How transition between sea water and liquid carbon dioxide affects its sequestration in deep oceans

Abstract

The study addresses capillary gravitational wave motions in relation to the sequestration of liquid carbon dioxide in the oceans. These waves propagate at great depths near the interface between sea water and the liquefied carbon dioxide. It is shown that length scales and stability of such waves depend on both thickness and profile of stratification in the transitional layer. A theoretical model outlined here predicts that the waves are mainly driven by capillarity if the thickness of the transitional layer is relatively small d≪d∗. Otherwise, when d≫d∗, the gravitational effect determines the flow. The value d∗ depends on the wave mode number, surface tension and the profile of stratification in the transitional layer. Fine structure of stratification in that layer could lead to drastic changes for the wave properties and even change the dispersion law for the solitary wave while geometry of the flow and the capillary effects both remain the same. An application of the theory to modelling of a safe sequestration of carbon dioxide in the deep oceans is considered and calculations accounting for the relevant physical properties of the sea water and the liquid carbon dioxide are presented. In natural conditions related to the carbon dioxide storage it is calculated that d∗∼1cm. Instability in the layer between sea water and the liquid carbon dioxide could occur solely due to the gravitational–capillary effects. It is shown that some profiles of stratification lead to the modulation instability and appearance of benthic storms or deep water rogue waves. It is concluded that as the depth of sequestration increases the fine structure of stratification becomes less important for determination of properties of the capillary–gravity waves.