Fracture Aperture Research Articles

Fracture Surface Evolution During Acidized Brine Injection in Calcareous Mudrocks.

During hydraulic fracturing, the oxic hydraulic fracturing fluid physically and chemically alters the fracture surface and creates a "reaction-altered zone". Recent work has shown that most of the physicochemical changes occur on the shale fracture surface, and the depth of reaction penetration is small over the course of shut-in time. In this work, we investigate the physicochemical evolution of a calcite-rich fracture surface during acidized brine injection in the presence of applied compressive stress. A calcite-rich Wolfcamp shale sample is selected, and a smooth fracture is generated. An acidized equilibrated brine is then injected for 16 h, and the pressure change is measured. A series of experimental measurements are done before and after the flood to note the change in physicochemical properties of the fracture. High resolution computed tomography scanning is conducted to observe the fracture aperture growth, which shows an increase of ∼8.3 μm during the course of injection. The fracture topography, observed using a surface roughness analyzer, is shown to be smoother after the injection. The calcite dissolution signature, i.e., surface stripping of calcite, is observed by X-ray fluorescence, and mass spectrometry of the timer-series of the effluent also points in the same direction. We conclude that mineral dissolution is the primary mechanism through which the fracture aperture is growing. The weakening of the fracture surface, along with the applied compressive stresses, promotes erosion of the surface generating fines which reduce the fracture conductivity during the course of injection. In this work, we also highlight the importance of rock mineralogy on the fracture evolution mechanism and determine the thickness of the "reaction altered" zone.

Three-dimensional high aspect ratio interface elements for simulating 3D hydraulic fracturing in deformable porous media

Hydraulic fracturing (HF) is a technique widely used in the oil industry to stimulate low permeability reservoirs and enable their production. However, to model the HF is necessary to consider at least three main coupling process: (i) the fluid pressure deforming the fracture walls, (ii) the fluid flow inside the fracture, and (iii) the fracture propagation through the porous medium. In this context, this work aims to expand the applicability of the high aspect ratio interface elements (HAR-IE) to simulate the formation and propagation of induced hydraulic fracture in three-dimensional scenarios. The proposed methodology considers a deformable porous media in which the fluid flow is governed via Darcy’s law. A proper tension continuum damage model is employed to deal with the fracture formation process and the classical cubic law defines the fluid flow in the fracture. A fully-coupled method solves the system of equations and the numerical results focus on the validation of the method via comparisons against analytical solutions. All the results showed that 3D HAR-IEs satisfactorily reproduce the main characteristics associated with HF, as fracture aperture, length and injection pressure.

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.

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.

Characterization methods for natural fractures distribution in shale and tight reservoirs

Aperture distribution and spatial arrangement are fundamental characteristics of natural fractures. Since it is impossible to directly measure the aperture of all existing fractures, a power law (fractal model) has been commonly used to describe fracture apertures, which has also been extended to estimate fracture spacing and macrofractures density. Although a power law (fractal model) has commonly been used to describe fracture apertures, data points in small and large fracture size ranges tend to deviate from this distribution. In this study, a Variable Shape Distribution (VSD) method was derived from a fractal theory to model fracture size distribution. The VSD method was compared with seven other commonly used models. Eleven fracture datasets collected from five countries on four continents were regressed using these methods. The scale-free methods of the VSD and power law models showed more advantages than the scale-dependent methods. The VSD method was found to best fit all variable aperture size distribution patterns, with an average coefficient of determination of 0.99. The average fractal dimension for all samples calculated by the VSD method (1.36) was slightly higher than that of the power law (1.06). This study is unique in showing that the VSD method can solve a boundary characterization problem that has been widely neglected in previous studies. With the assumption of an even fracture distribution, the VSD method was further applied to estimate average fracture spacing, predict a threshold fracture length that controls the linkage of fractures, and predict fractures outside of the measurement range. This study not only proposes an advanced fractal method to model aperture size distributions in shale and tight rocks but also helps to better understand the importance of fractal dimensions and boundary characterizations.

