## 6 Discussion  
The estimated porosity from numerical modelling concurs with the relatively high Young's modulus and rock strength, indicating that Clashach's core sample is a moderately hard rock according to the US National Engineering Handbook [69]. The deformation of the core sample alters the pore volume (porosity) and the pore network. The decrease in the porosity of the reservoir under the action of externally applied stress enhances the oil recovery from the reservoir [70]. The study provides insights into the relationship between stress and porosity in naturally fractured tight reservoir samples. Understanding this relationship is crucial for predicting fluid flow behavior and devising strategies to enhance oil recovery from the reservoir. The Clashach core's permeability reduces by 1.3% with a nearly 0.13% reduction in porosity, which highlights the pore space's weak connectivity. The intact rock's contribution to the determined strain and conductivity of the fractured core decreases because of the minimal pore strain and low permeability. Moreover, this indicates that the intact rock's contribution to the determined strain and conductivity of the fractured core is low due to minimal pore strain and low permeability. This implies that the fractured rock's properties dominate the overall behavior of the rock mass rather than the intact rock. The results provide insights into the behavior of fracture apertures under externally applied stress and highlight the importance of understanding these phenomena in various geological and engineering applications.  
Figure 12: Relative permeability variations at different stress loadings.  
In addition, when comparing the variations in \(k_{f}\) with the variations in \(k_{mat}\) (in Figure 6), it can be observed that the fracture permeability is much higher than the matrix permeability, as expected [7, 71]. Furthermore, the decrease in fracture permeability is more significant than that in matrix permeability for the same stress loading. This is because fracture permeability is affected by rock compaction and fracture closure, but matrix permeability is affected by rock compaction. Thus, to upgrade computational efficiency, it is logical to obtain matrix and fracture permeabilities by coupling the fracture with the matrix, instead of modelling them separately. Consequently, based on the simulation results, the computational efficiency can be improved by coupling the disconnected and narrow aperture's effects under different external stress loadings. These findings show that stress-dependent fracture closure plays a significant role in the multiphase flow characteristics of fractures in subterranean formations. In terms of the external stress being applied to the rock matrix, it can be seen that it has a significant impact on the relative permeabilities of both oil and water, as well as on water saturation. It can be seen that when increasing external stress loading, the relative permeability of oil decreases, while the relative permeability of water increases. However, external stress also causes a shift in water saturation, which in turn affects the relative permeabilities. This is because the water saturation is dependent on the injected water volume \(V_{\text{w}}\), as discussed earlier in Section 5.5. Thus, an in-depth understanding of the interdependencies between the injected water volume, water saturation and the relative permeabilities is essential for petroleum engineers when predicting oil recovery from fractured tight reservoirs, as this provides a quantifiable criterion for making informed decisions about the effectiveness of oil recovery methods.