Colloids and Surfaces A : Physicochemical and Engineering Aspects, 83 (1994) 273-284

2730927-7757/94/$07 .00

C9 1994- Elsevier Science B.V . All rights reserved .

Dewatering of crude oil emulsions4. Emulsion resolution by the application of anelectric field

T.Y. Chena, R.A. Mohammed', A.I . Bailey', P.F. Luckham", S.E. Taylorb'Department ofChemical Engineering and Chemical Technology, Imperial College of Science,Technology and Medicine, Prince Consort Road, London SW7 2BY, UKbSurface and Colloid Science Group, BP Research Centre, Chertsey Road, Sunbury-on-Thames,Middlesex TW16 7LN, UK

(Received 23 August 1993 ; accepted 26 September 1993)

Abstract

The effect of the application of an a .c . electric field on the structure of a water-in-crude oil emulsion has beeninvestigated both experimentally and using a molecular dynamics simulation . In both cases, long chains of droplets areseen to grow between the electrodes as a function of time. This results from an induced dipole on the water dropletsin the presence of an external electric field, similar to that seen in electrorheological fluids . In the presence of a rigidinterfacial film, resulting from adsorbed crude oil components such as asphaltenes, no coalescence of the drops wasapparent. Simulations were also carried out to study the coalescence of water droplets in our emulsion, typical of thosein which the asphaltene film was disrupted by the presence of added demulsifier . Coalescence was observed in themicroscopic analysis . The results show that the solid interfacial film is a key factor for the prevention of coalescencebetween droplets in the electric field .

Key words: Crude oil; Electric field effect ; Emulsion ; Resolution

Introduction

The electrostatic resolution of water-in-crude oilemulsions is very common in the oil industry .During oil production, water is separated from theemulsion by applying a high electric field of1--10 kV cm I onto the flowing petroleum emul-sion to cause the coagulation and coalescence ofwater droplets. Pioneering work on electricallyenhanced coalescence to resolve water-in-crude oilemulsions was carried out by Cottrell [ I ] in 1911 .Two principal mechanisms of the coalescence ofwater droplets in low dielectric constant liquids bythe application of high voltage electric fields have

-Corresponding author.

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been described by Waterman [2] . These aredipole-dipole coalescence and "electrofining".Moreover, the effect of a d .c. electric field on thecoalescence of water drops in a water-heptanesystem containing a surfactant was studied byAllan and Mason [3] . They found that the applica-tion of the electrical force greatly enhanced therate of film drainage reducing the drop lifetime .Brown and Hanson [4,5] have also drawn similarconclusions in their study of the effect of an a .c.electric field on the stability of water-in-keroseneemulsions .

Bailes and Larkai [6] used insulated electrodesin order to promote droplet-droplet coalescenceof water-in-oil (w/o) dispersions by applying pulsedd.c . electric fields . They claimed that it is essential

274

to insulate the electrodes in order to avoidelectrode short circuiting caused by drops bridgingthe electrodes as they align in the direction of thefield . The so-called coalescence parameter was usedto gauge the effect of the electric field on coales-cence- This coalescence parameter is the ratio ofthe depth of the dispersion band in the gravitysettler that is incorporated in the arrangement ofthe electrostatic coalescer when the field is on, tothe depth of the dispersion band at zero field .Bailes and Larkai also demonstrated experimen-tally that more efficient separation can be achievedby using pulsed rather than constant dc . fields,and that there exists an optimum frequency, in therange of 5 Hz in their case, at which the best phaseseparation can be obtained . They attributed theinefficient separation, observed when applying aconstant d .c . field to the dispersion, to the loss ofthe field strength resulting from leakage throughthe insulating material for a given thickness of theelectrode coating . However, Galvin [7] dismissedBailes and Larkai's claims concerning the use ofinsulated electrodes to improve the efficiency ofthe separation process, and showed in his analysisthat electrode insulation serves no purpose otherthan preventing short circuiting, and it onlyincreases the applied voltage required to producethe desired coalescence rate . Furthermore, heshowed that the design of an electrical coalescerrequires detailed analysis of the power supply . Itwas concluded that it is perfectly possible to designefficient electrical coalescers operating at the mainsfrequency of 240 V .

