Physics-informed Convolutional Recurrent Surrogate Model for Reservoir
  Simulation with Well Controls
Jungang Chen Eduardo Gildin John E. Killough
This paper presents a novel surrogate model for modeling subsurface fluid
flow with well controls using a physics-informed convolutional recurrent neural
network (PICRNN). The model uses a convolutional long-short term memory
(ConvLSTM) to capture the spatiotemporal dependencies of the state evolution
dynamics in the porous flow. The ConvLSTM is linked to the state space
equations, enabling the incorporation of a discrete-time sequence of well
control. The model requires initial state condition and a sequence of well
controls as inputs, and predicts the state variables of the system, such as
pressure, as output. By minimizing the residuals of reservoir flow state-space
equations, the network is trained without the need for labeled data. The model
is designed to serve as a surrogate model for predicting future reservoir
states based on the initial reservoir state and input engineering controls.
Boundary conditions are enforced into the state-space equations so no
additional loss term is needed. Three numerical cases are studied,
demonstrating the model's effectiveness in predicting reservoir dynamics based
on future well/system controls. The proposed model provides a new approach for
efficient and accurate prediction of subsurface fluid flow, with potential
applications in optimal control design for reservoir engineering.