Discrete Fracture Network Method Research Articles

Existence analysis of hydraulic conductivity representative elementary volume in fractured rocks based on three-dimensional discrete fracture network method

The complexity of fractures in rocks results in heterogeneity and anisotropy of their hydraulic properties. The existence of hydraulic conductivity representative elementary volume (KREV) is a fundamental question in comprehending the hydraulic behavior of fractured rock masses. This article introduces an analytical procedure for determining the existence of KREV in fractured rock masses, which considers the distribution of underground apertures using a discrete fracture network (DFN) model. The procedure follows four basic steps: inverse modeling to generate a 3D DFN; calibration of the effective aperture by combining the results of packer tests and flow simulation using finite difference methods; calculation of the equivalent conductivities in 10 domains and 31 different flow directions; analysis of the fit error between the conductivity ellipsoid to determine the existence of KREV. The proposed approach is applied to the fractured rocks surrounding the 3013 exploration adit near the underground powerhouse of the Three Gorges Project as a case study. The results show that most fractures in the study area have apertures ranging from 0.06 to 0.25 mm and follow a lognormal distribution. The KREV size is 14–16 times the fracture spacing. Investigation of this model has significant implications for understanding flow through fracture networks in related fields.

Embedded discrete fracture network method for numerical estimation of long-term performance of CO2-EGS under THM coupled framework

In enhanced geothermal system (EGS), the artificial fracture networks created by hydraulic fracturing provide highly conductive channel for heat extraction. Very complicated thermo-hydro-mechanical (THM) coupled processes will be involved during cold CO2 injection into the hot fractured reservoir. In this work, a new THM coupled approach is proposed for simulating the long-term performance of CO2-EGS based on embedded discrete fracture networks (DFNs). Due to significant temperature difference between the injection fluid and surrounding, the heat flow in fractures is governed by local thermal non-equilibrium theory. The THM coupling process is achieved by coupling the mechanical simulator FLAC3D and hydraulic-thermal simulator TOUGH2MP. The feasibility of proposed approach is verified and validated through comparing it with analytical solution and other method. The CO2 injection into a reservoir with stochastically generated DFNs is simulated for a period of 20 years, to study the flow behavior, fracture deformation, and thermal performance. The channeling flow is observed by streamlines of fluid and heat flow. The thermal stress due to temperature drop will enhance the fracture width, further decreasing the injection pressure, which shows the significance of incorporating the THM coupling effect in such high temperature reservoirs. This approach also enriches the tools for CO2-EGS simulation.

Impacts of T-type intersections on the connectivity and flow in Complex two-dimensional fracture networks

Natural fractures usually form T-type intersections, but the impacts of T-type intersections on the connectivity and flow results (such as permeability and fluid production) in complex fracture networks are rarely investigated. Here, a stochastic discrete fracture network method is implemented to construct complex two-dimensional fracture networks, denoted as original fracture networks. By implementing the rule-based fracture growth algorithm, the corresponding kinematic fracture networks are generated with a substantial proportion of T-type intersections. The connectivity and flow results of both the single-phase and two-phase flow simulations in these two types of fracture networks are systematically investigated. The results show that kinematic fracture networks tend to connect more fractures with fewer intersections and yield better connectivity than the original ones. Most kinematic fracture networks have larger permeability in the single-phase flow simulation and higher cumulative gas production in the two-phase flow simulation than original fracture networks under the same boundary conditions. The proportions of permeability and production enhancement are 68% and 77%, respectively. Flow results have strong positive correlations with the connectivity of fracture networks, but they are nonequivalent and strongly impacted by the number of inlets and outlets.