The application of an electric field to dielectricliquid drops dispersed in a non-conductingmedium enhances the attraction between the drops .These attractive interactions between dropletsresult from electrostatic interactions . Earlierexperiments have shown that if the emulsion dropsare surrounded by a rigid interfacial film, stablechains of drops will develop, ultimately bridgingthe gap between the electrodes [8] . It has alsobeen observed that the drops tend to deform intoan ellipsoidal shape and redisperse into the

T.Y Chen et al./Colloids Surfaces A : Yhysicocheni . Eng . Aspects 83 (1994) 273-284

medium. This results from the imbalance betweeninterfacial tension and the electrostatic force [2] .Taylor [8] reported that the dehydration of 5%w/o emulsions made from Kuwait, Romashkinoand Ninian crudes showed two distinct types ofbehaviour designated as type I for emulsions ofwater-in-Ninian and water-in-Kuwait crudes andtype Il for emulsions of water-in-Romashkinocrude. Type I occurred on the application of ana.c. field and showed the formation of very stablechains of droplets between the electrodes . As aresult, current leakage through the chains occurred,leading to an increase in the emulsion conductivityand hence short circuiting . Incompressible inter-facial films hindered drop-drop coalescence .However, on the addition of 300 prim of an oil-soluble surfactant (Span 80) to the emulsion beforeelectrification, the type I characteristics reverted totype Il . Type II behaviour indicates the lack ofany chain formation through rapid droplet coalesc-ence. This was attributed to the enhanced mobilityof the interfacial film in the presence of thesurfactant .

In this work, we have investigated the behaviourof water-in-Buchan crude oil emulsions in highelectric fields . The formation of droplet chains andthe coalescence of adjacent droplets in the chainswere monitored by microscopic observations .Furthermore, we have modelled the behaviourusing a molecular dynamics simulation in order togain more insight into the physics of the behaviourof emulsion resolution by electrical means .

Experimental aspects

A microscopic stage cell was constructed tocarry out observations . The design of the cell issimilar to Taylor's design [8] . Figure 1 shows thedesign of the microscopic cell which consists of aPerspex block and a pair of parallel electrodesmade from brass . In the microscopic observation,the cell was placed on the stage of the microscopeand connected to an a.c. power supply unit, whichwas set tip to deliver 2 kV at a maximum current

T.Y. Chen et al./Colloids Surfaces A: Physicochem . Eng. Aspects 83 (1994) 273-284

to - V

03

Izo

-

~-oa

tL_t

, ,pr ng-Push

--

i

-a

svl ; Y4s5senhl' 2 I L

Fig. 1 . A schematic representation of the microscope cell used to investigate the effect of electric fields on emulsion stability .

of 10 mA over a frequency range 1-20 Hz . Thisa.c. power supply unit includes a modulator totransfer a high voltage d.c. input from a d .c.generator into an a.c. output by a low voltagesinusoidal signal, fed from a function generator .The arrangement of parallel electrodes allows theapplication of an external electric field to theemulsions . Typically a field strength of100 V mm- t was applied to a sample of 2 mlof freshly prepared 5-20% water-in-Buchan crudeemulsion. The system was imaged by using a videomicroscope technique . An image printer was usedto print the results of the observations .

Molecular dynamics simulation of a water-in-oilemulsion in an electric field

A molecular dynamics simulation was performedto study the behaviour of water-oil emulsions bycalculating the movement of water droplets whensubject to an external a .c. electric field . By thiscomputer technique, both long-range and short-range interactions have been examined to revealtheir influence on the reorientation of water drop-lets in the water-in-oil emulsions .

In the case of water droplets moving in crudeoil under an external electric field, the electrostatic,thermal (Brownian) and hydrodynamic forces need

275

61 C C

J

K

to be taken into account when calculating thelong-range interaction between droplets . In addi-tion to these long-range interactions, the hard-sphere model was adopted to describe the inter-actions between droplets with a rigid asphaltenefilm at short range. However, the coalescence willoccur in touching droplets without these solidfilms .

