Spatial estimation is the process of inferring the value of one or multiple variables in a target subsurface using a number of samples of the variable. As the main application of spatial estimation is in mining and petroleum engineering, these variables are usually indicative of the presence of mineralization or hydrocarbon concentrations. Because of that, it is crucial to find spatial estimation methods that lead to accurate and reliable projections of these variables in order to properly locate and quantify deposits and reservoirs.
One of these methods is Collocated Cokriging which is based on a multivariate approach to spatial estimation. In this method, one secondary variable is estimated using the Kriging spatial estimation method, which is just a geological extension of linear regression, and the values generated in that process are used to estimate the primary variable of interest. In this project, a data set located at the East Texas oil fields is studied where multiple spatial variables have been extensively sampled. The primary variable of interest is effective porosity and the results of its estimation, first generated by Kriging and then by Collocated Cokriging using three other variables (oil saturation, effective water saturation, and bulk mass fraction of oil) are compared and analyzed. Since Collocated Cokriging is a novel estimation method and its performance on different geological settings has not been fully explored, it is important to test its capacities on a petroleum data set, which is the subject of this project.
The results show that Collocated Cokriging improves the quality of estimation, which is reflected in the reduction of estimation variance, over Kriging. Moreover, Collocated Cokriging improves estimation quality in parts of the domain with very few samples, which are areas that this improvement is most needed. Finally, it is concluded that Collocated Cokriging produces more precise results for secondary variables with a higher correlation to the primary variable. All these conclusions prove Collocated Cokriging's merit as a method of spatial estimation.