Inverse modeling of subsurface flow during CO2-enhanced oil recovery using deep learning approach with adaptive learning strategy

Inverse modeling plays a crucial role in oil-gas reservoir development for characterizing subsurface geological properties, minimizing prediction uncertainties, and forecasting production sequences. However, balancing the contradiction between computational costs and accuracy remains a challenge in previous inverse modeling approaches. To alleviate such contradictions, this study integrates the adaptive learning (AL) strategy into the iterative ensemble smoother (IES) approach. Unlike traditional numerical simulators, forward modeling of the multiphase flow processes is performed using surrogate models based on a combination of convolutional and recurrent neural networks (CNN-LSTM). The transfer learning technique is adopted to improve the efficiency of the CNN-LSTM surrogate. To test the performance of the proposed AL-CNN-LSTM-based IES approach, two-dimensional CO₂-EOR simulations are conducted with four different sets of permeability fields (${\sigma }_{\ln K}^2$ = 0.15, 0.30, 0.45 and 0.60 mD²) generated by stochastic modeling. Results demonstrate that the transfer learning technique significantly improves the efficiency of the CNN-LSTM surrogate with the average computation time reduced from 639.882 s to 115.212 s. By comparing the real permeability fields with the estimated results obtained from the AL-CNN-LSTM-based IES, the CNN-LSTM-based IES, and the Eclipse-based IES approaches, it is evident that the AL-CNN-LSTM-based IES approach outperforms traditional inversion approaches in terms of computational costs ($t=302.373s$) and accuracy ($RMSE=0.167$). Furthermore, the newly proposed AL-CNN-LSTM-based IES model demonstrates low sensitivity to permeability field variance, making it applicable for diverse geological scenarios in subsurface multiphase flow problems.