Coastal and offshore infrastructure must be designed to withstand extreme wave-induced loading conditions. Extreme Value Analysis (EVA) is often employed to infer probabilistic distributions that provide information about extreme design conditions. In traditional practices, EVA is performed under the assumption of stationarity. This means that the probability of extreme events is constant in time. However, hydraulic loading conditions are expected to exhibit temporal variability in severity and frequency as a result of climate change. Therefore, the assumption of stationarity becomes questionable. Nonstationary extreme value analysis (NEVA) for inferring extreme hydraulic loads have become more attractive in recent years. However, the applicability of NEVA models is debatable ansd differs on a case-by-case basis. Large scale oceanic bodies can be characterized by spatially and temporally varying extreme wave characteristics. Clustering analyses have proven to be successful to identify regions exhibiting similar extreme wave characteristics. Creating clusters based on similar extreme wave characteristics can potentially improve extreme value modelling because intra-cluster information can be pooled to derive more accurate extreme value models.

This research presents a practical assessment of the applicability of clustering analysis and non-stationary extreme value modeling of extreme wave statistics at cluster level in the North Sea. The primary objectives of this research are: (1) Study the temporal variability extreme significant wave height (Hm0) and extreme wind speeds (U10) in the North Sea domain, (2) Investigate how hierarchical clustering analysis (HAC) can be employed to cluster grid points that exhibit similar extreme wave characteristics, (3) How the obtained clusters and temporal variability can be employed to derive extreme value models describing extreme Hm0 statistics at cluster level and (4) assess whether NEVA models at cluster level form a practical alternative compared to conventional stationary analysis in the design and risk assessment of hydraulic infrastructure in light of climate change.

Temporal trend analysis of Hm0 in the North Sea showed that the period between 1990 and 2020 can be characterized by a decreasing trend. Between 1950 and 2020, a decrease in Hm0 intensity is observed in the Western regions and an increase is observed in the East. This is reason to believe that the variability in extreme wave climate is cyclical rather than monotonic. There is reason to believe that temporal variations of extreme U10 are responsible for the temporal variability of extreme Hm0. Initial clustering results partition the North Sea domain into 50 clusters based on characteristic values for the significant wave height (Hm0), peak period (Tp), and dominant wave directions (θ1 and θ2). After splitting clusters based on geo-location and merging clusters based on the intra-cluster statistical properties of the wave parameters, 63 clusters are obtained. The identified clusters and temporal variability are used to define NEVA models describing extreme Hm0 statistics at cluster level. Intra-cluster Hm0 observations are detrended before fitting the GEV parameters by means of Bayesian Inference. Informative priors are constructed by pooling the GEV parameter information from the intra-cluster grid points. Potential non-stationarity is accounted for by adding the Theil-Sen parameters (b and b0) to the location parameter (μ∗), making the location parameter a linear function of time. The model parameters subsequently read: Hm0 ∼ GEV (μ∗ + (b · t + b0) , σ∗, ξ∗). Using the extreme Hm0 data from the clustering centroid yields the most promising results for describing extreme Hm0 statistics at cluster level under the condition that the intra-cluster exhibits homogeneous values for b and b0.

The applied HAC analysis presented in this research is not the optimal strategy. The identified clusters exhibit heterogeneous values for b and b0 Because non-stationarity ofHm0 was not accounted for during the HAC analysis. This hinders the performance of the NEVA models at cluster level. Also, whether the derived methodology can be applied for the long-term projection of future extreme wave events in the North Sea is debatable. The non-stationary of extreme Hm0 is best described by a cyclic pattern. Without a thorough understanding of the underlying causes of the non-stationary in Hm0 and without future projections of the extreme wave climate, the applicability of NEVA for deriving extreme Hm0 design conditions in light of climate change cannot be guaranteed.

The mobilization of the trapped residual oil is an important part of Enhanced Oil Recovery. The desaturation of nonwetting fluids from porous media is often described using capillary numbers which are a ratio of viscous forces over the capillary forces between the wetting and the nonwetting fluids. Twodimensional microfluidic devices (micromodels) play an important role as they allow for the visualization of the two phase flow in porous media. Even though the existing definitions for capillary numbers work fine for describing the mobilization of the trapped nonwetting phase in geological rock, problems arise when applying these definitions for capillary numbers on micromodels. The conventional definition of the capillary numbers do not allow to visualize the desaturation of nonwetting phases in different micromodels on a single trend. This research presents the derivation of a new definition of a capillary number that can be used to better analyze the mobilization of trapped nonwetting ganglions inside micromodels. The new capillary number is based on a force balance on a trapped ganglion and the corresponding mobilization criteria of the trapped nonwetting phase. The new definition of the capillary number consists of the conventional definition of the capillary number and a geometric term that accounts for the geometry of the micromodel, including the sizes of the pore bodies and throats as well as the ganglion length. The functionality of similar definitions of the capillary number for roughened fractures has previously been published by Al Quaimi and Rossen (2017). The functionally of the new capillary number has been tested by analyzing published desaturation data for various micromodels, each using different wetting and nonwetting phase combinations using both the conventional and the new definition of the capillary number. It is found that the new definition allows for better analysis of the mobilization of the trapped nonwetting fluid inside micromodels, as the desaturation curves for different models can now be visualized by a single trend. Also, it is suggested that the geometrical parameters of the new equation are more significant for describing the mobilization of the trapped nonwetting phase than the of the medium and the interfacial properties of the wetting and nonwetting phases.