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Abstract

Summary

In this work, Physics-informed Neural Networks (PINNs) are employed for history-matching data from core-scale countercurrent spontaneous imbibition (COUCSI) tests. To our knowledge this is the first work exploring the variation in saturation function solutions from COUCSI tests. 1D flow was considered: two phases flow in opposite directions driven by capillary forces with one boundary open to flow.

The Partial Differential Equation (PDE) depends only on a saturation-dependent capillary diffusion coefficient (CDC). Static properties porosity, permeability, interfacial tension, and fluid viscosities, are considered known. In contrast, the CDC or its components (relative permeability and capillary pressure), are considered unknown. We investigate the range of functions (CDCs or RP/PC combinations) that explain different (synthetic or real) experimental COUCSI data: recovery from varying extent of early- and late-time periods, pressure transducers, and in-situ saturation profiles.

History matching was performed by training a PINN to minimize a loss function based on observational data, and terms related to the PDE, boundary- and initial conditions. The PINN model was generated with feed-forward neural networks, Fourier/inverse-Fourier transformation, and adaptive tanh activation function and trained using full-batching. The trainable parameters of both the NN and saturation functions were initialized randomly. Different solutions were obtained through different initializations.

The PINN method successfully matched observed data and returned a range of possible saturation function solutions. When a full recovery curve was provided (recovery data reaching close to its final value) unique CDC functions and correct spatial saturation profiles were obtained. However, different RP/PC combinations composing the CDC were calculated. For limited amounts of recovery data, different CDCs matched the observations equally well but predicted different recovery behavior beyond the collected data period. With limited recovery data, all still following a square root of time trend, a CDC with low magnitude and peak shifted to high saturations gave same match as a CDC with high magnitude and peak shifted to low saturations. Recovery data with sufficient points not being proportional to the square root of time strongly constrained how future recovery would behave and thus which CDCs could explain the results. Pressure data calibrated PC towards unique solutions matching the input. The RPs were also constrained, but the CDC is virtually independent of the highest fluid mobility. However, each RP could be determined at its lower values. Adding artificial noise in the recovery data increased the range of the estimated CDCs.

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/content/papers/10.3997/2214-4609.202331054
2023-10-02
2025-07-11

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/content/papers/10.3997/2214-4609.202331054
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Application of Physics-Informed Neural Networks for Estimation of Saturation Functions from Countercurrent Spontaneous Imbibition Tests
Conference Proceedings 2023, 1 (2023); https://doi.org/10.3997/2214-4609.202331054
/content/papers/10.3997/2214-4609.202331054
/content/papers/10.3997/2214-4609.202331054
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