Methods for history matching under geological constraints

Two geostatistical methods for history matching are presented. Both rely on the sequential simulation principle for generating geologically sound realizations. The first method relies on perturbing the sequential simulation through the perturbation of the conditional distribution models; the second method relies on the perturbation of random numbers. We show that both approaches are general in the sense that a large variety of geological scenarios can be generated while history matching. However, the conditional probability method is more efficient due to the ability to change the random path during the history matching procedure. We demonstrate these methods on two synthetic examples: a first example demonstrates how history matching can be performed under a training image based geological model constraint using multiple-point geostatistics; a second example shows how a combinations with an existing streamline-based history matching algorithm can provide efficient history matching yet maintaining geological consistency.