scholarly journals Analyzing the correlation between stochastic fracture networks geometrical properties and stress variability: a rock and fracture parameters study

2021 ◽  
Vol 11 (2) ◽  
pp. 685-702
Author(s):  
Meysam Khodaei ◽  
Ebrahim Biniaz Delijani ◽  
Mastaneh Hajipour ◽  
Kasra Karroubi ◽  
Ali Naghi Dehghan

AbstractIn this study, the correlation between geometric properties of the fracture network and stress variability in a fractured rock was studied. Initially, discrete fracture networks were generated using a stochastic approach, then, considering the tensorial nature of stress, the stress field under various tectonic stress conditions was determined using finite-difference method. Ultimately, stress data were analyzed using tensor-based mathematical relations. Subsequently, the effects of four parameters including rock tensile strength, rock cohesion, fracture normal stiffness and fracture dilation angle on the stress perturbation distribution were evaluated. The obtained results indicated that stress perturbation and dispersion are directly related to fracture density, which is expressed as the number of fractures per unit area utilizing the window sampling approach. It was also demonstrated that they are inversely related to power-law length exponent which represents the length of fracture. It was observed that stress distribution, among the evaluated parameters, is more sensitive to the fracture normal stiffness and the effects of rock parameters on stress distribution are negligible. It was concluded that the highest stress distribution is created when the fracture network is dense with fractures having high length and low normal stiffness value.

Fractals ◽  
2019 ◽  
Vol 27 (04) ◽  
pp. 1950057 ◽  
Author(s):  
TONGJUN MIAO ◽  
SUJUN CHENG ◽  
AIMIN CHEN ◽  
YAN XU ◽  
GUANG YANG ◽  
...  

Fractures with power law length distributions abound in nature such as carbonate oil and gas reservoirs, sandstone, hot dry rocks, etc. The fluid transport properties and morphology characterization of fracture networks have fascinated numerous researchers to investigate for several decades. In this work, the analytical models for fracture density and permeability are extended from fractal fracture network to general fracture network with power law length distributions. It is found that the fracture density is related to the power law exponents [Formula: see text] and the area porosity [Formula: see text] of fracture network. Then, a permeability model for the fracture length distribution with general power law exponent [Formula: see text] and the power law exponent [Formula: see text] for fracture length versus aperture is proposed based on the well-known cubic law in individual fracture. The analytical expression for permeability of fractured networks is found to be a function of power law exponents [Formula: see text], area porosity [Formula: see text] of fracture network, and the micro-structural parameters (maximum fracture length [Formula: see text], fracture azimuth [Formula: see text] and fracture dip angle [Formula: see text]). The present model may shed light on the mechanism of seepage in fracture networks with power law length distributions.


2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiaolin Wang ◽  
Liyuan Yu ◽  
Hanqing Yang

The equivalent permeability of fractured rock masses plays an important role in understanding the fluid flow and solute transport properties in underground engineering, yet the effective predictive models have not been proposed. This study established mathematical expressions to link permeability of 2D fracture networks to the geometric properties of fractured rock masses, including number density of fracture lines, total length of fractures per square meter, and fractal dimensions of fracture network structures and intersections. The results show that the equivalent permeability has power law relationships with the geometric properties of fracture networks. The fractal dimensions that can be easily obtained from an engineering site can be used to predict the permeability of a rock fracture network. When the fractal dimensions of fracture network structures and intersections exceed the critical values, the effect of randomness of fracture locations is negligible. The equivalent permeability of a fracture network increases with the increment of fracture density and/or fractal dimensions proportionally.


2021 ◽  
Vol 11 (2) ◽  
pp. 839-856
Author(s):  
Erfan Hosseini ◽  
Mohammad Sarmadivaleh ◽  
Zhongwei Chen

