Prediction and History Matching of Observed Production Rate and Bottomhole Pressure Data Sets from in Situ Cross-Linked Polymer Gel Conformance Treatments Using Machine Learning Methods

Abstract

Abstract The objective of this study is to develop a computationally efficient methodology for the prediction of oil rate, water rate, and injection bottomhole pressure (BHP), and history matching of such well outputs to estimate important rock and fluid parameters that have a significant impact on reservoir conformance after in situ polymer gel treatment. Two different machine learning (ML) proxy methods are investigated for performing prediction and history matching of well output data such as oil production rate, water production rate, and/or injection BHP that may be acquired before and after polymer gel treatment. One of the ML methods used is the least-squares support vector regression (LS-SVR) and the other is the long short-term memory (LSTM) network, a deep learning method based on the recurrent neural network (RNN). The LS-SVR and LSTM proxy models are built on training sets of BHP and rate data generated with a high-fidelity commercial numerical simulator. The high-fidelity model is based on compositional flow simulation using double permeability fracture models. The reservoir models used in history matching are calibrated by using synthetic BHP, oil, and/or water production rate data sets before and after polymer gel treatment. The ensemble smoother multiple data (ES-MDA) method is used for history matching and prediction for the uncertainty assessment of the polymer gel treatment period, while a high-fidelity simulator is used for history matching. When the high-fidelity simulator is replaced with any of the ML-based methods, we use a randomized maximum likelihood estimation (RMLE) method where the gradients are analytically computed for the LS-SVR surrogate model, while the LSTM is replaced by the high-fidelity simulator, we compute the gradients of the LSTM by stochastic simplex approximate gradient (StoSAG) method. Results show that the LS-SVR and LSTM methods provide significant computational savings over the conventional simulation and history matching with a high-fidelity model. LSTM provides better predictions than LS-SVR for the same size of training sets. However, for larger training sets, LSTM provides a significant computational gain over LS-SVR. In addition, the results also identify the key parameters that have a significant impact on the performance of in situ polymer gel treatment. These parameters are the relative permeability curves of oil and water, absolute fracture permeability, polymer and cross-linked concentrations, and residual resistance factors (RRFT) are the key parameters in the performance of in situ polymer gel treatment.