Generation of correlated properties in heterogeneous porous media

The spatial distribution of rock properties in porous media, such as permeability and porosity, often is strongly variable. Therefore, these properties usefully may be considered as a random field. However, this variability is correlated frequently on length scales comparable to geological lengths (for example, scales of sand bodies or facies). To solve various engineering problems (for example, in the oil recovery process) numerical models of a porous medium often are used. A need exists then to understand correlated random fields and to generate them over discretized numerical grids. The paper describes the general mathematical methods required to do this, with one particular method (the nearest neighbor model) described in detail. How parameters of the mathematical model may be related to rock property statistics for the nearest neighbor model is shown. The method is described in detail in one, two, and three dimensions. Examples are given of how model parameters may be determined from real data.