Numerical simulation of fracturing and imbibition in shale oil horizontal wells

The shale oil reservoir is characterized by tight lithology and ultra-low permeability, and its efficient exploitation requires the technology of multi-stage and multi-cluster hydraulic fracturing in horizontal wells and shut-in imbibition. After multi-stage and multi-cluster hydraulic fracturing, a complex fracture network is formed, and a large volume of frac fluid is stored within the fracture network. During shut-in, imbibition and exchange between oil and water occurs under the action of the capillary force and osmotic pressure, and the formation pressure builds up in the shale reservoir. On basis of the characteristics of shale oil reservoir, we establish a model of imbibition during fracturing injection and shut-in by coupling oil–water two-phase flow and saline ion diffusion in the hydraulic fractures (HFs) network, natural fractures (NFs) and matrix system under the action of capillary force and osmotic pressure. The DFN method and the multiple continuum method are introduced to characterize fluid flow between the HF and the NF and that between the NF and the matrix respectively, which avoids the problem of a large amount of computation of seepage within the complex fracture. Then, the discrete fracture network (DFN) model and the multiple continuum model are solved with the finite element method, and it is verified in flow field, saturation field and concentration field that the models are accurate and reliable. We propose the imbibition exchange volume for quantitative evaluation of the imbibition degree and a method of calculating the imbibition exchange volume. Simulation of oil and water flow in the fracturing and shut-in stages is performed based on these models. It is found that imbibition in the shale reservoir is driven by mechanisms of pressure difference, capillary force and osmotic pressure. The osmotic pressure and capillary force only cause an increase in the imbibition rate and a reduction in the imbibition equilibrium time and do not lead to variation in the peak of imbibition exchange volume. The imbibition equilibrium time under the action of the capillary force and osmotic pressure is reduced from 150 to 45 d compared with that under the action of the pressure difference. If imbibition equilibrium is reached, low initial water saturation, strong rock compressibility, high formation water salinity and high matrix permeability enhance imbibition and exchange of oil and water in the reservoir. The leakoff volume of frac fluid is generally larger than the imbibition exchanged volume. Leakoff equilibrium occurs slightly earlier than imbibition equilibrium. The imbibition equilibrium time is mainly affected by reservoir permeability and NF density. The number of interconnected fractures mainly affects the frac fluid volume within the hydraulic fracture in the fracturing process. The stimulated reservoir volume (SRV) mainly affects frac fluid imbibition exchange in the shut-in process.

A Numerical Study of Elastic Wave Arrival Behavior in a Naturally Fractured Rock Based on a Combined Displacement Discontinuity-Discrete Fracture Network Model

The arrival behavior of elastic waves in a naturally fractured rock is studied based on numerical simulations. We use the discrete fracture network method to represent the distribution of a natural fracture system and employ the displacement discontinuity method to compute the propagation of elastic waves across individual fractures. We analyze macroscopic wavefield arrival properties collectively arising from the interaction between elastic waves and numerous fractures in the system. We show that the dimensionless angular frequency ῶ = ωZ/κ exerts a fundamental control on the arrival behavior of a plane wave traveling through the fractured rock, where ω, Z, and κ are the angular frequency, seismic impedance, and fracture stiffness, respectively. An asynchronous arrival phenomenon of the wave energy occurs and becomes more significant with an increased ῶ. Two regimes are identified according to the two-branch dependency of the fractal dimension D of the FFAW on ῶ, where the wave arrival behavior is within a non-fractal regime for ῶ smaller than the critical frequency ῶc ≈ 1.0, and enters the fractal regime for ῶ ≥ ῶc. The self-affine properties of the FFAW, i.e., the roughness exponent α and the correlation length lc, both linearly decrease as a function of the exponent ξ (with ῶ = 10ξ) in the fractal regime. Early breakthrough of wave transport occurs in regions with relatively low fracture density, while late-time arrival happens in regions of high fracture density.

