News & Events
- July 15th, 2008Flowasta released
Driving Force
Flowasta uses the hydrate growth (kinetics) model by Skovborg (1994). It is a simplification of a model by Englezos et al. (1987), which considers three coupled reactions: 1) Transport of molecules from a hydrocarbon (gas) phase across an aqueous film; 2) diffusion from the aqueous bulk to the surface of the hydrate lattice; 3) adsorption of hydrocarbon molecules in the cavities of a hydrate lattice.
By analyzing hydrate growth data by Bisnoi et al. (1985 and 1986) Skovborg found that the first step was rate limiting.
Flowasta considers two sub-systems, one hydrocarbon (vapor and/or liquid) and one aqueous (water and hydrates) system. Both systems are assumed to be in internal equilibrium, while there may be a component transport across the film boundary separating the two systems as is illustrated in the figure below. When hydrates form, the dominant component transport is hydrate guest molecules crossing the phase boundary from the hydrocarbon side to the aqueous side to be adsorbed in a growing hydrate structure.
The mass transfer between the two sub-systems is expressed in terms of fugacities as expressed by Krejbjerg and Sørensen (2005).
A is the contact area between the hydrocarbon and the aqueous phases and ki is the mass transfer number for component i. The mass transfer number, ki can be written as Di/δ where Di is the diffusion coefficient of component i and δ is the effective thickness of the stagnant aqueous film.
The fugacities of each component in each of the two sub-systems are determined by utilizing the flash options and thermodynamic models known from PVTsim. The interfacial contact area is estimated from liquid hold-up and geometric considerations. It is not obvious how to determine the thickness of the stagnant film layer and Flowasta instead finds the mass transfer coefficients, ki, from the dimensionless groups, Sherwood (Sh), Reynolds (Re), Schmidt (Sc) and Weber (We).
Flowasta effectively handles sub-cooling, although it does not use a dedicated sub-cooling model. When a reservoir well stream is let into a sub-sea pipeline it may experience rapid cooling and the gas solubility in the water phase will increase. Diffusion of gas from the hydrocarbon phases to the water phase is on the other hand a slow process and that limits how fast the gas concentration in the water phase can increase. When the system reaches the temperature, at which hydrates would have formed, had the whole system been at equilibrium, too few hydrate-forming molecules are present in the aqueous sub-system for hydrate formation to start. More hydrate forming molecules must be transferred into the aqueous phase before hydrates can start to form. When that happens, the temperature may have further dropped and the system will exhibit an apparent sub-cooling.
Formation of hydrates will stop when the two sub-systems reaches equilibrium and the components fugacities in both sub-systems become identical. That will not always happen within the pipeline residence time, since the contact area between the hydrocarbon and water phases decreases as water is converted into hydrates. For systems with hydrate inhibitors added, hydrate formation may on the other hand stop long before all the water has been used to form hydrates.
