Unraveling the Effects of Fracture Density and Intensity on Reservoir Connectivity and Flow Behavior

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Sahu, Sanika M. Mokashi, Mansi P. Joshi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7493136/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract Understanding the factors that influence fluid flow in fractured reservoirs is crucial for optimizing production and enhancing reservoir management. While extensive studies have focused on network characterization, the direct influence of density and intensity of fractures on flow behavior remains largely unexplored, which is a critical aspect of fracture modeling. This study aims to investigate the relative importance of fracture density versus intensity in determining fluid flow behavior in fractured rock formations. This research analyzes geometrical parameters of a set of seven Odling’s fracture outcrops from the Devonian sandstone of the Hornelen Basin, Norway. Fracture density and intensity are evaluated with the application of Matlab toolbox, FracPaQ2D. Additionally, node-based connectivity is assessed through relative abundance of fractures, while percolation connectivity is estimated based on geometric extension of fracture traces. Flow simulations are performed using TRACE3D, by converting these fracture maps into permeability grids through the application of Fracture Continuum model. A comparative analysis of these parameters, examines how variations in density and intensity impact key flow parameters such as time of flights (TOFs) and fluid recovery. The results indicate that, although both fracture density and intensity are important, the fracture intensity exerts a more significant influence on fluid flow within a fractured media. This is because fracture intensity directly controls the percolation connectivity of the fracture network, which is a critical determinant of flow pathways. Specifically, it is influences by the formation and extent of the largest spanning clusters that facilitate fluid movement. Consequently, variations in fracture intensity can significantly alter reservoir permeability and fluid flow. These findings have significant implications for improving reservoir characterization and modeling, ultimately aiding in the optimization of hydrocarbon extraction, geothermal energy production, and carbon sequestration strategies. Fracture Networks Density Intensity Connectivity Flow Simulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1 Introduction Fluid flow in fractured reservoirs is a highly complex process as it is influenced by various geological and geo-mechanical properties of the subsurface rock mass. Among these, fracture density and intensity are particularly significant in determining hydrocarbon extraction, groundwater movement, geothermal energy production, and carbon storage. Understanding the relative impact of fracture density and intensity on fluid flow is crucial for production enhancement and optimizing reservoir management through state-of-art predictive modeling techniques [ 1 , 2 ]. Fracture density, defined as the number of fractures within a given area or volume, generally improves node-based connectivity [ 3 ], facilitating fluid flow in the network due to intersection and abutments of fracture traces. However, if fractures are discontinuous or poorly connected, increased density may not necessarily enhance the permeability of the reservoir. On the other hand, fracture intensity refers to the proportion of rock volume occupied by fracture clusters, which generally improves percolation-based connectivity, providing insights into both permeability and storage capacity [ 4 ]. A high fracture intensity indicates a greater volume of fracture clusters, generally spreading along the rock-mass area, which can support the fluid movement from one end to the other in a reservoir [ 4 , 5 ]. In fractured reservoirs of type III category as classified by R. E. Nelson [ 2 ], with high fracture porosity and permeability and low matrix porosity and permeability, fluid is storage and movement primarily occurs in fractures. This emphasizes the connectivity of a fracture network as a critical factor in controlling fluid flow [ 4 , 5 , 6 , 7 ]. Thus, the flow behavior indirectly depends on whether fracture density or intensity has a greater influence on the network connectivity. Hence, their lies a great interest in investigating the relative importance of fracture density versus intensity in determining fluid flow behavior in fractured reservoirs. In this research, the geometrical parameters i.e.; density and intensity of a set of seven Odling’s fracture outcrops from the Devonian sandstone of the Hornelen Basin, Norway are evaluated by application of Matlab toolbox, FracPaQ2D. These set of seven Odling’s fracture maps are used in this study, because its various statistical and geometrical characteristics are analysed by numerous researchers [6, 8, 9, 10. 11]. In the next step, the node-based connectivity of this maps are expressed as a single number ( N c ), through evaluation of the relative abundance of fracture intersections ( X -nodes) and abutments ( Y -nodes), using the concepts developed by Manzocchi [ 3 ]. As the node-based connectivity ( N c ) is dependent on the number of intersections and abutments, therefore it is moreover directly controlled by the fracture density. The percolation connectivity ( N p ) is estimated based on geometric spanning of the largest fracture clusters over map area. As the percolation connectivity ( N p ) is represented by the extension of fractures, therefore it is directly controlled by fracture intensity. In the final step, flow simulations are performed using TRACE3D, by converting these discrete fractures maps into permeability structures on a grid, through the application of Fracture Continuum model as described by [ 12 , 13 , 14 , 15 ]. This is done in a manner such that each cell gets a characteristic porosity and permeability value depending on whether or not it is occupied by a fracture. The fluid recovery values and time of flights (TOFs) are obtained from simulating flow through these fracture networks. A comparative analysis of the influence of node-based connectivity ( N c ) and percolation connectivity ( N p ) on fluid recovery is done to examine how variations in density and intensity impact the fluid flow behavior. The results indicate that, although both fracture density and intensity are important, the fracture intensity which controls the percolation connectivity, exerts a more significant influence on fluid flow in fracture maps. Specifically, flow behavior is influenced by the formation and extent of the largest spanning fracture clusters that facilitate fluid movement. Consequently, reservoir storage capacity and fluid transport is altered by the variations in fracture intensity. The findings of this study have significant implications for improving reservoir characterization and predictive geo-modeling of flow in fractured reservoirs. ultimately aiding in the, geothermal energy production, and carbon sequestration strategies. Beyond optimization of hydrocarbon extraction in petroleum reservoirs, the importance of fracture intensity and density extends to other subsurface applications, including geothermal energy production, carbon sequestration, nuclear waste disposal, and groundwater management. 