Copula Modeling and Uncertainty Propagation in Field-Scale Simulation of CO2 Fault Leakage

Subsurface storage of ${\mathrm{C}\mathrm{O}}_2$ is an important means to mitigate climate change, and the North Sea hosts considerable potential storage resources. To investigate the fate of ${\mathrm{C}\mathrm{O}}_2$ over 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 subject to high uncertainty. We present a computational framework for forward propagation of uncertainty, including stochastic upscaling and copula representation of multivariate distributions for a ${\mathrm{C}\mathrm{O}}_2$ storage site model with faults. The Vette fault zone in the Smeaheia formation in the North Sea is used as a test case. The stochastic upscaling method reduces the number of stochastic dimensions and the cost of evaluating the reservoir model. 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 the upscaled flow functions are accurately captured by a data-driven transformation model. The uncertainty in upscaled flow functions and other uncertain parameters are efficiently propagated to leakage estimates using numerical reservoir simulation of a two-phase system of CO₂ and brine. The expectations of leakage are estimated by an adaptive stratified sampling technique which effectively allocates samples in stochastic space. We demonstrate cost reduction compared to standard Monte Carlo of one or two orders of magnitude for simpler test cases, and factors 2–8 cost reduction for stochastic multi-phase flow properties and more complex stochastic models.