Exact expressions for finite-volume Kirkwood–Buff (KB) integrals are derived for hyperspheres in one, two, and three dimensions. These integrals scale linearly with inverse system size. From this, accurate estimates of KB integrals for infinite systems are obtained, and it is shown that they converge much better than the traditional expressions. We show that this approach is very suitable for the computation of KB integrals from molecular dynamics simulations, as we obtain KB integrals for open systems by simulating closed systems.

Knowledge of the mechanical properties of clathrate hydrates is central for studying the mechanical properties of hydrate-bearing sediments, their associated applications in wellbore stability, exploitation in stratum deformation, geological disaster prevention, and risk assessment of CO₂ buried in oceans. However, because of the limited understanding of hydrate formation conditions and limited methods to investigate these, the understanding of the mechanical properties of hydrates is still poor and even controversial to some extent. This paper reviews current experimental and theoretical results on mechanical properties of hydrates, and discusses the typical difficulties faced in this area. On the experimental side, the most important problem is obtaining pure hydrate samples. Theoretically, the essential origin of the mechanical properties has not been explained in terms of molecular interactions. The hope is to resolve these issues by combining novel macroscopic experiments and microscopic methods. In order to avoid difficulties caused by impurities, it is proposed to use molecular dynamics simulations. This technique can be used to reveal the nature of the mechanical characteristics of hydrates at the molecular and nanometre scale. The goals of this paper are to establish a bridge between the micromechanical nature and the macromechanical properties of hydrates, and to lay a solid theoretical basis for the study of the mechanical properties of hydrate-bearing sediments. These goals are important for the future safe and efficient exploitation of natural hydrates, hydrate-induced seabed geological disaster prevention, the safety of CO₂ geological burial, and the deployment of a reliable long-term seabed-borehole coupled hydrate observation system in the integrated Ocean Drilling Program.