2 Methodology 2.1 Mapping Natural Fracture Networks Outcrop analogs have been widely utilized by researchers to investigate both the ‘static’ and ‘dynamic’ properties of naturally fractured reservoirs [ 16 , 17 ]. This study employed a series of seven nested natural fracture maps derived from outcrop mapping and low-altitude aerial photography of fractures within well-exposed Devonian sandstones of the Hornelen Basin, Norway [ 18 ]. Each map was digitized, with fracture trace junctions automatically adjusted based on an estimated digitizing error corresponding to the thickness of the map lines [ 19 ]. This method ensures that the connectivity of the original map is accurately preserved in the digitized data. The set of seven nested natural fracture maps are shown in Fig. 1 . Numerous studies have examined these fracture networks in relation to various statistical and geometrical characteristics [ 8 , 9 , 10 , 20 ] and hence they form a suitable candidate for this research. These maps capture a range of fracture lengths, with the shortest constrained by image resolution and the longest by the mapped area [ 19 ]. Although, these fracture maps are considered to belong to a single fractal-fracture system characterized by a specific fractal dimension [ 10 , 21 ], a visual assessment of these maps revealed that the appearance of fracture traces is influenced by both the scale and resolution at which they were mapped. Hence, it would be interesting to investigate the relative importance of fracture density versus intensity in determining fluid flow behavior in fracture maps. 2.2 Estimation of Density & Intensity of Fractures Fracture density and fracture intensity are both measures used to describe the fracture characteristics of a rock mass, but they differ in their specific focus. The fractures density is defined as the number of fracture traces upon the mapped area. The most common measure is representing the number of fractures intersecting a line (e.g., a borehole) per unit length. Areal density, often used in 2D fracture maps is defined as the number of fractures per unit area, while the less commonly used volumetric density (3D) is represented as the number of fractures per unit volume. The fracture intensity is commonly defined as the extension of fractures over a mapped area. The 2D fracture intensity is expressed as the length of fracture traces per unit area, whereas the 3D fracture intensity is the total fracture surface area per unit volume. In essence, fracture intensity provides a more comprehensive view of fracturing by considering the scale and extent of the fractures, while fracture density primarily focuses on the frequency of fractures. In this study the fracture density (metre − 1 ) and intensity (metre − 2 ) of the set of seven Odling’s fracture maps are quantified using FracPaQ [ 22 ]. It is an open source MATLAB™ toolbox for the quantification of fracture patterns. Lengths and orientations are derived from the geometry of the input fracture traces, while the intensity and density are quantified using published methods. The density and intensity are estimated from the fracture maps using the circular scan window method of Mauldon et al. [ 23 ], applied to the coordinate geometry of the fracture trace and segment network. Here, fracture density was estimated as m/2πr 2 where m is the number of fractures terminating within a circle of radius r and fracture intensity as n/4r , where n is the number of fractures intersecting the perimeter of a circle of radius r . FracPaQ generates a 2D grid of evenly spaced circular scan windows to fit within the fracture trace map area, where the scan circle diameter is defined as 0.99 of the grid spacing in x and y to avoid overlapping scan circles. The code then calculates the intersections ( n ) and terminations ( m ) of the fracture segments within these circles, and calculates the estimated density and intensity values for the centre of each circle. This grid of values is then contoured using the standard MATLAB triangulation function to produce the maps of estimated fracture intensity (P21) and estimated fracture density (P20). 2.3 Estimation of Node-based Connectivity and Percolation Connectivity The connectivity of a fracture network is a useful tool to forecast the fluid flow and transport characteristics in a fractured reservoir. Two fundamentally different concepts are mostly used to estimate the connectivity of a fracture network. Connectivity can be referred as either a measure of the degree to which the elements of a network are interconnected through different nodes in a network; or a percolation threshold, below which the network is unconnected and above which it is connected. Node-based connectivity and percolation connectivity both deal with understanding of how fracture networks become connected, but they differ fundamentally in their definitions, approaches and applications. Node-based connectivity is analyzed based on network topology, which may be analysed on the basis of the proportions of isolated ( I ), abutting ( Y ) and crossing ( X ) nodes [ 3 , 24 ]. This is typical in graph theory representations, where fractures are modeled as nodes, and pathways between them are edges. In opening-mode fracture systems (joints and veins) many fractures terminate as abutments against other fractures to form connections with a Y geometry. (Dershowitz and Einstein; 1988). An increased prevalence for the formation of Y connections with increasing fracture interaction contributes to higher node based connectivity [ 26 ]. Figure 2 illustrates the X , Y and I nodes present in a fracture network. Manzocchi [ 3 ] showed that the connectivity can also be expressed in terms of a single parameter, n, defined by Eq. (1): \(\:n=\left[4\right(1-PI)/(1-PX\left)\right]\) 1 Where, PI = Proportion of I (isolated) nodes, PX = Proportion of X (intersection) nodes, PY = Proportion of Y (abutment) nodes. Percolation connectivity refers to the ability of a fracture network to form continuous, spanning pathways that allow for fluid flow and transport across a domain [ 27 ]. Percolation theory originates from statistical physics and is used to model connectivity in random networks [ 9 ]. The critical point at which a system transitions from being disconnected to connected is known as percolation threshold. The percolation cluster is the largest spanning fracture cluster over the map area. Hence, one of the important parameter affecting the percolation connectivity is fracture length distribution [ 13 ]. In the context of fractured reservoirs, percolation theory helps to quantify how fractures contribute to overall connectivity and the conditions under which a connected cluster of fractures emerges to generate a pathway for fluid flow [ 28 ]. In essence, percolation connectivity looks at whether a continuous path exists across the entire fracture network, once the percolation threshold is surpassed. Figure 3 shows a fracture network, its percolation cluster along with the network’s TOF. The TOF which is generated from flow simulation through the fracture network using TRACE3D is seen to be very similar to the percolation cluster of the network. Hence, the flow pathway is preferably the largest spanning cluster over the fracture map which connects its two ends. Theoretically, it can be presumed that node-based connectivity helps you understand how individual fracture traces link together, and this can be ideal for understanding flow in reservoirs with an individual well-planned or deterministic networks. Whereas the percolation connectivity represents if there's enough random connectivity for represented by the percolation connectivity for flow and transport, common in naturally fractured reservoirs. 