scholarly journals Evaluating Flow in Fractal-Fracture Networks: Effect of Variable Aperture

2021 ◽  
Vol 56 ◽  
pp. 117-128
Author(s):  
Ajay K. Sahu ◽  
Ankur Roy
Keyword(s):  
Practical Interest ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Aperture ◽  
High Porosity ◽  
Fracture Networks ◽  
Building Models ◽  
Variable Aperture ◽  
Almost All ◽  
Fractal Fracture

Abstract. While fractal models are often employed for describing the geometry of fracture networks, a constant aperture is mostly assigned to all the fractures when such models are flow simulated. In nature however, almost all fracture networks exhibit variable aperture values and it is this fracture aperture that controls the conductivity of individual fractures as described by the well-known cubic-law. It would therefore be of practical interest to investigate flow patterns in a fractal-fracture network where the apertures scale in accordance to their position in the hierarchy of the fractal. A set of synthetic fractal-fracture networks and two well-connected natural fracture maps that belong to the same fractal system are used for this purpose. A set of dominant sub-networks are generated from a given fractal-fracture map by systematically removing the smaller fracture segments with narrow apertures. The connectivity values of the fractal-fracture networks and their respective dominant sub-networks are then computed. Although a large number of fractures with smaller aperture are eliminated, no significant decrease is seen in the connectivity of the dominant sub-networks. A streamline simulator based on Darcy's law is used for flow simulating the fracture networks, which are conceptualized as two-dimensional fracture continuum models. A single high porosity value is assigned to all the fractures. The permeability assigned to fractures within the continuum model is based on their aperture values and there is nearly no matrix porosity and permeability. The recovery profiles and time-of-flight plots for each network and its dominant sub-networks at different time steps are compared. The results from both the synthetic networks and the natural data show that there is no significant decrease in fluid recovery in the dominant sub-networks compared to their respective parent fractal-fracture networks. It may therefore be concluded that in the case of such hierarchical fractal-fracture systems with scaled aperture, the smaller fractures do not significantly contribute to connectivity or fluid flow. In terms of decision making, this result will aid geoscientists and engineers in identifying only those fractures that ultimately matter in evaluating the flow recovery, thus building models that are computationally less expensive while being geologically realistic.

Influence of Aperture Distribution on Flow in Fractal-Fracture Networks

2021 ◽  
Author(s):  
Ajay Kumar Sahu ◽  
Ankur Roy
Keyword(s):  
Practical Interest ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Aperture ◽  
Fracture Networks ◽  
Fracture Systems ◽  
Fractal System ◽  
Porosity And Permeability ◽  
Aperture Distribution ◽  
Fractal Fracture

<p>While fractal models are often employed for describing the geometry of fracture networks, a constant aperture is mostly assigned to all the fractures when such models are flow simulated. While network geometry controls connectivity, it is fracture aperture that controls the conductivity of individual fractures as described by the well-known cubic-law. It would therefore be of practical interest to investigate flow patterns in a fractal-fracture network where the apertures also scale as a power-law in accordance to their position in the hierarchy of the fractal. A set of synthetic fractal-fracture networks and two well-connected natural fracture maps that belong to the same fractal system are used for this purpose. The former, with connectivity above the percolation threshold, are generated by spatially locating the fractured and un-fractured blocks in a deterministic and random manner. A set of sub-networks are generated from a given fractal-fracture map by systematically removing the smaller fracture segments. A streamline simulator based on Darcy's law is used for flow simulating the fracture networks, which are conceptualized as two-dimensional fracture continuum models. Porosity and permeability are assigned to a fracture within the continuum model based on its aperture value and there is nearly no matrix porosity or permeability. The recovery profiles and time-of-flight values for each network and its dominant sub-networks at different time steps are compared.</p><p>The results from both the synthetic networks and the natural maps show that there is no significant decrease in recovery in the dominant sub-networks of a given fractal-fracture network. It may therefore be concluded that in the case of such hierarchical fractal-fracture systems with scaled aperture, the smaller fractures do not significantly contribute to the fluid flow.</p><p><strong>Key-words: </strong>Fractal-fracture; Connectivity; Aperture; Dominant Sub-networks; Streamline Simulator; Recovery</p>

scholarly journals Clustering, Connectivity and Flow Responses of Deterministic Fractal-Fracture Networks