Inclusion of anisotropy in understanding rock deformation and inter-well fracture growth in layered formation through CZM based XFEM

In layered formations such as the Wufeng-Longmaxi marine shale, mechanical rock properties may be uniform horizontally within a layer, but vary vertically, and from layer to layer. In this study, we implement Newton-Raphson method within a rigorous two-dimensional scheme for computing fluid-solid coupling at every time increment in an anisotropic rock frame. The investigated domain consists of intercalations of soft and hard rock layers with a consideration of a cluster of three horizontal wells. The linear convection equation describing the fluid flow is discretized using upwind scheme whose integration points are determined by the intersection between the crack geometry and the underlying discretization of the extended finite element method (XFEM). A normalized slurry concentration averaged over the fracture width is used to establish a basis for analysing fluid viscosity effects with subsequent XFEM computation indicating that an increased slurry concentration leads to increasing fracture aperture. We further conduct a thorough investigation of an inter-well fracture development with the analyses revealing that the fractures kink at the interfaces of the intercalations of soft and hard layers. It is also observed that, when the elastic contrast between the soft and hard strata decreases, fracture kinking reduces and the inter-well fracture interference mechanism switches to linking or coalescence. Before the linking, the fluid pressure fields inside the separate fractures are independent, whereas an equilibrated pressure field develops inside the inter-linked fracture system. Oriented initial perforations show no link-growth of fractures. However, we observe that the highest inclination angle, which is 75° in our case, yields the highest treatment pressure of 62.8 MPa, whereas the lowest inclination angle of 15° yields the lowest treatment pressure of 56.3 MPa. We validate our results through comparison with a triaxial fracturing cell experiment, and Kristianovich-Geertsma-de Klerk (KGD) fracture problem. In all cases, the findings agree with the numerical results.

Improving reservoir permeability by electric pulse controllable shock wave

Controllable shock wave (CWS) parameters such as amplitude, operating area and number of operations are easy to control and have received extensive attention as a potential new technology for reservoir permeability enhancement. Based on the continuous-discontinuous element method (CDEM) and considering the coupling mechanism of reservoir deformation, failure, pore seepage and fracture flow, a multiphysical field coupling model of reservoir permeability enhancement under CWS is proposed. Under the fluid–solid coupling condition, the formation and development dynamic process of reservoir fractures are obtained, and the change of reservoir permeability is also obtained. The compression fracture zone, tensile fracture zone and undamaged zone are formed around the wellbore. After repeated impact, the number of fractures is more sensitive to tectonic stress, the fracture aperture is more sensitive to reservoir strength. Different from hydraulic fracturing, a large number of fractures in different directions will appear around the main fracture after repeated impact, forming a complex fracture network similar to spider web, which may be beneficial to improve reservoir permeability. The permeability of reservoirs with different tectonic stresses and strengths increases nonlinearly and monotonicly with repeated impacts. Based on CDEM, the change of reservoir permeability with tectonic stress, strength and impact times is obtained, which is a nonlinear monotonic three-dimensional relationship. Based on that relationship, the parameters of CWS can be controlled to predict the change of reservoir permeability, such as peak pressure, duration, impact times, etc. Therefore, it can optimize the reservoir fracturing scheme and improve the reservoir fracturing efficiency, which has considerable practical significance in engineering.

Mesoscopic Deformation of a Hydraulic and Mechanical Aperture of a Single Fracture under Normal Stress

