Comparison of Different Univariate and Multivariate Geostatistical Methods by Porosity Modeling of an Iranian Oil Field

Abstract

Geostatistical methods are grouped in two main divisions: univariate and multivariate. When there is adequate amount of primary data, univariate methods such as kriging and SGS give a good representation of property distribution in the reservoir, but practical difficulties appear when there is no sufficient data. In such a case it is necessary to choose multivariate geostatistical methods in which some covariables are contributed to model the primary variable. Multivariate geostatistics is a broad term that encompasses all geostatistical methods that utilize more than one variable to predict some physical property of the earth. Bivariate geostatistics is obviously the simplest subset of the multivariate techniques and thus the standard cokriging technique can be called multivariate geostatistics. Cokriging estimates the unsampled value using the primary and secondary variable values from all primary variable sampled locations and also the covariable at an unsampled location, thus there is a need to construct the secondary and cross covariograms. Hence, it is a time-consuming approach. Collocated cokriging is a valuable alternative to full cokriging, which overcomes these problems. It only requires the covariable sample to be available at every location where the principal variable must be estimated. The authors used this in the framework of sequential simulation to produce various realizations. They compare moving average, kriging, and SGS as univariate methods to collocated cokriging and collocated cosimulation as multivariate methods by porosity modeling of an Iranian oil field, although there were only 7 wells available.