2020 ◽  
Vol 54 ◽  
pp. 149-156
Author(s):  
Ajay K. Sahu ◽  
Ankur Roy
Keyword(s):  
Fractal Dimension ◽  
Spatial Clustering ◽  
Flow Behavior ◽  
Flow Simulation ◽  
Fractal Dimensions ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Fracture Models ◽  
Fractal Fracture

Abstract. It is well known that fracture networks display self-similarity in many cases and the connectivity and flow behavior of such networks are influenced by their respective fractal dimensions. In the past, the concept of lacunarity, a parameter that quantifies spatial clustering, has been implemented by one of the authors in order to demonstrate that a set of seven nested natural fracture maps belonging to a single fractal system, but of different visual appearances, have different clustering attributes. Any scale-dependency in the clustering of fractures will also likely have significant implications for flow processes that depend on fracture connectivity. It is therefore important to address the question as to whether the fractal dimension alone serves as a reasonable proxy for the connectivity of a fractal-fracture network and hence, its flow response or, if it is the lacunarity, a measure of scale-dependent clustering, that may be used instead. The present study attempts to address this issue by exploring possible relationships between the fractal dimension, lacunarity and connectivity of fractal-fracture networks. It also endeavors to study the relationship between lacunarity and fluid flow in such fractal-fracture networks. A set of deterministic fractal-fracture models generated at different iterations and, that have the same theoretical fractal dimension are used for this purpose. The results indicate that such deterministic synthetic fractal-fracture networks with the same theoretical fractal dimension have differences in their connectivity and that the latter is fairly correlated with lacunarity. Additionally, the flow simulation results imply that lacunarity influences flow patterns in fracture networks. Therefore, it may be concluded that at least in synthetic fractal-fracture networks, rather than fractal dimension, it is the lacunarity or scale-dependent clustering attribute that controls the connectivity and hence the flow behavior.

Clustering and Connectivity of Fractal-Fracture Networks: Are they related?

2020 ◽  
Author(s):  
Ajay Kumar Sahu ◽  
Ankur Roy
Keyword(s):  
Fractal Dimension ◽  
Spatial Clustering ◽  
Flow Behavior ◽  
Fractal Dimensions ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Fractal System ◽  
Clustering Behavior ◽  
Fractal Fracture

<p>It well known that fracture networks display self-similarity in many cases and the connectivity and flow behavior of such networks are influenced by their respective fractal dimensions. One of the authors have previously implemented the concept of lacunarity, a parameter that quantifies spatial clustering, to demonstrate that a set of 7 nested natural fracture maps belonging to a single fractal system, but different visual appearances have different clustering attributes. Any scale-dependency in the clustering of fractures will also likely have significant implications for flow processes that depend upon fracture connectivity. It is therefore important to address the question as to whether the fractal dimension serves as a reasonable proxy  for the connectivity of a fractal-fracture network or is it the lacunarity parameter that may be used instead. The present study attempts to address this issue by studying the clustering behavior (lacunarity) and connectivity of fractal-fracture patterns. We compare the set of 7 nested fracture maps mentioned earlier which belong to a single fractal system, in terms of their lacunarity and connectivity values. The results indicate that while the maps that have the same fractal dimension have almost similar connectivity values, there exist subtle differences such that both the connectivity and clustering change systematically with the scale at which the networks are mapped. It is further noted that there appears to be an exact correlation between clustering and connectivity values. Therefore, it may be concluded that rather than fractal dimension, it is the lacunarity or scale-dependent clustering attribute that control connectivity in fracture networks.</p>

Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations

2013 ◽  
Author(s):  
Hannes Hofmann ◽  
Tayfun Babadagli ◽  
Günter Zimmermann
Keyword(s):  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Network Development ◽  
Complex Fracture ◽  
Fracture Patterns ◽  
Fracture Systems ◽  
Fracture Development ◽  
Complex Fracture Network ◽  
Treatment Designs

