PhysicsNeMo-Sym reservoir simulation

01 · Overview

Reservoir simulation examples in PhysicsNeMo-Sym

A family of open-source examples, authored end to end, that show how physics-informed neural operators replace the forward simulator in reservoir engineering and carbon storage, from training through to Bayesian history matching.

2D and 3D black-oil

Forward problems with FNO, PINO and AFNO surrogates, trained with data and the PDE residual.

Norne

Forward and inverse problems on the Norne field model.

CCUS

CO2-brine flow for carbon capture, utilisation and storage, with a physics-constrained neural operator.

Generative workflows

Latent priors from variational autoencoders and diffusion models for history matching.

Numerical solvers

A black-oil simulator, a CO2 convective-mixing simulator and a history-matching solver.

02 · Carbon storage

CO2-brine flow with a physics-constrained neural operator

Geological storage of CO2 needs forecasts of the plume and the pressure over hundreds of years, for many realisations of the subsurface. The CCUS example couples a CO2-brine thermodynamic model (phase split by flash, phase densities and viscosities) with a physics-constrained neural operator whose loss includes the discretised mass-conservation residuals of both components. The physics-informed operator keeps its accuracy over the full storage period where a data-only operator drifts, at a fraction of the simulator's cost.

**CO2 injection, PINO surrogate against the simulator**Pressure, brine and gas saturation of a CO2 injection over the storage period: numerical reference, physics-informed neural operator and their difference.

**CO2 injection, data-driven FNO**The same injection with a Fourier neural operator trained on data alone, for comparison with the physics-informed model.

**Execution time**The PhysicsNeMo (Modulus) surrogate against the flow simulator on the CO2-brine forward problem: 44.41 s against 3.51 s, a factor of 13.

**CO2 gas saturation accuracy, FNO against PINO**R2 over 500 years of storage: the physics-informed operator stays above 0.94, the data-only FNO drifts.

**Pressure accuracy, FNO against PINO**The physics-informed operator holds pressure at R2 near 0.998 over the storage period.

**Brine saturation**R2, L2, SSIM and the combined loss of FNO and PINO at every report time.

**Gas saturation, R2 and L2**Accuracy of the CO2 plume over time.

**Pressure, R2 and L2**Accuracy of the pressure field over time.

03 · Movies

Neural operators at work

**2D waterflood, PINO against the numerical solver**Pressure and saturations predicted by the physics-informed neural operator beside the numerical reference.

**Water saturation in 3D**The waterflood front advancing through the reservoir.

**Oil saturation in 3D**Oil displaced toward the producers.

**3D black-oil, PINO**A three-dimensional forward problem with the physics-informed operator.

**Generative workflow, numerical reference**The forward problem of the generative history-matching workflow.

04 · Results

Forward and inverse problems

**Generative history matching**A variational convolutional autoencoder learns a latent prior; alpha-REKI updates the latent ensemble with the PINO forward model.

**Surrogates against the solver, 2D**Production predicted by FNO, PINO and AFNO variants against the numerical reference.

**Surrogate accuracy**RMSE of the surrogate families on the 2D problem.

**Recovered permeability**Initial, best, mean and true permeability after history matching.

**Misfit reduction**Cost of the ensemble before and after inversion.

**Prior ensemble**Production of the prior ensemble.

**Posterior ensemble**Production after history matching.

**Surrogates against the solver, 3D**The same comparison on the 3D problem.

**Generative workflow**Surrogate production against the numerical reference.

05 · Live demo

Ensemble history matching in the browser

Ensemble history matching in miniature. Two unknowns, near-well permeability and inter-well connectivity, control when water breaks through at two producers. Choose alpha-REKI, the adaptive regularised ensemble Kalman inversion, which picks each inflation alpha from the data misfit and stops when the sum of 1/alpha reaches one, or ES-MDA with a fixed number of assimilations. Watch the ensemble collapse onto the hidden truth and the predictions onto the data.

Method Ensemble size ES-MDA assimilations Observation noise

A two-parameter teaching example of the ensemble update, computed in your browser. The results above come from the PhysicsNeMo-Sym examples.

A toy forward model of breakthrough curves stands in for the neural operator; the update is the full ensemble Kalman step with the ensemble covariances and perturbed observations.

06 · Code

Explore the examples

Examples on GitHub NVIDIA PhysicsNeMo-Sym Norne history matching (arXiv 2024)

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Other featured work

Featured workPINO · Norne Featured workMixed precision HomeClement Etienam