  History matching based on monitoring data will enable uncertainty reduction,
and thus improved aquifer management, in industrial-scale carbon storage
operations. In traditional model-based data assimilation, geomodel parameters
are modified to force agreement between flow simulation results and
observations. In data-space inversion (DSI), history-matched quantities of
interest, e.g., posterior pressure and saturation fields conditioned to
observations, are inferred directly, without constructing posterior geomodels.
This is accomplished efficiently using a set of O(1000) prior simulation
results, data parameterization, and posterior sampling within a Bayesian
setting. In this study, we develop and implement (in DSI) a deep-learning-based
parameterization to represent spatio-temporal pressure and CO2 saturation
fields at a set of time steps. The new parameterization uses an adversarial
autoencoder (AAE) for dimension reduction and a convolutional long short-term
memory (convLSTM) network to represent the spatial distribution and temporal
evolution of the pressure and saturation fields. This parameterization is used
with an ensemble smoother with multiple data assimilation (ESMDA) in the DSI
framework to enable posterior predictions. A realistic 3D system characterized
by prior geological realizations drawn from a range of geological scenarios is
considered. A local grid refinement procedure is introduced to estimate the
error covariance term that appears in the history matching formulation.
Extensive history matching results are presented for various quantities, for
multiple synthetic true models. Substantial uncertainty reduction in posterior
pressure and saturation fields is achieved in all cases. The framework is
applied to efficiently provide posterior predictions for a range of error
covariance specifications. Such an assessment would be expensive using a
model-based approach.