AbstractThe role of natural fractures in future reservoir performance is prominent. The fractured porous media is composed of an interconnected network of fractures and blocks of the porous medium where fractures occur in various scales and have a strong influence either when most of the flow is concentrated and them or when they act as barriers. A general numerical model for discrete fracture networks (DFN) is usually employed to handle the observed wide variety of fracture properties and the lack of direct fracture visualization. These models generally use fracture properties’ stochastic distribution based on sparse and seismic data without any physical model constraint. Alternatively, a DFN model includes usual numerical geomechanical approaches like boundary element and finite element. But here, a geostatistical methodology has been used to generate a DFN model. In this paper, an alternative modeling technique is employed to create the realization of an anisotropic fractured rock using simulated annealing (SA) optimization algorithm. There is a notable positive correlation between fracture length and position. There are three principal subjects in a study of fractured rocks. Firstly, the network’s connectivity, secondly, fluid flows through the system, and thirdly, dispersion. Here, connectivity of generated networks is considered. Continuum percolation is the mathematical model to study the geometry of connected components in a random subset of space. Different random realizations from the S.A. algorithm in four different sizes of L = 100, 150, 200, 250 at post-threshold condition are used as disordered media in percolation theory to compute percolation properties using Monte Carlo simulation. The percolation threshold (critical fracture density) and two crucial scaling exponents (β and υ) that dictate the model’s connectivity behavior are estimated to over 200 realizations.


Solid Earth ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 1731-1746
Author(s):  
Romesh Palamakumbura ◽  
Maarten Krabbendam ◽  
Katie Whitbread ◽  
Christian Arnhardt

Abstract. Understanding the impact of fracture networks on rock mass properties is an essential part of a wide range of applications in geosciences from understanding permeability of groundwater aquifers and hydrocarbon reservoirs to erodibility properties and slope stability of rock masses for geotechnical engineering. However, gathering high-quality, oriented-fracture datasets in the field can be difficult and time-consuming, for example, due to constraints on field work time or access (e.g. cliffs). Therefore, a method for obtaining accurate, quantitative fracture data from photographs is a significant benefit. In this paper we describe a method for generating a series of digital fracture traces in a geographic information system (GIS) environment, in which spatial analysis of a fracture network can be carried out. The method is not meant to replace the gathering of data in the field but to be used in conjunction with it, and it is well suited when field work time is limited or when the section cannot be accessed directly. The basis of the method is the generation of the vector dataset (shapefile) of a fracture network from a georeferenced photograph of an outcrop in a GIS environment. From that shapefile, key parameters such as fracture density and orientation can be calculated. Furthermore, in the GIS environment more complex spatial calculations and graphical plots can be carried out such as heat maps of fracture density. Advantages and limitations compared to other fracture network capture methods are discussed.


Solid Earth ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 2119-2140
Author(s):  
Billy James Andrews ◽  
Zoe Kai Shipton ◽  
Richard Lord ◽  
Lucy McKay

Abstract. Fault architecture and fracture network evolution (and resulting bulk hydraulic properties) are highly dependent on the mechanical properties of the rocks at the time the structures developed. This paper investigates the role of mechanical layering and pre-existing structures on the evolution of strike–slip faults and fracture networks. Detailed mapping of exceptionally well exposed fluvial–deltaic lithologies at Spireslack Surface Coal Mine, Scotland, reveals two phases of faulting with an initial sinistral and later dextral sense of shear with ongoing pre-faulting, syn-faulting, and post-faulting joint sets. We find fault zone internal structure depends on whether the fault is self-juxtaposing or cuts multiple lithologies, the presence of shale layers that promote bed-rotation and fault-core lens formation, and the orientation of joints and coal cleats at the time of faulting. During ongoing deformation, cementation of fractures is concentrated where the fracture network is most connected. This leads to the counter-intuitive result that the highest-fracture-density part of the network often has the lowest open fracture connectivity. To evaluate the final bulk hydraulic properties of a deformed rock mass, it is crucial to appreciate the relative timing of deformation events, concurrent or subsequent cementation, and the interlinked effects on overall network connectivity.


Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050014
Author(s):  
XIAOSHAN WANG ◽  
YUJING JIANG ◽  
RICHENG LIU ◽  
BO LI ◽  
ZAIQUAN WANG

This paper presents a numerical study on the equivalent permeability of a fractured rock. A series of two-dimensional discrete fracture network (DFN) models for the calculation of equivalent permeability are generated based on discrete element method (DEM). A sufficient large “parent” DFN model is generated based on the data obtained from a site investigation result of Three Gorges Project in China. Smaller DFN models are extracted from the large “parent” DFN model to calculate the equivalent permeability with an interval of rotation angle of [Formula: see text]. Fluid flow through fractures in both horizontal and vertical directions is simulated. The results show that when the side length of DFN models are larger than 40[Formula: see text]m, the equivalent permeability of both [Formula: see text] and [Formula: see text] become stable, indicating that a DFN model size of 40[Formula: see text]m can be approximated as a representative elementary volume (REV) for those studied rocks. Penetration ellipses are fitted using the least square method on the basis of the calculated equivalent permeability tensor and the main seepage directions of this fractured rock were determined as 63–67[Formula: see text]. Fractal characteristics of DFN models are analyzed with box-counting method by changing the fracture trace length and fracture density, and the results show that equivalent permeability exhibits a logarithmic increasing trend with the increment of fractal dimension.