The model emulsion used in this simulationcomprises a disperse phase, which consists ofmonodisperse water droplets having a diameter aand dielectric constant Ea, and a continuous phase,which is a crude oil of dielectric constant E 0 it . Inaddition, this emulsion was constrained between apair of parallel electrodes . Figure 2 illustrates thegeometry and coordinates of the system used inthis simulation. The size of the gap between thetwo electrodes is represented as lx in length and 1,in width . The spherical coordinate system is alsoshown in Fig- 2 to represent the relative positionbetween any droplet i and droplet j, where eii isthe angle between the direction of the electric fieldand the centre of droplet i to the centre of dropletj . Moreover, an a .c . electric field, E= En sin (2rrft)e ,was applied across the gap, where Eo is the maxi-mum electric field, t is time, f is the appliedfrequency and e . is the unit vector in the z direction .

The movement of any droplet i in the emulsion

276

4Electrode

s

Fig. 2 The geometry and coordinates of the model system .

can be described in terms of an equation of motion(i .e . inertial force on any droplet i is equal to allforces acting on this droplet) . Hence Newton'sequation of motion for droplet i can be written as

d2R,M dt2 =L,Fl(R=)

T.Y. Chen et al./Colloids Sur/aces A : Physicochem . Eng. Aspects 83 (1994) 273-284

dielectric particles in an electrorheological fluid :

AR* _ [ YFe' *(Rti,B ;i) + EFj* (Rii,Bil).it(

i+YF;1rep,droplets* (R ; i) + F pelectrode*,

;ra

(h)]At+i

(2)

(1)

where m is the mass of each droplet in the emulsion,R, is the position of droplet i and F1 is any possibleforce applied to the droplet. Consequently, themovement of droplet i can be demonstrated bythis equation of motion (Eq.(I)) . Integration ofEq. (1) will give information about the position ofdroplet i at any arbitrary time point. In order toattain the solution for this equation of motion, thepossible forces which may be involved in thephenomenon should be considered . In this study,electrostatic, thermal and hydrodynamic forces aretaken into account as long-range forces and ahard-sphere model is used for the short-rangeinteraction between the droplets which areassumed to be covered by thin asphaltene films (ora coalescence procedure is adopted to simulate thewater droplets which are not covered by asphaltenefilms) . These forces are all discussed in theAppendix. The governing equation for the move-ment of water droplets in the crude oil emulsionunder an a.c . electric field is similar toKlingenberg's equation [9] for the movement of

where AR; is the movement of droplet i, At is thetime interval, Fj (R 11 , B;1) is the induced dipole-di-pole interaction between droplet i and neighbour-ing droplet j, Fiji (Rij, Oi) represents the pairinteraction between the ith droplet and the imageof droplet j and the sum of this interaction is equalto the interaction between any droplet i and oneof the electrodes, F;7 drOp 1 L2t(R ; 1 ) is the short-rangerepulsive force between any two droplets,Flep,electrode(h) is the short-range repulsive forcebetween any droplet i and the electrode, and theasterisk indicates a dimensionless variable .

The molecular dynamics simulation was per-formed to study the movement of droplets in theemulsion using 57 droplets in a system of l* _1x/o=30 and 1t=de/a=30. Consequently, the areafraction of droplets in the emulsion for this two-dimensional simulation was about 0 .05. Moreover,the a.c . frequency f, the dimensionless cut-off radiusR* and time interval At* were chosen as 6 Hz, 5 .0and 0.0001 respectively . The initial position of thedroplets was randomly decided to represent a well-dispersed emulsion .

All forces exerted on every droplet were calcu-lated at any time t for further usage in the equationof motion to determine the movement of droplets .hence the small movement of any droplet i (AR*)can be estimated by the product of the total forcesmultiplied by the time interval . As a result, thenew position of any droplet can be determinedfrom the superposition of original position andsmall movement. In other words, the position ofdroplets can be monitored step by step. If theprocedure is repeated again and again by increas-ing another time increment, the equilibrium struc-ture may be attained .

