# Bulk Dynamics of Droplets in Liquid-Liquid Axial Cyclones

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## Abstract

Separation of oil and water is an essential step in the treatment of the production streams from fossil oil wells. Settling by gravity is a robust though voluminous process and therewith expensive method at remote locations, leading to a need for smaller separation equipment. In this thesis, we describe the research performed on the development of an inline axial cyclone for oil/water separation. This work is part of ISPT project OG-00-004 and has an experimental nature: a flowrig has been constructed to test different cyclones at flow rates up to 60 m3/h in a 10 cm diameter tube in which brine and low-viscosity lubricant oil can be mixed in almost any proportion. Results are compared with numerical datasets resulting from the same ISPT project. Three different swirl elements have been developed for this project: a strong swirl element and a weak swirl element with 10 cm diameter, and one element with a 26 cm diameter in combination with a tapered tube section. For all three swirl elements, the velocity profile of water has been measured with Laser Doppler Anemometry (LDA). The strong swirl element has a swirl number of 3.7, the weak of 2.3 and the large diameter element of 3.9. The axial velocity profile normalized with the bulk velocity shows vortex breakdown (upstream flow in the center), where the severeness of the breakdown normalized with the upstream bulk velocity shows proportionality with the swirl number. For the azimuthal velocity, the velocity profile was proportional to the bulk velocity. The non-dimensional azimuthal velocity was similar for all three swirl elements in the region |r/D| < 0.2. Outside that region the relative velocity is strongly influenced by the swirl element. Time series obtained with single phase LDA studies were used to estimate the effect of turbulent dispersion on droplet trajectories. A simplified equation of motion based on centrifugal buoyancy, drag and turbulent dispersion was solved for many fictitious droplet paths. The measured, chaotic axial velocity time series was used to mimic the radial component of the velocity fluctuations. With this model, we can predict the smallest droplet size that can be separated with a certain cyclone and the largest droplet size before it is broken by the flow. Model results show good agreement with overall bulk data obtained in the experimental flow rig. With an intrusive endoscope technique, we measured the droplet size distribution at various positions in the axial cyclone. From this, Hinze’s theory for the droplet size in turbulent pipe flow is confirmed. Furthermore, the inverse correlation between azimuthal velocity and median droplet size is shown and quantified: a lower velocity allows larger droplets to survive. Different designs were tested to understand which parameters have a large influence on the industrially relevant parameter of separation performance. This question is answered by variation of the swirl element, swirl tube length, pickup tube diameter, flow rate and droplet size. Changes that affect the droplet size have a severe effect on separation, these are the swirl element and flow rate. Changes that increase the droplet size lead to better phase separation. The other geometrical changes can be used to optimize performance, but are not identified as parameters leading to breakthrough improvements. Two non-dimensional numbers can be used to explain the behavior of the cyclone: the Weber number (We) based on the droplet size upstream of the swirl element and the maximum velocity obtained in the gaps of the swirl element, and the Reynolds number (Re_?) for the droplets downstream of the swirl element based on their median diameter and the azimuthal liquid velocity. Separation is better for a smaller We number, because droplets are less vulnerable for breakup under that condition. A large Re? number is beneficial since the droplets then experience a large centrifugal acceleration which is larger than turbulent dispersion. Both trends are confirmed with experimental data obtained in this project. We propose that there is a function for the maximum possible separation efficiency based on both non-dimensional numbers. The inverse coupling between We and Re_? via the azimuthal velocity makes optimization of separation efficiency difficult. Application of a large diameter swirl element (low velocity and therefore limited droplet breakup) in combination with a gradual tapering of the tube (increasing the azimuthal velocity) is a possibility to obtain both a large We and Re? number. Another option is to place multiple axial cyclones in series, with a stepwise increase of the swirl strength in each subsequent cyclone. In such a configuration, each step is capable of separating smaller droplets than the previous step, without immediate breakup of large droplets. This method should increase the overall quality of the phase separation.