Abstract
Background:
Productivity index (PI) is a diagnostic tool in investigating the “health” of wells. This must be done accurately for correct forecasting and production optimization. Estimating PI is more complex for complex deltaic formations (e.g., Niger Delta formation) and in horizontal wells compared to vertical wells. Traditional analytical models, such as those of Borisov, Joshi, Renard-Dupuy, and so on, are limited by oversimplifications and often lead to erroneous estimation in complex formation settings. These traditional analytical models also fail to capture explicitly, for instance, flow regime and geometry, and some other complexities associated with horizontal wells; hence, the need to look for methods to overcome these drawbacks and estimate with a good degree of accuracy.

Aim:
The study aims to explore the robustness and accuracy of machine learning (ML) models in capturing these complexities that the traditional analytical model fails to capture in the Niger Delta formation and in horizontal wells by comparing the performance of single machine learning models and ensemble models in predicting PI of horizontal wells in the highly complex Niger Delta formation.

Methods:
Five ML models, namely, linear regression (LR), random forest (RF), support vector machine, XGBoost, and a developed ensemble model, were trained and evaluated on synthetically expanded datasets generated using a variational auto encoding to address these gaps. Preprocessing and hyperparameter tuning were performed.

Results:
The results show that XGBoost outperforms other models and traditional correlations, including the developed ensemble model, with LR and RF also ranking high. Although the developed ensemble achieved the highest R² (0.9417), XGBoost, RF, and LR delivered better overall error metrics. Ensemble ML models show a high degree of accuracy by handling complexities associated with heterogeneous Niger Delta formation and horizontal wells compared to single ML models in estimating PI.

Conclusion:
The study shows that ML models can be deployed to estimate PI in complex geologic conditions and flow regimes, saving time, cost, and reducing the probability of problems throughout the entire life of the well.

Key words: Productivity index; Horizontal wells; Machine learning; Linear regression; Random forest; Support vector regression; XGBoost; Ensemble model; Reservoir heterogeneity