Results and discussion

Video recordings of the behaviour of water dropsin the 5% water-in-Buchan crude oil emulsion

T.Y. Chen ei al ./Colloids Surfaces A : Physlcochens. Eng . Aspects 83 (1994) 273 284

under the influence of an electric field revealed anumber of possible mechanisms governing theaction of the field under which droplets coalesce .It was observed that there was movement of thesolvent under the effect of the electrical forces(electro-osmosis) . Large drops tended to elongateinto an ellipsoidal shape owing to the induction ofa dipole . The commonest observation, however,was the formation of long chains of drops travers-ing the electrodes in a direction parallel to that ofthe field. The motion of the drops usually followedthat of the direction of the applied field . At afrequency in the range of 2-10 Hz, long chainstraversing the electrodes were formed as shown inFig. 3 . Higher frequencies (16-20 Hz) caused thedrops to form shorter chains of typically 5-15drops per chain; coalescence was also seen at thisfrequency. Experiments were also performed at

277

high frequencies (up to 100011z) where, again,short (5-10 drops) chains of droplets were formed.These are shown in Fig . 4. Figure 3 shows clearlythat the drops are aligning in the direction of thefield . The response to the field is rapid as it takesbetween 2 and 6 s to form chains . These illustrationshave been obtained from stills of video recordings .Figure 5 shows a sequence of photomicrographsat different stages during the formation of dropletchains for a sample of 20% water-in-Buchan crudeoil emulsions under the influence of electrical forcesas a result of applying a 485 V mm' field gradientat 50 Hz using Taylor's cell which employed insu-lated electrodes . The formation of chains of drop-lets is due to the droplets becoming polarised inan electric field, as has been shown to be the casein electrorheological fluids [10] . Thus thefollowing results (Fig . 6) from molecular dynamic

Fig . 3 . The effect of imposed electric field on 5% water-in-Buchan crude emulsion drops (frequency, 6 Hz ; field strength, 100 VTop left : before subjecting emulsion drops to the field . Top right : after 2 s of imposing electric field . Bottom right: after

6 s . Bottom left : after 25 s .

278

Fig . 4 . The effect of the imposed electric field on 5% water-in-Buchan crude emulsion drops (frequency, 16 Hz; field strength, 100 V(r.m .s.) mm- ') . Top left : before subjecting emulsion drops to the field . Top right: after 1 s of imposing electric field . Bottom right: after

3 s . Bottom left : after 35 s .

simulations are used as evidence to support thisthesis .

Before subjecting the emulsion droplets to theimposed electric field, the droplets were randomlydispersed in the medium to represent a well-dispersed emulsion . Figure 6(a) shows the randomdistribution of droplets in the Buchan crude oil atzero field . Once the electric field is applied, dropletsare polarised immediately owing to the redistribu-tion of surface charges . Therefore dipole momentsare induced in the droplets. This induced dipole-in-duced dipole interaction may cause the approach .separation, rotation and translation of a pair ofdroplets, which are dependent on the initial posi-tion of this droplet pair . As a result, clusters canbe seen in Fig . 6(b) . After a longer time period,droplet chains are formed in the water-in-crude oilemulsion. Figures 6(c)-6(e) reveal the formation of

T. Y. Chen et al,/Colloids Surfaces A : Physicochem . Eng . Aspects 83 (1994) 273-284

droplet chains in the presence of an external electricfield. If the applied electric field lasts longer, theshort droplet chains are aggregated to form longerdroplet chains. Figure 6(f) demonstrates the struc-ture of droplets in an imposed a.c. electric field .Figure 6 is in good qualitative agreement with themicroscopic observation on the development ofthe chain structure in the previous section (seeFigs. 3 and 4) .

