Sequential Gaussian simulation using multi-variable cokriging

Kiki (Hong) Xu, Jian Sun, Brian Russell, Kris Innanen

ABSTRACT

Uncertainty analysis is a key element in reservoir properties prediction, and many techniques have been developed, such as simulation, which is usually performed by least square method. Least square estimation is a classic and well known approach as a best fit solver, which is equivalent to simple kriging or cokriging system in case of geostatistics filed. Inspired by the distinction of simple and ordinary system in geostatistics and benefited from the extended cokriging system, for reservoir properties prediction, we propose an approach to implement sequential simulation with multiple priori information using the extended cokriging system. As it implies, the conditional mean and variance in the posterior distribution are obtained by performing the extended cokriging system. Comparison between this approach and traditional sequential simulation using least square method are discussed in sense of semivariogram. The advantage are further analyzed through the estimated error map, which indicates that simulation using the extended geostatistics method can produce an more an accurate map, especially dealing with the data has the dramatical changes.

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