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Emulsions of Heavy Crude Oils. II. ViscousResponses and Their Influence on Emulsion StabilityMeasurementsAnne Silset a , Andreas Hannisdal b , Pl Viggo Hemmingsen c & Johan Sjblom aa Ugelstad Laboratory, Department of Chemical Engineering , Norwegian University ofScience and Technology (NTNU) , Trondheim, Norwayb Aibel Technology , Billingstad, Norwayc StatoilHydro, Research Centre , Trondheim, NorwayPublished online: 17 Sep 2010.

To cite this article: Anne Silset , Andreas Hannisdal , Pl Viggo Hemmingsen & Johan Sjblom (2010) Emulsions of HeavyCrude Oils. II. Viscous Responses and Their Influence on Emulsion Stability Measurements, Journal of Dispersion Science andTechnology, 31:10, 1432-1445, DOI: 10.1080/01932690903210341

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Emulsions of Heavy Crude Oils. II. Viscous Responsesand Their Inuence on Emulsion Stability MeasurementsAnne Silset, 1 Andreas Hannisdal, 2 Pa l Viggo Hemmingsen, 3 and

Johan Sjoblom1

1Ugelstad Laboratory, Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway2Aibel Technology, Billingstad, Norway3StatoilHydro, Research Centre, Trondheim, Norway

The stability of 30 heavy crude oil emulsions was studied in a parallel-plate laboratory coalescer(DC eld). Particularly, viscous responses and their inuence on the emulsion stability measure-ments were investigated. In addition to highlighting previous results from the same experimentalsetup and discussing these based on recent experience, new results at different temperatures andvolume fractions of water were presented. A new semi-empirical model for the characteristic timeof the destabilization process was presented. The electrical forces were modelled with a

point-dipole approximation and the hydrodynamic resistance to droplet transport was modelledwith an empirical term including the logarithmic viscosity of the oil phase. The new model clearlyperformed much better than the previous model, particularly for very viscous crude oils. Studies of the performance of industrial electrocoalescers have showed that simple electrostatic theory canpotentially explain complex separation phenomena when the resistance to the coalescence step isreduced by an efcient demulsier. The ultimate goal is to build a model for both the laboratorysetup and the industrial coalescer so that laboratory experiments can be used to predict thebehavior of the industrial process.

Keywords Crude oil, electrocoalescence, emulsion stability, point-dipole approximation,temperature, viscosity, water cut

1. INTRODUCTIONIn the petroleum industry, stable water-in-oil (w =o)

emulsions will be formed when oil and coproduced wateris mixed in the reservoir during transportation from thewellhead to the platform or in the process plant. The waterhas to be removed before rening takes place. It is veryimportant to be aware of the properties that inuence theformation of emulsionsas well as the destabilizationmechanisms of the emulsion system. The destabilizationmechanism of an emulsion involves two general steps occulation and coalescence. Depending on the method-ology of separation, the occulation step is at leastcontrolled by factors such as the density and viscosity of the continuous oil phase and the sizes of the dispersed

water droplets. The coalescence step is controlled bynatural surfactants within the crude oil and indigenous

compounds like naphthenic acids, resins, and asphaltenes,which stabilize the interfacial lm on the water droplets.Inorganic solids, made interfacially active by adsorptionof organic molecules, can also contribute considerably tothe overall stability of the interfaces. The interfacialchemistry of petroleum w =o emulsions has been studiedin detail previously. [15]

Several techniques exist for enhancing the separation of w=o emulsions in industrial processes, such as chemical, [6,7]

gravitational, or centrifugal settling, [8] heat treatment andelectrostatic destabilization. [9,10] In the petroleum industry,the electrocoalescence separation concept has been usedboth for water knock-out processes and polishing pro-

cesses. Strong electrical elds create attractive forcesbetween conductive water droplets (with salt), which aredispersed in the insulating crude oil. The forces enhanceboth the occulation and the coalescence step in thedehydration process. [11,12]

Cottrell and Speed [11] led the rst patent on electrocoa-lescence, observing the coalescence mechanism when a highpotential was applied to a pair of wire electrodes in a w =o

Received 3 December 2008; accepted 29 December 2008.The authors would like to acknowledge the nancial support

from the participants in the Joint Industry Project, Flucha III,hosted by the Ugelstad Laboratory at the Norwegian Universityof Science and Technology.

Address correspondence to Andreas Hannisdal, AibelTechnology, Bergerveien 12, 1396, Billingstad, Norway. E-mail:[email protected]

Journal of Dispersion Science and Technology, 31:14321445, 2010Copyright # Taylor & Francis Group, LLCISSN: 0193-2691 print =1532-2351 onlineDOI: 10.1080/01932690903210341

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emulsion. Chains of aqueous drops extended from oneelectrode to the other. Coalescence of adjacent drops ineach chain then occurred and the drops next to the electro-des became larger as new drops were acquired by the chain.Almost any type of high electric eld will assist the separ-ation of w =o dispersions to some extent. [13] Alternatingcurrent (AC), direct current (DC), pulsed DC, or combina-tions of them are being utilized in the separation of water-in-crude oil emulsions. Each eld type acts accordingto different mechanisms. Most of the available commercialelectrocoalescers work in AC because of their high watertolerance, effective power consumption, and low tendencyfor electrolytic corrosion. The DC electric eld has beenless common in the past. In 1981, the concept of pulsedDC elds was introduced, together with insulated electro-des. Since then, this has become more common in theelectrocoalescence technology. Pulsed DC and AC eldsare especially useful, when the aqueous phase content of the emulsion is high, to prevent short circuiting the electri-cal system. [14]

