Ensemble Machine Learning for Predicting Viscosity of Nanoparticle-Surfactant-Stabilized CO2 Foam
Authors: Olukoga Toluwalase , Totaro Micheal , Feng Yin 
Published: June 2022

Summary
This paper investigates the computational behaviors of simple-to-use, relatively fast, and versatile machine learning (ML) methods to predict apparent viscosity, a key rheological property of nanoparticle-surfactant-stabilized CO2 foam in unconventional reservoir fracturing.
The first novelty of our study is the investigation of the predictive performance of ML approaches as viable alternatives for predicting the apparent viscosity of NP-Surf-CO2 foams. The predictive and computational performance of five nonlinear ML algorithms were first compared. Support vector regression (SVR), K-nearest neighbors (KNN), classification and regression trees (CART), feed-forward multilayer perceptron neural network (MLPNN), and multivariate polynomial regression (MPR) algorithms were used to create models. Temperature, foam quality, pressure, salinity, shear rate, nanoparticle size, nanoparticle concentration, and surfactant concentration were identified as relevant input parameters using principal component analysis (PCA). A data set containing 329 experimental data records was used in the study. In building the models, 80% of the data set was used for training and 20% of the data set for testing.
Another unique aspect of this research is the examination of diverse ensemble learning techniques for improving computational performance. We developed meta-models of the generated models by implementing various ensemble learning algorithms (bagging, boosting, and stacking). This was done to explore and compare the computational and predictive performance enhancements of the base models (if any).
To determine the relative significance of the input parameters on prediction accuracy, we used permutation feature importance (PFI). We also investigated how the SVR model made its predictions by utilizing the SHapely Additive exPlanations (SHAP) technique to quantify the influence of each input parameter on prediction. This work’s application of the SHAP approach in the interpretation of ML findings in predicting apparent viscosity is also novel.
On the test data, the SVR model in this work had the best predictive performance of the single models, with an R2 of 0.979, root mean squared error (RMSE) of 0.885 cp, and mean absolute error (MAE) of 0.320 cp. Blending, a variant of the stacking ensemble technique, significantly improved this performance. With an R2 of 1.0, RMSE of 0.094 cp, and MAE of 0.087 cp, an SVR-based meta-model ensembled with blending outperformed all single and ensemble models in predicting apparent viscosity. However, in terms of computational time, the blended SVR-based meta-model did not outperform any of its constituent models. PCA and PFI ranked temperature as the most important factor in predicting the apparent viscosity of NP-Surf-CO2 foams. The ML approach used in this study provides a comprehensive understanding of the nonlinear relationship between the investigated factors and apparent viscosity. The workflow can be used to evaluate the apparent viscosity of NP-Surf-CO2 foam fracturing fluid efficiently and effectively.