## 4 Results
### Karst Network Modelling and Topology Analysis
#### 4.4.2 Fracture Network Topology  
Figures 10c and 11c showed the trace length distribution in two different scale datasets. Both histograms illustrate a wide range of lengths and a comparable unimodal distribution of fracture trace lengths with a positive skew. The most abundant lineament lengths vary from 150 m to 225 m, whereas the dominant outcrop-scale fracture lengths range from 0.7 cm to 1.4 cm.  
Figure 10: (**a**) Satellite image of Subis build-up covered by high-intensity of vegetation. (**b**) Two-dimensional DFN model based on the lineament traces. Nodes in black circles and trace mid-points in red circles were used to represent the traces. (**c**) Length distribution. (**d**) Estimated density of the fractures (P20). (**e**) Estimated intensity of fractures (P21) [scale: 100 pixels = 1 km].  
Fracture Density (P20), Intensity (P21), and Connectivity (I-X-Y)  
Figure 10d,e and Figure 11d,e depict the fracture density (P20), which represents the number of fractures per unit area, as well as the intensity (P21), which reflects the total length of fractures per unit area. For examination purposes, both regional- and outcrop-scale traces were confined by a square box. The northern part of the Subis Limestone build-up had the most fractures and the longest overall length of fractures. Meanwhile, the outcrop-scale fractures were denser in the northwest direction of the outcrop. These two parameters, however, cannot be used directly in the 3D fracture modelling as they are directionally dependent on either the measurements or on boundary sensitivity.  
The I-X-Y topology was analysed to quantify the connectivity of the fracture networks and is represented by the average number of connections per line (\(\mathrm{C_{L}}\)). [PERSON] and [PERSON] [56] described the values of two contour lines. Lineaments at the regional scale (Figure 12a-d) and fractures at the outcrop scale (Figure 12e,h) were interpreted. The triangular plots depict the detailed topological analyses of nodes and branches for regional- and outcrop-scale fractures, as indicated by the fracture network's relative proportions of isolated (I), splay or abutment (Y), and intersection (X) nodes.  
Figure 11: (**a**) Enlarged open fractures due to dissolution. (**b**) Two-dimensional DFN model based on the outcrop-scale fracture traces. Nodes in black circles and trace mid-points in red circles were used to represent the traces. (**c**) Length distribution. (**d**) Estimated density of the fractures (P20). (**e**) Estimated intensity of fractures (P21) [scale: 800 pixels = 2.5 m].  
Based on the I-X-Y models for the dataset utilised in this study, I nodes or isolated nodes are the predominant node type for the regional scale lineaments (I = 0.93) with  
Figure 12: The connectivity of traces (isolated (I), splay or abutment (Y), and intersection (X) for regional lineaments (**a–d**) and outcrop fractures (**e,h**). A ternary plot of fracture segment connectivity (**b,f**) lineaments and fracture traces on (**a,e**). (**c,g**) Heat maps of I nodes and (**d,h**) X + Y nodes.  
relatively low values in the X-Y or intersection-abutment nodes (X = 0.04, Y = 0.03). Similarly, at the outcrop scale, the dominant type of nodes are I nodes (I = 0.74) with comparatively low values in the X-Y nodes (X = 0.20, Y = 0.06). The heat maps of X + Y nodes for both scales in the Subis Limestone reveal a low proportion of X + Y nodes, indicating that the fracture patterns are poorly connected (Figure 12d,h). According to the results of the I-X-Y connectivity models, naturally fractured reservoirs are characterised by isolated fractures with poor connectivity, without considering the karst-related porosity effect on the fracture.