岩体裂隙网络非线性渗流特性研究

基于人工交叉裂隙模型,通过室内透水试验,利用电荷耦合元件（CCD）照相机可视化技术,对流体在裂隙交叉点内的非线性流动特性进行研究。建立两种离散裂隙网络（DFN）模型,考虑两种边界条件,改变模型进口和出口之间的压力,直接求解Navier-Stokes（简称N-S）方程,对DFN的非线性渗流特性进行研究。结果表明,室内试验可以观测到与出口3相连的裂隙单元内发生了明显的非线性流动,且通过模型的流量Q和模型两端的压力P具有非线性关系。数值计算结果也表明,在水力梯度J较大时（比如J > 0.1）,通过DFN的Q和P具有非线性关系,而当J较小时（比如J < 10-4）,Q与P线性相关;根据文中的算例,建议利用局部立方定律求解DFN内每条裂隙的渗流特性的临界条件为J ≤10-4;裂隙表面粗糙会造成通过DFN渗流量的降低,但对相对流量误差的影响可忽略不计。     

Review: Mathematical expressions for estimating equivalent permeability of rock fracture networks

Fracture networks play a more significant role in conducting fluid flow and solute transport in fractured rock masses, comparing with that of the rock matrix. Accurate estimation of the permeability of fracture networks would help researchers and engineers better assess the performance of projects associated with fluid flow in fractured rock masses. This study provides a review of previous works that have focused on the estimation of equivalent permeability of two-dimensional (2-D) discrete fracture networks (DFNs) considering the influences of geometric properties of fractured rock masses. Mathematical expressions for the effects of nine important parameters that significantly impact on the equivalent permeability of DFNs are summarized, including (1) fracture-length distribution, (2) aperture distribution, (3) fracture surface roughness, (4) fracture dead-end, (5) number of intersections, (6) hydraulic gradient, (7) boundary stress, (8) anisotropy, and (9) scale. Recent developments of 3-D fracture networks are briefly reviewed to underline the importance of utilizing 3-D models in future research.     

Flow and transport predictions during multi-borehole tests in fractured chalk using discrete fracture network models

Multi-borehole pumping and tracer tests on the 10 to 100-m scale were conducted in a fractured chalk aquitard in the Negev Desert, Israel. Outcrop and core fracture surveys, as well as slug tests in packed-off intervals, were carried out at this site to obtain the parameters needed for construction of a stochastic discrete fracture network (DFN). Calibration of stochastic DFNs directly to the multiple borehole test data was inadequate. Instead, two equivalent deterministic DFN flow models were used: the vertical-fractures (VF) model, consisting of only vertical fractures, and the fractures’ intersections (INT) model, consisting of vertical and horizontal fractures with enhanced transmissivity at their intersections. Both models were calibrated against the multi-borehole response of one pumping test and their predictions were tested against three other independent pumping tests. The average accuracies of all transient drawdown predictions of the VF and INT models were 65 and 66%, respectively. In contrast to this equality in average drawdown predictions of both models, the INT model predicted better important breakthrough curve features (e.g., first and peak arrival times), than the VF model. This result is in line with previously assumed channeled flow, derived from analytical analysis of these pumping and tracer tests. Ronit Nativ, deceased, may her memory be blessed.     

Cubic law with aperture-length correlation: implications for network scale fluid flow

Previous studies have computed and modeled fluid flow through fractured rock with the parallel plate approach where the volumetric flow per unit width normal to the direction of flow is proportional to the cubed aperture between the plates, referred to as the traditional cubic law. When combined with the square root relationship of displacement to length scaling of opening-mode fractures, total flow rates through natural opening-mode fractures are found to be proportional to apertures to the fifth power. This new relationship was explored by examining a suite of flow simulations through fracture networks using the discrete fracture network model (DFN). Flow was modeled through fracture networks with the same spatial distribution of fractures for both correlated and uncorrelated fracture length-to-aperture relationships. Results indicate that flow rates are significantly higher for correlated DFNs. Furthermore, the length-to-aperture relations lead to power-law distributions of network hydraulic conductivity which greatly influence equivalent permeability tensor values. These results confirm the importance of the correlated square root relationship of displacement to length scaling for total flow through natural opening-mode fractures and, hence, emphasize the role of these correlations for flow modeling.     

Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.     