The response time can also be estimated in thissimulation. Since the dimensionless time interval(At* =At/ta ) was chosen as 0.00001, the real timestep can be determined by calculating thecharacteristic time (tr =3at7 . i,a 2 (3/16)nc0so„aeff2Eo)where n o;, is the viscosity of the oil, (t is thedielectric mismatch between the disperse phase andthe dispersion medium, and ce is the dielectricconstant in vacuum . For a water-in-Buchan crude

T.Y. Chen et al.lColloids Surfaces A : Physicochem . Eng. Aspects 83 (1994) 273-284

(e)

Fig. 5 . Photomicrographs of a 20% water-in-Buchan crude oil emulsion at 50 Hz, 1 .6 kV, showing drop aggregation at different timeintervals : (a) 0 s; (b) 22 s; (c) 108 s; (d) 251 s ; (e) 693 s.

(b)

(d)

279

2811

(a)

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oil emulsion, the physical properties of theemulsion are ?lo;,=100 mPas, ax10_'m,E,=100 V mm- ', ca =8.854 x 10- ' 2 (' 2 J - ' m - ',cw =78.54 and coil = 3. Hence the characteristic time

T_Y Chen el a1 ./Catloids Surfaces A: Physicochem . Eng. Aspects 83 (1994) 273-284

(d)

40000 STEPS

n

8 80°

0 0o °

0

o

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o0 0°0

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8 oG 0o °

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o

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~ O8° o 8

(()1400000 STEPS

N

Fig. 6 . Computer simulations showing the formation of droplet chains in a 5% water-in-Buchan crude oil emulsion under an ac.electric field .

can be determined as 7 .5 s on a real time scale .Furthermore, the real time, step can be computedas 7.5 x 10_ 5 s. As a consequence, the requiredtime to reach the structure, shown in Fig. 6(f), is

T.Y Chen et ai ./Colloids Surfaces A: Physicochem . Eng. Aspects 83 (1994) 273-284

about 100s. We note that in the microscopic

observations (Fig . 3) it takes 25 s for the droplet

chains to form . The agreement between simulation

and experiment is therefore good .

Since the interdroplet force is strongly dependent

on the application of an external electric field, the

formation of chain structures will be influenced by

the rate of change of the direction and magnitude

(b)

(c)

00

0 0

° °

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O 000

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O ° O O 0° O O P•

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of the applied electric field . The magnitude and

direction of the applied sinusoidal field, E=

Eu sin(2irfr)e,, which will influence the charge

redistribution and hence the induced dipoles of

water droplets, is dominated by the applied a.c .

frequency. A fast reversal in the field direction will

be expected at high a .c. frequencies. However,

during this time, the droplets may be able to

(e)

(f)

281

Fig 7 . Computer simulations illustrating the coalescence of water droplets in a 5% water-in-Buchan crude oil emulsion under an a .c.electric field as a function of time .

wmo ..ms

°o °

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00

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282

respond to the fast change of the field . Thereforethe lower frequencies may be more effective inpromoting droplet chain formation.

Coalescence was also simulated in this study,representing the situation where no rigid film existson the droplets. Figure 7 illustrates the coalescenceprocess of water droplets in a water-in-oil emulsionunder the effect of an a.c. electric field . Once again,the water-in-oil emulsion is assumed to be initiallywell dispersed with a random position of dropletsin the crude oil (shown in Fig. 7(a)) . After applyingthe electric field, the neighbouring droplets tend tocoagulate and coalesce to form larger droplets.This is displayed in Fig . 7(b) . As time passes, thesize of droplets increases while the number ofdroplets decreases (see Figs . 7(c)-7(e)) . Finally, asmaller number of larger droplets are found toremain in the water-in-oil emulsion (Fig . 7(f)) .

Conclusions

The qualitative and quantitative similarity of theexperimental and simulation results shows that inthe presence of an electric field the water dropletsform chains owing to the induction of a dipole .We note that the simulation presented here issimilar to those presented to describe the chainingof particles in water-activated electrorheologicalfluids, suggesting that similar forces are involvedand that if coalescence can be avoided, then water-in-oil emulsions should also exhibit electrorheolog-ical effects . However, if the interfacial film is com-pressible, then coalescence is likely before chainformation can take place. In both microscopicobservation and simulation, the shorter chainsobserved at the higher a.c . frequencies are presuma-bly formed as a result of the droplets havinginsufficient time to respond to the rapidly changingalternating current .

