Study on Electrical Dispersion Characteristics of Two-Dimensional Rock Based on LBM

In the process of oil and gas field exploration and development, the complex resistivity spectral logging technology utilizes the dispersion characteristics of rock impedance, which can more accurately distinguish oil, gas, and water layers. Currently, the study of rock complex resistivity dispersion stays in the macroscopic equivalent parameter model, and it is difficult to explain the mechanism of rock electric dispersion from the microscopic point of view. In this study, a mesoscopic model of rock electric dispersion is established based on the Lattice Boltzmann method(LBM), and the effects of external electric field frequency and rock porosity on the electric dispersion characteristics of rocks are discussed by simulating the complex resistivity dispersion response of two-dimensional pore channels at different frequencies based on the interfacial polarization theory. The simulation results show that the mesoscopic model can successfully reflect the motion law of ions in the porous medium under the external electric field, and at the same time, the larger the porosity of the rock, the more the valley of the imaginary part of the complex resistivity of the model response moves to the direction of increasing frequency, which is consistent with the experimental law of the actual rock electric frequency dispersion. The mesoscale model established by this research can be used for the study of the micro-mechanisms of the rock electric frequency dispersion, and provide theoretical basis for the application of complex resistivity logging technology in the exploration and development of oil and gas.