Improved Understanding of Naturally Fractured Reservoirs Using Data Assimilation

Seabra, Gabriel Serrao; Hoop, S. De; Voskov, Denis; Vossepoel, F.C.

doi:10.3997/2214-4609.202221095

Cited by 3 publications

(3 citation statements)

References 5 publications

(9 reference statements)

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“…Utilizing neural network surrogate models for speeding up data assimilation has been explored in various studies, see also 18 for a review. In [19][20][21][22] , generative deep learning has been used for high-dimensional state-and parameter estimation. However, none of these approaches performed sequential assimilation of the data.…”

Section: Introductionmentioning

confidence: 99%

The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification

Mücke,

Bohté,

Oosterlee

2024

Preprint

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In Data Assimilation, observations are fused with simulations to obtain an accurate estimate of the state and parameters for a given physical system. Combining data with a model, however, while accurately estimating uncertainty, is computationally expensive and infeasible to run in real-time for complex systems. Here, we present a novel particle filter methodology, the Deep Latent Space Particle filter or D-LSPF, that uses neural network-based surrogate models to overcome this computational challenge. The D-LSPF enables filtering in the low-dimensional latent space obtained using Wasserstein AEs with modified vision transformer layers for dimensionality reduction and transformers for parameterized latent space time stepping. As we demonstrate on three test cases, including leak localization in multi-phase pipe flow and seabed identification for fully nonlinear water waves, the D-LSPF runs orders of magnitude faster than a high-fidelity particle filter and 3-5 times faster than alternative methods while being up to an order of magnitude more accurate. The D-LSPF thus enables real-time data assimilation with uncertainty quantification for physical systems.

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Section: Introductionmentioning

confidence: 99%

The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification

Mücke,

Bohté,

Oosterlee

2024

Preprint

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“…However, these models may not accurately represent the complex relationship between aperture values and stress state, displacement history and fracture parameters such as orientation, length, and surface roughness. In Seabra et al (2023), those complex relations are included, albeit without shear displacement. They calculate fracture apertures as a function of effective normal stress obtained from a geomechanical simulation and subsequently reduce the uncertainty in the global model parameters with DA.…”

Section: Introductionmentioning

confidence: 99%

Prior with Far-Field Stress Approximation for Ensemble-Based Data Assimilation in Naturally Fractured Reservoirs

Liem,

Conti,

Matthai

et al. 2023

Preprint

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Fractures are frequently encountered in reservoirs used for geothermal heat extraction, CO2 storage, and other subsurface applications. Their significant impact on flow and transport requires accurate characterisation for performance estimation and risk assessment. However, fractures, and particularly their apertures, are usually associated with large uncertainties. Data assimilation (or history matching) is a well-established tool for reducing uncertainty and improving simulation results. In recent years, ensemble-based methods like the ensemble smoother with multiple data assimilation (ESMDA) have gained popularity. A key aspect of those methods is a well-constructed prior ensemble that accurately reflects available knowledge. Here, we consider a geological scenario where fracture opening is primarily created by shearing and assume a known fracture geometry. Generating prior realisations of aperture with geomechanical simulators might become computationally prohibitive, while purely stochastic approaches might not incorporate all available geological knowledge. We therefore introduce the far-field stress approximation (FFSA), a proxy model in which this stress is projected onto the fracture planes and shear displacement is approximated with linear elastic theory. We thereby compensate for modelling errors by introducing additional uncertainty in the underlying model parameters. The FFSA efficiently generates reasonable prior realisations at low computational costs. The resulting posterior ensemble obtained from our ESMDA framework matches the flow and transport behaviour of the synthetic reference at measurement locations and improves the estimation of the fracture apertures. These results markedly outperform those obtained from prior ensembles based on two naïve stochastic approaches, thus underlining the importance of accurate prior modelling.

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“…Utilizing neural network surrogate models for speeding up data assimilation has been explored in various studies (see [23] for a review). In [107,118,139,162], generative deep learning has been used for high-dimensional state-and parameter estimation. However, none of these approaches performed sequential assimilation of the data.…”

Section: Introductionmentioning

confidence: 99%

Deep Learning for Real-Time Inverse Problems and Data Assimilation with Uncertainty Quantification for Digital Twins

Mücke

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We develop novel approaches to enhance the functionality and efficiency of digital twins through deep learning techniques. Digital twins, sophisticated virtual models of physical systems, serve as dynamic counterparts, mirroring real-world entities' behavior and performance. Their primary role includes real-time monitoring, flaw detection, automated control, and proactive maintenance. To perform such tasks it is necessary to use various methods from scientific computing to combine data with physics models. Furthermore, to assess the reliability of a digital twin, it is important to not only make predictions, but also quantify the uncertainty of estimations and predictions. In this regard, Bayesian methods serve as a natural framework to pose the problems. However, the complexity and real-time operation requirements pose significant computational challenges. The thesis explores the integration of deep learning in scientific computing for enabling digital twins. The focus is on overcoming the computational hurdles in real-time data assimilation and inverse problem-solving through surrogate modeling. Deep learning, with its capability to handle high-dimensional functions in both deterministic and stochastic settings is shown to be a viable solution to these challenges. This work investigates several key areas, beginning with a brief introduction to digital twins, data assimilation, and inverse problems. It proceeds to elaborate on the role of Bayesian inversion problems in static and dynamic contexts, highlighting the importance of uncertainty quantification. The focus is on the challenges of real-time computation and the potential of Bayesian methods, despite their computational intensity. The thesis investigates deep learning architectures like dense and residual neural networks, convolutional neural networks, recurrent neural networks and transformers. The core contributions are presented in the four main chapters of the thesis: 1) Reduced Order Modeling for Parameterized Time-Dependent Partial Differential Equations: Introducing a deep learning framework for solving parameterized PDEs using spatially and memory-aware neural networks, demonstrated on linear advection and incompressible Navier-Stokes equations. 2) Markov Chain Generative Adversarial Neural Networks: Enhancing Bayesian inversion for static problems with sparse observations using a unique algorithm combining MCMC and GANs, demonstrated on a Darcy flow problem and pipe flow leakage detection. 3) Probabilistic Digital Twin for Leak Localization: Developing a probabilistic framework using supervised Wasserstein Autoencoders for leak localization in water distribution networks, tested on several network models. 4) The Deep Latent Space Particle Filter: Proposing a real-time nonlinear data assimilation method for dynamic PDEs with uncertainty quantification, using transformer-based dimensionality reduction and time-stepping in particle filters, demonstrated on various dynamic systems. This thesis contributes significantly to digital twins, addressing computational limitations and opening new avenues for practical applications in various industries.

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Improved Understanding of Naturally Fractured Reservoirs Using Data Assimilation

Cited by 3 publications

References 5 publications

The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification

The Deep Latent Space Particle Filter for Real-Time Data Assimilation with Uncertainty Quantification

Prior with Far-Field Stress Approximation for Ensemble-Based Data Assimilation in Naturally Fractured Reservoirs

Deep Learning for Real-Time Inverse Problems and Data Assimilation with Uncertainty Quantification for Digital Twins

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