Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fields

TL;DR

This work introduces a single Fourier Neural Operator (FNO) surrogate that learns the solution operator for Darcy-style reservoir flows, generalizing across unseen permeability fields, well locations, and variable well counts. By integrating input channels that encode well locations/controls and employing a data-augmentation strategy, the model achieves error levels under 5% for most predictions and can extrapolate in time, while delivering predictions in seconds instead of hours. The approach handles both single-phase pressures and two-phase pressures with saturations (via a unified architecture, enhanced by U-FNO constructs) and demonstrates substantial acceleration over traditional CMG IMEX simulations, enabling efficient history matching and reservoir optimization. The combination of discretization-invariant learning, adaptive masking, and augmentation paves the way for practical reservoir digital twins and rapid scenario assessment in hydrocarbon and carbon storage applications.

Abstract

Simulating Darcy flows in porous media is fundamental to understand the future flow behavior of fluids in hydrocarbon and carbon storage reservoirs. Geological models of reservoirs are often associated with high uncertainly leading to many numerical simulations for history matching and production optimization. Machine learning models trained with simulation data can provide a faster alternative to traditional simulators. In this paper we present a single Fourier Neural Operator (FNO) surrogate that outperforms traditional reservoir simulators by the ability to predict pressures and saturations on varying permeability fields, well locations, well controls, and number of wells. The maximum-mean relative error of 95\% of pressure and saturation predictions is less than 5\%. This is achieved by employing a simple yet very effective data augmentation technique that reduces the dataset size by 75\% and reduces overfitting. Also, constructing the input tensor in a binary fashion enables predictions on unseen well locations, well controls, and number of wells. Such model can accelerate history matching and reservoir characterization procedures by several orders of magnitude. The ability to predict on new well locations, well controls, and number of wells enables highly efficient reservoir management and optimization.

Figures (12)

• Figure 1: U-FNO architecture.
• Figure 2: Pressure Well controls (BHP) for a single $(5x5x40)$ sample for demonstration purposes only.
• Figure 3: Data augmentation. Column (1) illustrates the statistical analysis of the first model trained with 250 unaugmented samples dataset. Column (2) illustrates the statistical analysis of the second model trained with 250 augmented samples dataset. Column (3) illustrates the statistical analysis of the third model trained with 1000 unaugmented samples dataset. Column (4) illustrates the statistical analysis of the fourth model trained with 1000 augmented samples dataset. In the second row, the two dashed lines represent the mean and mean plus two standard deviations respectively, and in the third row, the gray, green, yellow, red areas are the mean, mean plus one, two, and three standard deviation respectfully.
• Figure 4: Model 1: pressure predictions for five testing samples over testing time range $[240, 440]$ days (red area) with new permeability fields, well locations, well controls, and number of wells. The first column is the permeability fields with the location of wells marked with white triangles on the same plot. The second column displays pressure predictions, the third column displays simulation pressure, the fourth column is the point-wise relative error, and the fifth column is the well controls for the testing time range. The horizontal black dash-line in the well controls plots is the initial pressure at $t=0$ days. The green and red areas represent the training and testing time range respectively. The two vertical dashed blue lines mark the 40 time-steps range of the test samples, and the vertical black dashline represents the timestep whose results are shown in the figure.
• Figure 5: (a) - pressure predictions (b) - saturation predictions for three testing samples with new permeability fields, well locations, well controls, and number of wells. First column is permeability fields with the location of wells marked with white triangles on the same plot, second column is initial condition, third column is prediction, fourth column is true value, fifth column is the point-wise errors (relative/absolute), and sixth column is well controls.