Abstract Studies have focused on describing the interactions between the fluid flow characteristics and structural deformation of fractures at the mesoscopic scale, which is a scale between the macroscale and the microscale. In this work, a three-dimensional numerical simulation based on the Navier-Stokes equation was carried out to investigate the effect of normal stress on the fracture morphology distribution, the fluid flow characteristics distribution, and the interdependence between the flow and stress in a single mesoscopic fracture. Two fracture surfaces of a mesoscopic rough-walled fracture model were created. Results suggest that the nonlinear relationship between the normal stress and deformation due to the area of the total closure increases unevenly. Distributions of the mechanical aperture are approximated well by a normal distribution. Change in the fluid flow is due to the increase in the fractional contact area. The low-velocity zones are surrounded by relatively smaller apertures, which gradually close and join the areas of total closure. Under the limitation of the total closure areas of the two fracture surfaces, the appearance of channel flow behavior. Compared with the flow in the X- and Y-directions, normal stress-induced flow anisotropy occurred. The mesoscopic quantitative relationship between the strains in terms of the mechanical/hydraulic aperture was determined and proven. A macroscopic relationship between the intrinsic permeability and the strain was deduced, which enhances the evaluation and design of various geological engineering applications in which fracture deformation is considered.

Coupled hydromechanical analysis of sparsely fractured crystalline rocks

This paper addresses the issue of evolution and coalescence of localized damage zones in sparsely fractured crystalline rocks. The approach incorporates a constitutive law with embedded discontinuity, which is phrased in terms of both the hydraulic and mechanical response. The formulation takes into account the hydromechanical interaction in regions intercepted by discontinuities. An internal length scale parameter is employed in the definition of equivalent hydraulic conductivity and the tangential stiffness operators, and the onset of newly developed macrocracks is detected by the bifurcation analysis. An enhanced mixed u-p finite element formulation is derived which considers the effect of progressive evolution of the fracture aperture in the weak statements of balance equations. Fully implicit temporal discretization is employed, and the finite element formulation is stabilized by invoking the Polynomial-Pressure-Projection (PPP) technique. A coupled FE analysis is conducted examining the response of Luc du Bonnet granite, with pre-existing fracture network, subjected to plane strain compression that triggers the crack propagation and coalescence. The approach is first verified on some benchmark problems that involve the presence of a dominant fracture. The results of simulations are compared with those obtained using a very fine mesh incorporating interface elements. Later, a series of coupled analyses are carried out examining the hydromechanical response in the presence of multiple fractures.

Digital Rock Analysis on the Influence of Coarse Micro-Fractures on Petrophysical Properties in Tight Sandstone Reservoirs

Tight sandstone reservoirs, as typical unconventional reservoirs, have attracted more and more attention worldwide. Compared to conventional reservoirs, the complex microscopic pore structures and micro-fractures of the tight reservoirs are developed, and fluid flow in the tight sandstone reservoir is very complicated. Therefore, studying the influence of fractures on the rock topological structure and the flow characteristics between micro-fractures and the matrix is critical to the development of tight sandstone reservoirs. In light of the intricate nature of micro-fractures, digital rock analysis technology is utilized to address this issue instead of traditional experimental methods. Firstly, the selected tight rock is scanned by X-ray computed tomography (XCT), and then the natural tight digital rock is reconstructed by filtering and binary segmentation. Secondly, micro-fracture with different shapes is added to the digital rock. Then, a pore network model extracted by the maximum ball method is adopted to conduct the flow simulation. The study finds that the distribution of pore throat radius changes with increasing fracture aperture and length and that the permeability and capillary pressure curves are influenced by fracture aperture and length in the direction of connectivity. The impact of micro-fracture dip angle on pore throat structure is significant with changes in permeability and fluid flow in different directions. Overall, the study emphasizes the importance of fracture aperture and length in determining the properties and behavior of tight sandstone reservoirs and highlights the usefulness of digital rock analysis technology in providing insights into complex microstructures.

Thermo-poro-elastic analytical model of the heat extraction performance of EGS inlaid with multi-linked fractures

