[Paper Review] A Physics-Constrained Deep Learning Model for Simulating Multiphase Flow in 3D Heterogeneous Porous Media

Bicheng Yan, D. R. Harp+2 more|arXiv (Cornell University)|Apr 30, 2021

Hydraulic Fracturing and Reservoir Analysis42 references4 citations

TL;DR

This paper proposes a physics-constrained deep learning model that accelerates 3D multiphase flow simulation in heterogeneous porous media by leveraging convolutional neural networks with continuity-based smoothing and temporal penalization. Trained on physics-based simulation data, it achieves ~1400× speedup with <0.3% average error in pressure and saturation predictions, enabling efficient use in inverse problems and coupled processes.

ABSTRACT

In this work, an efficient physics-constrained deep learning model is developed for solving multiphase flow in 3D heterogeneous porous media. The model fully leverages the spatial topology predictive capability of convolutional neural networks, and is coupled with an efficient continuity-based smoother to predict flow responses that need spatial continuity. Furthermore, the transient regions are penalized to steer the training process such that the model can accurately capture flow in these regions. The model takes inputs including properties of porous media, fluid properties and well controls, and predicts the temporal-spatial evolution of the state variables (pressure and saturation). While maintaining the continuity of fluid flow, the 3D spatial domain is decomposed into 2D images for reducing training cost, and the decomposition results in an increased number of training data samples and better training efficiency. Additionally, a surrogate model is separately constructed as a postprocessor to calculate well flow rate based on the predictions of state variables from the deep learning model. We use the example of CO2 injection into saline aquifers, and apply the physics-constrained deep learning model that is trained from physics-based simulation data and emulates the physics process. The model performs prediction with a speedup of ~1400 times compared to physics-based simulations, and the average temporal errors of predicted pressure and saturation plumes are 0.27% and 0.099% respectively. Furthermore, water production rate is efficiently predicted by a surrogate model for well flow rate, with a mean error less than 5%. Therefore, with its unique scheme to cope with the fidelity in fluid flow in porous media, the physics-constrained deep learning model can become an efficient predictive model for computationally demanding inverse problems or other coupled processes.

Motivation & Objective

• To develop a fast, accurate surrogate model for 3D multiphase flow in heterogeneous porous media, particularly for computationally expensive applications.
• To address the challenge of maintaining spatial continuity and transient flow fidelity in deep learning-based flow simulations.
• To reduce training cost and improve efficiency by decomposing the 3D domain into 2D image slices for CNN processing.
• To enable real-time prediction of well flow rates using a separate surrogate model post-processing the deep learning outputs.
• To ensure physical consistency by embedding conservation laws and penalizing transient region errors during training.

Proposed method

• The model uses a 3D-to-2D decomposition strategy, converting the 3D spatial domain into 2D cross-sectional images to reduce computational cost and increase training data diversity.
• A convolutional neural network (CNN) is employed to learn spatial topology and predict temporal-spatial evolution of pressure and saturation fields.
• An efficiency-enhancing continuity-based smoother is integrated to enforce spatial continuity in predicted flow responses.
• Transient regions are penalized during training to improve accuracy in dynamic flow zones, particularly during early and intermediate time steps.
• A separate surrogate model is trained to predict well flow rates from the predicted state variables, reducing error to <5%.
• The model is trained on high-fidelity physics-based simulation data from CO2 injection into saline aquifers, ensuring physical consistency.

Experimental results

Research questions

• RQ1 Can a physics-constrained deep learning model achieve high accuracy in predicting 3D multiphase flow in heterogeneous porous media while drastically reducing computational cost?
• RQ2 How effectively can a 2D image-based CNN architecture preserve the spatial continuity and dynamics of 3D flow fields in porous media?
• RQ3 To what extent does penalizing transient regions during training improve prediction accuracy in evolving flow systems?
• RQ4 Can a post-processing surrogate model accurately predict well flow rates with minimal error when fed predictions from the primary deep learning model?
• RQ5 How does the physics-constrained deep learning framework compare to full physics-based simulations in terms of speed and accuracy for complex flow scenarios?

Key findings

• The physics-constrained deep learning model achieves a speedup of approximately 1400 times compared to traditional physics-based simulations.
• The average temporal error in predicted pressure plumes is 0.27%, and for saturation plumes, it is 0.099%, indicating high predictive fidelity.
• The surrogate model for well flow rate prediction achieves a mean error of less than 5% across test cases.
• The 2D decomposition strategy significantly reduces training cost while increasing the number of training samples and improving training efficiency.
• The inclusion of continuity-based smoothing and transient region penalization enhances model accuracy, particularly in dynamic flow regions.
• The model maintains strong physical consistency by embedding conservation principles and penalizing deviations from flow continuity.