Generally, two main designs of coalescers are common;cellular units, which may consist of coated or uncoated elec-trodes and either internal or external settlers, and tankunits, with bare electrodes in which coalescence and settlingtake place simultaneously, as commonly used in the oilindustry. Traditional electrocoalescers have nonisolatedelectrodes and are for that reason placed downstream nor-mal gravity separators to avoid too high water loading andshort circuiting followed by collapse of the electric eld.Recently, other nontraditional electrostatic coalescer unitshave appeared in the market, that is, the Compact ElectroCoalescer (CEC) from Aker Solutions (Oslo, Norway),the Vessel Internal Electrostatic Coalescer (VIEC) from

Aibel (Asker, Norway), and the Dual Polarity Treater fromNatco (Houston TX, USA). All these products havepartially or completely isolated electrodes to reduce thepotential for short circuiting at high water cuts. [15,16] TheCEC is an inline AC coalescer, the VIEC is built as a wallof AC coalescer elements in the rst or second stageseparator, and the Dual Polarity Treater is a compact dehy-drator tank utilizing both DC and AC elds. The character-istics and geometry of the electrodes and the electrical elddetermine the performance of the electrostatic coalescer.

To our knowledge, Kilpatrick and Speicker [17] wereamong the rst to use electrical elds in a parallel-platecapacitor to evaluate w =o emulsion stability. The experi-mental setup was similar to the one used in this study: par-allel nonisolated electrodes, direct current, and constantlyincreasing eld strength until instability occurred. Thepoint of instability was identied by monitoring the currentthrough the emulsion. Aske et al. [18] used the same labora-tory setup to investigate which analytical and physico-chemical parameters that contributed to emulsionstability in electrical elds. Using multivariate data

analysis, the emulsion stability was correlated tophysicochemical properties such as molecular weight,density, viscosity, interfacial tension, interfacial elasticity,total acid number (TAN), and SARA (saturates, aro-matics, resins, asphaltenes) composition for a crude oilmatrix consisting of 21 samples. It was concluded thatthe asphaltene content, the state of asphaltene aggregation,and interfacial elasticity were the most important factorswith regard to emulsion stability. Chiesa et al. [19]

performed a fundamental study on the combined effect of viscosity and electrostatic forces on two water dropletscolliding in an electric eld. According to Chiesa et al., vis-cosity inuenced indirectly the rest time of coalescing waterdroplets since the impact velocity and consequently thekinetic energy of colliding water droplets was dependenton both the strength of electrical forces and on the viscosityof the surrounding oil. Less et al. [20] studied the electro-rheological behavior of petroleum emulsions. Droplettransport and coalescence processes were studied in electricelds. Less demonstrated the reversibility of droplet chain

formation caused by electric forces at low shear rates. Thisphenomenon was not observed at high shear. Hemmingsenet al.[21] studied the rheology and the stability of 27 heavycrude oils in DC electric elds. Emulsion stability wasmeasured with the same parallel-plate capacitor as theone used in the current study. The magnitude of theelectrical eld was constantly increased with a step rate,dE 0=dt , until destabilization occurred. Hemmingsen et al.realized that viscous responses greatly inuenced thereorganization of water droplets in the electric eld. Tem-perature and dilution effects were studied. Based on thendings by Hemmingsen et al., [21] Hannisdal et al. [22]

extended the work and included experiments with varying

dE 0=dt . Thirty crude oils were analyzed with respect to dif-ferent bulk properties, interfacial properties, spectroscopicsignatures, and emulsion stability. Emulsion stability wasmeasured with the same parallel-plate capacitor as theone used in the current study. The experimental resultswere compared to a simplied theoretical model thatdescribed the destabilization process by taking drag forcesand dielectrophoretic forces into account. To a largeextent, the results could be explained by the rate of droplettransport and the viscosity of the continuous phase. Givenenough time, water-in-heavy oil emulsions could be desta-bilized even at very low electrical eld magnitudes. Eventhough water-in-heavy crude oil emulsions are expectedto have a considerable barrier to drop coalescence throughthe lm strength, such interfaces seemed to provide limitedstability to electrically induced disintegration. Atten [23]

came to the same conclusion when the performance of acoaxial cylindrical electrocoalescer (AC eld) was evalu-ated. Beetge and Horne [24] studied the electrical destabiliza-tion of emulsions with different amount of water to nd therelative amount of energy required for occulation and

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coalescence. Crude oil blends and model oil emulsions hadin some cases a distinct barrier toward coalescence, whichdiminished by introducing demulsier. Even though thetheoretical analyses and the interpretation of results differslightly, the observations by Beetge and Horne are inharmony with results from the current study.

Here, emulsions of 30 crude oils, previously studied byHemmingsen et al. [21] and Hannisdal et al. [22] have beeninvestigated in a parallel-plate DC laboratory coalescer.In addition to highlighting previous results and discuss-ing these based on recent experience, new results arepresented. The focus is on viscous responses and theirinuence on the emulsion stability measurements in thelaboratory coalescer. A new semi-empirical model thatexplains the experimental ndings is presented. Themodel accounts for varying water cuts, magnitudes of the electrical eld, and a broad range of oil viscosities,both for different crude oils and for oils at differenttemperatures.

