Learning and Inferring Multiphase Flow Dynamics in Porous Media using Scientific Machine Learning: Application to the "FluidFlower" CO2 Injection Experiment

This paper presents a scientific machine learning framework that combines a convolutional neural network surrogate with Bayesian inference to efficiently predict and calibrate multiphase CO2-brine flow dynamics in porous media, demonstrating significant improvements in parameter identification and simulation accuracy over traditional methods using high-resolution "FluidFlower" experimental data.

The Gist

Imagine you are trying to predict how a drop of ink spreads through a sponge, but this sponge is made of different types of sand, has hidden cracks (faults), and the ink is actually carbon dioxide gas being injected underground. This is the challenge of geological carbon storage: figuring out exactly where the gas will go and how it will get trapped so we can store it safely.

The problem is that the physics involved are incredibly complex. To get a perfect answer using traditional computer models, you have to run massive, slow simulations. If you want to know how uncertain you are about the answer (e.g., "What if the sand is slightly more porous?"), you would need to run those slow simulations thousands of times. That takes too long and costs too much computing power.

This paper presents a clever solution using Scientific Machine Learning (SciML) to speed things up and make better predictions. Here is how they did it, explained simply:

1. The "Speedy Apprentice" (The Surrogate Model)

Think of the traditional, high-fidelity computer simulation as a master chef who can cook the perfect dish but takes three days to do it. You can't ask the master chef to cook 1,000 variations of the dish just to see which one tastes best.

The authors trained a Convolutional Neural Network (CNN)—which they call a "surrogate"—to act like a speedy apprentice.

• Training: They fed the apprentice 98 examples of the master chef's work (simulations of CO2 moving through the "FluidFlower" tank).
• Learning: The apprentice learned the patterns: how the gas rises, how it spreads sideways, and how it gets stuck in different layers of sand.
• The Result: Once trained, the apprentice can predict the outcome of a new scenario in a fraction of a second. It is millions of times faster than the master chef, yet it still gets the big picture right. It captures the main shape of the gas cloud (the "plume") and how it moves, even if it misses some tiny, chaotic swirls (fingering) that are hard to predict.

2. The "Detective Game" (Bayesian Inference)

Now that they have a fast apprentice, they needed to solve a detective problem: What are the hidden properties of the underground rock?

In the real world, we don't know the exact permeability (how easy it is for fluid to flow) or the pressure of every layer of rock. We only have a few measurements.

• The Old Way: Scientists used to guess the rock properties, run the slow master chef simulation, compare it to the experiment, and tweak the guess. They did this manually, looking at just a few big numbers (like "how big is the gas cloud at 1 hour?").
• The New Way: The authors used the fast apprentice inside a Bayesian inference framework (a statistical method). They let the computer run thousands of "what-if" scenarios instantly.
• The Twist: Instead of just looking at a few numbers, they fed the computer the entire video of the experiment. They compared the whole picture of the gas cloud moving over time against the apprentice's predictions.

3. What They Found

• Better Accuracy: By using the full video and the fast apprentice, their model matched the real experiment much better than the previous manual attempts. It correctly predicted how the gas cloud hit a "fault" (a crack in the rock) and how it spread under a "seal" (a layer that stops the gas from escaping).
• The "Fingerprint" Problem: They discovered that different combinations of rock properties can sometimes produce the same-looking gas cloud. It's like two different fingerprints leaving the same smudge on a window. This means there isn't just one "perfect" answer for the rock properties; there are several plausible ones. The machine learning framework helped them map out all these possibilities, rather than just picking one.
• Timing Matters: They tested how much data they needed. They found that once the gas cloud interacted with the major geological features (like the faults and seals), the data became very informative. Adding more data after that point didn't help much more. It's like solving a puzzle: once you find the corner pieces and the main image, adding a few more edge pieces doesn't change the picture much.

The "FluidFlower" Experiment

The whole study was tested on a real-life experiment called "FluidFlower." Imagine a large, transparent tank filled with different layers of sand. Scientists inject CO2 (which turns blue in the water due to a pH indicator) and watch it move. Because the tank is clear, they can take photos of the entire gas cloud as it evolves. This provided the "ground truth" to test if their AI apprentice was actually learning the right physics.

The Bottom Line

This paper shows that by combining a fast AI "apprentice" with a statistical detective game, scientists can:

1. Predict how carbon dioxide moves underground much faster than before.
2. Use real-world experimental data to figure out the hidden properties of the rock.
3. Understand the limits of what we can know (identifying which rock properties are easy to guess and which are ambiguous).

This is a major step toward creating "digital twins" of underground storage sites—virtual models that are accurate enough to help us make safe decisions about storing carbon dioxide to fight climate change.

