## 3 Results and Discussion
### Evaluation of New Engineered Feature  
From the results of the feature selection techniques, the GR, DEN, NEU, POR and Sw logs were selected as candidates for feature selection for the NMR T\({}_{2}\)LM prediction. The variety of logs selected are because the best performing feature selection techniques selected all of these logs as relevant. These logs also relate to properties on which wettability occurs. Simple feature engineering techniques were employed in this study to combine existing features into new variables, and these are shown as:  
* New Feature 1: Addition (DEN, Sw)
* New Feature 2: Addition (DEN, NEU)
* New Feature 3: Addition (POR, Sw)
* New Feature 4: Product (POR, Sw)
* New Feature 5: Square root (Product (DEN, GR))
* New Feature 6: Round Sw (2))
* New Feature 7: Scaled (Sw)  
The performance of the new feature was analysed using accuracy and Permutation Feature Importance (PFI) on test data. The XGBoost model was used to evaluate the performance of all features in NMR T\({}_{2}\)LM predictions. In terms of the analysis, the XGBoost feature importance identified Sw and POR as having a low correlation which disagrees with the literature. For the well data used, the most important feature was the DEN log which is a formation dependent log. Figure 11 showed the feature performance of all the 9 variables used in predicting T2 LM before feature engineering.  
The PFI results of the performance of the new feature for NMR T\({}_{2}\)LM predictions are illustrated in Figure 12. This study used a similar train/test split in the final XGBoost model prediction to maintain consistency. The initial testing R\({}^{2}\) without the new features was 0.8148. The importance score is computed in a way that higher values represent better predictive power. The importance of the values for the most relevant features represents a significant fraction of the accuracy score. From the results, many of the input variables have a considerably low importance score. This outcome suggests that the predictive power of these input variables is condensed into a small number of variables. The permutation importance plot shows that permuting a feature drops the accuracy by at most 0.12. This analysis suggests that some of the features are important. This outcome is consistent with the computed high test accuracy.  
Figure 11: XGBoost feature importance in predicting NMR T2 LM.  
Figure 12: Permutation feature importance on all input variables for T\({}_{2}\)LM prediction.  
This outcome goes on to support the engineering of the new feature. As density relates to porosity and the spaces where wettability is formed, these logs should be paramount, whereas saturation relates to fluid interactions. Based on the hypothesis that these logs are important in determining wettability, they had inherent important information for the generalisation of the model. The new feature 1 with DEN and Sw incorporated achieved a much higher relevance score, improving the model's performance and confirming the hypothesis that they have important information that helped improve the model generalisation. By omitting this important feature engineering step and this critical feature would have caused the model to over- or under-fit, which should not be the case. Since there are variabilities from one model to the other on features considered the most important ones, feature engineering needs to be performed based on domain knowledge.  
Further analysis was performed using 6 different models for the most important features to ascertain if the new features will be deemed as important when different models are used. This result is shown in Table 7. The models used are the LGBoost, AdaBoost, Bagging, Decision Tree, XGBoost and Extra Tree. All the top performing models assessed some features as not important. The most common irrelevant features are the DEN, Res_Dep and Res_Med logs. However, New feature 1, PERM and GR variables were commonly selected as important features.