References

1 F.G . Cottrell . U .S. Patent 987, 114, 1911 .23

1'.Y. Chen et al ./Colloids Surfaces A : Physicochem. Eng. Aspects 83 (1994) 273-284

4 A.H. Brown and C . Hanson. Trans. Faraday Soc,61(1965) t754.

5 A .H . Brown and C. Hanson, Chem. Eng . Set., 23 (1968) 841 .6 P.J . Bailes and S.K.L . Larkai, Trans. Inst. Chem. Eng ., 59

(1981) 229 .7 C .P . Galvin, Inst . Chem . Eng . Symp., Ser . 88, p . 101 .8 S.E . Taylor. Colloids Surfaces,29 (1988) 29 .9 D .J . Klingenberg, F.S. Swol and CF . Zukoski, J. Chem .

Phys.,91 (1989)7888 .10 H. Conrad, M . Fisher and A.F. Sprecher. in Proc. 2nd Int .

Coal. ER Fluids, Technomics, Lancaster, PA, 1990, p. 63 .11 R .B . Bird, W .E. Stewart and EN . Lightfoot, Transport

Phenomena. Wiley. New York, 1960 .12 M. Righy, E.B . Smith, W .A. Wakeham and G .C. Maitland,

The Forces between Molecules, Oxford University Press,Oxford, 1986 .

13 J . Israclachvili, Intermolecular and Surface Forces,Academic Press, London, 1992 .

14 M.P. Allen and D .J. Tildesley, Computer Simulation ofLiquids, Clarendon Press, Oxford, 1987 .

15 D .J . Klingenberg . F .S . Swol and C .F. Zukoski, 1. Chem .Phys.,91 (1989) 7888 .

Appendix

Hydrodynamic force

The hydrodynamic force (represented as P'') isa consequence of the relative motion of droplet ito the surrounding crude oil in the emulsion electri-fication . for a very slow motion of a microsizedspherical droplet through an incompressible fluid,the "creeping flow" model is adequate to describethis motion. In this approximation, the inertialforce (mass x acceleration) can he neglected com-pared with the viscous forces . Thus the equationof motion can be simplified by setting the left-handside of Eq. (1) to zero. Furthermore, the hydrody-namic force can be represented by a drag force .This drag force was derived by Stokes (see Ref. 11)as

F"Ya=-3ntrho ;ldR ;dt

where il .i, is the viscosity of the dispersion medium,crude oil in this case .

Electrostatic force

L.C. Waterman, Chem . Eng. Prog,61 (1965) 51 .R .S. Allan and S.L. Mason, Trans . Faraday Soc ., 57 When high dielectric water droplets dispersed in(1961) 2027 . a non-conducting oil are subject to an external

T . Y. Chen et a1./Colloids Surfaces A : Physimchem. Eng. Aspects 83 ( 1994) 273-284

electric field, the dominant electrostatic responsefor the droplets is interfacial polarisation, whicharises from the redistribution of charges on thesurface of the droplets. As a consequence of inter-facial polarisation, dipole moments are induced inthe droplets by the application of an electric field .This induced dipole moment in an a .c . electric fieldis given as [12,13]

gird = 7E

where a is the polarisability of the water droplets,which can be expressed in terms of the water andcrude oil dielectric constants and the dielectricmismatch fl between the disperse phase and disper-sion medium, i .e .

a=( 1 /2)neoc°ua'fl R=(c..-cwi)/(cw+2e°,i)

where co is the dielectric constant in vacuum.If an a .c. electric field (E= E 0 sin(2nft)e,) is

applied to the system, the magnitude of the dipolemoment becomes

it, = ( 1/2)nEOEmia 3fEn sin(21rft)

For R > a/2, the interaction energy between twoinduced dipoles in the electric field can be derivedas [12,13]

Uei(Ri;, dij)= - go(3 cost B-1)/(4neoc°uR )

where R ;; is the separation between two dropletsand B ; 1 is the angle shown in Fig . 2. The induceddipole-induced dipole force between two waterdroplets can be obtained by differentiating theinteraction energy [14] :

Fe"(R+i , O) = V Uel(Ri l . Bji)

3p4ncae ° ,,R ;.

x (L(3 cos2 B„ -1 )e, + (sin 20 i4ea l }

A similar force for two polarised particles inn ))) asuspension of dielectric particles suspended in non-conducting oil under a uniform (d .c .) electric fieldhas been obtained by Klingenberg et al, [15] by

283

means of solving Laplace's equation and integ-rating Maxwell's stress tensor along the surface ofone particle .

