Fo rces and movement of small water droplets in oil due to …

Nordic Insulation Symposium Tampere, June 11-13, 2003

Forces and movement of small water droplets in oil due to applied electric field

A. Pedersen Norwegian University of technology and science Norway

E. Ildstad Norwegian University of technology and science Norway

A. Nysveen Norwegian Unive rsity of technology and science Norway

1. Introduction

The wellstream in offshore oil production comprises various types of hydrocarbons, water and sometimes sand. During the production removal of water from the oil is made by using large gravity separation tanks. The efficiency of oil / water separation depends on several factors and varies from reservoir to reservoir. Electric field, so called electrocoalescense, is used to increase the size of the water droplets which will result in higher settling speed in the gravitational separators[1]. In order to optimise and reduce the size of these separators it is important to know more about the mechanism involved. In this article the focus is on the forces due to polarization of water droplets. It is common to describe these forces assuming that the droplet behaves as a small dipole. This work has tested the validity of this assumption. The electric force acting on a water droplet in an electric field has been experimentally examined, indirectly through the measurements of drag forces, on the droplet in two distinct ways, (a) force on one fa lling droplet in an divergent field, and (b) force in droplet - droplet interactions.

2. Forces on droplets in electric field

In an external electric field the distribution of charge on the surface of the water droplet will result in attractive forces between the water droplets and subsequently enhance coalescense of water droplets. In a stagnant fluid the sum of forces acting will result in an acceleration of the water droplet:

mp

dv dt

=

Fg

+ Fe

+ Fd

(1)

where mp is the mass of the droplet, v is the velocity of the droplet, Fg is the gravitational force, Fe is the electric force acting on the droplet in the direction of the field and Fd is the viscous force acting in the direction opposite to the direction of movement. In the following these forces will be described in some detail.

2.1 Fe, electric force acting on the droplet

When a neutral water droplet is placed in an electric field it becomes polarized and surface charges will be induced on its surface.

For a water droplet in an uniform field, fig. 1a, the magnitude of the forces acting on each side of the water droplet will be equal, resulting in zero translation force. If the external

+ + + + + + + + + +

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-

+

-

-

+

-

Fe

-------

-

+ + + +

++

+ + +

Fe

-

+ + +

-

+

-

+

-

+ +

-

+

--

+ + +

-------

-

-

(a)

(b)

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field is nonuniform the forces acting will be larger on the high stress side. This is illustrated in fig. 1b. This gives rise to a net force pulling the small water droplet towards the region where the field is strongest, a phenomena usually called dielectrophoresis. If the water droplet is small and the degree of inhomogenity is low this net dielectrophoretic force acting on the droplet can with good approximation be expressed by[3]:

Fe = ?E .

(2)

Where ? is the dipole and ( is the average external field acting on it. In case of a small

neutral water droplet this can be expressed as: [4]

Fe1

=

2a30oil

-----w---a---t--e--r---?-------o---i--lwater + 2oil

E

2

(3)

For both AC and DC fields the net translation force will always be directed toward the

region with strongest field. In an strong inhomogenous electric field, and in case of strong

droplet-droplet interaction, the droplets themselves alter the electric field and this general

dipole approximation will not be valid. An alternative approach is then to calculate the

surface charge and the resulting electric field surrounding the droplet. The density of sur-

face charge on the water droplet can then be expressed as [2]:

= Ei(water ? oil)0 sin

(4)

where (L is the field inside the droplet and ZDWHU and RLO are the relative dielectric constants of the water and oil, respectively. The force acting on the droplet then becomes:

Fe2 = ExdA

(5)

A

where ([ is the field in the direction of movement.

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The resulting gravitational force acting on the water droplet is given by

Fg

=

4-- a3 ( 3

water

?

oil)g

(6)

Where D is the radius of the droplet, J is the gravitational acceleration, ZDWHU and RLO are

the densities of the water and oil.