2.4 Fracture Modeling and Flow Simulation While information on network geometry and connectivity helps in modeling fracture networks, geo-modelers and reservoir engineers are ultimately interested in understanding how fractures influence fluid flow in the subsurface. In order to simulate flow in fracture networks, the Fracture Continuum (FC) model [ 12 , 13 , 14 , 15 ] is implemented where discrete fractures are converted into permeability structures on a grid. In this study, similar FC models are built from raster images of fracture maps such that each pixel represents a cell which is much smaller than the smallest fracture. Each cell is assigned a characteristic porosity and permeability value depending on whether or not it represents part of a fracture. The FC model is computationally efficient and also, details of the fracture network are preserved by the use of very small cell size. Using this approach, each of the seven fracture maps of size 1042 x 1042 pixels were converted into a permeability structured grid block of 1042 x 1042 x 1 cells. Hence, each pixel of the networks’ image (raster data) is represented by a cell which is the smallest possible grid that can be used in the FC model. It therefore preserves the minutest details of the original network that helps in accurately modeling the flow behavior of such maps [ 29 ]. Each cell of the FC models thus generated, is then assigned a porosity and permeability value according to whether they represent fracture, 95% and 10 6 md respectively, or matrix, 5% and 10 2 md respectively [ 30 , 31 ]. These values were chosen such that flow occurs mostly through fractures because in this research, fractured reservoirs of Type-1 [ 2 ] is considered where natural fractures are the main contributors to fluid flow in terms of permeability and porosity. Thus the focus is on evaluating fracture network geometry from flow responses. All the FC models are flow simulated using TRACE3D [ 32 , 33 ] at a constant boundary condition with reservoir pressure of 2480 psia and an injection rate of 500 bbl/day for a period of 1000 days. A pair of injector and producer are placed at the two diagonal corners, (1, 1) and (1000, 1000) of the model fracture network and, (1, 1) and (1042, 1042) of the fracture maps to obtain a total areal sweep of the reservoir fluids. The overall recovery values for the seven natural fracture maps are considered for quantitative characterization of fluid flow, which can help in evaluating the effect of fracture network geometry on flow behavior. The time of flight (TOFs) are used to visualize the fluid-front movement from the injector to producer through the fracture networks. 3 Results 3.1 Density and Intensity of Fracture Networks The fracture density (pixel − 1 ) and intensity (pixel − 2 ) of the set of seven Odling’s fracture maps are quantified using FracPaQ are shown in Fig. 4 and Fig. 5 respectively. It is observed in Fig. 4, that the density of fracture maps trends to increase from map 1 to map 7. Also, a vivid difference of fracture density is observed in map 3 and map 4, although this two maps cover the same map area of 90m x 90m. The density is observed to increase directly with increase of the scale of the maps. It is evident, as the larger scale maps have more number of shorter fractures which also generates a higher number of node interactions. This suggests that, a fracture map with higher density can contribute to a higher value of node-based connectivity. Figure 5 shows that the fracture intensity increases from map 1 to map 2 and then gradually decreases till map 7. Also, for map 3 and map 4 the intensity plots appear to be somewhat similar as these two maps cover the same map area of 90m x 90m and have a stubble difference in the arrangements of their fracture traces. The trend of intensity plots of the fracture maps suggests that the intensity of fracture maps is moreover affected by the resolution of the maps, i.e.; the higher resolution maps have higher intensity due the exposure of longer fracture traces mapped at higher resolution. It can be presumed that a higher fracture intensity can contribute of a higher value of percolation connectivity, which is dependent on the presence of longest spanning clusters in fracture maps. Figure 5 . Density maps of the seven nested natural fracture maps generated using FracPaQ2D. 3.2 Node-based Connectivity and Percolation Connectivity The node-based connectivity, evaluated based on the proportions of X , Y and I nodes using the Eq. 1 is plotted in Fig. 5 . Two distinct trends are observed, one in map 1–3, where the node-based connectivity decreases from map 1 to map 3. The other trend in observed in map 4–7, where the node-based connectivity decreases from map 4 to map 7. It can be stated that the resolution and scale of the map influences the overall connectivity of the maps. However, it’s astonishing that map 3 and map 4 are the outcrop area mapped at same scale of 90 x 90 m only at different resolutions, but their node-based connectivity is very different. Also, Odling [ 18 ], mentions that the fractures in map 2 are more connected and spread out over the mapping area. Hence, map 2 should have the highest overall connectivity and contribute to fluid flow. The percolation connectivity, evaluated based on the largest spanning cluster in a fracture network is plotted in Fig. 6 [ 5 ]. It is observed that the highest percolation connectivity value is for map 2 and lowest for map 7, whereas the it remains almost same for map 3 and map 4. It suggests that the percolation connectivity of each of these maps is sensitive to the presence of longer traces with respect to the domain size that span over the entire map [ 7 , 18 , 19 , 20 , 34 ]. The presence of large number of short fracture traces with respect to the domain size cannot guarantee good connectivity as these “short” fractures may be less connected than a fewer long fractures. The small scale high resolution maps have “longer” traces relative to the map area, hence, are better connected than the large scale, low resolution maps with large number of “short” fractures. This percolation connectivity study also aligns well with the overall connectivity estimated by Odling, 1997. Figure 6 . Percolation connectivity (Pc) of the seven nested natural fracture maps [ 5 ]. 3.3 Fluid Recovery The fluid recovery obtained by flow simulation of each of the fracture maps (as described in section 2.4) are shown in Fig. 7 . The recovery values appear to be very similar to the percolation connectivity. This can possibly be attributed to the fact that recovery is directly controlled by the extend of longer spanning clusters of the networks. The latter in turn, is related to fracture intensity which is quantified by the length of fracture traces per area of the map. As the fracture length distribution of networks are different in each of the fracture maps, there exists differences in intensity, which leads to differences in percolation connectivity and ultimately differences in of fluid transport path from the injection point to the production point of the fractured domain. The heterogeneity in fracture networks can be vividly visualize in the TOFs generated using streamline-based flow simulators. The concept of time of flight (TOF) introduced by Datta-Gupta and King [ 33 ], is a spatial coordinate representing the distance along streamline to where the reservoir will be contacted. Map-1 and map-6 along with their respective TOFs for different time steps: 500, 750 and 1000 are shown in Fig. 6 . The fracture area contacted in map-1 is higher than that of map-6 at each time step. This shows that the fluid movement is along the percolation cluster that provides an amicable flow pathway from the injector to the producer. The resultant of this can be obtained as a high recovery value of map 1 over map 6 although for the same time period of flow simulation. 