Erratum: Properties of a pair of fracture networks produced by triaxial deformation experiments: insights on fluid flow using discrete fracture network models

Results of a series of deformation experiments conducted on gabbro samples and numerical models for computation of flow are presented. Rocks were subjected to triaxial tests (σ1 > σ2 = σ3) under σ3 = 150 MPa confining pressure at room temperature, to generate fracture network patterns. These patterns were either produced by keeping a constant confining pressure and loading the sample up to failure (conventional test: CT), or by building up a high differential stress and suddenly releasing the confining pressure (confining pressure release test: CPR). The networks are similar in overall density but differ primarily in the orientation of smaller fractures. In the case of CT tests, a conjugate fracture set is observed with one dominant fracture zone running at about 20° from σ1. CPR tests do not show such a conjugate pattern and the mean fracture orientation is at around 35° from σ1. Discrete fracture network (DFN) methodology was used to determine the distribution of flow and hydraulic head for both fracture sets under simple boundary conditions and uniform transmissivity values. The fracture network generated by CT and CPR tests exhibit different patterns of flow field and hydraulic head configurations, but convey approximately the same amount of flow at all scales for which DFN models were simulated. The numerical modelling results help to develop understanding of qualitative differences in flow distribution that may arise in rocks of the same mineralogical composition and mechanical properties, but under the influence of different stress conditions, albeit at similar overall stress magnitude.

     

Machine learning for graph-based representations of three-dimensional discrete fracture networks

Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks (Hyman et al. Comput. Geosci. 84, 10–19 2015) are designed to simulate flow and transport in such porous media. Flow and transport calculations reveal that a small backbone of fractures exists, where most flow and transport occurs. Restricting the flowing fracture network to this backbone provides a significant reduction in the network’s effective size. However, the particle-tracking simulations needed to determine this reduction are computationally intensive. Such methods may be impractical for large systems or for robust uncertainty quantification of fracture networks, where thousands of forward simulations are needed to bound system behavior. In this paper, we develop an alternative network reduction approach to characterizing transport in DFNs, by combining graph theoretical and machine learning methods. We consider a graph representation where nodes signify fractures and edges denote their intersections. Using random forest and support vector machines, we rapidly identify a subnetwork that captures the flow patterns of the full DFN, based primarily on node centrality features in the graph. Our supervised learning techniques train on particle-tracking backbone paths found by dfnWorks, but run in negligible time compared to those simulations. We find that our predictions can reduce the network to approximately 20% of its original size, while still generating breakthrough curves consistent with those of the original network.     

Combining a connected-component labeling algorithm with FILTERSIM to simulate continuous discrete fracture networks

Because modeling the flow of gas and oil in fractured media is increasingly important, multipoint geostatistics approaches, such as single normal equation simulation and FILTERSIM, have become a focus of research in the simulation of sedimentary faces. However, there are problems when these methods are applied to the simulation of discrete fracture networks (DFNs). The biggest problem is that the generated fractures are discontinuous, behaving as separated and isolated points. This paper proposes an improved approach we call CCL-FILTERSIM, which combines FILTERSIM with a run-based, connected-component labeling algorithm to generate more continuous fractures. This paper focuses on the continuity of the simulated fracture network and adopts the scan of the training image, classification of the patterns, and the sequential simulation proposed by FILTERSIM. The principle innovation of the CCL-FILTERSIM approach is the choice of data pattern. Only patterns that form better continuous object patterns are chosen. This is realized by a connected-component labeling algorithm that calculates the connected runs of selected patterns and chooses the pattern with the least runs. Some cases are presented to compare realizations from CCL-FILTERSIM and FILTERSIM, which show that CCL-FILTERSIM yields more continuous objects than FILTERSIM. The DFNs generated by this method provide better conditions for subsequent fluid flow research.     

