## 2 Methodology

Table 1: Geometric characteristics of the model and elastic strength properties of the casing. channels are subjected to multiple cycles of loading and unloading. The experience of experimental studies has shown that, after the third cycle, such deformations of the rock are not observed, which confirms the choice of a poroelastic model for this study. 3. Cement stone has been accepted as impenetrable, which is to some extent an assumption. However, experiments show that the permeability of cement stone can manifest itself during gas filtration due to its greater mobility compared to liquid. Nevertheless, when modeling an environment saturated with water and oil, cement stone can be considered practically impenetrable. Experimental studies of cement have also shown that the dependence of stress on deformation is close to linear. In this regard, an elastic medium was set for the cement support. 4. The calculations did not take into account phase permeability; that is, it was assumed that only oil is filtered, and residual water saturation does not affect the phase permeability of oil. It is important to note that the following parameters were set in the ANSYS software package to determine the convergence criterion: the accuracy of the stress calculation is \(1\times 10^{-8}\), and the accuracy of the pressure calculation is \(1\times 10^{-10}\). If we set a lower accuracy, for example, for stresses of \(1\times 10^{-9}\), then the numerical calculation stopped converging. Considering the above, the finite element model contains the following boundary conditions:  
1. Vertical movements were fixed at the lower boundary;
2. Movements along the normal to the surface were fixed at the left and right lateral boundaries;
3. wo boundary conditions were set at the outer lateral surface:
* Fluid pressure based on the differential pressure drawdown and the pressure on the supply circuit: \[\mathrm{P}=\mathrm{P_{b}}-\Delta\mathrm{P}\frac{\ln\mathrm{r}/\mathrm{r_{w}}}{ \ln\mathrm{r_{b}}/\mathrm{r_{w}}},\] (6) where \(\mathrm{p}\) is the determined pressure value; \(\mathrm{P_{b}}\) is the pressure on the supply circuit; \(\Delta\mathrm{P}\) is the differential pressure drawdown; \(\mathrm{r_{b}}\) is the radius of the supply circuit; \(\mathrm{r_{w}}\) is the radius of the well; \(\mathrm{r}\) is the radius from the center of the well, for which we determine the pressure value;
* Horizontal stress based on the values of vertical stress and Poisson's ratio;
4. Vertical movements were set at the upper boundary for the casing and cement stone (imitation of a cased well); vertical stresses were applied to the rock, based on the reservoir depth and the average volume weight of the overlying rock stratum;
5. Fluid pressure was set inside the well and in the perforation channels, taking into account the pressure drawdown value. To determine the rock permeability, we calculated the average effective stresses in each finite element of the model according to the following ratio: \[\sigma_{av}=\frac{\sigma_{1}+\sigma_{2}+\sigma_{3}}{3},\] (7) where \(\sigma_{av}\) is the average effective stress; \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are the main effective stresses. To assess the stability of the rocks and the occurrence of plastic deformations, we applied the Mohr-Coulomb criterion to the main effective stresses: \[\sigma_{1}-\alpha p=\sigma_{c}+(\sigma_{3}-\alpha p)\frac{1+sin\varphi}{1-sin\varphi},\] (8) where \(\sigma_{1}\) and \(\sigma_{3}\) are the main maximum and minimum stresses; \(\sigma_{c}\) is the ultimate rock strength under uniaxial compression; \(\varphi\) is the angle of internal friction; \(\alpha\) is the Biot coefficient. The elastic strength properties of cement stone, shown in Table 2, were determined in the framework of earlier studies ([PERSON] and [PERSON], 2018). The physical properties of reservoir rock and the permeability dependence on average effective stresses, presented in Table 3 and Figure 2, were also determined in previous studies ([PERSON] and [PERSON], 2018).