Equivalent Fracture Models Research Articles

A New Hydro-Mechanical Coupling Numerical Model for Predicting Water Inflow in Karst Tunnels Considering Deformable Fracture

The accurate prediction of groundwater inflow in tunnels in karst regions has been a difficult problem to overcome for a long time. This study proposes an equivalent fracture model that takes into account unsaturated seepage and fracture deformation to predict tunnel water inflow, which is constructed based on the TOUGH-FLAC3D framework. The proposed model with complete failure mechanisms of fracture, including shear failure and tensile failure, was applied to predict the water inflow of the Jianxing Tunnel in Guizhou Province to verify its effectiveness. The results indicate that the proposed numerical model was found to be comparable to on-site observations in predicting inflow rate. The inflow rate in a fractured network reaches a steady state faster than that in a non-fractured network. There is a significant difference of 100 times between the highest transient rate and the stable rate between the fracture network and the non-fractured model. The excavation-induced stress redistribution resulted in slip fracture occurring within a distance of approximately 8.2 m from the tunnel wall, which can increase the fracture width and in turn increases the amount of water flowing into the tunnel by about 50%. In addition, this paper also analyzes the impact of the factors of fracture density, incline angle, stress anisotropy, and initial fracture width on the inflow rate during tunnel construction. The study emphasizes the significance of considering deformable fractures and provides valuable insights for improving numerical tools for inflow prediction during tunnel construction.

The Impact of Fracture Geometries on Heterogeneity and Accuracy of Upscaled Equivalent Fracture Models

Abstract Fractures are widely distributed in the upper crust, which is important to transport processes in groundwater, geothermal, and hydrocarbon reservoirs. Little attention has been paid to the heterogeneity and accuracy of upscaled equivalent fracture models (EFMs) regarding the complex fracture geometries during numerical reservoir simulation. This paper investigates how fracture geometric properties affect the accuracy of highly heterogeneous EFMs. An ensemble of synthetic fractured porous rocks is generated stochastically with varied fracture length, fracture density, and aperture-length correlation. Each realization is upscaled to EFM with the recently developed multiple boundary method. Flow problems are solved for EFMs and discrete fracture models (DFMs) simultaneously, and their flow rates are compared. The results demonstrate that the heterogeneity of EFMs decreases with the number and length of fractures and increases with the aperture-length correlation component. The flow rates calculated by EFMs fit well with those by DFMs with a slope around 1.08 and R2 coefficient above 0.98. The accuracy of the upscaled EFM decreases when the aperture-length correlation changes from sublinear to linear. The uncertainty of upscaling accuracy decreases with dimensionless fracture density. The findings of this study can help for a better understanding of the effect of the discrete fracture geometries on the performance of upscaled EFMs and choosing the appropriate models for different kinds of fractured reservoirs.

Equivalent Permeability Distribution for Fractured Porous Rocks: The Influence of Fracture Network Properties

Equivalent fracture models are widely used for simulations of groundwater exploitation, geothermal reservoir production, and solute transport in groundwater systems. Equivalent permeability has a great impact on such processes. In this study, equivalent permeability distributions are investigated based on a state-of-the-art numerical upscaling method (i.e., the multiple boundary method) for fractured porous rocks. An ensemble of discrete fracture models is created based on power law length distributions. The equivalent permeability is upscaled from discrete fracture models based on the multiple boundary method. The results show that the statistical distributions of equivalent permeability tensor components are highly related to fracture geometry and differ from each other. For the histograms of the equivalent permeability, the shapes of k x x and k y y change from a power law-like distribution to a lognormal-like distribution when the fracture length and the number of fractures increase. For the off-diagonal component k x y , it is a normal-like distribution and its range expands when the fracture length and the number of fractures increase. The mean of diagonal equivalent permeability tensor components increases linearly with the fracture density. The analysis helps in generating stochastic equivalent permeability models in fractured porous rocks and reduces uncertainties when applying equivalent fracture models.

Equivalent Permeability Distribution for Fractured Porous Rocks: Correlating Fracture Aperture and Length

Estimating equivalent permeability at grid block scale of numerical models is a critical issue for large-scale fractured porous rocks. However, it is difficult to constrain the permeability distributions for equivalent fracture models as these are strongly influenced by complex fracture properties. This study quantitatively investigated equivalent permeability distributions for fractured porous rocks, considering the impact of the correlated fracture aperture and length model. Two-dimensional discrete fracture models are generated with varied correlation exponent ranges from 0.5 to 1, which indicates different geomechanical properties of fractured porous rock. The equivalent fracture models are built by the multiple boundary upscaling method. Results indicate that the spatial distribution of equivalent permeability varied with the correlation exponent. When the minimum fracture length and the number of fractures increase, the process that the diagonal equivalent permeability tensor components change from a power law like to a lognormal like and to a normal-like distribution slows down as the correlation exponent increases. The average dimensionless equivalent permeability for the equivalent fracture models is well described by an exponential relationship with the correlation exponent. A power law model is built between the equivalent permeability of equivalent fracture models and fracture density of discrete fracture models for the correlated aperture-length models. The results demonstrate that both the fracture density and length-aperture model influence the equivalent permeability of equivalent fracture models interactively.

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

Efficiency and accuracy of equivalent fracture models for predicting fractured geothermal reservoirs: the influence of fracture network patterns

We evaluate the accuracy and efficiency of equivalent fracture models with a Cartesian grid regarding the variation of fracture network patterns. We apply both the standard finite volume method and the mimetic finite difference method for discretizing the flow equation in the equivalent fracture models. The study underlines that the equivalent fracture models yield accurate and efficient results for predicting the temperature in geothermal reservoirs. The equivalent fracture models based on the mimetic finite difference method yields comparable results with those based on the standard finite volume method. Whereas their accuracy is influenced by the orientations of sparsely distributed fractures.