The existing analytical model of the heat extraction performance of EGS ignored the influences of both thermo-poro-elastic effect and multi-linked fractures. Therefore, a thermo-poro-elastic analytical model was proposed to simulate heat extraction performance of EGS inlaid with multi-linked fractures. First, the mathematical models of fluid flow, heat transfer, and fracture aperture variation were established based on the conservation of energy and mass. Second, the partial differential equations were converted to ordinary differential equations by Laplace transformation, and the analytical solutions of water and rock temperatures were obtained. Then, the proposed model was verified with the published single-fracture model, which has been demonstrated to be efficient. Finally, the influencing factors, including geothermal reservoir parameters, production parameters, thermo-poro-elastic effect, and fracture morphology, were systematically analyzed and discussed. The results indicated that both the thermo-poro-elastic effect and multi-linked fractures have significant influence on the heat extraction performance of the EGS. The thermo-poro-elasticity effect tends to cause the fracture aperture to increase. The heat extraction performance of the EGS inlaid with multi-linked fractures is much better than that of single fracture EGS. Compared to the uncoupled situation, the production temperature is lowered and the output energy is increased by the thermo-poro-elastic effect at a constant flow rate in the fracture due to the increase in injection rate caused by the increase in fracture aperture. With the increasing of initial fracture aperture, the production temperature gradually decreases, while the output energy first increases and then decreases, so that the optimal initial fracture aperture is 2 mm. The results can provide important guidance for the design and production of an EGS inlaid with multi-linked fractures.

A 3D hybrid DFPM-DFM Model for gas production from fractured shale reservoirs

Hydraulic fracturing as a key technology has been applied to improve gas productivity from shale reservoirs. Both induced hydraulic fractures (HFs) and inherent natural fractures (NFs) delineate a shale reservoir into matrix and fracture domains. Accurate characterizations of matrix and fracture are critical in evaluating gas production. In this work, an in-house built 3D discrete fracture model (DFM) was proposed to explicitly represent the distribution of the NFs network. Gas flow in shale matrix containing multiscale pores in inorganic matters (IOM) and organic matters (OM) was represented by a dual-fractal permeability model (DFPM). Consequentially, a hybrid DFPM–DFM model was proposed to couple gas flow and geomechanics the model was solved by commercial software based on the finite element method. The proposed model was verified using field data from a shale reservoir. The model was further employed to investigate the impacts of fractally-distributed pore size and fracture attributes on the evolutions of permeability and the associated gas production. The results showed that the fractally distributed pore size of IOM accounts for the diverse profiles of permeability evolution that exhibits a downward trend before rebounding. The impacts of pore diameter and tortuosity index on cumulative gas production were quantitatively analysed. We also highlighted the remarkable effects of fracture patterns (fracture connectivity, aperture and number) on cumulative gas production. This work provides a framework to explore the multiscale structural heterogeneities on hydrocarbon recovery and shale deformation.

How high can fracture porosity become in the ultra-deep subsurface?

Knowledge of how high can fracture porosity become in the ultra-deep burial conditions is important but remains problematic. Fracture aperture and porosity are measured using X-ray computed tomography (CT) at atmospheric pressure and then calculated by image logs. Special attention is paid to how high fracture porosity can become in ultra-deep (>6000 m) settings, and which situations will result in high fracture porosities. In situ stress magnitudes, which can be calculated using well logs, control fracture performances, and dissolution along fracture improve fracture porosity at ultra-deep burial depths. Low horizontal stress difference (Δσ < 25 MPa), very high fracture density will result in a high fracture porosity. Fracture porosity can keep as high as 2.0% in relatively low in situ stress conditions even at ultra-deep burial depths. In intense in situ stress conditions (Δσ > 45 MPa), a high degree of dissolution along the fracture dramatically increases fracture porosity. Dissolution will result in the vuggy fracture planes and improve fracture porosity up to 2.0%. The results provide insights into the detection, characterization, and modeling of subsurface fractures.

Experimental study of montmorillonite erosion in low ionic strength water under stagnant and flow conditions in artificial fractures