Besides these interdroplet forces, the forcesresulting from the interaction with the twoelectrodes also need to be calculated during thesimulation. A simple approximation which may beutilised is that the electrodes can be represented asthe images which are mirrored on the electrodesby all the dipoles in the system . Thus the inter-action force between any droplet i and one of theelectrodes can be given by the sum of the pairinteractions between the ith droplet and the imagesof all the droplets [15] .

Brownian force

The Brownian force kT/a is a random thermalforce likely to disperse the droplets into the crudeoil. This force may cause the destruction of thechain-like structure of droplets whereas the inter-droplet forces arising from polarisation of thedroplets lead to formation of the droplet chains,so there must be a competition between two forcesconcerning the formation of structure . A compari-son between the magnitude of Brownian and elec-trostatic forces exerted on any droplet i is shownas

~F ;;.I

3nc ae° ;laa /32 Eo sin 2(2nft)(5 cos' By

+ 5 cost 0u -1)/R,

From the experimental condition for the waterdroplets dispersed in the Buchan crude oil,T,:298 K, k=1.381 x 10-23 J K- ', a x 10 gm,Ea= I00 V mm - ', e a =8.854 x 10-12 C2 J- ' m

1,

E µ,=78.54 and E°;,= 3 . The ratio of the Brownianforce on any droplet i to the electrostatic force onthe same droplet from the other droplet at R ;;=aand 0 ;;=0 was estimated as being of the order of10 -5 . The effect of this thermal force seems farsmaller than that of the electrostatic force. Sincewe are interested in the chain-like structure ofdroplets observed by the microscopic experiments,

kTa

284

the Brownian force can be safely ignored in thisstudy .

Short-range force

Hard-sphere modelIn the presence of asphaltene films on the surface

of the droplets, the droplets generally retain theirspherical shape during the microscopic experi-ments; only the largest droplets exhibit deviationsfrom sphericity. Hence the assumption of hardspheres for these non-deformable droplets can beused in the simulation . In this simulation, the Bornrepulsion [12,13] was chosen to represent thedroplets with asphaltene films . This repulsive forcebetween any two droplets can be written as

raRdropfete - (R;J - a)F; ;

(R;;) = C exp

e0.01

where C is a constant which is chosen to balancethe attractive force to avoid the overlap of dropletsat the touching point. In this case, C was chosenas

C=3/16ns0Coaaz(fE~

A similar approximation for the short-rangeforce between the droplets and the electrodes wasalso used, but R te was replaced by h+1/2o, whereh is the distance from the centre of the droplet to

T.Y. Chen et al./Colloids Surfaces A : Physicochem. Eng. Aspects 83 (1994) 273-284

the electrode wall. Hence the short-range forcebetween any droplet i and the electrode can bewritten as

ep .electrode

--05c)(h)=Cexp

_(h

0.01- eF)

CoalescenceThe coalescence of droplets occurs because drop-

lets are not covered by asphaltene films . In thiscase, the hard-sphere model is no longer valid asa short-range interaction force in the simulation .Instead of this short-range force, a coalescenceprocedure was introduced. If a pair of droplets ofdiameters D; and D) were found to overlap, thentheir volumes were combined to form a new dropletof diameter

D;; = (D3 + D3)t /s

The centre of the new droplet was located at thecentre of mass of a pair of droplets involved in thecoalescence. The actual bodily movement of thetwo droplets during their coalescence was notsimulated. In addition, the wetting phenomenonon the surface of electrodes was not considered inthis study. Furthermore, the induced dipole-dipoleinteraction is strongly dependent on the dropletsize. Hence the change of the interdroplet force inthis simulation of the coalescence phenomenonshould be considered .