Fracture sealing and its impact on the percolation of subsurface fracture networks

Current uderstanding of the impact of fracture sealing on macro-scale fluid flow is insufficient. Here, we generate well-connected orthogonal fracture networks in two- and three-dimensions using a discrete fracture network method. The fracture sealing is simulated by dividing fractures into segments (2D) and blocks (3D). Impacts of fracture sealing on the percolation status of orthogonal fracture networks are systematically studied. Different aperture shapes, segment lengths, and spacing distributions are broadly considered. We find that a small amount of sealing can prevent the formation of spanning clusters, suggesting that global connectivity is rarely realized. Local clusters can trigger hydraulic responses if their sizes are large enough. The connectivity reduction caused by fracture sealing can be reversed by significant stress perturbations, such as hydraulic fracturing. The well-connected and critically oriented fractures become critically stressed and slide because of the increased pore pressure. Partially sealed and mechanically stable fractures can also contribute to fluid flow by enlarging the stimulated reservoir volume (SRV). A new procedure to estimate the SRV size is proposed, and the estimated results are qualitatively consistent with microseismicity maps and field observations.

Complexity analysis of three-dimensional stochastic discrete fracture networks with fractal and multifractal techniques

Systematic analysis of the complexity of fracture systems, especially for three-dimensional (3D) fracture networks, is largely insufficient. In this work, we generate different fracture networks with various geometries with a stochastic discrete fracture network method. The fractal dimension (D) and the singularity variation in a multifractal spectrum (Δα) are utilized to quantify the complexity of fracture networks in different aspects (spatial filling and heterogeneity). Influential factors of complexity, including geometrical fracture properties and system size, are then systematically studied. We generalize the analysis by considering two critical (percolative and over-percolative) stages of fracture networks. At the first stage, κ (fracture orientation) is the most significant parameter for D, following a (fracture length) and L (system size). FD (fracture positions) has a weak correlation with D but a strong correlation with Δα. At the second stage, the sensitivity results of each geometrical parameter and the system size are the same as in stage one for D. For Δα, κ and FD become more significant. For both stages, there is a weak finite-size effect for D and no finite-size effect for Δα. Therefore, a large fracture system is more suitable for a stable fractal dimension estimation, but no requirement for the estimation of Δα. D and Δα are almost independent. Therefore, they can separately quantify different aspects of complexity.

Impacts of fracture properties on the formation and development of stimulated reservoir volume: A global sensitivity analysis

Stimulated reservoir volume (SRV), the highly permeable fracture network created by hydraulic fracturing, is essential for fluid production from low-permeable reservoirs. However, the configuration of SRV and its impacting factors are largely unknown. In this work, we adopt the stochastic discrete fracture network method to mimic natural fractures in subsurface formations and conduct a global sensitivity analysis with the Sobol method. The sensitivity of different fracture properties, including geometrical properties (fracture lengths, orientations, and center positions), mechanical properties (fracture roughness and fracture strength), fracture sealing properties (probabilities of open fractures and segment lengths), and the fracture intensity, are investigated in two and three-dimensional fracture networks. JRC-JCS model is adopted to identify critically stressed fractures. We find that critically stressed fractures compose the backbone of SRV, while partially open fractures can significantly enlarge the size of SRV by connecting more critically orientated fractures. The fracture roughness is the most influential factor for the total length (area) of critically stressed fractures. For the relative increase of SRV (RI) in 2D/3D fracture networks, the probability of open fractures is the most significant factor. The fracture lengths and center positions are essential factors for RI in 2D fracture networks but insignificant in 3D fracture networks. This work provides a realistic scenario of the subsurface structure and systematically investigates the influential factors of SRV, which is useful for estimating the size of SRV and predicting shale gas reservoirs’ production in an accurate and physically meaningful way.

Development and verification of three-dimensional equivalent discrete fracture network modelling based on the finite element method