4 Conclusions Identifying the differences between fracture intensity and fracture density within a network, particularly when networks share the same fractal dimensions offers critical insights with wide-ranging applications across geosciences and engineering disciplines. This study demonstrates that variations in key geometric properties, such as connectivity, as well as differences in fluid recovery behavior, are more strongly governed by fracture intensity rather than by fracture density. These findings also highlight the need to distinguish between these two parameters when modeling fracture networks, as fracture intensity plays a more dominant role in controlling fluid flow and overall network behavior. The novelty of this study lies in such a focused comparison of fracture intensity and fracture density, which has not been systematically explored before, providing new insights into how subtle differences in fracture characterization can lead to significant variations in reservoir performance and flow modeling. Through accurate characterizing and distinguishing these network properties, professionals in the fields of hydrology and reservoir engineering can make more informed decisions, optimize resource extraction, enhance safety, and mitigate environmental impacts. Declarations Competing Interests: The authors declares no competing interests with any individual/organization anywhere Funding: This work is not funded by any agency, rather it is an effort of the authors investigation using opensource softwares. Author Contribution Dr. A K S has explored the initial idea of this research and also have worked on all the analysis, coding and result analysis. 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Sahu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYFCCA2AygYG9AcpkYDAAI8JaeA4wHDhAnBYGqBaJBJh2Aur5Gw8/k2D4Y5dncPN14uGPbXcSG9ibt0kwFNzBqUXiwDEzCca25GKD27kbDhxse5bYwHOsTILB4BkerxwAamlgTtwA1rLtcGKDRI4ZUMthnDrkDxz/BnRYfeKGm2ehWuTf4NdicOAMUAHb4cQNN3hhtvDg12J44EyxRWLb8cSZZ4AOO/vvmXEbT1qxRQIeLXI3jm+88eFPdWLf8bObP1ScuSPbz34YJIJbCzDIWEAxAg8NBjYQlYBdMQTwNzB/QOIewKd2FIyCUTAKRigAALa5aFsIpGEUAAAAAElFTkSuQmCC","orcid":"","institution":"MIT World Peace University","correspondingAuthor":true,"prefix":"","firstName":"Ajay","middleName":"K.","lastName":"Sahu","suffix":""},{"id":513861806,"identity":"0ab7ed78-24e1-43e6-b258-f006668d7cf0","order_by":1,"name":"Sanika M. Mokashi","email":"","orcid":"","institution":"MIT World Peace University","correspondingAuthor":false,"prefix":"","firstName":"Sanika","middleName":"M.","lastName":"Mokashi","suffix":""},{"id":513861809,"identity":"3c61f54a-7a26-49f8-abf8-94672c5f4c3a","order_by":2,"name":"Mansi P. Joshi","email":"","orcid":"","institution":"MIT World Peace University","correspondingAuthor":false,"prefix":"","firstName":"Mansi","middleName":"P.","lastName":"Joshi","suffix":""}],"badges":[],"createdAt":"2025-08-30 06:23:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7493136/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7493136/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91457469,"identity":"7f0d51b7-588a-4303-bea8-c3a202e05003","added_by":"auto","created_at":"2025-09-16 16:36:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":117587,"visible":true,"origin":"","legend":"\u003cp\u003eA set of seven nested natural fracture outcrops from the Devonian sandstone of Hornelen Basin, Norway. The mapping technique is also highlighted along with their scale [19].\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/ddb6005dba5f722f694b27f4.png"},{"id":91457470,"identity":"189c65e8-2bab-4b90-8486-b597e209e1ec","added_by":"auto","created_at":"2025-09-16 16:36:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":25331,"visible":true,"origin":"","legend":"\u003cp\u003eA schematic description of the X-node (Blue squares), Y-node (red triangles), and I-node (green circles) in a fracture network.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/98e4202923ccd918f0021722.png"},{"id":91458448,"identity":"6500d16c-7501-4588-b668-18eb96239eb1","added_by":"auto","created_at":"2025-09-16 16:44:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":36941,"visible":true,"origin":"","legend":"\u003cp\u003eA schematic representation of fracture network (left), its percolation cluster (centre), and its TOF (right) which depicts flow pathways of fluids.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/516450375130ea91b0f982dd.png"},{"id":91458449,"identity":"59790d40-b0c3-489d-b623-e0ad9ae66c6a","added_by":"auto","created_at":"2025-09-16 16:44:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1482942,"visible":true,"origin":"","legend":"\u003cp\u003eDensity maps of the seven nested natural fracture maps generated using FracPaQ2D.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/c1d84d505f8f3ab758942311.png"},{"id":91458991,"identity":"52475db4-d3ed-4422-808d-28d4974d9258","added_by":"auto","created_at":"2025-09-16 16:52:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":2282188,"visible":true,"origin":"","legend":"\u003cp\u003eIntensity maps of the seven nested natural fracture maps generated using FracPaQ2D.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/df2899d1d800f81d1b0a3fb1.png"},{"id":91458450,"identity":"4ed020b4-da04-4bd2-be10-e95fe92ae108","added_by":"auto","created_at":"2025-09-16 16:44:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":18472,"visible":true,"origin":"","legend":"\u003cp\u003eNode-based connectivity (Nc) of the seven nested natural fracture maps.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/46fd30dc7cf49f5e821c9b25.png"},{"id":91460071,"identity":"4d0a8af1-5ed6-443d-b2ad-63d9930eb5d2","added_by":"auto","created_at":"2025-09-16 17:00:04","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":20174,"visible":true,"origin":"","legend":"\u003cp\u003ePercolation connectivity (Pc) of the seven nested natural fracture maps [5].\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/e4a5720734720631631827b2.png"},{"id":91457474,"identity":"8a0c69c3-6350-4bda-8959-f3eddd544aeb","added_by":"auto","created_at":"2025-09-16 16:36:04","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":16629,"visible":true,"origin":"","legend":"\u003cp\u003eFluid recovery of the seven nested natural fracture maps [5].\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/006160cc868566dbbab47105.png"},{"id":91457478,"identity":"1634cc57-1484-4b3e-b34c-da9b07458c7b","added_by":"auto","created_at":"2025-09-16 16:36:04","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":660280,"visible":true,"origin":"","legend":"\u003cp\u003eTOFs of map 1 and map 6, showing flow pathways are representatives of the percolation cluster which is influenced by the intensity of fracture maps [5].\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/f44ff1143fb184132c70deed.png"},{"id":91460506,"identity":"b96e055c-fb13-4fb2-9f6e-04ec0c156fed","added_by":"auto","created_at":"2025-09-16 17:08:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4787612,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7493136/v1/01193e42-45df-4d85-af65-fde43270bb92.