Comparison of IK, SISIM and SNESIM in reconstructing 2D porous media

Great progress has been made in the mechanics of fluids flow in porous media, which is based on Darcy's law and widely used in many engineering fields. The two-dimensional reconstruction of porous media is of great significance to the research of mechanisms of fluid flow in porous media. However, it is quite difficult to reconstruct the unknown information only by some sparse known data in the process of reconstruction. Therefore, some interpolation methods are used to reconstruct the unknown region for better results. Some interpolation methods including indicator kriging (IK), sequential indicator simulation (SISIM) and single normal equation simulation (SNESIM) are typical interpolation methods for reconstruction of porous media. IK is a famous interpolation method in geoscience and it does not guarantee that the probabilities monotonically increase and are bound between 0 and 1 for the continuous case and that they are all positive summing to one for the categorical case. SISIM combines IK with the sequential method to simulate non-parametric continuous or categorical distributions. SNESIM scans a training image using a data template to get the probabilities of occurrences of data events. The three methods are tested on the two-dimensional reconstruction of sandstone. The reconstructed images and the original image are compared. The experimental results demonstrate that the structures of porous media reconstructed through SNESIM are most similar to those of original data.