The discrete fracture network (DFN) method is essential for estimating the mechanical properties of naturally fractured rock masses. A three-dimensional (3D) equivalent DFN model was proposed and thoroughly validated for fractured rock masses. In the equivalent DFN modelling, the Monte Carlo method and 3D rock failure process analysis (RFPA3D) software were used. Additionally, the fracture and its spatial distribution were described explicitly, and the strength and deformability of complex fractured rock masses were investigated. A case study was conducted at the dam site area of Lianghekou Hydropower Station's the left bank slope. The ShapeMetriX3D system was used to acquire the geometric parameters and probability distribution of fractures via digital photogrammetry. Additionally, a series of numerical models were created by combining the proposed equivalent DFN method with the fracture geometry information from the case study. Based on the concept of scale effect and anisotropy, the representative element volume (REV) and mechanical parameters of fractured rock masses were determined. The mechanical parameters of slope rock masses obtained by the proposed DFN modelling and generalized Hoek Brown strength criterion were compared. Furthermore, the applicability and reliability of the proposed model were validated using site data and numerical verifications. The proposed 3D equivalent DFN modelling can analyze the scale effect and anisotropy of mechanical properties of fractured rock masses effectively. Finally, the influence of water head on the hydraulic characteristics of fractured rock masses was analyzed based on the proposed model. Results showed that fractures were the main pathway of water.

Modeling study on supercritical CO2 fracturing applicability and capacity to stimulate reservoirs with different permeabilities

Hydraulic fracturing (HF) using water-based fluids is an effective approach for reservoir stimulation in the exploitation of unconventional resources. Recently, supercritical carbon dioxide (S–CO2) has been proposed as a prospective fracturing fluid in reservoir stimulation because it exhibits higher fracturing capacity compared with water-based fracturing fluid. However, S–CO2 appears to have a distinct drawback of intensifying leak-off when used in reservoirs with relatively high rock matrix permeability (RMP). In this work, a modeling study on water fracturing and S–CO2 fracturing (SCF) was implemented in reservoirs with varied RMPs to assess their applicability. In the modeling, the natural fracture system in the reservoir was considered through the discrete fracture network method for simulating different reservoirs. The lower viscosity and density of S–CO2 compared with those of water enable the easier fracturing of reservoir rocks and allow the generation of more complex fracture networks. However, the intensifying leak-off of S–CO2 due to fracture propagation can hamper the build-up of hydraulic pressure and affect fracture propagation, especially in reservoirs with relatively high RMP. The inflection of fracture length development during HF can also reflect the impact of fluid leak-off. Permeability determines the final fracture network of SCF, and the injection rate increase can offset the leak-off to a certain extent; however, the improvement in fracturing results becomes limited. The modeling results clearly demonstrate the importance of RMP, which can directly determine the applicability and capacity of SCF.

A novel method for modeling the 3D discrete fracture network from a single 2D exemplar

Fracture network modeling is an important prerequisite for studying many rock mechanics and permeability topics. At present, the fracture morphology in the most discrete fracture network (DFN) models is expressed by Euclidean geometries. In order to improve the accuracy of natural fracture description, this paper proposes using the block texture synthesis method to generate large-scale models of 2D fractured coal rock. The results show that these large-scale models remain the original texture or fracture structures from the exemplars. In addition, this paper presents using the idea of physical cover to transform exemplar that is used to generate 3D DFN models. The results show that the fracture density of the 3D DFN model generated by uncovered fracture structures is low. In contrast, the fracture structures with texture or random coverage can generate high-quality 3D DFN models. Furthermore, compared with the traditional DFN model, the texture-based DFN model has an excellent restoration of natural fractures in orientation, roughness, fluctuation, aperture, density, and connectivity. Therefore, the texture-based DFN method can provide a new idea for constructing 3D DFN models.

Equivalent discrete fracture network method for numerical estimation of deformability in complexly fractured rock masses

Equivalent continuum models estimating the deformability of complexly fractured rock masses may incur significant discrepancies. This paper proposes an equivalent discrete fracture network (E-DFN) method to proficiently capture the non-continuous characteristics of rock masses while significantly reducing computational cost compared with traditional discrete fracture network (DFN) models. A significance index of individual fractures is defined to quantitatively evaluate their impact on the elastic modulus. Accumulative significance indices are then generated to define E-DFNs containing representative quantities of fractures. Numerical simulations are conducted with E-DFN models using UDEC (universal distinct element code). The relationship between elastic moduli of complexly fractured rocks and models with E-DFNs is established by an extrapolation function obtained through regression analyses based on an assumption of the marginal diminishing effect of modulus reduction. The proposed method is validated by stochastic DFNs with different geometric configurations. The results show that reasonable estimation with small errors is achieved by the extrapolation of density-reduced E-DFN models. The E-DFN method strikes a balance between result reliability and computational intensity.

