Application of Machine Learning to Interpret Steady State Drainage Relative Permeability Experiments

Abstract

Abstract 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, three different machine learning models was developed to assist in a faster estimation of these curves from steady-state drainage coreflooding experimental runs. The three different models that were tested and compared were extreme gradient boosting (XGB), deep neural network (DNN) and recurrent neural network (RNN) algorithms. Based on existing mathematical models, a leading edge framework was developed where a large database of Kr and 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 utilized to estimate 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 machine learning model. The entire data set was split into 80% for training and 20% for testing. K-fold cross validation technique was applied to increase the model accuracy by splitting the 80% of the training data into 10 folds. In this manner, for each of the 10 experiments, 9 folds were used for training and the remaining one was used for model validation. Once the model is trained and validated, it was subjected to blind testing on the remaining 20% of the data set. The machine learning model learns to capture fluid flow behavior inside the core from the training dataset. The trained/tested model was thereby employed to estimate Kr curves based on available experimental results. The performance of the developed model was assessed using the values of the coefficient of determination (R2) along with the loss calculated during training/validation of the model. The respective cross plots along with comparisons of ground-truth versus AI predicted curves indicate that the model is capable of making accurate predictions with error percentage between 0.2 and 0.6% on history matching experimental data for all the three tested ML techniques (XGB, DNN, and RNN). This implies that the AI-based model exhibits better efficiency and reliability in determining Kr curves when compared to conventional methods. The results also include a comparison between classical machine learning approaches, shallow and deep neural networks in terms of accuracy in predicting the final Kr curves. The various models discussed in this research work currently focusses on the prediction of Kr curves for drainage steady-state experiments; however, the work can be extended to capture the imbibition cycle as well.