SS: High Pressure Gas-Liquid Separation: High-pressure droplet-deposition: from experiments to closure laws
Authors: Dupuy Pablo Matas , Jakobsen Hugo Atle , Fernandino Maria , Svendsen Hallvard , Gaebler Ansor 
Published: July 2010

Abstract
Complete computational models that can be trusted at high pressures will enable a more accurate prediction of high pressure separation performance, valuable to vendors that design and supply separation equipment to the industry. The Population Balance Equation (PBE) is a promising modeling tool because it can simulate different physics for each droplet size coupled with CFD. This work discusses how to incorporate information on droplet to wall deposition into this framework. Droplet-wall collision experiments have been run at pressures up to 100 bars. The results are used as deposition closure laws in the PBE.
A practical example is given as application note where the change in efficiency due to the bouncing from the wall leads to a variation in the efficiency of one order of magnitude in the Stokes number.

Introduction
Many stages of gas cleaning are achieved at relatively low pressures because the phase separation is easier than at high pressures. In addition, there is little knowledge about and a lack of trusted simulation capability of hydrocarbon droplet streams at high pressure. The mechanisms of separations like droplet deposition need therefore to be investigated and implemented in a modelling frame in order to be able to simulate a whole separator device.
Different techniques can be applied for the simulation of separation devices (Hoffmann and Stein 2008). The key is the correct description of the dispersed phase. The Muschelknautz (1970, 1990, 1991) method has been applied for more than 40 years for cyclone separators. It consists of a pseudo empirical model for computation of the overall separation efficiency of particles by estimation of the cut-off particle diameter of the inner vortex.
Computational fluid dynamics is widely used for modeling the fluid field flow and visualizing fluid patterns and structure inside these devices. CFD has been applied to separators, where the dispersed phase is incorporated by either a Lagrangian or Eulerian approach (Crowe et al. 1998).
In general terms, a Lagrangian approach better describes the evolution of a particle with a given characteristic like size. But the Lagrangian approach has the disadvantage of being resource demanding. The interaction of the dispersed phase with the continuous phase can be achieved either by one-way or two-way coupling. The two-way coupling is the most demanding in terms of complexity and resources. For a recent application of computational fluid dynamics for the modeling of cyclone separators see Derksen (2003, 2005) and Derksen et al. (2006).
The eulerian method models the dispersed phase as a continuum after an averaging process (Jakobsen 2008). If only moments of the particle distribution function are tracked, like volume fraction, a lot of information is lost at the local level of interaction, i.e. many assumptions must be made to determine a collision outcome since neither droplet size nor droplet velocity are known. The tracking of the entire population in an eulerian fashion is achieved by applying the Population Balance Method (PBM). This method is nearly as descriptive as the lagrangian one, with the benefit of modeling the bidirectional interaction between both phases at different particle sizes (analoge to the two-way coupling of the eulerian method). However, the disadvantage of the PBM is to have the velocity internal coordinate integrated. This means that while the approaching velocity is critical for determining a collision outcome, it is not tracked individually in a PBM formulation, but statistically. The particle approaching velocity needs to be estimated as it wil be explained in this work. For the recent development of PBM applied to separation and wall/film interaction see Dorao et al. (2009) and Patruno et al. (2009a, 2009b, 2009c).