Introducing Coherent-Control Koopman Modeling to Reservoir Scale Porous Media Flow Studies

TL;DR

This paper introduces Coherent-Control Koopman Modeling (CCKM), a robust surrogate modeling approach for reservoir dynamics that outperforms classical methods under regime shifts, enabling reliable real-time reservoir management.

Contribution

The paper presents CCKM, a novel control-coherent Koopman model that maintains stability and accuracy during regime shifts, improving upon classical DMDc methods for reservoir flow prediction.

Findings

CCKM remains stable and accurate under regime shifts.

CCKM achieves sub-bar mean absolute error in pressure predictions.

Classical DMDc exhibits large errors during control transients.

Abstract

Accurate and robust surrogate modeling is essential for the real-time control and optimization of large-scale subsurface systems, such as geological CO2 storage and waterflood management. This study investigates the limits of classical Dynamic Mode Decomposition with control (DMDc) and introduces CCKM, as a robust alter-native, in enforcing control in pressure and water saturation reservoir dynamics under challenging prediction scenarios. We introduced a control-coherent incremental ({\Delta}) CCKM formulation, in which the field update is driven by actuator changes rather than rather than actuator levels as in the original level formulation and compared them both against DMDc and a Hybrid B-only surrogate that re-uses DMDcs bottom-B (same-step feed-through), showing that only CCKM remains stable and accurate under regime shifts. Two representative cases are considered: (i) an out-of-distribution shut-in and restart case, and (ii) an in-distribution bottomhole pressure (BHP) drawdown. Results show that only CCKM consistently maintains stability and accuracy across both scenarios, achieving sub-bar mean absolute error and sub-percent Frobenius norm percent change error (FPCE) even under regime shifts, while DMDc exhibit large unphysical errors during control transients. The findings demonstrate that strict control-coherence is critical for reliable surrogate modeling, particularly in settings with abrupt changes in control strategy. The proposed framework is broadly applicable to real-time reservoir optimization and can be integrated seamlessly into existing optimization and monitoring workflows, enabling fast and trustworthy deci-sion support in the presence of both expected and unexpected actuation regimes.