2021 ◽  
Author(s):  
Maximilian O. Kottwitz ◽  
Anton A. Popov ◽  
Steffen Abe ◽  
Boris J. P. Kaus

Abstract. Predicting effective permeabilities of fractured rock masses is a key component of reservoir modelling. This is often realized with the discrete fracture network (DFN) method, where single-phase incompressible fluid flow is modelled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in significant computational costs. Equivalent continuum models (ECM) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While this has the advantage of lower computational costs and the possibility to include matrix properties, choosing the right cell size for discretizing the fracture network into an ECM is crucial to provide accurate flow results and conserve anisotropic flow properties. Whereas several techniques exist to map a fracture network onto a grid of continuum cells, the complexity related to flow in fracture intersections is often ignored. Here, numerical simulations of Stokes-flow in simple fracture intersections are utilized to analyze their effect on permeability. It is demonstrated that intersection lineaments oriented parallel to the principal direction of flow increase permeability in a process termed intersection flow localization (IFL). We propose a new method to generate ECM's that includes this effect with a directional pipe flow parametrization: the fracture-and-pipe model. Our approach is tested by conducting resolution tests with a massively parallelized Darcy-flow solver, capable of representing the full permeability anisotropy for individual grid cells. The results suggest that as long as the cell size is smaller than the minimal fracture length and larger than the maximal hydraulic aperture of the considered fracture network, the resulting effective permeabilities and anisotropies are resolution-independent. Within that range, ECM's are applicable to upscale flow in fracture networks, which reduces computational expenses for numerical permeability predictions of fractured rock masses. Furthermore, incorporating the off-diagonal terms of the individual permeability tensors into numerical simulations results in an improved representation of anisotropy in ECM's that was previously reserved for the DFN method.


2009 ◽  
Vol 12 (01) ◽  
pp. 48-52 ◽  
Author(s):  
Shawn C. Maxwell ◽  
Charles Waltman ◽  
Norman R. Warpinski ◽  
Michael J. Mayerhofer ◽  
Neda Boroumand