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Unraveling the Effects of Fracture Density and Intensity on Reservoir Connectivity and Flow Behavior","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eFluid flow in fractured reservoirs is a highly complex process as it is influenced by various geological and geo-mechanical properties of the subsurface rock mass. Among these, fracture density and intensity are particularly significant in determining hydrocarbon extraction, groundwater movement, geothermal energy production, and carbon storage. Understanding the relative impact of fracture density and intensity on fluid flow is crucial for production enhancement and optimizing reservoir management through state-of-art predictive modeling techniques [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eFracture density, defined as the number of fractures within a given area or volume, generally improves node-based connectivity [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], facilitating fluid flow in the network due to intersection and abutments of fracture traces. However, if fractures are discontinuous or poorly connected, increased density may not necessarily enhance the permeability of the reservoir. On the other hand, fracture intensity refers to the proportion of rock volume occupied by fracture clusters, which generally improves percolation-based connectivity, providing insights into both permeability and storage capacity [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. A high fracture intensity indicates a greater volume of fracture clusters, generally spreading along the rock-mass area, which can support the fluid movement from one end to the other in a reservoir [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn fractured reservoirs of type III category as classified by R. E. Nelson [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], with high fracture porosity and permeability and low matrix porosity and permeability, fluid is storage and movement primarily occurs in fractures. This emphasizes the connectivity of a fracture network as a critical factor in controlling fluid flow [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Thus, the flow behavior indirectly depends on whether fracture density or intensity has a greater influence on the network connectivity. Hence, their lies a great interest in investigating the relative importance of fracture density versus intensity in determining fluid flow behavior in fractured reservoirs.\u003c/p\u003e\u003cp\u003eIn this research, the geometrical parameters i.e.; density and intensity of a set of seven Odling\u0026rsquo;s fracture outcrops from the Devonian sandstone of the Hornelen Basin, Norway are evaluated by application of Matlab toolbox, FracPaQ2D. These set of seven Odling\u0026rsquo;s fracture maps are used in this study, because its various statistical and geometrical characteristics are analysed by numerous researchers [6, 8, 9, 10. 11]. In the next step, the node-based connectivity of this maps are expressed as a single number (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e), through evaluation of the relative abundance of fracture intersections (\u003cem\u003eX\u003c/em\u003e-nodes) and abutments (\u003cem\u003eY\u003c/em\u003e-nodes), using the concepts developed by Manzocchi [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. As the node-based connectivity (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e) is dependent on the number of intersections and abutments, therefore it is moreover directly controlled by the fracture density. The percolation connectivity (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e) is estimated based on geometric spanning of the largest fracture clusters over map area. As the percolation connectivity (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e) is represented by the extension of fractures, therefore it is directly controlled by fracture intensity.\u003c/p\u003e\u003cp\u003eIn the final step, flow simulations are performed using TRACE3D, by converting these discrete fractures maps into permeability structures on a grid, through the application of Fracture Continuum model as described by [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. This is done in a manner such that each cell gets a characteristic porosity and permeability value depending on whether or not it is occupied by a fracture. The fluid recovery values and time of flights (TOFs) are obtained from simulating flow through these fracture networks.\u003c/p\u003e\u003cp\u003eA comparative analysis of the influence of node-based connectivity (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e) and percolation connectivity (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e) on fluid recovery is done to examine how variations in density and intensity impact the fluid flow behavior. The results indicate that, although both fracture density and intensity are important, the fracture intensity which controls the percolation connectivity, exerts a more significant influence on fluid flow in fracture maps. Specifically, flow behavior is influenced by the formation and extent of the largest spanning fracture clusters that facilitate fluid movement. Consequently, reservoir storage capacity and fluid transport is altered by the variations in fracture intensity.\u003c/p\u003e\u003cp\u003eThe findings of this study have significant implications for improving reservoir characterization and predictive geo-modeling of flow in fractured reservoirs. ultimately aiding in the, geothermal energy production, and carbon sequestration strategies. Beyond optimization of hydrocarbon extraction in petroleum reservoirs, the importance of fracture intensity and density extends to other subsurface applications, including geothermal energy production, carbon sequestration, nuclear waste disposal, and groundwater management.\u003c/p\u003e"},{"header":"2 Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Mapping Natural Fracture Networks\u003c/h2\u003e\u003cp\u003eOutcrop analogs have been widely utilized by researchers to investigate both the \u0026lsquo;static\u0026rsquo; and \u0026lsquo;dynamic\u0026rsquo; properties of naturally fractured reservoirs [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. This study employed a series of seven nested natural fracture maps derived from outcrop mapping and low-altitude aerial photography of fractures within well-exposed Devonian sandstones of the Hornelen Basin, Norway [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Each map was digitized, with fracture trace junctions automatically adjusted based on an estimated digitizing error corresponding to the thickness of the map lines [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. This method ensures that the connectivity of the original map is accurately preserved in the digitized data. The set of seven nested natural fracture maps are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eNumerous studies have examined these fracture networks in relation to various statistical and geometrical characteristics [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] and hence they form a suitable candidate for this research. These maps capture a range of fracture lengths, with the shortest constrained by image resolution and the longest by the mapped area [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Although, these fracture maps are considered to belong to a single fractal-fracture system characterized by a specific fractal dimension [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], a visual assessment of these maps revealed that the appearance of fracture traces is influenced by both the scale and resolution at which they were mapped. Hence, it would be interesting to investigate the relative importance of fracture density versus intensity in determining fluid flow behavior in fracture maps.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Estimation of Density \u0026amp; Intensity of Fractures\u003c/h2\u003e\u003cp\u003eFracture density and fracture intensity are both measures used to describe the fracture characteristics of a rock mass, but they differ in their specific focus. The fractures density is defined as the number of fracture traces upon the mapped area. The most common measure is representing the number of fractures intersecting a line (e.g., a borehole) per unit length. Areal density, often used in 2D fracture maps is defined as the number of fractures per unit area, while the less commonly used volumetric density (3D) is represented as the number of fractures per unit volume. The fracture intensity is commonly defined as the extension of fractures over a mapped area. The 2D fracture intensity is expressed as the length of fracture traces per unit area, whereas the 3D fracture intensity is the total fracture surface area per unit volume. In essence, fracture intensity provides a more comprehensive view of fracturing by considering the scale and extent of the fractures, while fracture density primarily focuses on the frequency of fractures.