i.e., the mechanical properties). The presented shear modelling approach and the sensitivity analysis results are useful for further hydro-mechanical investigations of fractured rocks.

Effect of roughness characteristics of hydraulic fractures on the proppant transport using supercritical CO2

The morphology of rough fractures significantly affects proppant transport in hydraulic fractures. The fracture roughness is even more critical in proppant transport using supercritical CO2 since supercritical CO2 produces rougher fractures than other conventional fracturing fluids. In this study, we used roughness characteristics of the fractures generated by using supercritical CO2 and real rock samples determined by direct measurement together with coupled CFD (Computational Fluid Dynamics)-DEM (Discrete Element Method) to investigate the effects of different roughness characterization parameters on the efficiency of proppant transport using supercritical CO2. Laboratory experimental data of proppant transport in supercritical CO2 within the fracture were used to verify the reliability of the model. The results show that as the ratio of proppant diameter to average width of rough fracture increases, the proppant is more likely to bridge or even form sand blockage when transported in rough fractures, while better transport can be obtained when the ratio is less than 0.4. The main form of proppant particle transport within the rough fractures are the scouring and throwing of particles as the slurry flows through the bridging locations. In addition, the variation of root mean square (RMS) of asperity height values and fractal dimensions can have dissimilar effects on the proppant transport in rough fractures. The distance of proppant transport within the fracture decreases with the increasing fractal dimension, but increasing the RMS of asperity height value will yield proppant transport to longer distance. The proppant is transported farther in rough fractures than in planar fractures, but also, the required pumping pressure is higher in rough fractures, and the pumping pressure is positively related to the fracture roughness. Since using supercritical CO2 for fracturing produces rougher fractures than that of water-based fracturing fluids, higher pump power is required for efficient proppant transport using supercritical CO2, otherwise sand plug may occur. The results of this study lead to a better insight into the proppant transport behavior using supercritical CO2 in rough rock fractures and, therefore, would be useful for the improved field design of waterless fracturing operations conducted by using supercritical CO2.

Geometric rules for the annihilation dynamics of step lines on fracture fronts.

The roughness of a fracture surface records a crack's complex path through a material and can affect the resultant frictional or fluid transport properties of the broken medium. For brittle fractures, some of the most prominent surface features are long, step-like discontinuities called step lines. In heterogeneous materials, the mean crack surface roughness created by these step lines is well captured by a simple, one-dimensional ballistic annihilation model, which assumes the creation of these steps is a random processes with a single probability that depends on the heterogeneity of the material, and that their destruction occurs via pairwise interactions. Here, through an exhaustive study of experimentally generated crack surfaces in brittle hydrogels, we examine step interactions and show that interaction outcomes depend on the geometry of the incoming steps. The rules that govern step interactions can be categorized into three unique classes and are fully described, providing a complete framework for predicting fracture roughness.

Study on Radial Leakage Model and Law of Fractured Formation Drilling Fluid

Wellbore leakage mostly occurs in structurally developed fractured formations. Analyzing the real-time leakage rate during the drilling process plays an important role in identifying the leakage mechanism and its rules on-site. Based on the principles of fluid mechanics and using Herschel-Bulkley (H-B) drilling fluid, by reasonably simplifying the drilling fluid performance parameters, fracture roughness characteristic parameters, pressure difference between the wellbore and formation, and the radial extension length of drilling fluid, the radial leakage model is improved to improve the calculation accuracy. Using the Euler format in numerical analysis to solve the model and with the help of numerical analysis software, the radial leakage law of this flow pattern in the fractures is obtained. The results show that the deformation coefficient of the fracture index, fracture aperture, pressure difference, leakage rate, and cumulative leakage rate are positively correlated. The larger the curvature of the fracture, the rougher the fracture, and the smaller the leakage rate and cumulative leakage rate. The larger the consistency coefficient of the drilling fluid, the greater the additional resistance between the fractures, and the smaller the leakage rate and cumulative leakage rate. As the extending length of the fracture increases, the invasion of drilling fluid decreases, the leakage rate slows down, and eventually reaches zero, with the maximum cumulative leakage rate.

Flow structure transition and identification of two-phase fluid flow through rough rock fractures

Flow structure transition and identification of two-phase fluid flow through rough rock fractures

Nonlinear flow and permeability anisotropy characteristics in hydraulic fracturing-induced rock fractures subjected to various normal compressive stresses

