SESSION 2

FLOW CHARACTERISTICS: MODELLING AND EXPERIMENTS

Chairmen: G.F. Hewitt, D. Stevens

MOTION OF SWARMS OF DROPLETS

I. Wagner, J. Stichlmair
Technische Universität München
Lehrstuhl A für Verfahrenstechnik
Arcisstr. 21,
D-80333 München
Germany
Tel.: 0049-89-28916506; Fax: 0049-89-28916510

The motion of a swarm of drops in liquid-liquid systems is a fundamental phenomenon in two-phase flow. The prediction of the settling velocity in mixer-settler devices, spray columns or sieve plate towers for heat and mass transfer is of practical importance. Due to this wide scope the fluiddynamic behavior of two-phase droplet flow has been target of countless investigations. The dispersed phase holdup as well as the flooding point is strongly dependent on the relative velocity of droplet swarm and continuous phase. It had been demonstrated by many investigations that the droplet motion in dispersions decreases significantly with holdup due to interactions between particles, wake effects and enhanced effective velocities.

Fluiddynamic behavior of fixed and fluidized beds of solid particles had been studied extensively by many researchers and there are numberless models available to predict pressure drop and bed extension. However due to the more complex behavior of liquid-liquid systems there is still a lack of predictive models to determine the settling velocity by taking into account the swarm effects. Existing models (Ishii and Zuber 1979, Pilhofer and Mewes 1979, Kumar and Hartland 1989) are not satisfying with respect to theoretical background, accuracy and range of validity. In this work we will develop a new, theoretically based model for the motion of droplet-swarms in liquid-liquid systems as well as a new way for predicting flooding rates in counter-current columns.

Because of the similar behavior of solid and fluid particles, the proceeding is based on the well known model for rigid particles of Stichlmair et al. 1989 which goes back to the work of Richardson and Zaki 1954. According to these authors, the ratio of the relative velocity in a swarm and the terminal velocity of a single particle is a function of the void fraction to the power of 4.65 for laminar and 2.325 for turbulent flow. Applying this relationship for the solid particles to any correlation for the terminal velocity of droplets a novel swarm model for fluid particles is achieved. Using a modified relationship for terminal velocities of single drops based on the equations of Ishii and Zuber 1979 and Hu and Kintner l955 results in a generalized correlation for the swann velocity valid for the whole range of Reynolds numbers. This procedure leads, in comparison to the turbulent flow around solid spheres, to a smaller dependency of the relative velocity on the holdup for oscillating drops. This finding is in agreement with other investigations. The equation was developed theoretically without any adjusted parameter and does reduce to a single drop correlation for very low holdup.

To prove the quality of the new developed model a data base comprising 534 experimental data points collected from different sources had been assembled. It could be shown that the model represents the data with an average relative deviation of 15.5 % for Reynolds numbers in the range of 2.4 · 10^-2 to 2.6 · 10³ , including oscillating droplets. The new equation can be applied to a dispersed phase holdup up to 52.3% which is equal to cubic arranged, dense packed spheres. At higher holdup deformation of the drops will influence the particle movement strongly.

The presentation will include all informations on the model development as well as a comparison with existing models. Additionally, a novel flooding point diagram for countercurrent operation will be presented.

REFERENCES

1. Hu, S. und Kintner, R. C.: AIChE J.1 (1955), 42/48
2. Ishii, M., Zuber, N.: AIChE J. 25 (1979), 843/855
3. Kumar, A., Hartland, C.: Can. J. Chem. Engng. 67 ( 1989),17/25
4. Pilhofer, Th., Mewes, D.: Reprotext, Verlag Chemie, Weinheim, New York,1979
5. Richardson, J. F., Zaki, W. N.: Trans. Inst. Chem. Eng. 32 (1954), 32/35
6. Stichlmair, J., Bravo, J. L., Fair, J. R.: Gas Sep. Purif. 3 (1989),19/28

THE EFFECT OF EMULSIFICATION ON THE FLOW BEHAVIOUR OF TWO IMMISCIBLE LIQUIDS IN HORIZONTAL PIPES

Dieter Mewes, Martin Nädler and Alexander Tokarz
Institut für Verfahrenstechnik, Universität Hannover
Callinstr. 36, 30167 Hannover, Germany
dms@c36.uni-hannover.de

Mixtures of water and oil are frequently being transported in pipelines over long distances. For the design of theses pipelines and the adhering pumping equipment, it is necessary to know in advance the flow pattern and pressure drop for given volumetric flow rates of the two phases.

