# The Electromagnetic Field Analytical Solution Analysis to Downhole Current Injection [PERSON]
## 3 Simulation Experiments
When the inclination angle of the observation points is \(0^{\circ}\), the detected magnetic field gradually decreases from top to bottom; when the inclination angles are \(5^{\circ}\) and \(10^{\circ}\), the detected magnetic field gradually increases from top to bottom due to the change in well spacing. The above variation trend is consistent with the principles of downhole current injection ranging detection. Keeping other simulation parameters constant, the excitation current was further increased to 300 mA and 500 mA, and analytical calculation and COMSOL-based numerical simulation were employed to obtain the results of converging current density and magnetic field distribution, respectively. Figure 7 shows the results of converging currents around the target well for different excitation levels. It can be observed that the convergent current increases proportionally with the excitation current, both in the analytical and numerical  
Figure 4: Convergent current simulation results. Figure 5: Schematic diagram of magnetic field detection point placement. representations. The analytical method provides smoother computational results because it is not affected by the number of mesh grids. The calculated results of the magnetic field at the corresponding detection locations under different excitations were obtained, as illustrated in Figure 8. It can be found that the magnetic field strength increases with the excitation current, exhibiting an approximately linear growth trend. The above analysis indicates that the computational results of the analytical method align well with the numerical results and demonstrate good adaptability to different excitation cases, thereby confirming the validity of the proposed analytical solution. Based on the model validity verification, the environmental suitability of the constructed analytical calculation model was further analyzed. With an excitation of 100 mA and other conditions held constant, the stratum conductivity was adjusted to 0.002 S/m, 0.02 S/m, and 0.2 S/m. The converging currents of the target casing and the observed magnetic fields at different locations were then calculated. Figure 9 shows the magnitude of the converging current along the surface of the target casing for different background conductivities. It can be observed that the converging current gradually decreases as the stratum conductivity increases. This phenomenon occurs because as the stratum conductivity increases, the difference between the stratum conductivity and the target casing  
Figure 6: Magnetic field simulation results. Figure 7: Simulation results of convergent current with different magnitude of excitation current. conductivity becomes smaller, weakening the current convergence ability of the metal casing. Furthermore, when the conductivity changes, the position of the extreme value of the converging current shifts slightly. This indicates that changes in the stratum conductivity also affect the electromagnetic transmission path. Accordingly, we also calculated the magnetic field for various conductivity cases to analyze the distribution pattern, with the results shown in Figure 10. It is evident that as the stratum conductivity increases, the observed magnetic field at the same location decreases rapidly, which is consistent with the change in converging currents. Notably, the change in stratum conductivity not only affects the magnitude of the magnetic field but also alters its distribution pattern. This observation aligns with the theoretical analysis and confirms that the constructed analytical results are consistent with the results obtained from COMSOL. Figure 8: Simulation results of magnetic field with different excitation currents. Figure 3:0 Effect of stratum conductivity on converging currents.