Prediction of spontaneous imbibition in porous media using deep and ensemble learning techniques

Spontaneous imbibition (SI), which is a process of displacing a nonwetting fluid by a wetting fluid in porous media, is of critical importance to hydrocarbon recovery from fractured reservoirs. In the present study, we utilize deep and ensemble learning techniques to predict SI recovery in porous media under different boundary conditions including All-Faces-Open (AFO), One-End-Open (OEO), Two-Ends-Open (TEO), and Two-Ends-Closed (TEC). An extensive experimental dataset reported in literature representing a multiplicity of non-wetting fluid recovery-time curves was used in our analysis. The prepared dataset was used to learn diverse ensemble and deep learning algorithms of Random Forest (RF), Gradient Boosting Machine (GBM), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Voting Regressor (VR), Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU). The training procedure provided us with robust models linking the SI recovery to the absolute permeability (k), porosity (phi), characteristic length (Lc), interfacial tension (sigma), wetting-phase viscosity (mu w), non-wetting-phase viscosity (mu nw), and imbibition time (t). To evaluate and validate the models' prediction, we used two well-established approaches: (i) 10-fold cross -validation and (ii) predicting the SI behavior of a set of unseen data excluded from the model training. Our results illustrate an excellent performance of deep and ensemble learning techniques for prediction of SI with the test RMSE values of 4.642, 4.088, 4.524, 3.933, 3.875, 3.975, 4.513, and 4.807 percent for RF, GBM, XGBoost, LightGBM, VR, CNN, LSTM, and GRU models, respectively. The models have significant benefits in terms of accuracy and generality. Furthermore, they alleviate the sophistications associated with tuning the traditional correlation functions. The findings of this study can pave the road toward a more comprehensive characterization of fluid flow in porous materials which is important to a wide range of environmental and energy-related challenges such as contaminant transport, soil remediation, and enhanced oil recovery.