A Simulation Model for Three-Phase Gravity Separators
Authors: Hallanger A. , Soenstaboe F. , Knutsen T. 
Published: December 2007

Abstract
A CFD model for three-phase gravity separators has been developed. The mathematical basis is the two-fluid model extended to three phases. The phases are taken to be incompressible and isothermal, solutions are then found for volume fractions, phase velocities and pressure on the numerical grid.
The local values of volume fractions are used to select one continuous and possibly two disperse phases in each control volume. The dispersed particles are assumed to be spherical and follow the drag law for solid particles. A viscosity increase from the collective influence of dispersed particles is included. A mixture model is used for water drops dispersed in oil. The drops are divided into classes with different diameters, and continuity equations solved for each class together with a momentum equation for the mixture phase. The water drops will either coalesce with free water, or be entrained with the oil. Constant turbulent viscosities are used taking the average internal velocities and heights of the of the stratification layers as the scales for the fluctuating velocities and eddy length respectively. A volumetric conservation law can be formulated for the total flow. The global volumetric conservation law is exploited in the boundary conditions in order to maintain overall volume conservation. The flow splits between the outlets are specified initially, and corrected during the simulation to account for the variations due to cross entrainment.
The model is applied on a first stage separator with a vertical inlet design and internal baffles to straighten the flow from the norwegian Oseberg field. Field measurements of water entrainment at different interface levels in the vessel are available. The correspondence between calculated and measured values are good.

Introduction
Design of separators has up to now mainly been based on the API design rules. It is then assumed that the phases are separated and stratified in the separator with completely uniform flow in each phase. The residence time of the phases can then be calculated together with cut-off drop sizes and K-factors for the gas phase.
The API rules are proven, but all effects from non-ideal flow due to inlet/outlets and internal equipment used to enhance separation are neglected. Considerable safety factors must therefore be used in design work. When weight and space are critical, as on offshore platforms or in sub-sea applications, the size of the vessel should be as small as possible. More accurate design methods are then required. One such tool is computational fluid dynamics (CFD), which has been used in single-phase simulations of separators. Several assumptions about the positions of the phase interfaces and the inlet flow pattern must then be made. To fully exploit the power of CFD, a complete multiphase separator model containing the fundamental physics should be formulated.
In this paper such a computational model for three-phase gas, oil and water flow in a gravity separator is described.

Theory
The mathematical basis for the simulation code is the two-fluid equations, which give the conservation of mass, momentum and energy for each phase. These equations are derived through time-averaging of the Navier-Stokes equations for single-phase flow. The subject is thoroughly treated by Ishii. The averaging formalism for two phases can easily be extended to an arbitrary number of phases. Through the averaging, detailed information about the shape and size of the fluid interfaces is lost and replaced by phase interactions terms. These terms are dependent on the flow and need to be modelled (closure laws).
We assume that the phases are incompressible. For high pressure separators the pressure differences are small compared with the operating pressure. The variations in gas density are then negligible. For operating levels closer to atmospheric conditions, small compression effects are possible at inlet and outlets regions and on bubbles in the liquid bulk. These effects are however under most conditions of a small magnitude. If the gas/liquid interface is displaced the density of the free gas phase in the vessel can vary. In the following such transients will be neglected.
We further assume that the flow in the separator is isothermal.
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