The creation of large complex fracture networks by hydraulic fracturing is imperative for enhanced oil recovery from tight sand or shale reservoirs, tight gas extraction, and Hot-Dry-Rock (HDR) geothermal systems to improve the contact area to the rock matrix. Although conventional fracturing treatments may result in bi-wing fractures, there is evidence by microseismic mapping that fracture networks can develop in many unconventional reservoirs, especially when natural fracture systems are present and the differences between the principle stresses are low. However, not much insight is gained about fracture development as well as fluid and proppant transport in naturally fractured tight formations. In order to clarify the relationship between rock and treatment parameters, and resulting fracture properties, numerical simulations were performed using a commercial Discrete Fracture Network (DFN) simulator. A comprehensive sensitivity analysis is presented to identify typical fracture network patterns resulting from massive water fracturing treatments in different geological conditions. It is shown how the treatment parameters influence the fracture development and what type of fracture patterns may result from different treatment designs. The focus of this study is on complex fracture network development in different natural fracture systems. Additionally, the applicability of the DFN simulator for modeling shale gas stimulation and HDR stimulation is critically discussed. The approach stated above gives an insight into the relationships between rock properties (specifically matrix properties and characteristics of natural fracture systems) and the properties of developed fracture networks. Various simulated scenarios show typical conditions under which different complex fracture patterns can develop and prescribe efficient treatment designs to generate these fracture systems. Hydraulic stimulation is essential for the production of oil, gas, or heat from ultratight formations like shales and basement rocks (mainly granite). If natural fracture systems are present, the fracturing process becomes more complex to simulate. Our simulation results reveal valuable information about main parameters influencing fracture network properties, major factors leading to complex fracture network development, and differences between HDR and shale gas/oil shale stimulations.

scholarly journals The Role of In Situ Stress in Organizing Flow Pathways in Natural Fracture Networks at the Percolation Threshold

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Chuanyin Jiang ◽  
Xiaoguang Wang ◽  
Zhixue Sun ◽  
Qinghua Lei
Keyword(s):  
Fluid Flow ◽  
Percolation Threshold ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
In Situ Stress ◽  
Natural Fracture ◽  
Fracture Aperture ◽  
Dilation Effect ◽  
Stress Dependent

We investigated the effect of in situ stresses on fluid flow in a natural fracture network. The fracture network model is based on an actual critically connected (i.e., close to the percolation threshold) fracture pattern mapped from a field outcrop. We derive stress-dependent fracture aperture fields using a hybrid finite-discrete element method. We analyze the changes of aperture distribution and fluid flow field with variations of in situ stress orientation and magnitude. Our simulations show that an isotropic stress loading tends to reduce fracture apertures and suppress fluid flow, resulting in a decrease of equivalent permeability of the fractured rock. Anisotropic stresses may cause a significant amount of sliding of fracture walls accompanied with shear-induced dilation along some preferentially oriented fractures, resulting in enhanced flow heterogeneity and channelization. When the differential stress is further elevated, fracture propagation becomes prevailing and creates some new flow paths via linking preexisting natural fractures, which attempts to increase the bulk permeability but attenuates the flow channelization. Comparing to the shear-induced dilation effect, it appears that the propagation of new cracks leads to a more prominent permeability enhancement for the natural fracture system. The results have particularly important implications for predicting the hydraulic responses of fractured rocks to in situ stress fields and may provide useful guidance for the strategy design of geofluid production from naturally fractured reservoirs.

Modelling large-scale fractured reservoirs efficiently for geothermal energy and groundwater flow

2020 ◽  
Author(s):  
Simon Oldfield ◽  
Mikael Lüthje ◽  
Michael Welch ◽  
Florian Smit
Keyword(s):  
Fluid Flow ◽  
Geothermal Energy ◽  
Large Scale ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Persistent Problem ◽  
Fracture Evolution ◽  
Rapid Generation

<p>Large scale modelling of fractured reservoirs is a persistent problem in representing fluid flow in the subsurface. Considering a geothermal energy prospect beneath the Drenthe Aa area, we demonstrate application of a recently developed approach to efficiently predict fracture network geometry across an area of several square kilometres.</p><p>Using a strain based method to mechanically model fracture nucleation and propagation, we generate a discretely modelled fracture network consisting of individual failure planes, opening parallel and perpendicular to the orientation of maximum and minimum strain. Fracture orientation, length and interactions vary following expected trends, forming a connected fracture network featuring population statistics and size distributions comparable to outcrop examples.</p><p>Modelled fracture networks appear visually similar to natural fracture networks with spatial variation in fracture clustering and the dominance of major and minor fracture trends.</p><p>Using a network topology approach, we demonstrate that the predicted fracture network shares greater geometric similarity with natural networks. Considering fluid flow through the model, we demonstrate that hydraulic conductivity and flow anisotropy are strongly dependent on the geometric connection of fracture sets.</p><p>Modelling fracture evolution mechanically allows improved representation of geometric aspects of fracture networks to which fluid flow is particularly sensitive. This method enables rapid generation of discretely modelled fractures over large areas and extraction of suitable summary statistics for reservoir simulation. Visual similarity of the output models improves our ability to compare between our model and natural analogues to consider model validation.</p>