Compacted bentonite has been proposed as a buffer material in several geological repository concepts for high-level radioactive waste. However, in dilute groundwater, bentonite, especially when dominated by Na-montmorillonite, has been found to be susceptible to erosion and excessive mass loss may compromise the safety of the repository. Herein, results from twelve erosion tests with either flowing or stagnant aqueous solutions, performed with custom-designed artificial fractures made of Poly(methyl methacrylate) are reported. The fracture aperture was 0.1 mm in all tests. Na-montmorillonite or an equal mix by weight of Na- and Ca-montmorillonite were employed. Eleven of the tests were performed with the fracture being vertical, and in one test the fracture was horizontal. The transparent artificial fracture setup allowed monitoring of the expansion of the montmorillonite into the fracture. In all but one test, the diameter reached a limit value, normally within one month of the start of the test. The final diameters varied between 5.9 and 8.7 cm and no clear correlation to flow rate, type of montmorillonite or ionic strength could be discerned. The initial diameter of the emplaced clay was 3.5 cm. The erosion was monitored regularly by turbidity measurements. In general, erosion rates decreased with time and were ultimately low enough that an extrapolation or upscaling of the results to repository scale and operating time would imply a total erosion below the critical value for repository safety. This was the case for all vertical fractures, regardless of montmorillonite type and ionic strength of the aqueous solution. The observed decrease in erosion rates was not due to depletion of montmorillonite at the source because at the end of each test 90% or more of the montmorillonite remained. Further, the ionic strengths were below the critical coagulation concentration, hence gelation cannot provide an explanation to the reduction in erosion rates. Finally, the diameters of the extruded montmorillonite reached the limit while the erosion rates continued to decrease. Consequently, the observed limited expansion was not due to a steady state between erosion and swelling. Rather, the expansion behaviour suggests the presence of frictional forces between the montmorillonite and the fracture walls. The results from this study are beyond the current understanding of montmorillonite colloid behaviour and cannot be explained by existing models.

Improved Fracture Segmentation from Unwrapped Drill-Core Images Using an Innovative Two-Stage Segmentation Approach

While machine learning (ML) provides a great tool for image analysis, obtaining accurate fracture segmentation from high-resolution core images is challenging. A major reason is that the segmentation quality of large and detailed objects, such as fractures, is limited by the capacity of the segmentation branch. This challenge can be seen in the Mask Region-based Convolutional Neural Network (Mask R-CNN), which is a common and well-validated instance segmentation model. This study proposes a two-stage segmentation approach using Mask R-CNN to improve fracture segmentation from unwrapped-core images. Two CNN models are used: the first model processes full-size unwrapped-core images to detect and segment fractures; the second model performs a more detailed segmentation by processing smaller regions of the images that include the fractures detected by the first model. In addition, the procedure uses a new architecture of Mask R-CNN with a point-based rendering (PointRend) neural network module that can increase segmentation accuracy. The method is evaluated on approximately 47 m of core from four boreholes and results in an improvement to previous fracture segmentation methods. It achieves an increase in the average intersection over union of approximately 27% from the baseline (one-stage segmentation with standard Mask R-CNN). The enhanced fracture segmentation provides a mean for obtaining an accurate fracture aperture with an average error of less than 1 mm, which represents a reduction of 0.5 mm from the baseline method. This work presents a novel contribution towards developing an ML-based workflow for core-image analysis.

The effect of fluid flow in the longitudinal fracture along a borehole axis on Stoneley wave propagation

The characterization of fractures is essential to increase the production of hydrocarbon and geothermal resources. In this study, we investigate the effect of the fluid flow in the longitudinal fracture along a borehole on the dispersion and attenuation behavior of Stoneley waves using numerical experiments. In general, incorporating a fracture with the aperture of several tens to hundreds of micrometers into 3D seismic modeling is challenging with high calculational costs. We develop a novel numerical scheme that includes a 2D fluid flow simulation embedded into a 3D wave propagation modeling to address this problem. We devise an approach for capturing the effects of the fluid flow in the fractures of arbitrary aperture widths, which could be much thinner than the grid spacing of a 3D wave propagation simulation. A comparison of the numerical results from our scheme with the analytical solution indicates good agreement, supporting the method’s validity. This developed scheme is applied to the coupled simulation between the Stoneley wave propagation along the borehole axis and induced fluid flow inside a longitudinal fracture with different fracture apertures, fluid viscosity, and dynamic hydraulic conductivity. The modified matrix pencil algorithm applied to the recorded waveforms estimates the dispersion and attenuation of the Stoneley mode. The numerical results reveal the effect of the fracture aperture and fluid viscosity on the dispersion and attenuation behavior of the Stoneley waves. Based on the results, we demonstrate our scheme is an innovative method for estimating the aperture of the fracture and viscosity of the fluid by analyzing the dispersion and attenuation properties of the Stoneley waves.

