(721c) Capturing the Phase Interface Using the Gradient Theory in the Mixing of Hydrocarbons and Supercritical Water

Mixing of hydrocarbons and supercritical water is used in an advanced refinery technology for upgrading heavy crudes or bio-crudes with a promising, high production rate of light hydrocarbons, less coke generation, and simultaneous reduction of heavy metals. The mixing is a tightly coupled process of multiphase flows, thermodynamics, and heat transfer. Tremendous modeling efforts are required to capture the coupled mass and heat diffusion across a phase interface, which is termed as the inter-phase diffusion. Because of the chemo-physical complexity on the interface, the state-of-the-art modeling works are mainly on 1-D geometries. In our previous works, we have proposed (a) a sharp interface method to accurately capture the inter-phase diffusion in 1-D, and we have also developed (b) a multi-dimensional interface capturing algorithm to handle the same inter-phase diffusion. Method (a) only handles 1-D geometries; however, because of the simplicity in 1-D, it can accurately capture the diminishing and/or emergence of an interface. Method (b) handles 2-D and 3-D geometries; however, it is currently impossible to capture the emergence of an interface, because when an interface appears in the formerly continuous, one-phase region, it is difficult to draft a numerical, geometric algorithm to create a new or even partial, non-closed surface in the bulk of fluids. (The emerged phase interface captured in our previous works refers to the phase separation of light hydrocarbons and extra-heavy hydrocarbons when mixing with supercritical water.)

Handling the emerged partial, non-closed phase interface in the mixture of hydrocarbons and supercritical water in 3-D is mathematically and numerically challenging, yet fascinating. The non-closed surface is usually cut off by the domain boundary in most cases. For example, we can have a hemisphere on a flat solid surface. The solid surface cut the sphere into a half, and the hemisphere is a non-closed surface cut off by the domain boundary, which is the solid surface. However, in the mixture of hydrocarbons and supercritical water, the non-closed surface can be random holes on an originally closed surface, for example, a sphere. Such holes are also not at all similar to the holes on the membrane of a live biological cell. The membrane with many holes is still a closed surface, while it is just that the dimension of its thickness is significantly small. The holes on the non-closed surface in the mixture of hydrocarbons and supercritical water are the regions, where the sharp phase interface physically and gradually grows into one-phase. It is a multi-scale coupled thermodynamics and transport phenomena, ranging from the molecular scale into the macro-scale.

In this talk, we present preliminary results of a novel multi-scale method coupling the Gradient Theory, thermodynamics, and transport models to capture the diminished and/or emerged multi-dimensional phase interface in the mixture of hydrocarbons and supercritical water. We propose to use novel methods to overcome the meta-stable phase behavior regions, where the non-ideal diffusional driving force does not cause the phase separation, while it should result in a phase separation based on the global minimization of the Gibbs energy. Results of our new method is compared with our former 1-D sharp interface method. Good agreement has been observed. The capability of capturing the partial, non-closed 3-D phase interface is demonstrated.