Effect of borehole design on cross-hole electrical impedance tomography (EIT) measurements

Electrical Impedance Tomography (EIT) is a sophisticated non-invasive tool to investigate the subsurface in engineering and environmental studies. To increase the depth of investigation, EIT measurements can be made in boreholes. However, the presence of the borehole may affect EIT measurements. Here, we aim to investigate the effect of different borehole components on EIT measurements using 2,5-D and 3D finite element modeling. The results showed that the unstructured mesh is more suitable than the structured mesh to investigate borehole effects because it was more flexible, required less elements to represent the borehole, and resulted in elements with more favorable aspect ratios than the structured mesh. The use of an unstructured mesh led to a decrease of modeling error from 4,96% to 0,002% as determined using the deviation from the analytical solution for a homogeneous medium. The computational time was also reduced by a factor of 10. Simulations with a variety of domain sizes revealed that the distance to the no-flow boundary affects the simulation results strongly. Therefore, it was attempted to find an unstructured mesh that provided a good compromise between modeling accuracy and computational time for different electrode configurations. Using the longest possible electrode configuration at the Krauthausen test site (worst case scenario), it was found that a mesh with a vertical domain size of 13 m (3,5 m below bottom electrode) and a horizontal domain size of 13 m (1,8 times the current electrode spacing) was a good compromise with a modeling accuracy of 2,15%. Smaller electrode configurations resulted in an even higher accuracy. To investigate the effect of different borehole components on EIT measurements, a variety of scenarios were designed. In particular, the effect of the water-filled borehole, the PVC casing, and the gravel filter were investigated relative to complex resistivity simulations for a homogenous medium with chain and electrode modules. It was found that the results of the complex resistivity simulations were best understood using the sensitivity distribution of the electrode configuration under consideration. In all simulations, the sensitivity in the vicinity of the borehole was predominantly negative. Therefore, the introduction of the water-filled borehole caused an increase in the real part of the impedance, and a decrease (more negative) in the imaginary part of the simulated impedance. The PVC casing mostly enhanced the effect of the water-filled borehole described above, although this effect was less clear for some electrode configuration. The effect of the gravel filter mostly reduced the effect of the water-filled borehole with PVC casing. For EIT measurements in a single borehole, the highest simulated phase error was 12% for a Wenner configuration with electrode spacing of 0,33 m. This error decreased with increasing electrode spacing. In the case of cross-well configurations, the error in the phase shit was as high as 6,5%. Here, it was found that the highest errors occur when both current electrodes are located in the same borehole. These results indicated that cross-well measurements are less affected by the presence of the borehole than measurements in a single borehole. Overall, it was concluded that finite element modeling with unstructured meshes is well suited to obtain detailed insights in the effect of different borehole components on EIT measurements