# Study on the Mechanism of Stress Sensitivity Changes in Ultra-Deep Carbonate Reservoirs
## 2 Stress-Sensitive Modelling of Ultra-Deep Carbonate Reservoirs
### Derivation of Equations for Stress Sensitivity Evaluation of Matrix-Type Carbonate Reservoir  
The change mechanism of stress sensitivity in matrix-type carbonate reservoirs is through the changes in the internal pore structure and skeletal structure of the rock. When the rock is subjected to stress, the internal pore structure of the rock tends to close, resulting in a reduction in porosity and permeability, which lowers the flow capacity of the reservoir. Additionally, the skeletal structure of carbonate reservoirs is relatively weak and undergoes plastic deformation under stress. It can cause a reduction in the volume of the rock and induce uncontrollable factors such as reservoir fracturing and crack formation [23]. Therefore, a physical experiment using true core samples was carried out to study the stress sensitivity of the ultra-deep carbonate matrix by the mentioned factors. Note:  
1. The samples were collected from ultra-deep carbonate samples of the Northwest Bureau of SINOPEC. 2. This study focuses on ultra-deep carbonate reservoirs that are deeply buried and difficult to obtain core samples from. During the sampling process, the cores were severely damaged. Therefore, we selected two relatively intact cores as representatives in this study, and the specific sample parameters can be found in Table 1.  
This experiment involved two test samples, sequentially numbered A1 and A2. The experiment was conducted under conditions of a confining pressure of 87 MPa, a temper \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Core Number** & **Diameter/mm** & **Permeability/mD** & **Porosity/\%** \\ \hline A1 & 69.246 & 0.032 & 0.1306 \\ A2 & 54.228 & 0.133 & 0.1528 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of the samples. ature of 120 \({}^{\circ}\)C, and nitrogen as the fluid medium. By maintaining a constant confining pressure on the core samples, changes in flow pressure were used to alter the effective stress experienced by the cores. Experimental Procedure:  
1. Measure the permeability and porosity of the samples before any loss occurs;  
2. Place the core samples into the core holder and initialize the core permeability tester;  
3. Ensure that the confining pressure remains constant and changes the flow pressure to 10 MPa, 15 MPa, 20 MPa, 25 MPa, 30 MPa, 35 MPa, 40 MPa, 45 MPa, and 50 MPa. After each pressure point stabilizes, measure the permeability of the rock sample and calculate the permeability loss rate;  
4. After all pressure-point tests are completed, turn off the equipment;  
5. Replace the core and repeat the aforementioned operations (Figure 1). The value of K0 is the original permeability of the formation, and Kh is the permeability measured under different fluid pressures that correspond to different effective stresses. Based on the data obtained in the high-temperature and high-pressure testing conditions (Tables 2 and 3), the permeability-effective stress relationship curve (Figure 2) and permeability loss rate (K\({}_{\text{h}}\)/K\({}_{0}\))-effective stress relationship curve (Figure 3) were drawn. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Core Number**} & \multirow{2}{*}{**Porosity/\%**} & \multirow{2}{*}{**Confining Pressure/MPa**} & \multirow{2}{*}{**Flow Pressure/MPa**} & \multirow{2}{*}{**Permeability/mD**} & **Rate of Change in Permeability/\%** \\ \cline{5-5}  & & 87 & 65 & 0.0541 & 0.0 \\ \cline{3-5}  & & 87 & 60 & 0.0453 & 16.4 \\ \cline{3-5}  & & 87 & 50 & 0.0352 & 34.9  
Figure 3: Depletion permeability-loss-rate curve.