Conditioning geological surfaces to horizontal wells

Abstract

AbstractKriging is a standard method for conditioning surfaces to observations. Kriging works for vertical wells, but may produce surfaces that cross horizontal wells between surface observations. We establish an approach that also works for horizontal wells, where surfaces are modeled as a set of correlated Gaussian random fields. The constraints imposed by the horizontal wells makes the conditional surfaces non-Gaussian. We present a method for exact conditional simulation and an approximation for prediction and prediction uncertainty. Thousands of constraints can be handled efficiently without numerical instabilities. The approach is illustrated with synthetic and real examples that show how the constraints influence the surfaces and reduce uncertainty.