Projection Onto Convex Sets (POCS): A new method for constrained stochastic simulation of rock properties for geotechnical design and fluid flow modeling

Numerical modeling of rock masses requires the accurate estimation of material properties throughout a rock volume. No matter how dense and accurate the sampling scheme may be, most of the rock mass remains unsampled. Thus a key step in creating useful numerical models is to accurately estimate material properties in unsampled regions. Estimation accuracy has improved over the past decade through the use and improvement of methods based upon the spatial correlation among data, such as geostatistics and fractal geometry. However, the spatial pattern of a particular property in a rock mass is a function of more than its spatial correlation. A new method, Projection Onto Convex Sets (POCS), offers an alternative way to constrain the estimated values for numerical models. Its primary advantage is that it can simultaneously enforce a large variety of geologically useful constraints. This paper provides an overview of the theory and numerical implementation of POCS, and illustrates an application to flow through fractures.