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When the water droplet is moving the oil will cause a net drag force on the droplet. In a

stagnant fluid this force can be expressed by the drag coefficient through the equation [5]:

Fd

=

1-2

oilCD

A

v2

(7)

where &' is the drag coefficient, $ is the representative area of the droplet and Y is the velocity of the droplet. &' is expressed as the function of the Reynolds number and the

correction factor because of internal motion in the droplet.

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Experiments were designed for visual observations of droplets or water in oil emulsions exposed to electric field. The electrode arrangement was put inside a small test cell (15x15x15)cm3, which was placed in an shadowgraphic setup using an optical bench as shown in fig. 2. A high speed video camera with a maximum frame rate of 32000 frames/ sec was used to record the trajectory of the moving droplets.The voltage source was a HV-

CMOS Camera Long Distance Microscope Test Cell

Background Light

Laptop

Test Cell

Translation stages

Cylindrical Setup

Stationar droplet Setup

(a)

(b)

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amplifier (+/- 20 kV, 0 - 20 kHz). In these experiments 50Hz sinusiodal voltage was used.

The oil used in the experiments was Nytro 10x, and the characteristics of the oil and water

are shown in table1.

Two different electrode systems were used in this study:

(i). Low nonuniform field, shown in fig. 2a where a cylindrical field was made using a rod as an inner electrode and a fine grid as a outer electrode. This grid had an inner radius, U\ = 3 cm, and a length of 4.5 cm. The inner electrode had a radius, UL = 0.5 cm.

(ii). Stationary droplet setup for droplet- droplet attraction using vertical electrode arrangement, schematically shown in fig. 2b.The gap of the electrodes where G = 2 cm. The highly nonuniform electric field was made by an energized water droplet attached to the tip of an glass capillary. The glass capillary was mounted in the centre of the grounded electrode. The capillary was metalized with a silver painting. In these experiments water with 3.5%wt NaCl was used. The capillary and the stationary water droplet were both connected to the grounded electrode.

Nytro 10 X

Dest. water

Dest water + 3.5 Wt NaCl

Dyn Viscosity (@ 20C mPas

13.7

Dyn Viscosity (@ 40C mPas

6.4

Density (@ 20C), g/cm3

0.875

0.998

Relative permittivity, r

2.2

80

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0HWKRG IRU PHDVXUHPHQWV RI IRUFHV LQ ORZ ILHOG WKH F\OLQGULFDO JHRPHWU\ By a glass capillary water droplets were injected between the two electrodes as shown in fig. 3. The droplet sedimented slowly due to gravity. When the droplet entered into the

Fd

x s

ry

ri

U

Fe

Fg

(b)

y

x

(a)

(c)

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frame of the video camera the 50Hz voltage was turned on. The droplet then started to

move toward the inner electrode. Fig. 3 shows a typically trajectory of the droplet record-

ed with the video camera. The radius of the water droplet D, its position and increment in

x-direction, G[, and y-direction, G\, and time between the frames GW were measured man-

ually from each frame of the videofilm. From this the speed of the water droplets was de-

rived using

v = -----d---x---2----+-----d---y---2

(8)

dt

Thus the electric force is equal to the drag force in x-direction

Fe1 = FDx

=

1-2

oi

lCDAv2

cos

(9)

where is the angle of the dragforce, shown in fig 3b.

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A water in oil emulsion (10% water) was mixed in a mixer (turax). The emulsion was injected in the gap via a syringe in the front of the stationary droplet. The diameter of the droplets were in the 5- 20?m range, allowing the emulsion to float like a cloud in the gap.

d

x

l

U

y

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The gap was energized after the emulsion had been injected. Small water droplets then

started to move towards the stronger field. The position of these droplets were recorded

by the video camera, resulting in a typically trajectory as shown in fig. 4.

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A 2-dimensional FEM model of the droplet-droplet interaction setup was used to calculate the electric field. Using the electrostatic axisymmetry. The field in the positions of the droplet was recorded and used in MATLAB to calculate the electric forces according to eq. 5. Simulations were made with and without the small water droplet included in the model. In these simulations the internal and external field were recorded at each position of the droplet.

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