Hybrid Mathematical Modelling and Uncertainty Quantification of Underground Hydrogen Storage #

Peter Castellucci, Igor Chernyavsky, Oliver Jensen, Radha Boya, Lin Ma

11:10 Tuesday in 3E11.

Part of the Liquid crystals and transport models session.

Abstract #

In order to slow the rapidly deteriorating climate crisis we need to drastically increase our use of cleaner, more renewable energy sources. Given that renewable sources are often subject to seasonal variations, the question of what to do with the excess energy has the potential to be answered by underground hydrogen storage systems. The storage security of underground hydrogen is largely determined by the quality of the dense porous-rock formation known as the caprock which sits on top of the storage site. To assess the potential for leakage, theoretical models need to be developed which can propagate the uncertainty in the spatially varying structure of the caprock (Ma et al., 2018) through to the macroscopic hydrogen transport dynamics. Our approach is to model the transport of hydrogen in the caprock as a diffusion-uptake process with first- order reaction kinetics and an oscillatory boundary condition to account for the seasonal variations. For the case when the spatial variation in diffusivity is weak we quantify the spatio-temporal variations in hydrogen distribution by modelling the diffusivity as a Gaussian random field with a squared exponential covariance function. We use a Green’s function approach (Price et al., 2022) to derive a perturbative approximation for the time-averaged variance in the 1D concentration profiles of hydrogen. This analytical approach allows a more insightful investigation into the relationship between the parameters of the problem and the variance in the concentration field than standard Monte-Carlo methods. Our results show that the uncertainty in the concentration of hydrogen increases non-monotonically with the correlation length of the diffusivity fluctuations. The peak variance in hydrogen concentration occurs when the correlation length is comparable to the steady- state penetration depth of hydrogen into the caprock. The uncertainty also increases non-monotonically with the ratio of the frequency of injection/withdrawal to the reaction rate and the analytical expression for the variance can be used to find an optimal frequency which minimises the uncertainty.

References Ma, L., Slater, T., Dowey, P.J., Yue, S., Rutter, E.H., Taylor, K.G., Lee, P.D., 2018. Hierarchical integration of porosity in shales. Sci Rep 8, 11683. https://doi.org/10.1038/s41598-018-30153-x Price, G.F., Chernyavsky, I.L., Jensen, O.E., 2022. Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization. Proc. R. Soc. A, 478:20220032. https://doi.org/10.1098/rspa.2022.0032