Reservoir History Matching of the Norne field with generative exotic priors and a coupled Mixture of Experts -- Physics Informed Neural Operator Forward Model

We developed a novel reservoir characterization workflow that addresses reservoir history matching by coupling a physics-informed neural operator (PINO) forward model with a mixture of experts' approach, termed cluster classify regress (CCR). The inverse modelling is achieved via an adaptive Regularized Ensemble Kalman inversion (aREKI) method, ideal for rapid inverse uncertainty quantification during history matching. We parametrize unknown permeability and porosity fields for non-Gaussian posterior measures using a variational convolution autoencoder and a denoising diffusion implicit model (DDIM) exotic priors. The CCR works as a supervised model with the PINO surrogate to replicate nonlinear Peaceman well equations. The CCR's flexibility allows any independent machine-learning algorithm for each stage. The PINO reservoir surrogate's loss function is derived from supervised data loss and losses from the initial conditions and residual of the governing black oil PDE. The PINO-CCR surrogate outputs pressure, water, and gas saturations, along with oil, water, and gas production rates. The methodology was compared to a standard numerical black oil simulator for a waterflooding case on the Norne field, showing similar outputs. This PINO-CCR surrogate was then used in the aREKI history matching workflow, successfully recovering the unknown permeability, porosity and fault multiplier, with simulations up to 6000 times faster than conventional methods. Training the PINO-CCR surrogate on an NVIDIA H100 with 80G memory takes about 5 hours for 100 samples of the Norne field. This workflow is suitable for ensemble-based approaches, where posterior density sampling, given an expensive likelihood evaluation, is desirable for uncertainty quantification.

A Novel A.I Enhanced Reservoir Characterization with a Combined Mixture of Experts -- NVIDIA Modulus based Physics Informed Neural Operator Forward Model

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.