  We have developed an advanced workflow for reservoir characterization,
effectively addressing the challenges of reservoir history matching through a
novel approach. This method integrates a Physics Informed Neural Operator
(PINO) as a forward model within a sophisticated Cluster Classify Regress (CCR)
framework. The process is enhanced by an adaptive Regularized Ensemble Kalman
Inversion (aREKI), optimized for rapid uncertainty quantification in reservoir
history matching. This innovative workflow parameterizes unknown permeability
and porosity fields, capturing non-Gaussian posterior measures with techniques
such as a variational convolution autoencoder and the CCR. Serving as exotic
priors and a supervised model, the CCR synergizes with the PINO surrogate to
accurately simulate the nonlinear dynamics of Peaceman well equations. The CCR
approach allows for flexibility in applying distinct machine learning
algorithms across its stages. Updates to the PINO reservoir surrogate are
driven by a loss function derived from supervised data, initial conditions, and
residuals of governing black oil PDEs. Our integrated model, termed
PINO-Res-Sim, outputs crucial parameters including pressures, saturations, and
production rates for oil, water, and gas. Validated against traditional
simulators through controlled experiments on synthetic reservoirs and the Norne
field, the methodology showed remarkable accuracy. Additionally, the
PINO-Res-Sim in the aREKI workflow efficiently recovered unknown fields with a
computational speedup of 100 to 6000 times faster than conventional methods.
The learning phase for PINO-Res-Sim, conducted on an NVIDIA H100, was
impressively efficient, compatible with ensemble-based methods for complex
computational tasks.
