An echo state network approach to data-driven modeling and optimal control of carbonate reservoirs with uncertainty fields

Abstract

Previous studies of reservoir simulation have shown that it is required to have every inherent carbonate reservoir physics available at the model development phase. However, this process while ideal is computationally intensive and time consuming especially for complex geological fields. In this study, Echo State Network (ESN) is proposed to predict two cases of reservoir waterflooding with integrated uncertainty properties in unstructured physical dimension and log-normal permeability fields. The generalization efficiency of ESN with respect to uncertainties in injection and production data is also investigated by tuning the ESN reservoir size (N). Consequently, adjoint based method is used to optimize the Net Present Value (NPV) via obtained injection well controls. Observation revealed that the developed ESN exhibits superior predictive accuracy in scenarios of low geological uncertainties, achieving an average test accuracy of 90.79%, and then declining to 86.19% as the uncertainty level is increased. Also, N is found to be significant in terms of ESN generalization efficiency with N = 40 achieving higher performance compared to N = 20, thereby validating its influence on ESN reservoir state to adapt to current data history during training. Lastly, the optimized scenario, derived from the initial well control predictions, demonstrated a higher NPV when compared with the base scenario of the developed oil reservoir model.