Modeling anisotropic flow and heat transport by using mimetic finite differences

Modeling anisotropic flow in porous or fractured rock often assumes that the permeability tensor is diagonal, which means that its principle directions are always aligned with the coordinate axes. However, the permeability of a heterogeneous anisotropic medium usually is a full tensor. For overcoming this shortcoming, we use the mimetic finite difference method (mFD) for discretizing the flow equation in a hydrothermal reservoir simulation code, SHEMAT-Suite, which couples this equation with the heat transport equation. We verify SHEMAT-Suite-mFD against analytical solutions of pumping tests, using both diagonal and full permeability tensors. We compare results from three benchmarks for testing the capability of SHEMAT-Suite-mFD to handle anisotropic flow in porous and fractured media. The benchmarks include coupled flow and heat transport problems, three-dimensional problems and flow through a fractured porous medium with full equivalent permeability tensor. It shows firstly that the mimetic finite difference method can model anisotropic flow both in porous and in fractured media accurately and its results are better than those obtained by the multi-point flux approximation method in highly anisotropic models, secondly that the asymmetric permeability tensor can be included and leads to improved results compared the symmetric permeability tensor in the equivalent fracture models, and thirdly that the method can be easily implemented in existing finite volume or finite difference codes, which has been demonstrated successfully for SHEMAT-Suite.

Geomechanical modeling of hydraulic fractures interacting with natural fractures — Validation with microseismic and tracer data from the Marcellus and Eagle Ford

We have developed a new geomechanical workflow to study the mechanics of hydraulic fracturing in naturally fractured unconventional reservoirs. This workflow used the material point method (MPM) for computational mechanics and an equivalent fracture model derived from continuous fracture modeling to represent natural fractures (NFs). We first used the workflow to test the effect of different stress anisotropies on the propagation path of a single NF intersected by a hydraulic fracture. In these elementary studies, increasing the stress anisotropy was found to decrease the curving of a propagating NF, and this could be used to explain the observed trends in the microseismic data. The workflow was applied to Marcellus and Eagle Ford wells, where multiple geomechanical results were validated with microseismic data and tracer tests. Application of the workflow to a Marcellus well provides a strain field that correlates well with microseismicity, and a maximum energy release rate, or [Formula: see text] integral at each completion stage, which appeared to correlate to the production log and could be used to quantify the impact of skipping the completion stages. On the first of two Eagle Ford wells considered, the MPM workflow provided a horizontal differential stress map that showed significant variability imparted by NFs perturbing the regional stress field. Additionally, a map of the strain distribution after stimulating the well showed the same features as the interpreted microseismic data: three distinct regions of microseismic character, supported by tracer tests and explained by the MPM differential stress map. Finally, the workflow was able to estimate, in the second well with no microseismic data, its main performance characteristics as validated by tracer tests. The field-validated MPM geomechanical workflow is a powerful tool for completion optimization in the presence of NFs, which affect in multiple ways the final outcome of hydraulic fracturing.

A physical model study of effect of fracture aperture on seismic wave

Based on Hudson’s theoretical hypothesis of equivalent fracture model, inserting aligned round chips in solid model can simulate fractured media. The effect of fractures on the propagation of P and S waves can be observed by changing the fracture thickness. The base model is made of epoxy resin, and the material of fractures is a kind of low-velocity mixture containing silicon rubber. With constant diameter and number of fractures in each model, one group of models can be formed through changing the thickness of fracture. These models have the same fracture density. By using the ultrasonic pulse transmission method, the experiment records time and waveform of P and S waves in the direction parallel and perpendicular to the fracture orientation. The result shows that, with the same fracture density, changing fracture aperture will affect both velocity and amplitude of P and S waves, and the effect on P-wave amplitude is much greater than that on the velocity. Moreover, the variation in velocity of S wave is more obvious in the slow shear wave (S2), while the variation in amplitude is more obvious in the fast shear wave (S1). These properties of wave propagation are useful for seismic data processing and interpretation.

Mechanical degradation of emplacement drifts at Yucca Mountain—A modeling case study—Part I: Nonlithophysal rock

This paper outlines rock mechanics investigations associated with mechanical degradation of planned emplacement drifts at Yucca Mountain, which is the designated site for the proposed US high-level nuclear waste repository. The factors leading to drift degradation include stresses from the overburden, stresses induced by the heat released from the emplaced waste, stresses due to seismically related ground motions, and time-dependent strength degradation. The welded tuff emplacement horizon consists of two groups of rock with distinct engineering properties: nonlithophysal units and lithophysal units, based on the relative proportion of lithophysal cavities. The term ‘lithophysal’ refers to hollow, bubble like cavities in volcanic rock that are surrounded by a porous rim formed by fine-grained alkali feldspar, quartz, and other minerals. Lithophysae are typically a few centimeters to a few decimeters in diameter. Part I of the paper concentrates on the generally hard, strong, and fractured nonlithophysal rock. The degradation behavior of the tunnels in the nonlithophysal rock is controlled by the occurrence of keyblocks. A statistically equivalent fracture model was generated based on extensive underground fracture mapping data from the Exploratory Studies Facility at Yucca Mountain. Three-dimensional distinct block analyses, generated with the fracture patterns randomly selected from the fracture model, were developed with the consideration of in situ, thermal, and seismic loads. In this study, field data, laboratory data, and numerical analyses are well integrated to provide a solution for the unique problem of modeling drift degradation.