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.

A hydro‐mechanically‐coupled XFEM model for the injection‐induced evolution of multiple fractures

AbstractIn this paper, a two‐dimensional eXtended Finite Element Method (XFEM) solution is presented for the hydro‐mechanically coupled hydro‐frac‐induced propagation of multiple fractures in rocks. Fractures are considered one‐dimensional objects, and the rock matrix is regarded as a two‐dimensional medium. Rules for improving the accuracy of the solution are included to deal with the transfer of variables between fractures and matrix in the coupling process. The main variables include fluid pressure and fracture aperture. The following assumptions are made: (1) the fluid pressure inside a fracture is applied as a net pressure; (2) fluid leak‐off is ignored; (3) the fluid front is regarded as a fracture front provided that the area of fluid lag has a small effect on fracture propagation compared to the area at which the fluid pressure is applied. The fluid flow is governed by the lubrication equation, while the XFEM is used to describe the behaviour of the elastic medium. The simulation results are compared with analytical solutions for a single hydraulic fracture model to verify and validate the proposed algorithm. A simulation with multiple hydraulic fractures is also performed to investigate the interference effect of multiple fractures and fracture propagation. The shadow effect caused by multiple fractures is analysed to manifest the stress variation along the propagation path.

A fractal model for estimating the permeability of tortuous fracture networks with correlated fracture length and aperture

Many fractures are present in the crust and dominate fluid flow and mass transport. This study proposes a fractal model of permeability for fractured rock masses that includes fractal properties of both fracture networks and fracture surface tortuosity. Using this model, a mathematical expression is derived based on the traditional parallel-plate cubic law and fractal theory. This expression functions as the equivalent permeability of the tortuous fracture network in terms of the maximum fracture length lmax, the fractal dimension of the length distribution Df, porosity ϕ, fracture orientation θ, and the proportionality coefficient between fracture length and aperture β. The fractal scaling law of the fracture length distribution and fractal permeability model is verified by comparison with published studies and fluid dynamic computation, respectively. The results indicate that the deviation of permeability values predicted by the models that do or do not consider the fracture surface tortuosity are as large as three orders of magnitude, which emphasizes that the role of tortuosity should be considered to avoid the overestimation of permeability due to the smooth fracture surface assumption. Further analyses show that the permeability increases with increasing fractal dimension Df, proportionality coefficient β, maximum fracture length lmax, and effective porosity ϕ but decreases with increasing tortuosity dimension Dtf and orientation θ. The fractal dimension of the fracture length distribution Df has the most significant influence on the permeability of the fracture network, followed by Dtf, β, lmax, θ, and ϕ, sequentially.

Permeability evolution and gas flow in wet coal under non-equilibrium state: Considering both water swelling and process-based gas swelling

Accurate knowledge of gas flow within the reservoir and related controlling factors will be important for enhancing the production of coal bed methane. At present, most studies focused on the permeability evolution of dry coal under gas adsorption equilibrium, gas flow and gas diffusion within wet coal under the generally non-equilibrium state are often ignored in the process of gas recovery. In this study, an improved apparent permeability model is proposed which accommodates the water and gas adsorption, stress dependence, water film thickness and gas flow regimes. In the process of modeling, the water adsorption is only affected by water content while the gas adsorption is time and water content dependent; based on poroelastic mechanics, the effective fracture aperture and effective pore radius are derived; and then the variation in water film thickness for different pore types under the effect of water content, stress and adsorption swelling are modeled; the flow regimes are considered based on Beskok’s model. Further, after validation with experimental data, the proposed model was applied to numerical simulations to investigate the evolution of permeability-related factors under the effect of different water contents. The gas flow in wet coal under the non-equilibrium state is explicitly revealed.