# Study on Permeability Stress-Sensitivity in
## 4 Simulation Results and Discussion
### Analysis of Permeability Stress-Sensitivity Simulation Results  
The relationship between permeability and effective stress can reveal the mechanism of permeability stress-sensitivity in gas reservoir depletion development. Figure 16 shows the variation of normalized permeability and average effective stress (\(\sigma_{\rm o}=(\sigma_{\rm x}+\sigma_{\rm y}+\sigma_{\rm z})/3\)) near the wells of LNY-06 and LNY-24 during gas reservoir development. The effective stress near the well increases and the permeability gradually decreases during depletion exploitation, exhibiting a high stress-sensitivity. Meanwhile, the figure shows the three-dimensional permeability of the fracture and matrix, with the greatest decay of permeability in the Z-direction of the fracture and the least decay of permeability in the Y-direction of the matrix.  
Figure 14: Elastic strain distribution of natural fractures in the target formation.  
Figure 15: Plastic strain distribution of natural fractures in the target formation.  
To further explore the permeability stress-sensitivity of the target formation, the evolutionary distributions of the matrix permeability and fracture permeability were plotted in Figures 17 and 18. The permeability gradually decreases with an average decrease of about 25% and a maximum decrease of about 39% by the end of the simulation. The trends in matrix permeability and fracture permeability are consistent, but the maximum decrease in fracture permeability is about 40%, the maximum decrease in matrix permeability is about 20%. The permeability stress-sensitivity of fracture system has a greater impact during gas reservoir development. The variation of matrix permeability and fracture permeability is different between the three-dimensions, with the largest permeability variation in the Z-direction, Figures 17c and 18c, and the smallest permeability variation in the Y-direction, Figures 17b and 18b, which is consistent with the three-dimensional effective stress variation. Thus, it shows that the heterogeneity of the reservoirs can have an impact on the evolution of permeability [39].  
Figure 16: Normalized permeability and mean effective stress around the well.  
Figure 17: Normalized permeability contours of matrix systems.  
Two types of models were used to simulate fixed production rate of the seven wells in the target formation. The first considered permeability stress-sensitivity while the second did not consider permeability stress-sensitivity. Figures 19 and 20 show the historical fitting  
Figure 18: Normalized permeability contours of fracture systems.  
results and bottom hole pressure error analysis for wells LNY-06 and LNY-24. Combining the data of the seven wells, the actual bottom hole pressure, the bottom hole pressure of the first type model and the bottom hole pressure of the second type model decreased to 79.64 MPa, 81.48 MPa and 83.42 MPa, respectively, after 2090 days of development. In the early stage of production, the formation pressure shows little change and the deformation is relatively small. The bottom hole pressure change curves for the two types models are basically equal. In the later stage of production, the pore pressure decreased significantly and the reservoir permeability decreased, while the rate of decline in bottom hole pressure increased. The mean square errors between the historical gas production results and the simulation results with and without permeability stress-sensitivity considered were 2.22 and 4.01, respectively. This indicates that the permeability stress-sensitivity is one of the factors affecting gas production.  
Figure 19: Production history matching.