Determining Optimum Estimation Methods for Interpolation and Extrapolation of Reservoir Properties: A Case Study

Abstract

ABSTRACT The accuracy of four-point estimation methods (simple averaging, fifth-degree bicubic spline, inverse weighted distance squared, and kriging) were compared in five reservoir layers using data sets consisting of five different reservoir properties (horizontal permeability, vertical-horizontal permeability ratio, thickness, porosity, and top of structure). This study had four objectives: (1) to determine if kriging could be applied to petroleum-related data sets; (2) to determine the optimum estimation method by layer for each reservoir property and to use that optimum method to assign values to grid blocks for use in a reservoir simulation study; (3) to determine if a correlation could be established between the optimum estimation method and a reservoir property; and (4) to determine if criteria could be established for choosing the optimum estimation method through initial evaluation of data set size, distribution, and spatial correlation. Kriging was found to be the optimum estimation method in 10 out of 12 cases for data sets having a normal or lognormal histogram distribution and a stable overall semivariogram. Simple averaging and inverse weighted distance squared were optimum in the other two cases. Fifth-degree bicubic spline proved to be the optimum estimation method for data sets that did not have a normal or lognormal histogram distribution. Simple averaging was found to be the optimum method for data sets that did not have stable overall semivariograms because of limited data set size. These results show that kriging can be applied to petroleum-related problems with a relatively small number of data points as compared to kriging's usual application in the ore industry with much larger data sets.