Application of Machine Learning to Interpret Steady-State Drainage Relative Permeability Experiments
Authors: Mathew Eric Sonny , Tembely Moussa , AlAmeri Waleed , Al-Shalabi Emad W. , Shaik Abdul Ravoof 
Published: March 2023

Summary
A meticulous interpretation of steady-state or unsteady-state relative permeability (Kr) experimental data is required to determine a complete set of Kr curves. In this work, different machine learning (ML) models were developed to assist in a faster estimation of these curves from steady-state drainage coreflooding experimental runs. These ML algorithms include gradient boosting (GB), random forest (RF), extreme gradient boosting (XGB), and deep neural network (DNN) with a main focus on and comparison of the two latter algorithms (XGB and DNN). Based on existing mathematical models, a leading-edge framework was developed where a large database of Kr and capillary pressure (Pc) curves were generated. This database was used to perform thousands of coreflood simulation runs representing oil-water drainage steady-state experiments. The results obtained from these simulation runs, mainly pressure drop along with other conventional core analysis data, were used to estimate analytical Kr curves based on Darcy’s law. These analytically estimated Kr curves along with the previously generated Pc curves were fed as features into the ML model. The entire data set was split into 80% for training and 20% for testing. The k-fold cross-validation technique was applied to increase the model’s accuracy by splitting 80% of the training data into 10 folds. In this manner, for each of the 10 experiments, nine folds were used for training and the remaining fold was used for model validation. Once the model was trained and validated, it was subjected to blind testing on the remaining 20% of the data set. The ML model learns to capture fluid flow behavior inside the core from the training data set. In terms of applicability of these ML models, two sets of experimental data were needed as input; the first was the analytically estimated Kr curves from the steady-state drainage coreflooding experiments, while the other was the Pc curves estimated from centrifuge or mercury injection capillary pressure (MICP) measurements. The trained/tested model was then able to estimate Kr curves based on the experimental results fed as input. Furthermore, to test the performance of the ML model when only one set of experimental data is available to an end user, a recurrent neural network (RNN) algorithm was trained/tested to predict Kr curves in the absence of Pc curves as an input.
The performance of the three developed models (XGB, DNN, and RNN) was assessed using the values of the coefficient of determination (R2) along with the loss calculated during training/validation of the model. The respective crossplots along with comparisons of ground truth vs. artificial intelligence (AI)-predicted curves indicated that the model is capable of making accurate predictions with an error percentage between 0.2% and 0.6% on history-matching experimental data for all three tested ML techniques. This implies that the AI-based model exhibits better efficiency and reliability in determining Kr curves when compared to conventional methods. The developed ML models by no means replace the need to conduct drainage coreflooding or centrifuge experiments but act as an alternative to existing commercial platforms that are used to interpret experimental data to predict Kr curves. The two main advantages of the developed ML models are their capability of predicting Kr curves within a matter of a few minutes as well as with limited intervention from the end user. The results also include a comparison between classical ML approaches, shallow neural networks, and DNNs in terms of accuracy in predicting the final Kr curves. The research presented here is an extension of the state-of-the-art framework proposed by Mathew et al. (2021). However, the two main aspects of the current study are the application of deep learning for the prediction of Kr curves and the application of feature engineering. The latter not only reduces the training/testing time for the ML models but also enables the end user to obtain the final predictions with the least set of experimental data. The various models discussed in this research work currently focus on the prediction of Kr curves for drainage steady-state experiments; however, the work can be extended to capture the imbibition cycle as well.