Ergodic and non-ergodic variogram uncertainty in Agbabu bitumen field porosity data

Abstract

A recent investigation estimated and modeled the variogram of the porosity attribute of the bitumen field located at Agbabu, south-west Nigeria. In spite of methodological interventions made during the estimation, the variogram estimates obtained are still uncertain due to preferential and limited sample data. This current research therefore assesses the uncertainty in the ergodic and non-ergodic variogram estimates. Multiple samples required for ergodic and non-ergodic variogram estimates have been drawn from simulated realizations of the porosity random field. Variogram estimates have been obtained (using a recently-formulated lag-cluster technique and conventional technique) for each sample. The sampling distributions of these estimates have been examined with histograms and Normal Q-Q plots. The estimates exhibit approximately Normal distributions. The uncertainty in the ergodic variogram increases from 1.4×10-7 at lag 16.7 m to 4.6×10-7 at lag 4601.4 m; thereafter, it appears to flatten out. For most lag distances, the uncertainty in the non-ergodic variogram is constant at about 1.8×10-7; it fluctuates at large lag distances. The uncertainty in non-ergodic estimates is observed to be lower than the uncertainty in ergodic estimates. Consequently, that the current well spacing and distribution in Agbabu field is deemed adequate in the context of variogram estimation.