Geostatistical Simulation and Reconstruction of Porous Media by a Cross-Correlation Function and Integration of Hard and Soft Data

A new method is proposed for geostatistical simulation and reconstruction of porous media by integrating hard (quantitative) and soft (qualitative) data with a newly developed method of reconstruction. The reconstruction method is based on a cross-correlation function that we recently proposed and contains global multiple-point information about the porous medium under study, which is referred to cross-correlation-based simulation (CCSIM). The porous medium to be reconstructed is represented by a reference image (RI). Some of the information contained in the RI is represented by a training image (TI). In unconditional simulation, only the TI is used to reconstruct the RI, without honoring any particular data. If some soft data, such as a seismic image, and hard data are also available, they are integrated with the TI and conditional CCSIM method in order to reconstruct the RI, by honoring the hard data exactly. To illustrate the method, several two- and three-dimensional porous media are simulated and reconstructed, and the results are compared with those provided by the RI, as well as those generated by the traditional two-point geostatistical simulation, namely the co-sequential Gaussian simulation. To quantify the accuracy of the simulations and reconstruction, several statistical properties of the porous media, such as their porosity distribution, variograms, and long-range connectivity, as well as two-phase flow of oil and water through them, are computed. Excellent agreement is demonstrated between the results computed with the simulated model and those obtained with the RI.