The porosity and permeability prediction methods for carbonate reservoirs with extremely limited logging data: Stepwise regression vs. N-way analysis of variance

- The significant variable cluster acquired by stepwise regression may not be optimal all the time.
- Improving robustness of fitting coefficients can make great contribution to stepwise regression.
- Stepwise regression and N-way analysis of variance have the capability to predict porosity and permeability.
- N-way analysis of variance is more suitable to deal with reservoir evaluation problems than stepwise regression.

The available theories and methods for logging interpretation have achieved lots of excellent outcomes in the silicate and carbonate formations. But due to the complicated pore-throat systems and developed fractures, many practical physical models suitable for the silicate formations often need to aid more parameters to character the carbonate, resulting in the difficulties increasing in the reservoir evaluation. As the multivariate linear regression has the capability to calculate targets only using fitting model as a simple linear equation, both useful algorithms of stepwise regression and N-way analysis of variance are proposed in the study of porosity and permeability prediction. The stepwise regression selects out the significant curves from the abundant logging data based on the variance contribution calculation and colinearity verification, thus making the established fitting model optimal. The N-way analysis of variance also performs well on the selection of the significant logs but its calculation only needs to conduct once. Additionally, according to the results of analysis of variance and multiple comparisons, those fitted values can be accurately corrected by the creative algorithm of fitting correction in further step. The logging data derived from three wells of LULA oilfield within Santos Basin are chosen to verify the proposed methods. In the porosity prediction, the mean absolute error of fitted results for the stepwise regression in all verified cases is 3.41, 3.87, 2.89, 3.62, 1.57, and for the N-way analysis of variance is 2.84, 2.68, 2.76, 2.92 and 1.19. In the permeability prediction, the error is 66.28, 1132 400, 146.8, 3617, 0.37 for the stepwise regression, and for the N-way is 48.34, 1098.4, 191.9, 3187.7 and 0.62. Through the verified effects of the cases, all the statistical results indicate that both proposed methods are capable to predict the porosity and permeability in a cost-efficient way. Meanwhile, through the multiple comparisons with the core data, the fitted values obtained by the N-way analysis of variance are more accurate than those from the stepwise regression in general.