2. THEORETICAL BACKGROUNDElectrocoalescence is governed by the effect of electro-

static forces. When an electric eld is applied to a w =oemulsion, a suspended droplet is subjected to differentforces. One mechanism leading to coalescence of small dro-plets is dielectrophoresis. Dielectrophoretic forces areattractive forces established in a nonuniform electric eldbetween droplets having permittivity, which differs fromthe permittivity of the carrying liquid. [23] These forces pullthe droplet toward the highest voltage gradient and areproportional to the droplet diameter and the oil conduc-tivity, as shown by: [26]

F DP 4pr3e0eW e0

eW 2e0 r E 2; 2:1where r is the droplet radius, E o and E w are the oil and waterpermittivities, the subscripted symbol indicates theircomplex value (equal to E j rx , where r and x are conduc-tivity and eld frequency), and r E is the electric eldgradient. Another possible mechanism is electrophoresis.Electrophoretic forces are both attractive and repulsiveforces established in a uniform voltage eld betweencharged droplets and the electrodes. The fundamental prin-ciple relies on the charge separation between the particlesurface and the surrounding uid. An applied electric eldacts on the resulting charge density, causing the particle,the surrounding uid or both to move. [27] Equation (2.2)shows the formulation of the electrophoretic force for adroplet charged by direct contact with an electrode at thetime t t0. This droplet will gradually lose its charge witha relaxation time s (e0=r 0).[26]

F EP p2

6 4pr2e0E 2er 0 te0 2:2

The remaining basic process is the dipolar force, whichcauses a mutual attraction between neighboring dropletsdue to the interaction of the dipoles induced by the electriceld.[23] This force arises because of the high conductivity

of the water, which has high salt content and accordingto Eow et al. [27] can be written as:

F d 24pe0E 2r6

s4 ; 2:3

where s is the distance between two droplets radii. Themain equations are now written and can be analyzed.The most obvious feature of all electrostatic forces is theimportance of the magnitude of the electric eld, E , whichappear in second order in all Equations (2.1) through (2.3).Equation (2.3) shows that the dipolar force is stronglydependent on the water droplets size and the spacingbetween them, which is reasonable since it is the presenceof nearby droplets, which actually create the force.Assuming that the water droplets have similar size andare homogeneously distributed, the spacing is inverselyproportional to the dispersed water volume fraction / w ,as shown by: [28]

s r 4=3p

/ w 4=3

: 2:4

Therefore, as the water content is reduced along the elec-trocoalescence process because of the ongoing separation(or just because the emulsion to be treated has a low watercontent, but still far from export quality), the spacing

between the droplets is large and the dipolar attractionbecomes less and less effective.

Equation (2.2) does not show the interaction of droppairs, but it can be mentioned that the interaction forcefollows the law by Coulomb, who showed that the forcebetween two point charges falls inversely with the squareof the distance between them. Under DC electric elds,because of the unchanging polarity, this force will inducethe charged droplets to migrate toward the oppositelycharged electrode in a continuous path with a velocitydetermined by the viscosity of the continuous phase. Indoing so, it is likely that droplets will collide with eachother, merging together. [29] In AC elds no net charge isimparted to the droplets, so they will just oscillate arounda mean position at a frequency twice that of the electriceld[26] and they will coalesce only by polarization effects.It has been shown that electrophoresis is by far thestrongest electrical mechanism available. [30] Unfortunately,the corrosion mechanisms promoted by the unidirectionalcurrents and the poor water tolerance have discouragedthe use of DC elds. [27]

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Equation (2.1) points out that the dielectrophoreticforce is still independent of the droplet spacing, but itdepends on the gradient of the electric eld. Dielectrophor-esis does not require charged particles and arises from thefact that any dipole has a nite separation of equalamounts of positive and negative charges. When a nonuni-form eld is in alignment with the dipole, one end of thedipole will be in a weaker eld, resulting in a net force pull-ing the dipole toward the place of greatest eld intensity.Dielectrophoresis is the key factor in dipole coalescence,where it can be thought that a pair of close water dropsin oil attracts each other, both trying to reach the pointof maximum eld intensity between them. [27] Although die-lectrophoresis requires nonuniform electric elds, it existsin uniform elds as well, since in practice the presence of several droplets always acts to distort the eld lines.Having much higher permittivity than the oil, the dielectro-phoretic force will pull the water droplets towards regionsof higher eld strength (positive electrophoresis). [26]

3. EXPERIMENTAL

3.1. MaterialsThirty dead crude oils were received from different oil

companies with production sites on the Norwegian Conti-nental Shelf, in the South China Sea, the Gulf of Mexico,the UK Continental Shelf, France, Brazil, West Africa,and Alaska, USA. About half of the oils are dened asheavy (< API 20), while the lightest sample has an APIgravity of 33.6. Some crude oils are extremely viscous(see Appendix 1). The crude oils have systematically beenanalyzed with regard to viscosity, density, SARA fraction-

ation, TAN, interfacial elasticity, and interfacial tension(IFT). [22] (Some characteristic properties are attached inAppendix 1.) Because of the great variety in crude oilproperties, the operators meet different challenges withrespect to ow assurance and quality of the well productdue to coproduced water solids, asphaltene precipitationor high viscosity of the oil phase. Some of the samples alsocontain wax, which can be seen from their Bingham plasticbehavior below 25 C. The wax content has been investi-gated by Hemmingsen et al. [21] All crude oils were sampledin a way that minimized contamination by productionchemicals. Some samples were received with considerableamount of coproduced water, which was removed by grav-itationally induced separation. For some samples with highviscosity, the residual water could not be removed easilyand the w =o systems were analyzed as received.