Slope instability analysis in Phyllitic rock in the Lesser Himalayan using three different modeling approach

The numerical methods for slope stability problems always have a serious concern related to their continuum and discontinuum nature. In continuum methods, such as the finite element method and limit equilibrium methods, rock materials are usually considered as having a continuous nature. Where commonly practiced, discontinuum methods, like the discrete fracture network method and the discrete element method, are typically controlled by their discontinuous behavior. One of the key objectives of the present article is to emphasize the stability analysis for the development of the religious road corridor, NH-7, in Uttarakhand using different numerical manifold methods (conventional method, continuous method and discontinuous method). To investigate these aspects, eight different sites have been chosen from the Lesser Himalayan region. The geotechnical data have been collected through site visits with the help of a number of rigorous field studies. The rock exposure on the sites is mostly discontinuous in nature, having Phyllitic rock mass characteristics. The safety factor resulting from numerical analysis incorporating the Mohr–Coulomb failure criteria showed that limit equilibrium analysis has a decent correlation with the discrete element method (<10%) than finite element results. The article also discusses the principal stresses, maximum and minimum displacements variation in FEM and DEM modelling. Also, the results from the present study reveal that not just a single mode of numerical analysis is appropriate to predict accurate results for initiating economic remedial measures.

Development of fluid flow and heat transfer model in naturally fractured geothermal reservoir with discrete fracture network method

Natural fractures have a significant effect on fluid flow and heat transfer in naturally fractured geothermal reservoirs. However, most previous studies have assumed that reservoir systems are either a single continuum or dual continuum model, while some studies have just considered a pipeline model. In this study, we developed a discrete fracture network (DFN) geothermal reservoir simulator. The DFN model developed was validated for synthetic fracture systems using a Tetrad; a comparison of the results revealed good agreement between two models. However, developed model is only a fracture model and cannot simulate fluid flow and heat transfer in the matrix. A matrix flow model will be added in the future.

Extracting Hydrocarbon From Shale: An Investigation of the Factors That Influence the Decline and the Tail of the Production Curve

AbstractUnderstanding physical processes that control the long‐term production of hydrocarbon from shale formations is important for both predicting the yield and increasing it. In this work, we explore the processes that could control the tail of the production curve by using a discrete fracture network method to calculate the total travel time from the rock matrix to small‐scale fractures to the primary hydraulic fracture network. The factors investigated include matrix diffusion, extent of the small‐scale fracture zone (or tributary fracture zone/TFZ) consisting of natural, reactivated and induced fractures, and the percentage of free hydrocarbon in the primary fracture network. Individual and combined parameter spaces are explored for each of these to understand the limits of these parameters as well as any systematic correlations between pairs of parameters. Although recent studies have shown that the matrix diffusion in virgin shale influences the production tail only after nearly 20 years, we demonstrate that matrix diffusion in the region of the TFZ significantly impacts production within the first year itself. Additionally, we found that the depth of TFZ fracturing region had no effect on the shape of the production curves although the total mass of the hydrocarbon produced increases with the depth. We also show that one can fit the production data using a site‐specific set of parameters representing the diffusion in the TFZ, depth of the TFZ, and the free hydrocarbon in the large‐scale fractures.

