Copula modeling and uncertainty propagation in field-scale simulation of CO$_2$ fault leakage
arxiv(2023)
摘要
Subsurface storage of CO$_2$ is an important means to mitigate climate
change, and to investigate the fate of CO$_2$ over several decades in vast
reservoirs, numerical simulation based on realistic models is essential. Faults
and other complex geological structures introduce modeling challenges as their
effects on storage operations are uncertain due to limited data. In this work,
we present a computational framework for forward propagation of uncertainty,
including stochastic upscaling and copula representation of flow functions for
a CO$_2$ storage site using the Vette fault zone in the Smeaheia formation in
the North Sea as a test case. The upscaling method leads to a reduction of the
number of stochastic dimensions and the cost of evaluating the reservoir model.
A viable model that represents the upscaled data needs to capture dependencies
between variables, and allow sampling. Copulas provide representation of
dependent multidimensional random variables and a good fit to data, allow fast
sampling, and coupling to the forward propagation method via independent
uniform random variables. The non-stationary correlation within some of the
upscaled flow function are accurately captured by a data-driven transformation
model. The uncertainty in upscaled flow functions and other parameters are
propagated to uncertain leakage estimates using numerical reservoir simulation
of a two-phase system. The expectations of leakage are estimated by an adaptive
stratified sampling technique, where samples are sequentially concentrated to
regions of the parameter space to greedily maximize variance reduction. We
demonstrate cost reduction compared to standard Monte Carlo of one or two
orders of magnitude for simpler test cases with only fault and reservoir layer
permeabilities assumed uncertain, and factors 2--8 cost reduction for
stochastic multi-phase flow properties and more complex stochastic models.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要