Clustering, Connectivity and Flow in Naturally Fractured Reservoir Analogs

2021 ◽  
Author(s):  
Ajay K. Sahu ◽  
Ankur Roy
Keyword(s):  
Fractal Dimension ◽  
Oil And Gas ◽  
Flow Behavior ◽  
Oil And Gas Industry ◽  
Fracture Network ◽  
Natural Fracture ◽  
Fractured Reservoir ◽  
Fracture Networks ◽  
Gas Industry ◽  
Network Geometry

Abstract A previous study by the authors on synthetic fractal-fracture networks showed that lacunarity, a parameter that quantifies scale-dependent clustering in patterns, can be used as a proxy for connectivity and also, is an indicator of fluid flow in such model networks. In this research, we apply the concepts thus developed to the study of fractured reservoir analogs and seek solutions to more practical problems faced by modelers in the oil and gas industry. A set of seven nested fracture networks from the Devonian Sandstone of Hornelen Basin, Norway that have the same fractal-dimension but are mapped at different scales and resolutions is considered. We compare these seven natural fracture maps in terms of their lacunarity and connectivity values to test whether the former is a reasonable indicator of the latter. Additionally, these maps are also flow simulated by implementing a fracture continuum model and using a streamline simulator, TRACE3D. The values of lacunarity, connectivity and fluid recovery thus obtained are pairwise correlated with one another to look for possible relationships. The results indicate that while fracture maps that have the same fractal dimension show almost similar connectivity values, there exist subtle differences such that both the connectivity and clustering values change systematically with the scale at which the fracture networks are mapped. It is further noted that there appears to be a very good correlation between clustering, connectivity, and fluid recovery values for these fracture networks that belong to the same fractal system. The overall results indicate that while the fractal dimension is an important parameter for characterizing a specific type of fracture network geometry, it is the lacunarity or scale-dependent clustering attribute that controls connectivity in fracture maps and hence the flow properties. This research may prove helpful in quickly evaluating connectivity of fracture networks based on the lacunarity parameter. This parameter can therefore, be used for calibrating Discrete Fracture Network (DFN) models with respect to connectivity of reservoir analogs and can possibly replace the fractal dimension which is more commonly used in software that model DFNs. Additionally, while lacunarity has been mostly used for understanding network geometry in terms of clustering, we, for the first time, show how this may be directly used for understanding the potential flow behavior of fracture networks.

scholarly journals Numerical Simulation of Hydraulic Fracture Propagation in Coal Seams with Discontinuous Natural Fracture Networks

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 113 ◽  
Author(s):  
Shen Wang ◽  
Huamin Li ◽  
Dongyin Li
Keyword(s):  
Hydraulic Fracture ◽  
Fracture Propagation ◽  
Fracture Network ◽  
Natural Fracture ◽  
Cohesive Element ◽  
Natural Fractures ◽  
Fracture Networks ◽  
Coal Seams ◽  
Hydraulic Fracture Network ◽  
Hydraulic Fracture Propagation

To investigate the mechanism of hydraulic fracture propagation in coal seams with discontinuous natural fractures, an innovative finite element meshing scheme for modeling hydraulic fracturing was proposed. Hydraulic fracture propagation and interaction with discontinuous natural fracture networks in coal seams were modeled based on the cohesive element method. The hydraulic fracture network characteristics, the growth process of the secondary hydraulic fractures, the pore pressure distribution and the variation of bottomhole pressure were analyzed. The improved cohesive element method, which considers the leak-off and seepage behaviors of fracturing liquid, is capable of modeling hydraulic fracturing in naturally fractured formations. The results indicate that under high stress difference conditions, the hydraulic fracture network is spindle-shaped, and shows a multi-level branch structure. The ratio of secondary fracture total length to main fracture total length was 2.11~3.62, suggesting that the secondary fractures are an important part of the hydraulic fracture network in coal seams. In deep coal seams, the break pressure of discontinuous natural fractures mainly depends on the in-situ stress field and the direction of natural fractures. The mechanism of hydraulic fracture propagation in deep coal seams is significantly different from that in hard and tight rock layers.