In particular, it is known that there is a strong dependence of the pressure drop on the flow regime present. Due to the turbulent energy dissipation, the formation of dispersions and emulsions of the immiscible phases is observed over a wide range of volume fractions. The flow behaviour of these emulsions may significantly defer from the flow behaviour of the single phases oil and water.

In the present study, the effect of the emulsification on the flow behaviour of oil and water in a horizontal tube is investigated. The flow rig consists of a horizontal pipe with an inner diameter of 59 mm the total length of which is 48 m. The liquid phases are fed into the test section in layers according to their density by a nozzle specifically designed to prevent entrance effects. By this methods, the observed dispersion downstream are solely due to the momentum transfer as a result of the flow. The investigated oil is a mineral white oil, the viscosity of which is varied between 22 and 35 mPas by controlling the temperature of the oil. The pressure drop of the two-phase mixture is measured at two different positions being at an entrance length of l_e/d = 225 and l_e/d = 680, respectively.

The results indicate that there is a maximum in the pressure drop for the flow of water-in-oil- emulsions at an input water fraction of approximately 10 %. This maximum is above the pressure drop for the single phase flow of the water as well as of the oil phase. It can partly be attributed to the rheological behaviour of the emulsions which determine the flow. Within this region of the water fraction, the emulsions flow in a significantly non-Newtonian manner. The apparent viscosity of the emulsion is larger than the viscosity of the pure oil even at high shear rates.

At the point of local phase inversion from the flow of an water-in-oil emulsion to the flow of a layer of a water-in-oil dispersion above a layer of pure water, a sharp decrease of the pressure drop is observed. At an input water fraction of around 40%, a pressure drop minimum is measured which is in the order of the value for the single phase flow of water. Transition regions at different input water fractions are observed where phase inversion occurs either locally within the dispersion layer or in the entire cross sectional area. No significant effect of the temperature on the flow characteristics is noticed.

A NOTE ON THE LAMINAR CORE-ANNULAR FLOW OF TWO IMMISCIBLE FLUIDS IN A HORIZONTAL TUBE

Sayavur I. Bakhtiyarov*, Dennis A. Siginer**
*Space Power Institute, Auburn University
Auburn, AL 86849-5820, USA
**Department of Mechanical Engineering, Auburn University
Auburn, AL 86849-5841, USA

ABSTRACT

Most crude oils are high in paraffin and asphaltene content. Deposits of these constituents on equipment and downhole cause severe problems which hamper and slow down production and transportation of crude oil. A simple, efficient and economically preferable method to prevent transportation problems caused by wax and asphaltene deposits on the inner surface of pipelines is to wet the inside wall with water based surfactants. The water film with surfactant additives acts as a barrier to prevent oil contact with the inner surface of the wall. If the film is replaced with a thicker layer, that is, if the water- oil ratio is increased, the use of surfactants may not be required, and the flow of oil may be lubricated by the water layer. Experiments on water- lubricated pipelining show that water in a stratified oil-water flow tends to encapsulate the oil. If the effects of gravity are negligible, the high-viscosity phase is centrally located; that is, the low viscosity fluid has a strong tendency to migrate to the region of high shear.

An experimental set-up based on an opto-mechanical principle to measure flow velocities is described in this note. The lubrication of a non-Newtonian liquid by a Newtonian fluid in the concentrically stratified laminar flow of two immiscible fluids in a horizontal tube is investigated experimentally and data for the interfacial velocity and the total volume flow rate for two zero shear rate viscosity ratios are reported. The results thus obtained can be used to validate the predictions of a theoretical solution to the core-annular flow problem .