A model oil system was used to study the effect of vary-ing the volume fraction of water in emulsions destabilizedby electrical forces. The model oil was made from analiphatic solvent with viscosity of 1.8 mPas (Telasol) and1 vol% sorbitan monooleate.

3.2. Destabilization of Emulsions in an Electrical Field:The E-Critical Cell

The critical electric eld cell, was used to investigate thew=o emulsion stability (Figure 1). The technique has beenused and described previously. [21,22,3234] The cell is madeup of a Teon plate with a hole in the center (r 5 mm),and a brass plate on each side. The distance between the

plates varied from 0.25mm up to 1.0 mm. The brass plateswere connected to a computer-controlled power supply(Agilent Model 6634B; Agilent, Santa Clara, CA, USA)that can deliver a maximum of 100 V DC. Electrodes withparallel-plate geometry were used. The cell was placed in aheating cabinet to control the temperature. The crude oilsamples were emulsied at 40 C and 60 C with an UltraTurrax T18 basic rotor-stator homogenizer (IKA; Staufen,Germany) at 24000 rpm for 2 minutes. The emulsionsamples were then injected into the cell. An increasing elec-tric eld magnitude was applied over the emulsion (startingfrom 0 V). Practical considerations (low voltage powersupply because of safety issues, 0100V) limited the eld

strength in the test to 4.0kV =cm. The current that passedthrough the sample was continuously measured. The criti-cal electric eld (CEF) was dened as the electric eldnecessary to achieve a sudden increase in the currentthrough the emulsion, caused by a short circuiting of theeld. Several parallels were performed for each sample toensure reproducible results.

3.3. Destabilization of Emulsions in an ACElectrical Field

Model oil emulsions with different volume fraction of water were studied to highlight the behavior of extremely

viscous emulsions. The setup consisted of a frequency gen-erator (1.8 kHz), and an amplier providing 1.5 kV =cm ACacross two curved, rectangular electrodes. A glass bottletube (100 ml) with the emulsion was placed between thetwo electrodes and served as electrical insulation from theelectrodes. The setup was presented schematically by Lesset al.[33]

FIG. 1. The gure shows the critical electric eld cell. Two brasselectrodes are connected to a power supply (DC) and an ampere meter.


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The practical importance of electrophoresis is dependingon the relaxation time of the charged droplet after being incontact with a noninsulated electrode. The charge will leakto the surrounding medium with a relaxation time s (e0=r 0).[26] The crude oil matrix studied here has an averageconductivity ( r ) of 3.7 10 8 S=m (variance 7.8 10 16)at 40 C and a dielectric constant ( e) of 2.52 (variance 0.06). This corresponds to a relaxation time constant of about 6.0 10 4 seconds. The charged droplets will quicklyloose their charge. It seems reasonable to assume that dipoleattraction and dielectrophoresis is the dominating mech-anism of electrocoalescence in the critical electric eld cell,even though the experimental setup has the potential forelectrophoretic forces also.

4.2. Viscous Responses The Effect of Increasing dE 0 /dt

The effect of an electric eld and the rate of which theeld magnitude was increased ( dE 0=dt) has been investi-gated. Previously, the motivation for applying a constantlyincreasing electric eld was to identify what was assumedto be a critical electric eld for droplet-droplet lm ruptureand coalescence. Consequently, the experimental methodgot its name: the E-critical, or the Ecrit method. [17,31]

Moreover, by applying a constantly increasing electriceld, a large range of crude oils could be covered in oneanalysis.

Hannisdal et al. [22] presented results for the 30 crude oilsused in the current study, versus the step rate of the electriceld (dE 0=dt). The data has been presented in Figure 4. Theraw data is presented in Appendix 1. Each point repre-sented 25 measurements of the same emulsion, with a

variance in the 00.25 kV =cm range (greatest for the moststable emulsions). The droplet size distributions of theemulsions were similar (mean size 6.2 2.2 mm). Emul-sions of heavy crude oils were generally more stable thanemulsions of lighter crude oils. Some viscous emulsionscould not be destabilized at all, and were assigned themaximum CEF value: 4.0 kV =cm. Moreover, the CEFvalues increased progressively with increasing eld ratewhich pointed in the direction of a viscous contribution

to the observed response parameter. The continuous phaseprovided a hydrodynamic resistance to droplet motionthrough its viscosity. Thus, with increasing eld rate, dro-plets were given less time to respond to the electric eldand the stability of the emulsion appeared to be greater.The relative contribution from the coalescence step wasat its maximum for experiments at low eld rates, whereasthe relative contribution from the occulation step domi-nated for experiments performed with high dE 0=dt.

The results clearly show how the viscosity of the oilphase affects the measured response parameter, the emul-sion stability, both for different crude oils and for crudeoils analyzed differently. The CEF value is highly depen-dent on how it is measured and will usually have a signi-cant contribution from viscous effects. This is important toremember when trying to explain emulsion stability byother physicochemical properties of the system, as wasdone previously. [18,32] The multivariate analysis can beweakened by the strong covariance between the responseparameter (CEF), the viscosity, and other properties of the crude oil.