\u003c/p\u003e\u003cp\u003eIn this study the fracture density (metre\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and intensity (metre\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) of the set of seven Odling\u0026rsquo;s fracture maps are quantified using FracPaQ [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. It is an open source MATLAB\u0026trade; toolbox for the quantification of fracture patterns. Lengths and orientations are derived from the geometry of the input fracture traces, while the intensity and density are quantified using published methods. The density and intensity are estimated from the fracture maps using the circular scan window method of Mauldon et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], applied to the coordinate geometry of the fracture trace and segment network. Here, fracture density was estimated as \u003cem\u003em/2πr\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e where \u003cem\u003em\u003c/em\u003e is the number of fractures terminating within a circle of radius \u003cem\u003er\u003c/em\u003e and fracture intensity as \u003cem\u003en/4r\u003c/em\u003e, where \u003cem\u003en\u003c/em\u003e is the number of fractures intersecting the perimeter of a circle of radius \u003cem\u003er\u003c/em\u003e. FracPaQ generates a 2D grid of evenly spaced circular scan windows to fit within the fracture trace map area, where the scan circle diameter is defined as 0.99 of the grid spacing in \u003cem\u003ex\u003c/em\u003e and \u003cem\u003ey\u003c/em\u003e to avoid overlapping scan circles. The code then calculates the intersections (\u003cem\u003en\u003c/em\u003e) and terminations (\u003cem\u003em\u003c/em\u003e) of the fracture segments within these circles, and calculates the estimated density and intensity values for the centre of each circle. This grid of values is then contoured using the standard MATLAB triangulation function to produce the maps of estimated fracture intensity (P21) and estimated fracture density (P20).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Estimation of Node-based Connectivity and Percolation Connectivity\u003c/h2\u003e\u003cp\u003eThe connectivity of a fracture network is a useful tool to forecast the fluid flow and transport characteristics in a fractured reservoir. Two fundamentally different concepts are mostly used to estimate the connectivity of a fracture network. Connectivity can be referred as either a measure of the degree to which the elements of a network are interconnected through different nodes in a network; or a percolation threshold, below which the network is unconnected and above which it is connected. Node-based connectivity and percolation connectivity both deal with understanding of how fracture networks become connected, but they differ fundamentally in their definitions, approaches and applications.\u003c/p\u003e\u003cp\u003eNode-based connectivity is analyzed based on network topology, which may be analysed on the basis of the proportions of isolated (\u003cem\u003eI\u003c/em\u003e), abutting (\u003cem\u003eY\u003c/em\u003e) and crossing (\u003cem\u003eX\u003c/em\u003e) nodes [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. This is typical in graph theory representations, where fractures are modeled as nodes, and pathways between them are edges. In opening-mode fracture systems (joints and veins) many fractures terminate as abutments against other fractures to form connections with a \u003cem\u003eY\u003c/em\u003e geometry. (Dershowitz and Einstein; 1988). An increased prevalence for the formation of \u003cem\u003eY\u003c/em\u003e connections with increasing fracture interaction contributes to higher node based connectivity [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the \u003cem\u003eX\u003c/em\u003e, \u003cem\u003eY\u003c/em\u003e and \u003cem\u003eI\u003c/em\u003e nodes present in a fracture network.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eManzocchi [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] showed that the connectivity can also be expressed in terms of a single parameter, n, defined by Eq.\u0026nbsp;(1):\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n=\\left[4\\right(1-PI)/(1-PX\\left)\\right]\\)\u003c/span\u003e\u003c/span\u003e 1\u003c/p\u003e\u003cp\u003eWhere, PI\u0026thinsp;=\u0026thinsp;Proportion of I (isolated) nodes, PX\u0026thinsp;=\u0026thinsp;Proportion of X (intersection) nodes, PY\u0026thinsp;=\u0026thinsp;Proportion of Y (abutment) nodes.\u003c/p\u003e\u003cp\u003ePercolation connectivity refers to the ability of a fracture network to form continuous, spanning pathways that allow for fluid flow and transport across a domain [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Percolation theory originates from statistical physics and is used to model connectivity in random networks [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The critical point at which a system transitions from being disconnected to connected is known as percolation threshold. The percolation cluster is the largest spanning fracture cluster over the map area. Hence, one of the important parameter affecting the percolation connectivity is fracture length distribution [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. In the context of fractured reservoirs, percolation theory helps to quantify how fractures contribute to overall connectivity and the conditions under which a connected cluster of fractures emerges to generate a pathway for fluid flow [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. In essence, percolation connectivity looks at whether a continuous path exists across the entire fracture network, once the percolation threshold is surpassed. Figure\u0026nbsp;3 shows a fracture network, its percolation cluster along with the network\u0026rsquo;s TOF. The TOF which is generated from flow simulation through the fracture network using TRACE3D is seen to be very similar to the percolation cluster of the network. Hence, the flow pathway is preferably the largest spanning cluster over the fracture map which connects its two ends.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTheoretically, it can be presumed that node-based connectivity helps you understand how individual fracture traces link together, and this can be ideal for understanding flow in reservoirs with an individual well-planned or deterministic networks. Whereas the percolation connectivity represents if there's enough random connectivity for represented by the percolation connectivity for flow and transport, common in naturally fractured reservoirs.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4 Fracture Modeling and Flow Simulation\u003c/h2\u003e\u003cp\u003eWhile information on network geometry and connectivity helps in modeling fracture networks, geo-modelers and reservoir engineers are ultimately interested in understanding how fractures influence fluid flow in the subsurface. In order to simulate flow in fracture networks, the Fracture Continuum (FC) model [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] is implemented where discrete fractures are converted into permeability structures on a grid. In this study, similar FC models are built from raster images of fracture maps such that each pixel represents a cell which is much smaller than the smallest fracture. Each cell is assigned a characteristic porosity and permeability value depending on whether or not it represents part of a fracture. The FC model is computationally efficient and also, details of the fracture network are preserved by the use of very small cell size.