Evaluating the Relationship Between Well Parameters and Production Using Multivariate Statistical Models: A Middle Bakken and Three Forks Case History
Authors: Lolon E. , Hamidieh K. , Weijers L. , Mayerhofer M. , Melcher H. , Oduba O. 
Published: January 2016

Abstract
Building a predictive statistical model for evaluating the impact of various fracture treatment and well completion designs on production has been of great interest in the oil and gas industry. The objectives of this study were to evaluate the benefits of advanced statistical and machine-learning techniques for predicting production from oil wells, highlight the strengths and weaknesses of these techniques, and gain insight into the relationship between well parameters and production. The predictive models are described through mathematical functions or algorithms that rely on well data (training set). The ongoing dilemma is that these models often result in poor predictions, even if they result in a high R-squared (0.7 or higher). The new perspective that this study brings is the importance of cross-validation with "hold-out" datasets in the workflow to develop reliable statistical models.
A database of available completion and production data has been assembled from the North Dakota Industrial Commission (NDIC) and Frac Focus websites and from internal completion documentation. To date, there are at least 6,800 horizontal wells completed in the Middle Bakken formation and 3,600 completed in the Three Forks formation on the North Dakota side of the Williston Basin. Various models such as multiple regression, random forests, and gradient boosting machine were built to predict the cumulative oil production of the Middle Bakken and Three Forks horizontal wells. Model predictive abilities were assessed by cross-validating the root mean squared errors (in cross-validation, a hold-out set was used to assess the modelis predictive ability).
The results showed the following conclusions about statistical evaluation techniques: 1) regression models that account for overfitting provided the best predictive ability, 2) gradient boosting model with the highest R-squared value had the worst predictive ability for the specific datasets in this paper— which shows why it is critical to not rely solely on R-squared value to assess a modelis predictive ability, but to also perform cross-validation, and 3) random forests and gradient boosting machine can be used for determining variable importance. Moreover, we observed that there is statistical evidence to support the presence of important interactions among variables in predicting cumulative oil production.
For the Middle Bakken and Three Forks wells included in this study, the results showed that water cut, which can be used as a proxy for reservoir quality, is the most important predictor for cumulative oil production. However, the most important completion-related variables for predicting oil production were total frac fluid and proppant pumped. The analysis and results presented in this paper will enable companies to apply the approach to their own data when building production prediction models and analyzing the complex relationships of variables that control well performance.