FIG. 4. Electrocoalescence of 30 water-in-crude oil emulsions(/ w 0.3 vol=vol) with a background DC eld. The ordinate axis repre-sents the maximum electric eld magnitude without short circuiting(CEF) as a function of the rate by which the electrical eld magnitudewas increased. The samples that are assigned the maximum eld magni-tude (4 kV =cm) could not be destabilized. (Printed with permission fromHannisdal et al. [22])

FIG. 3. Viscosity as a function of time and corresponding voltageapplication for emulsions ( / w 0.3) in low shear rate (6 s 1) and highshear rate (500 s 1) experiments. Printed with permission from Lesset al. [20] .


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Hannisdal et al. [22] modeled the droplet transportprocess in an electric eld with a simple model, previouslypresented by Atten. [23] The hydrodynamic resistance todroplet motion was explained by Stokes law, whereas thepoint-dipole approximation accounted for electric forcesacting on spherical droplets at large drop separations (s =r >> 1) lying on similar eld line. By also assuming a mono-disperse emulsion and an initial repartition of the drops onthe vertices of a cubic lattice, the characteristic time fordroplet approach was modelled as:

s theo 8g15eE 20

p6/ w

5=3

1" #: 4:1With the viscosity ( g), the permittivity ( e0) of the continu-ous phase, and the water cut ( / w). By taking into accountthat the electric eld magnitude was increased linearly withtime at a rate, dE 0=dt, the characteristic time of dropletapproach could be expressed as:

s theo 8g

5e 1=3 dE 0

dt 2=3 p

6/ w 5=3

1" #1=3

: 4:2

The theoretical time of droplet approach was comparedto the experimental time, sexp , which followed directly fromthe experimental CEF value and the eld rate, dE 0=dt.Although very simplied, this approximation could capturethe most underlying effects, the drag on droplets(point-dipoles) in an electric eld. Hannisdal et al. [22] ident-ied a clear dependency between stheo and sexp for the 30different crude oils. Figure 5 shows the experimental versus

theoretical time for experiments with a rate, dE 0=dt 0.004 kV=cm s 1. Hannisdal et al. showed that theexperimental times, sexp , were approximately 10 timesgreater than the theoretical times, stheo , as indicated bythe broken line. The discrepancy between theoretical andexperimental times was discussed and it was showed thatalso surfactant-free emulsions had characteristic timesmuch greater than expected from Equation (4.2). There-fore, the large experimental times could not be explainedby a signicant contribution from a barrier to the coalesc-ence step as may be anticipated from classical lm stabili-zation mechanisms in petroleum emulsions. In fact, avery low electric eld magnitude was sufcient to destabi-lize the w=o interface. The time to break the emulsion of crude oil no. 6 (goil 2269cP, 40 C) at constant electriceld (0.44.0kV=cm) magnitude (Figure 6) followedexactly the same trend as experiments performed atincreasing eld strength (Figure 5). The characteristic timewas underestimated by a factor of 10.

With new experience, we can conrm that the conclu-sions by Hannisdal and et al. [22] were correct. For this

specic crude oil matrix, the underestimation of thecharacteristic time is generally not a result of a barrier tocoalescence (thermodynamically stable), but a result of reduced droplet transport. One may thus argue whetheror not critical electric eld is the proper name for the analy-sis as this name gives expectations about a threshold eld

FIG. 5. The characteristic time of destabilization ( sexp ) of emulsions(/ w 0.3, T 40 C) in the DC eld is compared to the theoretical ( s theo )

value of droplet approach as predicted from equation (4.2). The experi-mental time was given by the measured CEF value and dE o=dt(0.004 kV=cm s 1). (Printed with permission from Hannisdal et al. [22])

FIG. 6. The experimental and theoretical times for emulsion no. 6under the inuence of a constant background eld with magnitude from0.4 to 4.0kV=cm. The theoretical time is calculated from Equation (4.2).(Printed with permission from Hannisdal et al. [22])


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strength for achieving separation, which is not always thecase. For reasonably low viscous crude oil emulsions, thediscrepancy between experimental and theoretical valuescan be solved simply by dening a factor b s theo =sexp .In Figure 5, b is equal to 10. If b mainly is a result of thespecic experimental setup or the electrocoalescergeometry, this opens up for huge possibilities when itcomes to predicting the performance of real processes fromlaboratory experiments. Even though it has been proposedthat b is mainly dependent on the geometry of the test celland droplet transport phenomena, it should still be poss-ible to identify crude oil emulsions with signicant barrierto the coalescence step, for example because of rigid dro-plets or particle-stabilized interfaces. These would appearon the left side of the broken line in Figure 5. In fact, someof the crude oils that are known to have nonstabilizedasphaltenes actually appear on the left side in Figure 5.When identied as a problematic emulsion, an optimizeddemulsier or inhibitor may bring the emulsion back tothe state where bulk properties dominate the overall emul-

sion stability. Beetge and Horne[24]

have done importantwork on understanding the relative contribution from theocculation and the coalescence in CEF experiments.

