A model to determine effective electrical resistivity of shale gas SEM images

Understanding electrical conductivity of organic shale plays an important role in unlocking mystery about pore network in shale. I present a systematic and novel approach to determine effective electrical conductivity of shale samples from readily available SEM images. The method includes (1) analyzing SEM images to identify different components like quartz, clay, organic matter, and pores and (2) use a numerical solver to solve voltage field imposed to the analyzed images to compute effective electrical resistivity of the sample. I extended the method to 3D images generated from SEM images and computed effective electrical conductivity of the generated 3D images. The study shows that electrical conductivity is sensitive to pore network and water saturation. I found estimated electrical conductivity of the 2D SEM images are very different from 3D images, hence not a good representative of the shale samples. I also compared numerical results with different analytical averaging techniques, e.g., arithmetic mean, harmonic mean, geometric mean, and the incomplete layer methods. None of the analytical methods predicts close enough to the numerical results, although incomplete layer method showed the closest results.