\u003c/p\u003e\u003cp\u003eUsing this approach, each of the seven fracture maps of size 1042 x 1042 pixels were converted into a permeability structured grid block of 1042 x 1042 x 1 cells. Hence, each pixel of the networks\u0026rsquo; image (raster data) is represented by a cell which is the smallest possible grid that can be used in the FC model. It therefore preserves the minutest details of the original network that helps in accurately modeling the flow behavior of such maps [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Each cell of the FC models thus generated, is then assigned a porosity and permeability value according to whether they represent fracture, 95% and 10\u003csup\u003e6\u003c/sup\u003e md respectively, or matrix, 5% and 10\u003csup\u003e2\u003c/sup\u003e md respectively [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. These values were chosen such that flow occurs mostly through fractures because in this research, fractured reservoirs of Type-1 [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] is considered where natural fractures are the main contributors to fluid flow in terms of permeability and porosity. Thus the focus is on evaluating fracture network geometry from flow responses.\u003c/p\u003e\u003cp\u003eAll the FC models are flow simulated using TRACE3D [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] at a constant boundary condition with reservoir pressure of 2480 psia and an injection rate of 500 bbl/day for a period of 1000 days. A pair of injector and producer are placed at the two diagonal corners, (1, 1) and (1000, 1000) of the model fracture network and, (1, 1) and (1042, 1042) of the fracture maps to obtain a total areal sweep of the reservoir fluids. The overall recovery values for the seven natural fracture maps are considered for quantitative characterization of fluid flow, which can help in evaluating the effect of fracture network geometry on flow behavior. The time of flight (TOFs) are used to visualize the fluid-front movement from the injector to producer through the fracture networks.\u003c/p\u003e\u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Density and Intensity of Fracture Networks\u003c/h2\u003e\u003cp\u003eThe fracture density (pixel\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and intensity (pixel\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) of the set of seven Odling\u0026rsquo;s fracture maps are quantified using FracPaQ are shown in Fig.\u0026nbsp;4 and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e respectively. It is observed in Fig.\u0026nbsp;4, that the density of fracture maps trends to increase from map 1 to map 7. Also, a vivid difference of fracture density is observed in map 3 and map 4, although this two maps cover the same map area of 90m x 90m. The density is observed to increase directly with increase of the scale of the maps. It is evident, as the larger scale maps have more number of shorter fractures which also generates a higher number of node interactions. This suggests that, a fracture map with higher density can contribute to a higher value of node-based connectivity.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows that the fracture intensity increases from map 1 to map 2 and then gradually decreases till map 7. Also, for map 3 and map 4 the intensity plots appear to be somewhat similar as these two maps cover the same map area of 90m x 90m and have a stubble difference in the arrangements of their fracture traces. The trend of intensity plots of the fracture maps suggests that the intensity of fracture maps is moreover affected by the resolution of the maps, i.e.; the higher resolution maps have higher intensity due the exposure of longer fracture traces mapped at higher resolution. It can be presumed that a higher fracture intensity can contribute of a higher value of percolation connectivity, which is dependent on the presence of longest spanning clusters in fracture maps.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Density maps of the seven nested natural fracture maps generated using FracPaQ2D.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Node-based Connectivity and Percolation Connectivity\u003c/h2\u003e\u003cp\u003eThe node-based connectivity, evaluated based on the proportions of \u003cem\u003eX\u003c/em\u003e, \u003cem\u003eY\u003c/em\u003e and \u003cem\u003eI\u003c/em\u003e nodes using the Eq.\u0026nbsp;1 is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Two distinct trends are observed, one in map 1\u0026ndash;3, where the node-based connectivity decreases from map 1 to map 3. The other trend in observed in map 4\u0026ndash;7, where the node-based connectivity decreases from map 4 to map 7. It can be stated that the resolution and scale of the map influences the overall connectivity of the maps. However, it\u0026rsquo;s astonishing that map 3 and map 4 are the outcrop area mapped at same scale of \u003cem\u003e90\u003c/em\u003e x \u003cem\u003e90\u003c/em\u003e m only at different resolutions, but their node-based connectivity is very different. Also, Odling [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], mentions that the fractures in map 2 are more connected and spread out over the mapping area. Hence, map 2 should have the highest overall connectivity and contribute to fluid flow.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe percolation connectivity, evaluated based on the largest spanning cluster in a fracture network is plotted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. It is observed that the highest percolation connectivity value is for map 2 and lowest for map 7, whereas the it remains almost same for map 3 and map 4. It suggests that the percolation connectivity of each of these maps is sensitive to the presence of longer traces with respect to the domain size that span over the entire map [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The presence of large number of short fracture traces with respect to the domain size cannot guarantee good connectivity as these \u0026ldquo;short\u0026rdquo; fractures may be less connected than a fewer long fractures. The small scale high resolution maps have \u0026ldquo;longer\u0026rdquo; traces relative to the map area, hence, are better connected than the large scale, low resolution maps with large number of \u0026ldquo;short\u0026rdquo; fractures. This percolation connectivity study also aligns well with the overall connectivity estimated by Odling, 1997.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Percolation connectivity (Pc) of the seven nested natural fracture maps [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Fluid Recovery\u003c/h2\u003e\u003cp\u003eThe fluid recovery obtained by flow simulation of each of the fracture maps (as described in section 2.4) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The recovery values appear to be very similar to the percolation connectivity. This can possibly be attributed to the fact that recovery is directly controlled by the extend of longer spanning clusters of the networks. The latter in turn, is related to fracture intensity which is quantified by the length of fracture traces per area of the map. As the fracture length distribution of networks are different in each of the fracture maps, there exists differences in intensity, which leads to differences in percolation connectivity and ultimately differences in of fluid transport path from the injection point to the production point of the fractured domain.