Still, as apparent from the Figure 5 some of the mostviscous emulsions did not follow the same trend as theremaining samples. These water-in-heavy oil emulsionswere destabilized sooner than expected from the behaviorof the remaining samples. Possible reasons were discussedin detail by Hannisdal et al. [22] Among these, different elec-trochemistry for crude oils was mentioned as a factor thatwas not taken into account. Recent studies have concludedthat difference in crude oil permittivity in Equation (4.1) or(4.2) cannot explain the behavior of the data set. The cor-

relation between experimental and theoretical character-istic time of droplet approach for heavy oils would notimprove dramatically by allowing permittivity to varybetween different crude oils. The variance is too low(5.3%). However, it should be mentioned that Equation(4.1) and (4.2) assumes perfect dielectric properties of thecrude oil, which is not the case. The conductivity of thecrude oils may differ signicantly, especially at high tem-peratures where the mobility of charge carriers in heavycrude oils is high. [3436] The conductivity of heavy crudeoils may be several orders of magnitude greater than lightcrude oils.

4.3. Viscous Responses The Effect of Increasing Temperature

The previous section highlighted the important viscouscontribution to droplet reorganization in electric elds,and how this also inuenced the measured maximum eldstrength in the critical electric eld cell. Since Equation(4.2) has already been tested for crude oils with differentviscosities, it was natural to change the temperature of

the same crude oil emulsions to produce different crudeoil viscosities. 14 of the crude oils in the data set were ana-lyzed with respect to emulsion stability (CEF) at 60 C.Figure 7 shows the maximum electric eld magnitude with-out short circuiting (CEF) versus the rate that the electriceld magnitude was increased for four water-in-crude oilemulsions (oil no. 8, 12, 18, and 20) ( / w 0.3) at 40 Cand 60 C. Generally, the 60 C results followed the sametrend with respect to increasing eld rate ( dE 0=dt ) as the40 C results. This conrmed that the trends observed wereviscous responses caused by the viscosity of the oil phase.

The absolute difference in CEF between 40 C and 60 Ctests increased progressively with the magnitude of theCEF. Figure 8 shows the experimental time of destabiliza-tion for emulsions at 40 C and 60 C at a single eld rate(0.008kV=cm s 1). Even though some results deviatedslightly from the trend, the relative difference in CEFbetween 40 and 60 C tests was constant for these 14 crudeoil emulsions (sexp (60)=sexp (40) 0.68).

According to Equation (4.2), when holding / w and econstant, the temperature increase should reduce the timefor droplet approach by a scaling factor [ g(60)=g(40)]1=3,where g(60) is the crude oil viscosity at 60 C. The crude oilshad already been analyzed with respect to viscosity at dif-ferent temperatures (Appendix 1). To get an impressionabout what to expect from experimentally measured times,the viscosity scaling factor [ g(60)=g(40)]1=3 was plotted withreference to the viscosity at 40 C in Figure 9 (opensquares). The plot clearly indicated that the relative differ-ence in time between 40 C and 60 C, stheo (60)=s theo (40),changed with increasing viscosity of the oil phase. Theobservation was a result of the characteristics of crude oil

FIG. 7. The gure shows the maximum electric eld magnitude with-out short circuiting (CEF) versus the rate that the electric eld magnitudewas increased for 4 water-in-crude oil emulsions (oil no. 8, 12, 18, and 20)(/ w 0.3) at 40 C and 60 C.


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viscosity and its temperature dependence. Still, the obser-vation was in contrast to Figure 8 where sexp (60)=sexp (40)was more or less constant. Additionally, Hemmingsenet al.[21] realized that the experimental CEF for 27 crudeoil emulsions ( / w 0.3) at different temperatures ( T 4 Cto 80 C) followed a linear relationship between CEF andthe logarithmic viscosity. Based on the observations madeby Hemmingsen et al., Equation (4.2) was modied with

a new term to take the inuence of viscosity for very heavycrude oils into account.

s theo ln g 85e

1=3 dE 0dt

2=3 p6/ w

5=3

1" #1=3

: 4:3

By allowing the theoretical time of droplet approach todepend on the logarithmic viscosity (in Pas), the viscosityterm in Equation (4.3) will respond differently than theterm in Equation (4.2), especially for very heavy oils withhigh viscosity. The scaling factor ln[( g(60)]=ln[g(40)] wasplotted in Figure 9 with reference to the viscosity at 40 C(lled squares). The new scaling factor was constant at highviscosities, but was more sensitive for viscosities less than10 cP. Figure 10 shows the comparison between experi-mental and theoretical time (Equation (4.3)) of destabiliza-tion for the results presented by Hemmingsen et al. [21] Theresults include 93 data points from experiments where

the step rate of the electric eld was 0.002 kV =cm s1

.The theoretical time ( s theo ) based on Equation (4.3) wasclearly very similar to the experimentally determined timeof destabilization, sexp . In addition, the least stable crudeoils separated faster than expected, probably because of gravitational separation and coalescence before the testwas started. Finally, the results from the experiments inFigure 4 were compared to the new time estimated fromEquation (4.3). The comparison is presented in Figure 11

FIG. 10. The characteristic time of destabilization ( sexp ) of emulsions(/ w 0.3, T 480 C) in the DC eld is compared to the theoretical(s theo ) value of droplet approach as predicted from Equation (4.3). Theexperimental time was given by the measured CEF value and dE o=dt(0.002 kV=cm s 1).

FIG. 8. Comparison between the experimental time of destabilizationfor emulsions at 40 C and 60 C. The times were calculated directly from

the eld rate (0.008kV =cm s1

) and the CEF values (kV =cm).

FIG. 9. Scaling factors to take viscosity for different crude oils at dif-ferent temperatures into account when predicting the time for dropletapproach according to Equations (4.2) and (4.3). The symbol: g(40) meansthe Newtonian viscosity in cP (or mPas) at 40 C.


