# Study on the Mechanism of Stress Sensitivity Changes in Ultra-Deep Carbonate Reservoirs
## 2 Stress-Sensitive Modelling of Ultra-Deep Carbonate Reservoirs
### Derivation of Stress-Sensitive Formulae for Fractured Carbonates  
In the field of geology and rock mechanics, fractures can be classified based on different modes of crack propagation, known as Mode I, Mode II, and Mode III fractures [24; 25]. These modes are associated with different types of stress conditions and deformation mechanisms, and they can affect the behavior and stability of rocks differently. Here is a brief explanation of each mode:  
Mode I fracture (opening mode): Mode I fractures occur when a crack propagates perpendicular to the direction of the applied tensile stress. This is commonly referred to as an opening-mode fracture, where the crack surfaces move away from each other. Mode I fractures are typically associated with tensile loading and are important in rock fragmentation and tension-induced failures. Mode II fracture (sliding mode): Mode II fractures occur when a crack propagates parallel to the direction of the applied shear stress. This mode is characterized by sliding along the plane of the crack surfaces. Mode II fractures are associated with shear loading and can occur in situations where rocks are subjected to lateral or sliding forces. Mode III fracture (tearing mode): Mode III fractures occur when a crack propagates perpendicular to the direction of the applied tearing stress. In this mode, the crack surfaces slide past each other and move parallel to the direction of the applied stress. Mode III fractures are less common in geological contexts but can be important in certain types of underground mining or faulting events. In ultra-deep carbonate reservoirs, fractures play a dominant role in the loss of formation pressure, exacerbating the stress sensitivity effect of the reservoir [26; 27; 28; 29; 30]. Through numerical simulations comparing the effects of factors, such as the magnitude of Young's modulus, Poisson's ratio, and the fracture dip angle on the permeability loss of ultra-deep carbonate reservoir-rich formations, the role of fractures in stress sensitivity could be determined. It was found that reservoirs with developed fractures were more stress-sensitive than those without fractures. Fracture density and dip angle were observed to significantly impact stress sensitivity. Therefore, it is important to factor in the impacts of fractures and corresponding stress sensitivity effects during exploration and development of ultradeep carbonate reservoirs, and to take appropriate measures to maximize reservoir development effectiveness. Taking into account the abundant development of fractures in carbonate reservoirs, stress sensitivity can usually be described by introducing a stress sensitivity coefficient of permeability using [PERSON] and Darcy's laws as a basis for derivation. Therefore, based on [PERSON]'s modulus and Poisson's ratio, a three-parameter numerical simulation model based on Young's modulus, Poisson's ratio, and effective stress is typically used to calculate the relationship between effective stress and permeability. This method enables a systematic description of stress sensitivity in carbonate reservoirs, and it can provide a solid foundation for further studies of stress sensitivity and corresponding adjustments to oil and gas reservoir monitoring, development, and exploration processes.