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\begin{document}

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



\author[1]{Michael Liem}%
\author[1]{Giulia Conti}%
\author[2]{Stephan K. Matthai}%
\author[3]{Patrick Jenny}%
\affil[1]{ETH Zürich}%
\affil[2]{University of Melbourne}%
\affil[3]{ETH Zurich}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\selectlanguage{english}
\begin{abstract}
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 na\selectlanguage{ngerman}ïve stochastic approaches, thus underlining the importance of
accurate prior modelling.%
\end{abstract}\selectlanguage{ngerman}%



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