Generation of three-dimensional isotropic permeability fields

Reservoir rock properties, such as permeability and porosity, vary in space and may be characterized by their distributions. These distributions are not totally random, but display some correlation structure. Because the properties are known only at the wellbore, some rational method is required to generate these property distributions for inclusion in fluid transport models. This paper presents a numerically efficient method of generating geostatistical random fields by the Source Point Method (SPM). The SPM is the most efficient method with regard to computer time and data storage compared to other methods of generating random fields. In addition, the SPM is extended to a three-dimensional Euclidean space for the generation of property distributions of a system. Using conditional covariances, a formula for a three-dimensional isotropic field is derived to prespecify the desired correlation length. Results show that for a three-dimensional isotropic medium the correlation length can be prespecified. Results from the SPM are also compared with the matrix decomposition method (MDM).