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for experiments at dE 0=dt 0.004 kV=cm s 1. Experimentswith different dE 0=dt gave the same slope between thetheoretical and experimental time. This indicated that themagnitude of the electrical eld was correctly accountedfor in Equation (4.3) and (4.2). The logarithmic viscosityterm in the semi-empirical model (Equation (4.3)) clearlyexplained the data much better than Equation (4.2)(Figure 5). For light crude oils, Equation (4.2) could safelybe used. However, for viscous samples, this model wouldfail. Further work should focus on explaining why the log-arithmic function is a good solution for explaining theinuence of high crude oil viscosities. Factors likethe mechanical lm thinning process, the invalidity of thedipole approximation as the inter-droplet distance reduces,and other phenomena should be considered.

4.4. Viscous Responses The Effect of Increasing theWater Cut

Previous results presented by Hemmingsen et al. [21]

showed that the CEF value was increased for emulsionswith lower volume of water droplets ( / w 0.1, 0.2, and0.3). Aske et al.[18,32] came to the same conclusions whenstudying emulsions with water volume fraction / w 0.2and 0.3. At lower water volume fraction, the distancebetween droplets in the emulsion increased and the dropletshad to move longer distances in order to form linear chainsbetween the two electrodes. This is according to theory(Equations (4.2) and (4.3)) a predicts longer characteristictime of droplet approach for lower water volume fractions.

The droplet approach is assumed to be due to dipole-dipoleforces even though the experimental setup allows forelectrophoresis also. Therefore, as the water content isreduced along the electrocoalescer in a commercial process,because of the ongoing separation or just because theemulsion to be treated has low water content, the spacingbetween the droplets is large and the dipolar attractionbecomes less and less effective.

Beetge and Horne [24] investigated the stability of emul-sions with different water cut in a critical electric eld cellwith alternating current (340Hz) and a step rate dE 0 =dt (150V=s)=(0.150 cm) 0.94 kV=cm s 1. They observed verystrong dependency between the recorded CEF value andthe water cut, and CEF values as high as 12 kV =cm forlow amounts of water. The trend was correctly explainedby a occulation controlled mechanism of destabilization.This is exactly in agreement with the topic of the currentpaper: Viscous responses to electrical elds. The steprate used by Beetge and Horne was several orders of mag-nitude greater than the step rate used in this and other

studies[18,21,22]

and must result in increasingly delayedresponses and high CEF values for low water cut, as forhigh viscosity of the oil. It was proposed that the CEFshould be inversely proportional to the amount of waterin the emulsion ( / w). Since Equations (4.2) and (4.3) statethat the CEF value (CEF sheo dE 0 =dt ) is proportional to[(p=6/ w)5=3-1]1=3, not 1=/ w , the two expressions have beencompared by using results from Beetge and Horne. TheCEF results were plotted as a function of X 1=/ w accord-ing to Beetge and Horne, and X [(p=6/ w)5=3-1]1=3 accord-ing to expressions by Atten. [23] The plot is presented inFigure 12 for experiments in the range from 120 F to

FIG. 11. The characteristic time of destabilization ( sexp ) of emulsions(/ w 0.3, T 40 C) in the DC eld is compared to the theoretical ( s theo )

value of droplet approach as predicted from equation (4.3). The experi-mental time was given by the measured CEF value and dE o=dt(0.004 kV=cm s 1).

FIG. 12. Critical electric eld for experiments performed at differenttemperatures (120 F to 180 o F). [24] The same data are plotted as a functionof X 1=/ w according to Beetge [24] and X [(p=6/ w)5=3 1]1=3 accordingto expressions by Atten. [23]


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180o F. To correctly explain the effect of increasing amountof water in the emulsion, the data series should be linear.The different position on the horizontal axis is not of importance. Both expressions seem to predict the increasein critical electric eld value relatively well. By looking atthe two expressions, Beetge and Horne clearly predictlarger CEF values at low amount of water than Atten.For this reason, the dotted lines curve slightly for thisparticular raw data. However, in the practical range of water cut (150%), both expressions will perform well.

Finally, we will highlight a phenomenon that relates toemulsions with large volume fraction of water and conse-quently high emulsion viscosity. Equation (4.1) through(4.3) only account for the viscosity of the continuous oilphase. However, for high water cut emulsions with smalldroplets, the viscosity of the emulsion may be so high thatit reduces the rate of droplet transport processes. Figure 13shows the viscosity of model oil emulsions with varyingwater volume fraction in the range from 0.3 to 0.7. Asexpected, the emulsions had shear-thinning behavior and

showed a signicant increase in emulsion viscosity withincreasing number of droplets. The droplet size wasconstant for all emulsions with a lognormal distributionin the range from 1 to 45 mm (all samples were made fromthe same / w 0.7 emulsion). The emulsions did not separ-ate any free water by gravity during two weeks. The sameemulsions (100ml) were destabilized in AC electric elds(1.8 kHz) between two insulated electrodes. The setupwas explained in the experimental section. Several experi-ments were performed by varying the water volumefraction, the time in the electrical eld and the magnitude

of the electric eld. From these experiments, it was possibleto determine the experimental time corresponding to thephase separation of 90% of the emulsied water at a eldstrength of, for example, 1.5 kV =cm. Figure 14 shows theexperimental time of destabilization for emulsions withdifferent volume fraction of water. As predicted by theory,the efciency of separation was increased dramatically by

increasing the volume fraction of water up to 0.1. However,with further increase of / w , the efciency of separationdecreased signicantly (longer time to achieve separation).We can only explain the phenomenon by the signicantincrease in emulsion viscosity that will also impact themobility of droplets. One could argue if the viscosity termin Equations 4.1 through 4.3 should account for emulsionviscosity instead of the continuous phase viscosity. How-ever, due to the non-Newtonian character of emulsions, itis difcult to dene the proper shear rate (see Figure 13).The water cut, the droplet size, and the level of turbulencewill change as droplets coalesce and separate.