Simulation of groundwater flow in fractured rocks using a coupled model based on the method of domain decomposition

Groundwater flow in fractured rocks is modeled using a coupled model based on the domain decomposition method. In the model, the fractured porous medium is divided into two non-overlapping sub-domains. One is the rock matrix, in which the medium is described using a continuum model. The other consists of deep fractures and fissure zones, where the medium is described using a discrete fracture network (DFN) model. The two models are coupled through the continuity of the hydraulic heads and fluxes on the common boundaries. The coupled model is used to simulate groundwater flow in a hydropower station. The results show that the model simulates groundwater levels that are in agreement with the measured groundwater levels. Furthermore, the model’s parameters relating to deep fractures and fissure zones are verified by comparing three different models (the continuum model, coupled model, and DFN model). The results show that the coupled model can capture and duplicate the hydrogeological conditions in the study domain, whereas the continuum model overestimates and the DFN model underestimates the measured hydraulic heads. A sensitivity analysis shows that fracture aperture has a considerable effect on the groundwater level. So, when the fracture aperture is large, the coupled model or DFN model is more appropriate than the continuum model in the fracture domain.     

Regional fracture network permeability using outcrop scale measurements

Estimating the hydraulic properties of fractured aquifers is challenging due to the complexity of structural discontinuities that can generally be measured at a small scale, either in core or in outcrop, but influence groundwater flow over a range of scales. This modeling study uses fracture scanline data obtained from surface bedrock exposures to derive estimates of permeability that can be used to represent the fractured rock matrix within regional scale flow models. The model is developed using PETREL, which traditionally benefits from high resolution data sets obtained during oil and gas exploration, including for example seismic data, and borehole logging data (both lithological and geophysical). The technique consists of interpreting scanline fracture data, and using these data to generate representative Discrete Fracture Network (DFN) models for each field set. The DFN models are then upscaled to provide an effective hydraulic conductivity tensor that represents the fractured rock matrix. For each field site, the upscaled hydraulic conductivities are compared with estimates derived from pumping tests to validate the model. A hydraulic conductivity field is generated for the study region that captures the spatial variability of fracture networks in pseudo-three dimensions from scanline data. Hydraulic conductivities estimated using this approach compare well with those estimated from pumping test data. The study results suggest that such an approach may be feasible for taking small scale fracture data and upscaling these to represent the aquifer matrix hydraulic properties needed for regional groundwater modeling.     

Hydromechanical modelling of the SEALEX experiments

Numerical modelling of coupled physical processes in bentonite–sand mixtures under the geological conditions is significant for designing and constructing sealing systems in deep underground repositories for highly radioactive nuclear waste. Within the framework of DECOVALEX 2015, Task A, this work presents the model validation of OpenGeoSys by numerical modelling of coupled hydromechanical (HM) processes in bentonite–sand mixtures. Parameters used in the HM model were determined by modelling the laboratory tests of the sealing experiment (SEALEX). Afterwards these parameters were applied for the modelling of a small-scale mock-up test considering the influence of technological gap and incidental fail of the seal in the sealing system. In order to investigate the availability of employing these HM parameters and numerical models directly to field predictions, the modelling results and measured data of an in situ SEALEX experiment were analysed comparatively. The modelling results reproduced well the main features in HM behaviour of the compacted bentonite–sand mixture, which denotes that the adopted HM models and parameters are adequate for describing the HM processes in the sealing system. It is necessary to take the elastoplastic behaviour and evolution of the permeability of bentonite–sand mixtures into account when using the adopted models to reproduce the HM processes of a sealing system.     

A methodology to constrain the parameters of a hydrogeological discrete fracture network model for sparsely fractured crystalline rock,exemplified by data from the proposed high-level nuclear waste repository site at Forsmark,Sweden

The large-scale geological structure of the crystalline rock at the proposed high-level nuclear waste repository site at Forsmark, Sweden, has been classified in terms of deformation zones of elevated fracture frequency. The rock between deformation zones was divided into fracture domains according to fracture frequency. A methodology to constrain the geometric and hydraulic parameters that define a discrete fracture network (DFN) model for each fracture domain is presented. The methodology is based on flow logging and down-hole imaging in cored boreholes in combination with DFN realizations, fracture connectivity analysis and pumping test simulations. The simulations suggest that a good match could be obtained for a power law size distribution where the value of the location parameter equals the borehole radius but with different values for the shape parameter, depending on fracture domain and fracture set. Fractures around 10–100 m in size are the ones that typically form the connected network, giving inflows in the simulations. The report also addresses the issue of up-scaling of DFN properties to equivalent continuous porous medium (ECPM) bulk flow properties. Comparisons with double-packer injection tests provide confidence that the derived DFN formulation of detailed flows within individual fractures is also suited to simulating mean bulk flow properties and their spatial variability.     