Technical Summary

Technical Summary: Learning and Inferring Multiphase Flow Dynamics in Porous Media using Scientific Machine Learning

Problem Statement
Accurate prediction and parameter identification for multiphase flow in porous media are critical for geological carbon dioxide storage (GCS) but remain challenging due to strong nonlinearities, high-dimensional parameter spaces, and sparse observational data. Traditional high-fidelity numerical simulations, while sophisticated, are computationally expensive, making them impractical for uncertainty quantification, inverse modeling, or real-time decision-making. Furthermore, the scarcity of field-scale data creates a mismatch between model validation and actionable insights. While controlled laboratory experiments like the "FluidFlower" benchmark provide high-resolution data, history matching against such data is often ill-posed, requiring iterative, expert-guided calibrations that may not fully utilize spatiotemporal information.

Methodology
The authors propose a Scientific Machine Learning (SciML) framework that integrates surrogate modeling with Bayesian inference to address forward prediction and inverse parameter estimation for CO2-brine flows.

1. Forward Surrogate Modeling:

   • Data Generation: High-fidelity numerical simulations of the "FluidFlower" experiment were generated using the MATLAB Reservoir Simulation Toolbox (MRST). These simulations solved mass balance equations for two-phase, two-component flow with hysteretic capillary pressure and relative permeability functions.
   • Architecture: A Convolutional Neural Network (CNN) based on the UNet architecture was trained to learn the mapping from geological parameter realizations to the evolution of CO2 saturation and dissolved CO2 concentration fields.
   • Input/Output: The model takes spatially structured parameter fields (permeability, capillary entry pressure, connate water saturation, and relative permeability exponents for three geological regions: storage sand, fault sand, and top seal) and time as inputs. It outputs the corresponding dissolved CO2 concentration and gas saturation fields on a uniform 64 × 128 grid.
   • Training: The surrogate was trained on 98 simulation runs (45,668 input-output pairs) and tested on unseen cases, achieving acceleration orders of magnitude faster than the original full-physics simulations.

2. Inverse Parameter Inference:

   • Framework: The trained surrogate was embedded within a Markov chain Monte Carlo (MCMC) framework (using the emcee ensemble sampler) to perform Bayesian inference.
   • Likelihood: The likelihood function was constructed by comparing experimentally observed binary maps of dissolved and gaseous CO2 plumes (derived from image processing of "FluidFlower" photographs) against thresholded surrogate predictions.
   • Goal: This approach enables efficient exploration of the 15-dimensional parameter space to identify posterior distributions of key petrophysical properties, avoiding the prohibitive cost of repeated full-physics simulations.

Key Results

• Forward Prediction Accuracy: The surrogate model accurately captures large-scale CO2 plume migration, buoyancy-driven upward movement, lateral spreading, and interactions with heterogeneous geological structures (faults and seals). While minor discrepancies exist in fine-scale fingering structures due to hydrodynamic instabilities, the model maintains high fidelity in macroscopic transport behavior. Quantitative analysis using the Optimal Transport Wasserstein Distance (OTWD) shows that surrogate predictions are consistently closer to reference solutions than typical training realizations, even as solution complexity increases over time.
• Inverse Inference Performance: The surrogate-assisted Bayesian inversion significantly improves the concordance between simulations and experimental observations compared to manually calibrated results. The inferred Maximum A Posteriori (MAP) solution better reproduces large-scale plume geometry, vertical extent, and migration pathways, particularly in regions influenced by faults and sealing layers.
• Parameter Identifiability: The analysis reveals that while some parameters (e.g., permeability multipliers in specific regions) are well-constrained by observations, others remain broadly distributed or exhibit multiple modes. This highlights the non-uniqueness of the inverse problem, where distinct parameter combinations can produce similar macroscopic plume behaviors.
• Observation Horizon Impact: The study demonstrates that observational data becomes substantially more informative once the plume interacts with major geological features (faults and sealing layers). Extending the observation horizon beyond the point where the plume establishes primary migration pathways yields diminishing returns for constraining large-scale transport behavior, as remaining discrepancies are dominated by sensitive, fine-scale fingering dynamics.

Significance and Claims
The paper claims that this framework provides a critical step toward data-driven digital twins for subsurface systems. By leveraging spatially and temporally resolved full-field experimental observations, the approach substantially improves macroscopic concordance between simulations and experiments compared to previous manual calibrations based on limited scalar quantities.

The authors emphasize that the surrogate model learns physically meaningful transport behavior rather than simple interpolation, maintaining robust performance even in complex, nonlinear flow regimes. The integration of SciML with Bayesian inference makes computationally tractable the exploration of high-dimensional parameter spaces, revealing both identifiable and non-identifiable parameter combinations. This capability supports uncertainty-aware prediction and decision-making, bridging the gap between high-fidelity simulations and actionable insights for risk assessment in geological carbon storage. The work also underscores the importance of the "FluidFlower" benchmark in validating these approaches against physical reality, moving beyond synthetic datasets.