scholarly journals The Propagation Behavior of Hydraulic Fracture in Rock Mass with Cemented Joints

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Yongxiang Zheng ◽  
Jianjun Liu ◽  
Yun Lei
Keyword(s):  
Hydraulic Fracturing ◽  
Univariate Analysis ◽  
Fracture Propagation ◽  
Fracture Network ◽  
Parameter Analysis ◽  
Natural Fracture ◽  
Hydraulic Fractures ◽  
Fracture Networks ◽  
Form Complex ◽  
Propagation Behavior

The formation of the fracture network in shale hydraulic fracturing is the key to the successful development of shale gas. In order to analyze the mechanism of hydraulic fracturing fracture propagation in cemented fractured formations, a numerical simulation about fracture behavior in cemented joints was conducted based firstly on the block discrete element. And the critical pressure of three fracture propagation modes under the intersection of hydraulic fracturing fracture and closed natural fracture is derived, and the parameter analysis is carried out by univariate analysis and the response surface method (RSM). The results show that at a low intersecting angle, hydraulic fractures will turn and move forward at the same time, forming intersecting fractures. At medium angles, the cracks only turn. At high angles, the crack will expand directly forward without turning. In conclusion, low-angle intersecting fractures are more likely to form complex fracture networks, followed by medium-angle intersecting fractures, and high-angle intersecting fractures have more difficulty in forming fracture networks. The research results have important theoretical guiding significance for the hydraulic fracturing design.

Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Hannes Hofmann ◽  
Tayfun Babadagli ◽  
Günter Zimmermann
Keyword(s):  
Fracture Network ◽  
Natural Fracture ◽  
Fracture Networks ◽  
Network Development ◽  
Complex Fracture ◽  
Fracture Patterns ◽  
Fracture Systems ◽  
Fracture Development ◽  
Complex Fracture Network ◽  
Treatment Designs

The creation of large complex fracture networks by hydraulic fracturing is imperative for enhanced oil recovery from tight sand or shale reservoirs, tight gas extraction, and hot-dry-rock (HDR) geothermal systems to improve the contact area to the rock matrix. Although conventional fracturing treatments may result in biwing fractures, there is evidence by microseismic mapping that fracture networks can develop in many unconventional reservoirs, especially when natural fracture systems are present and the differences between the principle stresses are low. However, not much insight is gained about fracture development as well as fluid and proppant transport in naturally fractured tight formations. In order to clarify the relationship between rock and treatment parameters, and resulting fracture properties, numerical simulations were performed using a commercial discrete fracture network (DFN) simulator. A comprehensive sensitivity analysis is presented to identify typical fracture network patterns resulting from massive water fracturing treatments in different geological conditions. It is shown how the treatment parameters influence the fracture development and what type of fracture patterns may result from different treatment designs. The focus of this study is on complex fracture network development in different natural fracture systems. Additionally, the applicability of the DFN simulator for modeling shale gas stimulation and HDR stimulation is critically discussed. The approach stated above gives an insight into the relationships between rock properties (specifically matrix properties and characteristics of natural fracture systems) and the properties of developed fracture networks. Various simulated scenarios show typical conditions under which different complex fracture patterns can develop and prescribe efficient treatment designs to generate these fracture systems. Hydraulic stimulation is essential for the production of oil, gas, or heat from ultratight formations like shales and basement rocks (mainly granite). If natural fracture systems are present, the fracturing process becomes more complex to simulate. Our simulations suggest that stress state, in situ fracture networks, and fluid type are the main parameters influencing hydraulic fracture network development. Major factors leading to more complex fracture networks are an extensive pre-existing natural fracture network, small fracture spacings, low differences between the principle stresses, well contained formations, high tensile strength, high Young’s modulus, low viscosity fracturing fluid, and large fluid volumes. The differences between 5 km deep granitic HDR and 2.5 km deep shale gas stimulations are the following: (1) the reservoir temperature in granites is higher, (2) the pressures and stresses in granites are higher, (3) surface treatment pressures in granites are higher, (4) the fluid leak-off in granites is less, and (5) the mechanical parameters tensile strength and Young’s modulus of granites are usually higher than those of shales.

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