Evaluation of Pore Size and Distribution Impacts on Uniaxial Compressive Strength of Lithophysal Rock

Discrete element method (DEM) has been extensively used for studying the properties of rock mass through numerical simulation, which includes bonded particle (or grain) model method (BPM) and discrete fracture network method. In this paper, utilization of BPM for modeling uniaxial compressive strength (UCS) of lithophysal rock is explored and associated stages are discussed and calibrated including generation of particles, sample scale, loading method, macro- and micro-parameters of BPM. In order to investigate the impacts of pore size and distribution of lithophysal tuff on UCS, various combinations of different pore sizes in one sample and different pore locations with the same pore size are simulated using BPM-DEM. The simulation results show that UCS significantly decreases due to the existence of pores with the same condition of porosity, and when the pore radii increase, the minimum value of UCS slightly declines. Moreover, combinations of different pore sizes in one sample show that greater proportion of small pore radii increases UCS of the sample, while the differences of UCS values decrease. Meanwhile, associated fracture has been observed to develop along the pore and generally tends to develop along the large pores at the edge of the sample in the process of uniaxial compression simulation, with relatively small associated UCS values.

A coupled macro- and meso-mechanical model for heterogeneous coal

A thorough understanding of the deformation behavior, damage accumulation, and progressive failure of heterogeneous coal is a prerequisite for effective control of the surrounding rock and efficient exploitation of resources in underground coal mines. Such understanding can be obtained by analyzing both the macro- and meso-responses of coal to loading. Accordingly, a coupled macro- and meso-mechanical model for heterogeneous coal is developed and implemented in FLAC3D in the present study. The model is based on elasto-plastic mechanics and the energy dissipation and release principle, and heterogeneity is incorporated by the combination of a statistical approach and the discrete fracture network method. The model is calibrated by experimental data and is used to simulate stress-strain responses, the evolution of acoustic emission (AE) events, and energy conversion in compressed coal. The results reveal that: (1) the model can efficiently capture the dependency of the deformability, compressive strength and AE characteristics on the confining pressure; (2) the anisotropic behavior of heterogeneous coal is realistically realized, and the initiation, propagation and coalescence of micro-cracks can be located and tracked; and (3) stress paths, the degree of heterogeneity, and the unloading rate of confining pressure significantly influence the axial stress-strain response and AE event evolution in the stressed coal. The proposed model produces reasonable values for the roof weighting interval and expansion of the excavation-damaged zone around the gate when compared to the field data measured at the Dongzhouyao mine of China.

Rock matrix-fractured media model for heterogeneous and fractured coal bed

Coal was considered rock matrix-fractured media composed of rock matrix and fractures, and the rock matrix-fractured media model for heterogeneous and fractured coal bed was presented. In this model the rock matrix is heterogeneous, and the mechanical parameters such as elastic modulus and strength follow Weibull distribution. Fractures in coal bed were generated with the discrete fracture network method, and the properties of fractures were simulated with Desai element. Then the virtual generating system (VGS) of natural heterogeneous and fractured coal bed was developed in Matlab 6.0. The coupled model of gas flow and deformation process based on the rock matrix-fractured media model method and VGS for heterogeneous and fractured coal bed was presented, and the numerical code was developed in Matlab 6.0. The gas flow process in the heterogeneous and fractured coal bed was simulated in a numerical case. The main conclusions are: 1) The natural heterogeneous and fractured coal bed could be simulated by the rock matrix-fractured media model and VGS; 2) The fractures connected with the well have much more effects on gas flow than those non-connected

Fractured reservoir modeling by discrete fracture network and seismic modeling in the Tarim Basin, China

Fractured reservoirs are an important target for oil and gas exploration in the Tarim Basin and the prediction of this type of reservoir is challenging. Due to the complicated fracture system in the Tarim Basin, the conventional AVO inversion method based on HTI theory to predict fracture development will result in some errors. Thus, an integrated research concept for fractured reservoir prediction is put forward in this paper. Seismic modeling plays a bridging role in this concept, and the establishment of an anisotropic fracture model by Discrete Fracture Network (DFN) is the key part. Because the fracture system in the Tarim Basin shows complex anisotropic characteristics, it is vital to build an effective anisotropic model. Based on geological, well logging and seismic data, an effective anisotropic model of complex fracture systems can be set up with the DFN method. The effective elastic coefficients, and the input data for seismic modeling can be calculated. Then seismic modeling based on this model is performed, and the seismic response characteristics are analyzed. The modeling results can be used in the following AVO inversion for fracture detection.