Hybrid deep learning and ES-MDA for pressure transient inversion in radial composite reservoirs

Accurate characterization of reservoir heterogeneity is important for improving reservoir management and production forecasting. This study presents a hybrid workflow for permeability estimation in structured radial composite reservoirs using deep learning (DL) and the Ensemble Smoother with Multiple Data Assimilation (ES-MDA). Prior to DL modeling, a quantitative sensitivity and identifiability analysis was performed to evaluate the information content of single-well pressure-transient data. The analysis examined the effects of inner-zone permeability, mobility ratio, and composite radius on pressure-derivative responses, showing that the dominant sensitivities are associated with near-well radial-composite parameters, while sensitivity decreases with increasing radial distance from the well. Two DL architectures-a convolutional neural network (CNN) and a fully connected (FC) network-were evaluated using synthetic pressure-derivative responses generated from radial composite reservoir realizations. The objective of the proposed framework is not to reconstruct arbitrary geological permeability fields, but rather to infer permeability distributions constrained by radial composite reservoir behavior. Both models achieved high prediction accuracy under noise-free conditions, while the CNN demonstrated greater robustness when Gaussian noise was added to the pressure-derivative inputs during testing. For history matching (HM), two initialization strategies were investigated: (i) random radial-composite initialization and (ii) AI-informed initialization derived from CNN predictions. Ten ensemble realizations were generated using ± 5% perturbations, followed by 20 ES-MDA assimilation steps with a constant inflation factor of α = 20. The AI-informed initialization achieved faster convergence and lower final pressure-derivative misfit than the random initialization. Overall, the proposed framework provides an efficient and physically consistent workflow for permeability estimation and history matching in structured radial composite reservoirs.