Improved permeability prediction using multivariate analysis methods



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Predicting rock permeability from well logs in uncored wells is an important task in reservoir characterization. Due to the high costs of coring and laboratory analysis, typically cores are acquired in only a few wells. Since most wells are logged, the common practice is to estimate permeability from logs using correlation equations developed from limited core data. Most commonly, permeability is estimated from various well logs using statistical regression. For sandstones, often the logs of permeability can be correlated with porosity, but in carbonates the porosity permeability relationship tends to be much more complex and erratic. For this reason permeability prediction is a critical aspect of reservoir characterization in complex reservoirs such as carbonate reservoirs. In order to improve the permeability estimation in these reservoirs, several statistical regression techniques have already been tested in previous work to correlate permeability with different well logs. It has been shown that statistical regression for data correlation is quite promising in predicting complex reservoirs. But using all the possible well logs to predict permeability is not appropriate because the possibility of spurious correlation increases if you use more well logs. In statistics, variable selection is used to remove unnecessary independent variables and give a better prediction. So we apply variable selection to the permeability prediction procedures in order to further improve permeability estimation. We present three approaches to further improve reservoir permeability prediction based on well logs via data correlation and variable selection in this research. The first is a combination of stepwise algorithm with ACE technique. The second approach is the application of tree regression and cross-validation. The third is multivariate adaptive regression splines. Three methods are tested and compared at two complex carbonate reservoirs in west Texas: Salt Creek Field Unit (SCFU) and North Robertson Unit (NRU). The result of SCFU shows that permeability prediction is improved by applying variable selection to non-parametric regression ACE while tree regression is unable to predict permeability because it can not preserve the continuity of permeability. In NRU, none of these three methods can predict permeability accurately. This is due to the high complexity of NRU reservoir and measurement accuracy. In this reservoir, high permeability is discrete from low permeability, which makes prediction even more difficult. Permeability predictions based on well logs in complex carbonate reservoirs can be further improved by selecting appropriate well logs for data correlation. In comparing the relative predictive performance of the three regression methods, the stepwise with ACE method appears to outperform the other two methods.