A recent study by the Energy Information Administration of the US Department of Energy  indicates that the share of natural gas, oil, and coal as  primary energy  sources will increase further by 2025. The same study gives a share of about  87% in 2025. A major concern would be global warming and efforts towards environmental stewardship. Provided carbon dioxide can be captured efficiently, its sequestration and its use in improved oil recovery can be much more efficient than current estimates. There may be a need to re-examine much of the material in the literature with respect to the interface modeling both in thermodynamics and in fluid mechanics. Some of the carbon dioxide  injection projects may also need re-examination. Our recent formulation of non-equilibrium phenomena when carbon dioxide is placed above a column of oil or water shows many interesting features. The most important aspect is rapid dissolution. Diffusion aspects of mixing and momentum balance across a moving interface coupled with special behavior of carbon dioxide when dissolved in water and in petroleum fluids all add to features that if properly recognized can give enormous benefits. In order to study various features of carbon dioxide there may be need to develop new numerical models for subsurface flow studies. Results using high-order numerical modeling(combined discontinuous Galerkin and mixed finite element) from carbon dioxide injection in fractured permeable media will be shown to demonstrate that carbon dioxide may not travel fast through the cracks in the subsurface. The mixing from diffusion results in high oil recovery.