花岗岩潜山储层裂缝建模表征方法——以渤海花岗岩潜山A油田为例

花岗岩潜山油气藏在世界范围内并不多见,当前对其表征还未形成系统完善的研究方法;同时,由于储层受风化、构造多种作用改造,导致储层内部孔、缝、洞并存,具有极强的非均质性,对其表征存在一定的难度。为此本文以渤海大型花岗岩潜山A油田为例,提出了一套花岗岩潜山储层建模表征方法。首先从成因分析入手,引入地貌学分析方法,通过地貌演化特征分析,确定裂缝发育主控因素,在此基础上建立不同成因的裂缝分布趋势体。其次,以井点统计的裂缝特征参数为先验信息,以裂缝分布趋势体为平面约束,建立DFN模型,并对其进行“等效”得到裂缝属性模型。最后,采用动静态资料对裂缝属性模型进行优选,严格控制模型质量,最终得到符合地质认识的裂缝模型。     

A hybrid modeling approach to evaluate the groundwater flow system at the low- and intermediate-level radioactive waste disposal site in Gyeong-Ju, Korea

The development and implementation of a hybrid discrete fracture network/equivalent porous medium (DFN/EPM) approach to groundwater flow at the Gyeong-Ju low- and intermediate-level radioactive waste (LILW) disposal site in the Republic of Korea is reported. The geometrical and hydrogeological properties of fractured zones, background fractures and rock matrix were derived from site characterization data and implemented as a DFN. Several DFN realizations, including the deterministic fractured zones and the stochastic background fractures, whose statistical properties were verified by comparison with in-situ fracture and hydraulic test data, were suggested, and they were then upscaled to continuums using a fracture tensor approach for site-scale flow simulations. The upscaled models were evaluated by comparison to in-situ pressure monitoring data, and then used to simulate post-closure hydrogeology for the LILW facility. Simulation results demonstrate the importance of careful characterization and implementation of fractured zones. The study highlighted the importance of reducing uncertainty regarding the properties and variability of natural background fractures, particularly in the immediate vicinity of repository emplacement.     

随机与确定耦合的裂隙岩体结构面三维网络模拟

离散裂隙随机网络模型中结构面的分布特征仅代表其统计规律,并非地质成因、结构模式、构造形迹的客观反映,以致后续力学计算及渗流模拟结果可信度偏低。针对国家高放废物处置库甘肃北山预选区出露良好的花岗岩体,基于实测结构面统计规律、内在成生关系及水力联系,在前期纯随机模型关键部位修正特征参数,并融入人工辨识的确定结构模式而构建“随机-确定”耦合模型。图形和渗流模拟两种定量检验结果表明：耦合模型结构面数量更接近客观实际,模型准确度提升约48.8%;耦合模型渗流路径与流量较之前更显客观真实,模拟结果与试验数据的接近程度比随机模型大约1/3。另外,不同孔位渗流结果显示：相比于随机结构面,确定性结构面对区域渗流控制作用更加明显,在渗流模拟中扮演更为重要角色。此耦合模型有益于拓宽结构面网络模拟的发展方向。     

The Hydro-Mechanically Coupled Response of Rock Fractures

Summary. In a fractured rock mass, variations in stress and fluid pressure induced by engineering activities can significantly affect the hydrogeological properties. A significant change in fracture transmissivities can also be experienced in the far-field. The simulation of this kind of change requires a Hydro-Mechanical (HM) coupled model. The purpose of this paper is to show how such a model can be used to analyse the evolution of deformation and pressure in a fracture subjected to fluid injection. A 2D BEM-FEM code is used to solve the non-linear system of equations that describe the dependency of transmissivity on local fracture closure. The results of a sensitivity analysis of the essential fracture parameters allow one to gain insight into the importance of the HM models in the framework of the hydrogeology of fractured rock masses. Results obtained from a system of two impervious blocks and a saturated fracture are reported, in order to show the possibilities offered by this technique.     

Advances in discrete element modelling of underground excavations

The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. Efficient numerical models have been obtained using techniques of parallel computing and coupling the discrete element method with finite element method. The discrete element algorithm has been applied to simulation of different excavation processes, using different tools, TBMs and roadheaders. Numerical examples of tunnelling process are included in the paper, showing results in the form of rock failure, damage in the material, cutting forces and tool wear. Efficiency of the code for solving large scale geomechanical problems is also shown.