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Likelihood-Free Inference and Hierarchical Data Assimilation for Geological Carbon Storage

W Teng, LJ Durlofsky - arXiv preprint arXiv:2410.15302, 2024 - arxiv.org
Engineering paper cs.LG Suggest

Data assimilation will be essential for the management and expansion of geological carbon storage operations. In traditional data assimilation approaches a fixed set of …

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@article{2410.15302v2,
Author        = {Wenchao Teng and Louis J. Durlofsky},
Title         = {Likelihood-Free Inference and Hierarchical Data Assimilation for
  Geological Carbon Storage},
Eprint        = {2410.15302v2},
ArchivePrefix = {arXiv},
PrimaryClass  = {cs.LG},
Abstract      = {Data assimilation will be essential for the management and expansion of
geological carbon storage operations. In traditional data assimilation
approaches a fixed set of geological hyperparameters, such as mean and standard
deviation of log-permeability, is often assumed. Such hyperparameters, however,
may be highly uncertain in practical CO2 storage applications where
measurements are scarce. In this study, we develop a hierarchical data
assimilation framework for carbon storage that treats hyperparameters as
uncertain variables characterized by hyperprior distributions. To deal with the
computationally intractable likelihood function in hyperparameter estimation,
we apply a likelihood-free (or simulation-based) inference algorithm,
specifically sequential Monte Carlo-based approximate Bayesian computation
(SMC-ABC), to draw posterior samples of hyperparameters given dynamic
monitoring well data. In the second step we use an ensemble smoother with
multiple data assimilation (ESMDA) procedure to provide posterior realizations
of grid-block permeability. To reduce computational costs, a 3D recurrent
R-U-Net deep learning-based surrogate model is applied for forward function
evaluations. A rejection sampling (RS) procedure for data assimilation is
applied to provide reference posterior results. Detailed posterior results from
SMC-ABC-ESMDA are compared to those from the reference RS method. Close
agreement is achieved with 'converged' RS results, for two synthetic true
models, in all quantities considered. Importantly, the SMC-ABC-ESMDA procedure
provides speedup of 1-2 orders of magnitude relative to RS for the two cases. A
modified standalone ESMDA procedure is introduced for comparison purposes. For
the same number of function evaluations, the hierarchical approach is shown to
provide superior results for posterior hyperparameter distributions and
monitoring well pressure predictions.},
Year          = {2024},
Month         = {Oct},
Url           = {http://arxiv.org/abs/2410.15302v2},
File          = {2410.15302v2.pdf}
}

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