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe heterogeneity in fracture networks can be vividly visualize in the TOFs generated using streamline-based flow simulators. The concept of time of flight (TOF) introduced by Datta-Gupta and King [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], is a spatial coordinate representing the distance along streamline to where the reservoir will be contacted. Map-1 and map-6 along with their respective TOFs for different time steps: 500, 750 and 1000 are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The fracture area contacted in map-1 is higher than that of map-6 at each time step. This shows that the fluid movement is along the percolation cluster that provides an amicable flow pathway from the injector to the producer. The resultant of this can be obtained as a high recovery value of map 1 over map 6 although for the same time period of flow simulation.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003eIdentifying the differences between fracture intensity and fracture density within a network, particularly when networks share the same fractal dimensions offers critical insights with wide-ranging applications across geosciences and engineering disciplines. This study demonstrates that variations in key geometric properties, such as connectivity, as well as differences in fluid recovery behavior, are more strongly governed by fracture intensity rather than by fracture density. These findings also highlight the need to distinguish between these two parameters when modeling fracture networks, as fracture intensity plays a more dominant role in controlling fluid flow and overall network behavior.\u003c/p\u003e\u003cp\u003eThe novelty of this study lies in such a focused comparison of fracture intensity and fracture density, which has not been systematically explored before, providing new insights into how subtle differences in fracture characterization can lead to significant variations in reservoir performance and flow modeling. Through accurate characterizing and distinguishing these network properties, professionals in the fields of hydrology and reservoir engineering can make more informed decisions, optimize resource extraction, enhance safety, and mitigate environmental impacts.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eCompeting Interests:\u003c/h2\u003e\u003cp\u003eThe authors declares no competing interests with any individual/organization anywhere\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e\u003cp\u003eThis work is not funded by any agency, rather it is an effort of the authors investigation using opensource softwares.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eDr. A K S has explored the initial idea of this research and also have worked on all the analysis, coding and result analysis. Dr. A K S has also written the first draft of the manuscript. S.M.M and M. P. J. has carried out the proof reading and have contributed extensively in the enhancement of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eWe extend our sincere thanks to Petroleum Engineering Department at MIT World Peace University for encouraging this study. A.K.S would like to thank Reservoir Research Initiative Lab at IIT Kharagpur for providing generous suggestions and data accusation during the research.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eVan Golf-Racht TD (1982) Fundamentals of Jointed Reservoir Engineering. Elsevier Scientific, New York\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNelson RA (2001) Geologic Analysis of Naturally Fractured Reservoirs, Gulf Professional Publishing Co, ISBN 0-88415-317-7\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eManzocchi T (2002) The connectivity of two-dimensional networks of spatially correlated fractures. 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While extensive studies have focused on network characterization, the direct influence of density and intensity of fractures on flow behavior remains largely unexplored, which is a critical aspect of fracture modeling. This study aims to investigate the relative importance of fracture density versus intensity in determining fluid flow behavior in fractured rock formations. This research analyzes geometrical parameters of a set of seven Odling\u0026rsquo;s fracture outcrops from the Devonian sandstone of the Hornelen Basin, Norway. Fracture density and intensity are evaluated with the application of Matlab toolbox, FracPaQ2D. Additionally, node-based connectivity is assessed through relative abundance of fractures, while percolation connectivity is estimated based on geometric extension of fracture traces. Flow simulations are performed using TRACE3D, by converting these fracture maps into permeability grids through the application of Fracture Continuum model. A comparative analysis of these parameters, examines how variations in density and intensity impact key flow parameters such as time of flights (TOFs) and fluid recovery. The results indicate that, although both fracture density and intensity are important, the fracture intensity exerts a more significant influence on fluid flow within a fractured media. This is because fracture intensity directly controls the percolation connectivity of the fracture network, which is a critical determinant of flow pathways. Specifically, it is influences by the formation and extent of the largest spanning clusters that facilitate fluid movement. Consequently, variations in fracture intensity can significantly alter reservoir permeability and fluid flow. These findings have significant implications for improving reservoir characterization and modeling, ultimately aiding in the optimization of hydrocarbon extraction, geothermal energy production, and carbon sequestration strategies.\u003c/p\u003e","manuscriptTitle":"Unraveling the Effects of Fracture Density and Intensity on Reservoir Connectivity and Flow Behavior","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-16 16:35:59","doi":"10.21203/rs.3.rs-7493136/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-16T05:03:52+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-18T17:57:48+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"247371523507407744540481060319948577988","date":"2025-10-10T04:15:34+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-04T22:01:21+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-02T09:00:34+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"240874428873800465786030803428380181969","date":"2025-09-11T21:12:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"212039254681080095161061229379236126039","date":"2025-09-11T17:12:50+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-09T08:55:58+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-30T08:02:44+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-30T08:01:13+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Petroleum Exploration and Production Technology","date":"2025-08-30T06:07:40+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":false,"email":"","identity":"journal-of-petroleum-exploration-and-production-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Journal of Petroleum Exploration and Production Technology","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"VoR Journals","inReviewEnabled":false,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8d618e81-73b5-4c82-9c8e-6d66f4074129","owner":[],"postedDate":"September 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-07T04:23:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-16 16:35:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7493136","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7493136","identity":"rs-7493136","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}