Mathematical Modelling Multiple-cone Concurrent Three-phase (CTP) Hydrocyclone Separation
Authors: Changirwa R.M.M. , Rockwell M.C. , Mutua D.K. 
Published: March 2010

Abstract
Recent developments in liquid-liquid and solid-liquid separation reveal that the conventional two- phase hydrocyclone is an indispensable tool in petroleum and allied industries. This is attributable to its simplicity of operation and numerous diverse applications. In spite of its many advantages, the hydrocyclone suffers a major drawback in the treatment of multiple-phase immiscible mixtures. Occurrence of these mixtures, as dispersions of oil and solids within liquids, can be epidemic and environmentally undesirable. In resolving this impediment, this research project has developed a concurrent three-phase (CTP) liquid-solid-liquid separation hydrocyclone by hydrodynamically incorporating a transverse aperture into a two-phase design. This paper discusses the concept, hydrodynamics and developments of the CTP hydrocyclone and its methodology and apparatus. The computed velocity spectra behaved asymptotically as they approached the hydrocyclone wall yielding steep velocity gradients in that region and thus maximum effective viscosity. In treating a three-phase system consisting of 1,000 ppm by weight of dispersed crude oil and a similar amount of sand in water, the CTP hydrocyclone reduced the underflow by 90% (44 microns) of solids and 85% of oil droplets (48 microns) at a transverse aperture of 6 mm. Increase in feed velocity enhanced sand efficiency and degenerated oil efficiency. Theoretical and experimental results were found to be in agreement.

Introduction
The occurrence of dispersions of oil and solid impurities within aqueous liquids is widespread and undesirable. Immediate cases that come to mind include reuse or disposal of produced water in offshore petroleum development and pollution control of industrial effluent. There is often the need to remove the dispersions of these impurities concurrently. Currently, a three-phase separation involves several stages, combining solid-liquid and liquid-liquid hydrocyclones in series-a process which is seldom effective or manageable. This impediment can be resolved through mathematical, simulation and experimental modelling. Several investigators have developed theoretical, computer simulation and experimental models of solid-liquid hydrocyclone separation systems(1–4). Others have dealt with liquid-liquid hydrocyclones(5–7). The various models have featured single-cone for solid-liquid and liquid-liquid hydrocyclones and seldom touched on multiple-cone hydrocyclones. An attempt(8) was made to establish experimentally the feasibility of three-phase separation using a twin-inlet single-cone hydrocyclone. However, little attention has been given to concurrent three-phase separation in a multiple-cone hydrocyclone. The theory developed in this paper derives the oil and solids efficiencies of the CTP and more so, correlating them. In order to assess the CTP performance, velocity spectra are analysed.

The Concept of CTP Hydrocyclone
The CTP concept involves separation of an oil-solids-water mixture in a single multiple-cone hydrocyclone into three individual phases. The concurrent separation of different phases can be improved by use of a multiple-cone hydrocyclone. The multiplecone concurrent three-phase hydrocyclone in this research is a hydrocyclone with at least two cones successively, architecturally structured in decreasing geometric angles downstream of the hydrocyclone as shown in Figure 1. There are reasons for the multiple-coned CTP hydrocyclone: