## 3 Results and Discussion
### The Geodynamic Model Examples
#### 3.2.3 Model of Rock Failure near the Borehole  
The borehole model (Figure 12) reflects irreversible geodynamic processes near wells. It mainly characterizes tensile deformations, due to which radial and azimuthal fracture cracks are formed. The development of fracturing and the accompanying process of filling the fractures with fluid will be accompanied by a change in the resistivity of the near-well space. As a result, the macroscopic geoelectric characteristics of the rock near the well become azimuthally anisotropic. To determine the effective electric conductivity of the rock near the well, we use the cylindrical coordinate system with new coordinates, namely \(\rho\), \(\phi\), and \(z\), where \(\rho\) is the radial coordinate, \(\phi\) the azimuthal coordinate, and \(z\) the vertical coordinate. As the homogenization volume, we select a segment bounded by an \(\Delta\phi\) angle, \(\Delta\rho\) radius, and \(\Delta z\) thickness. We consider the model of the media to be uniform along the \(Z\) axis. The inclusions have sizes of \(\Delta\rho_{1}\), \(\Delta\phi_{1}\), and \(\Delta z_{1}\) and electric conductivity of \(\sigma_{1}\), while the size of the pore space is \(\Delta\rho_{0}\) with electric conductivity of \(\sigma_{0}\)(Figure 12). In the general case, the electric conductivity in the entire homogenization volume cannot be represented as a product of isolated functions of coordinates. However, in each separate layer, bounded in Figure 12 by the dotted line, electric conductivity has the following appearance. Therefore, we first average the electric conductivity in each layer over the spatial coordinates. At \(\rho\in\Delta\rho_{1}\),  
\[\sigma^{eff}= \begin{pmatrix}\sigma_{1}\frac{\Delta\rho_{1}}{\Delta\rho}+\sigma_{0 }\frac{\Delta\rho_{0}}{\Delta\rho}&0&0\\ 0&\frac{1}{\frac{1}{\sigma_{1}}\frac{\Delta\rho_{1}}{\Delta\rho}+\frac{1}{ \sigma_{0}}\frac{\Delta\rho_{0}}{\Delta\rho}}&0\\ 0&0&\sigma_{1}\frac{\Delta\rho_{1}}{\Delta\rho}+\sigma_{0}\frac{\Delta\rho_{0 }}{\Delta\rho}\end{pmatrix} ,\]  
where \(\Delta\rho=\Delta\phi_{1}+\Delta\phi_{0}\); if \(\rho\in\Delta\rho_{0}\), \(\sigma^{eff}=\sigma_{0}\). With this operation, the transition to the (radially) layered anisotropic model (1.6) is carried out. Passing this to the entire homogenization volume, i.e., averaging (radially) layered anisotropic media, we finally obtain  
\[\sigma^{eff}= \begin{pmatrix}\sigma_{11}&0&0\\ 0&\sigma_{22}&0\\ 0&0&\sigma_{33}\end{pmatrix} , \tag{10}\]  
where \(\Delta\rho=\Delta\rho_{1}+\Delta\rho_{0}\);  
Figure 12: The model of rock destruction near the borehole of the rock corresponds to the fractured-capillarity type of pore space (bianisotropic media). A simplified view of a borehole area is shown with a zoomed-in permeable formation depicting the invasion zone of the well. Right: A cut piece of a round clock specimen of layered rocks. \(\sigma_{0}\) and \(\sigma_{1}\) are electric conductivities of pore and inclusion spaces. The size of the pore space is \(\Delta\rho_{0}\), \(\Delta\varphi_{0}\), and \(\Delta z_{0}\). The inclusions have sizes of \(\Delta\rho_{1}\), \(\Delta\varphi_{1}\), and \(\Delta z_{1}\). The dimensions of the rock media are \(\Delta\rho=\Delta\rho_{0}+\Delta\rho_{1}\), \(\Delta\rho=\Delta\varphi_{0}+\Delta\varphi_{1}\). The media is uniform along the vertical axis \(Z\). The anisotropy coefficients of the effective electricity are  
\[