Summary Microseismic mapping is extensively used in the Barnett Shale to map hydraulic fracture complexity associated with interactions of the stimulation with pre-existing fractures (fracs). Previous studies have indicated a fair correlation between the well performance and extent of the seismically active volume. However, in addition to this measure of the extent of the stimulated fracture network, the characteristics of this fracture network is also expected to impact the well performance. In particular, the fracture spacing is believed to be an important factor controlling the potential gas flow. In this paper, we use the density of the total seismic moment release (a robust measure of the microseism strength) as an indication of the seismic deformation that may correlate to the fracture density. The study uses a set of microseismic maps of hydraulic fracture stimulations, including cases in which the stimulated reservoir volume measured by the extent of the seismically active region poorly correlated with the well performance. Incorporating the seismic moment density to assess the fracture density with the network extent, an improved correlation with the well performance was observed. Introduction Microseismic mapping of hydraulic fracture stimulations has become a common technique to map the fracture growth and geometry (Warpinski et al. 2004; Fisher et al. 2002; Maxwell et al. 2002; Fisher et al. 2004; Rutledge et al. 2004; Shapiro et al. 2004; Chambers et al. 2008; Lu et al. 2008; Warpinski et al. 2005). Microseismic images provide details of the fracture azimuth, height, length, and complexity resulting from interaction with pre-existing fratures. The resulting images can be used to calibrate numerical simulations of the fracture growth, allowing more confident modeling of other stimulations in the field, and a better identification of the stimulated region that may ultimately be drained by the well. Arguably, the Barnett Shale is the field that has had the most fracs mapped over the last several years. Microseismic mapping in the Barnett Shale has repeatedly demonstrated extreme fracture complexity resulting from interaction between the injection and a pre-existing fracture network (Fisher et al. 2002; Maxwell et al. 2002; Fisher et al. 2004; Rutledge et al. 2004; Shapiro et al. 2004; Chambers et al. 2008; Lu et al. 2008; Warpinski et al. 2005; Mayerhofer et al. 2006). Even between neighboring wells, the geometry of the stimulated fracture network shows a high degree of variability caused by localized differences in the fracture network (Fisher et al. 2002). The Barnett Shale has a low-intrinsic matrix permeability, and the permeability enhancement associated with the fracture stimulation results in permeable fracture networks sufficient for economic gas recovery in the field. Previous studies have shown a correlation between the volume of the reservoir stimulated as measured by the volume of the reservoir that emits microseisms during the stimulation, and the production ultimately realized from the well (Fisher et al. 2002; Fisher et al. 2004; Mayerhofer et al. 2006). The correlation is attributed to larger fracture networks being stimulated in wells in which a large microseismically active volume of the reservoir has been realized, resulting in more permeable fracture pathways connected to the well and therefore a higher potential for gas flow to the well. Recently, many operators in the Barnett Shale have attempted horizontal completions, which have allowed large volumes of the reservoir to be stimulated with large fracture networks. Many of these completions use perforated, cemented liners, and the microseismic images allow for indentification of improved perforation staging to maximize the stimulated reservoir volume (SRV) (Fisher et al. 2004). Many of the Barnett Shale stimulations are water fracs in which large volumes of water are injected at a high rate (Mayerhofer et al. 1997). One possible mechanism for the success of waterfracs is that increased fluid pressure in natural fractures induced shear failure, resulting in fracture dilation associated with mismatched surfaces on opposite sides of the fracture. Within this conceptual framework, the microseismic events correspond to the actual fracture movement. The earlier investigations of the SRV measured the total volume of the microseismically active region. However, this measure of the stimulated volume does not take into account the properties of the fracture network, which has also been indicated to impact well performance (Mayerhofer et al. 2006). Furthermore, the permeability enhancement of the fracture may be related to deformation associated with fracturing. Beyond the basic hypocentral locations of the microseisms used to calculate the SRV, additional seismic signal characteristics allow investigation of the source of the mechanical deformation resulting in the microseisms. In particular, the seismic moment (Aki and Richards 1980), a robust measure of the strength of an earthquake or microearthquake can be used to quantify the seismic deformation (Maxwell et al. 2003). In this paper, we examine several published microseismic projects in the Barnett Shale formation for correlation between the production and seismic-deformation attributes. In the next section, we describe seismic moments and the calculation of seismic deformation. We illustrate how a seismic moment can be used to remove a recording bias present in most microseismic monitoring applications and the importance for calculating the seismic deformation. Finally, we present the comparison between production, seismic deformation, and SRV for several published datasets.


2019 ◽  
Author(s):  
Romesh Palamakumbura ◽  
Maarten Krabbendam ◽  
Katie Whitbread ◽  
Christian Arnhardt

Abstract. Understanding the impact of fracture networks on rock mass properties is an essential part of a wide range of fields in geosciences, from understanding permeability of groundwater aquifers and hydrocarbon reservoirs to erodibility properties and slope stability of rock masses for geotechnical engineering. However, gathering high quality, oriented-fracture datasets in the field can be difficult and time consuming, for example due to constraints on time or access (e.g. cliffs). Therefore, a method for obtaining accurate, quantitative fracture data from photographs is a significant benefit. In this paper we describe and evaluate the method for generating a series of digital fracture traces in GIS-environment, in which spatial analysis of a fracture network can be carried out. The method is not meant to replace the gathering of data in the field, but to be used in conjunction, and is well suited where fieldwork time is limited, or where the section cannot be accessed directly. The basis of the method is the generation of the vector dataset (shapefile) of a fracture network from a georeferenced photograph of an outcrop in a GIS environment. From that shapefile, key parameters such as fracture density and orientation can be calculated. Furthermore, in the GIS-environment more complex spatial calculations and graphical plots can be carried out such as heat maps of fracture density. There are a number of advantages to using a digital method for gathering fracture data including: time efficiency, generating large fracture network datasets, flexibility during data gathering and consistency of data.


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