Enhancing the Parameterization of Reservoir Properties for Data Assimilation Using Deep VAE-GAN

Technical Deep Dive: Enhancing Reservoir Properties Parameterization with VAE-GAN

Overview

This work proposes a novel approach to improve the parameterization of reservoir properties for data assimilation, by combining the strengths of Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) into a hybrid VAE-GAN model. The key goals are:

1. Generate geologically realistic reservoir descriptions
2. Achieve good history matching performance with lower errors

Problem & Context

• Current state-of-the-art ensemble-based methods like ESMDA have limitations:
  • Use of finite ensemble sizes leads to spurious correlations
  • Rely on Gaussian assumptions which degrade performance for non-Gaussian reservoir properties
• Parameterization approaches like Truncated Pluri-Gaussian and PCA-based methods have been explored, but face challenges with complex 3D cases
• Recent deep learning techniques like Convolutional VAEs and GANs show promise, but have tradeoffs:
  • GANs generate more geologically plausible realizations, but poorer data assimilation
  • VAEs perform better for data assimilation, but generate less realistic reservoir models

Methodology

The key innovations in this work are:

1. Developing a hybrid VAE-GAN model that combines the strengths of both:
   • VAE component learns a structured latent space amenable to data assimilation
   • GAN component improves the realism of generated reservoir realizations
2. Integrating the VAE-GAN model with the ESMDA data assimilation algorithm
3. Evaluating the approach on two synthetic datasets:
   • Categorical facies model
   • Continuous permeability field from a carbonate reservoir benchmark

Data & Experimental Setup

• Categorical dataset: 48x48 grid, 80,000 realizations generated using SNESIM
• Continuous dataset: 65x65 grid, 15,000 realizations cropped from UNISIM-II-H benchmark
• Both datasets normalized to [-1, 1] range
• Reservoir simulation with 9 producers, 4 injectors in a 5-spot pattern
• History data: production rates, BHP at 90-day intervals over 10 periods

Results

Training Performance

• DCGAN, DCVAE, and VAE-GAN models were trained on both datasets
• VAE-GAN achieved the best balance, with FRD (Fréchet Reservoir Distance) of 5.12 for categorical and 8.32 for continuous, outperforming standalone GAN and VAE
• VAE-GAN also showed good performance on static geostatistical metrics like variogram, connectivity, and PCA correlation

Data Assimilation

• When integrated with ESMDA, the VAE-GAN model provided the best history matching, preserving ensemble variance and matching production data across most wells
• The GAN-only model struggled with data assimilation, likely due to the discontinuous and non-monotonic latent space
• VAE and VAE-GAN models were better able to transform the non-Gaussian distributions to the Gaussian assumptions of ESMDA

Interpretation

• The hybrid VAE-GAN architecture successfully combined the advantages of both generative models:
  • GAN's ability to generate high-quality, geologically realistic reservoir images
  • VAE's capacity to learn a structured latent space suitable for data assimilation with ESMDA
• This synergistic integration allowed the VAE-GAN model to outperform standalone GAN and VAE approaches in both realistic image generation and effective history matching

Limitations & Uncertainties

• The training process for VAE-GAN is more complex, requiring careful hyperparameter tuning to achieve stability
• Performance may degrade for larger 3D reservoir models due to increased complexity
• The synthetic nature of the test cases limits the ability to fully evaluate real-world applicability

What Comes Next

• Investigate the VAE-GAN approach on larger, more complex 3D reservoir models
• Explore methods to accelerate the VAE-GAN training process for improved scalability
• Validate the approach on real field data to assess performance on realistic geological scenarios