Well productivity after hydraulic fracturing is strongly affected by the flow behaviors in created fracture complexity. In this study, gas flow tests were conducted in splitting fractures (induced by Brazilian splitting) and hydraulic fractures (created by hydraulic fracturing) to study the nonlinear fluid flow behaviors in rough fractures. 3D fracture surfaces were first digitally reproduced with a scanner and then the fracture geometry parameters (roughness profile index R_{p}, the root mean square of the fracture profile wall slope Z_{2}), aperture distributions were computed for both fractures. The influence of the fracture geometry characteristics on the nonlinear flow behaviors were systematically analyzed. The permeability anisotropy was numerically examined in detail. The results show that R_{p}, Z_{2} and mean aperture of hydraulic fractures are relatively smaller, indicating that the fracture surfaces are smoother. The transmissivity of splitting fracture is relatively higher than that of hydraulic ones, and the ratio of splitting to hydraulic one varies from 2.51 at sigma_{c} = 1 MPa to 60.95 at sigma_{c} = 40 MPa. By contrast, splitting fractures have larger critical Reynolds number and lower critical pressure gradient, implying that nonlinearity is easier to occur in splitting fractures. The average Forchheimer coefficient for splitting fractures is 0.00577, which is 1.5 times larger than that (0.0041) for hydraulic ones. In addition, the fractures exhibit strong permeability anisotropy and this anisotropic effect is significantly dependent on the loading stress. In general, the permeability anisotropy in hydraulic fracture is more significant, showing that their permeability anisotropy ratios K are larger and more sensitive to the loading. The obtained results confirm that there exist some discrepancies in flow behaviors between splitting and hydraulic fractures and for more accurate evaluation in engineering practice, hydraulic fractures should be fully considered.

Proppant embedment in rough fractures considering shale hydration

Shale reservoirs are significantly hydrated owing to the presence of large amounts of clay minerals. However, the mechanical properties of the hydration layer on the rock surface decline, resulting in severe proppant embedding. In this study, we established a mathematical model of proppant embedding based on the rock surface indentation experiment and Hertz contact theory, carried out shale spontaneous imbibition experiments to develop a mathematical model for the hydration depth, and built a proppant embedded mathematical model of rough fractures considering the elastic–elastoplastic–plastic whole-stage. We analyzed the proppant embedding laws by considering the hydration layer under closing stress. Our observations were as follows: the surface mechanical properties of hydrated shale decreased by 35.7% after 15 days of hydration intrusion; spontaneous imbibition water absorption in horizontal bedding was greater than that in the vertical bedding; the degree of proppant embedding increased with the increase in shale hydration time. As the closing stress increased, the degree of proppant embedding in the slick water liquid shale became significantly weaker than that in the distilled water liquid shale. This research provided a theoretical basis for shale reservoir fracturing design and fracture effectiveness analysis after fracturing.

Comparative study on hydraulic fracturing using different discrete fracture network modeling: Insight from homogeneous to heterogeneity reservoirs

Conventional discrete fracture network (DFN) modeling is used to simulate hydraulic fracture propagation in fractured low permeability reservoirs. However, natural fractures have a certain degree of roughness, and reservoir rocks have significant heterogeneity characteristics. Therefore, it is necessary to compare the differences in hydraulic fracturing simulation of homogeneous and heterogeneous reservoirs caused by conventional and rough DFN modeling methods. Herein, new-generation algorithms for different DFNs are proposed. Combined the combined finite-discrete element method and different DFNs, four different simulation models are established, covering hydraulic fracturing models from relatively homogeneous to heterogeneous reservoirs. Then, the differences from different DFN modeling methods are compared and discussed. The results show that the relatively homogeneous and heterogeneous models established by conventional DFN may underestimate the bending propagation characteristics and fracturing time and overestimate the proportion of tensile failure. Meanwhile, when the nonuniform distribution of the mechanical parameters of rock blocks is considered, the bending propagation becomes more marked; thus, the fracturing time and the proportion of shear failure are further increased. The above results imply that to accurately predict the hydraulic fracture propagation in a real reservoir, it is vital to consider the roughness of real natural fractures and the nonuniform distribution of mechanical parameters in reservoir hydraulic fracturing modeling.

Numerical study of the wall-retardation effect on proppant transport in rough fractures

Proppant transport and distribution in fractures is critical to evaluate the effectiveness of hydraulic fracturing of unconventional reservoirs such as shale and tight sandstone. This study reproduced the process of proppant transport in rough fractures by two fluid method (TFM) and investigated the wall-retardation effect on proppant migration and settlement. Based on our previous work, the solid–liquid drag model considering wall-retardation effect was further discussed by Lattice Boltzmann method (LBM). The characteristics of rough surfaces of shale and tight sandstone samples were analyzed, and the 4 m × 0.3 m (length × height) rough fracture models were constructed based on these characteristics. The proppant transport and distribution in smooth fractures, sheared fractures and joint fractures were compared, and then the effects of fracture morphology, aperture and mated state on the retarded proppant transport were explored. In smooth fractures, the effect of wall retardation will disappear when the eccentric factor is more than 2.5. In rough fractures, the wall-retardation effect on proppant transport is further enhanced by the unevenly distributed fracture aperture. Both vertical and horizontal velocity of proppant decrease in rough fractures, and this phenomenon is strengthened when the wave-shaped texture or stratification is vertical to the flow direction. The none-flow zones formed by the contact of fracture surfaces will even destroy the continuity of flow filed and block up the proppant transport. However, the morphology of rough fractures will produce little impact on proppant transport when the mean fracture aperture overs the critical fracture aperture. For sheared fractures, the critical fracture aperture is around 6 mm, while for joint fractures, the critical fracture aperture is much less than 4 mm.