A Framework for Efficient Well Control Modeling in Machine Learning Surrogates

Abstract

Numerical reservoir simulators are computationally prohibitive for many-query tasks such as field development planning; which motivates a new generation of machine learning surrogates that promise significant speed ups over traditional solvers. A persistent challenge in that work is the treatment of dynamic well controls and sparse, time-dependent well data. Surrogates that reproduce cell-centered fields accurately often leave the quantities an engineer actually depend on, namely bottomhole pressure, phase rates, water cut, and gas-oil ratio, either outside the model or regressed by unconstrained output heads that need not respect rate control or the underlying inflow physics. We address this by coupling a three-dimensional Temporal Neural Operator (TNO), whose branch and trunk factorization decouples spatial geological heterogeneity from temporal well control inputs, to an analytic and fully differentiable black-oil well module placed inside both the training graph and the forecast loop. TNO predicts pressure, water saturation, and gas saturation on the Norne benchmark model. The well module samples those fields at the 504 completion cells belonging to 36 wells, evaluates black-oil properties and three-phase mobilities, corrects each completion pressure to a common bottomhole datum, and recovers the rate-controlled bottomhole pressure in closed form. Phase rates are aggregated per well and the computed pressure returns to the operator input, closing the loop. We trained the TNO on 400 Norne cases and evaluated on 50 held-out cases over a 61-step sequential forecast, the model reaches a pressure MAE of 0.559 bar, a bottomhole pressure MAE of 2.99 bar, and a water cut MAE of 0.034. Scheduled rate closure holds by construction rather than by fit, so the well responses stay physically consistent at the cost of a forward pass rather than a simulation run. This framework presents a step toward fast, physically consistent proxies that closed-loop reservoir management requires.