Sorbitan monooleate was used to stabilize the waterdroplets (1vol%, which is far above the critical micelle con-centration of the surfactant). The self-aggregation of thesurfactant molecules produced much greater relative emul-sion viscosities than what can be expected for petroleumemulsions. However, the same phenomenon has also beenobserved for real crude oil emulsions, even though to asmaller extent. The experimental setup had insulated elec-trodes and a constant magnitude of the imposed electrical

FIG. 13. Viscosity of model oil emulsions (aliphatic hydrocarbon with1 vol% sorbitan monooleate and viscosity 1.8 mPas, 3.5 wt% NaCl water,droplet size 145 mm).

FIG. 14. Time necessary to separate 90% of the water from 100mlmodel oil emulsions (aliphatic hydrocarbon with 1 vol% sorbitan mono-

oleate, 3.5 wt% NaCl water, droplet size 145 mm). The characteristicsof the electrical eld were: AC 1.8kHz, 1.5 kV =cm. The triangles showthe experimental results whereas the full line shows the last term of Equa-tion (4.2): constant x [( p=6/ w)5=3 1]1=3.


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eld (1.5kV=cm). Still, it cannot be excluded that thedielectric properties of the emulsion may have some impacton the eld distribution and the magnitude of electricforces.

5. CONCLUSIONS

The stability of heavy crude oil emulsions were studiedin a parallel-plate DC laboratory coalescer. Particularly,viscous responses and their inuence on the emulsion stab-ility measurements were investigated. In addition to high-lighting previous results from the same experimentalsetup and discussing these based on recent experience,new results were presented. These included experimentsat different temperatures and volume fractions of water(/ w). A new semi-empirical model for the characteristictime of the destabilization process was presented.

s theo ln g 8

5e 1=3 dE 0

dt 2=3 p

6/ w 5=3

1

" #1=3

:

The new model clearly performed much better than theprevious model, especially for very viscous crude oils. Thelogarithmic viscosity ( g) of the continuous phase success-fully predicted the behavior of 30 heavy crude oil emulsionsin DC electric elds. The magnitude of the electric eld wasconstantly increased with a step rate dE 0 =dt until destabili-zation occurred. The relative contribution from thecoalescence step was at its maximum for experiments atlow eld rates, whereas the relative contribution from theocculation step dominated for experiments performedfor high dE 0 =dt. Experimental results at different step ratesconrmed that the term ( dE 0=dt ) 2=3 properly explainedthe magnitude of the electric eld in the destabilizationprocess.

Studies of the performance of industrial electrocoales-cers (still yet to be published) have showed that simpleelectrostatic theory can potentially explain complex separ-ation phenomena when the resistance to the coalescencestep is reduced by an efcient demulsier. The ultimategoal is to build a model for both the laboratory setupand the industrial coalescer so that laboratory experi-ments can be used to predict the behavior of the industrialprocess.

REFERENCES[1] Speicker, P.M. and Kilpatrick, P.K. (2004) Langmuir , 20:

40224032.[2] Horvath-Szabo , G., Masliyah, J.H., Elliott, J.A.W.,

Yarranton, H.W., and Czarnecki, J. (2005) J. Colloid Interface Sci. , 283: 517.

[3] Freer, E.M. and Radke, C.J. (2004) J. Adhesion , 80:481496.

[4] Wang, Y., Zhang, L., Sun, T., Zhao, S., and Yu, J. (2004)J. Colloid Interface Sci. , 270: 163170.

[5] Goual, L., Horvath-Szabo , G., Masliyah, H., and Xu, Z.H.(2005) Langmuir , 21: 82788289.

[6] Mohammed, R.A., Luckham, P.F., and Taylor, S.E. (1994)Colloids Surf. A , 83: 261271.

[7] Lissant, K.J. (1983) Demulsication: Industrial Application,Surfactant; Science Series, 13. New York: Marcel Dekker.[8] Sun, D., Duan, X.D., and Zhou, D. (1999) Colloids Surf. A ,

150: 6975.[9] Goto, M., Kondo, K., and Nakashio, F. (1989) J. Chem.

Eng. Jpn. , 22 (4): 401406.[10] Mohammed, R.A., Luckham, P.F., Taylor, S.E. (1993)

Colloids Surf. A , 80: 223235.[11] Cottrell, F.G. (1911) Separating and collecting particles of

one liquid suspended in another liquid, US Patent 987.[12] Cottrell, F.G. (1911) Process for separating and collecting

particles of one liquid suspended in another liquid, US Patent98, 421 Edition.

[13] Bailes, P.J. (1984) Chem. Eng. , 62: 3338.

[14] Eow, J.S. and Ghadiri, M. (2002) Chem. Eng. , 85: 357368.[15] www.aibel.com; Accessed September 30, 2010.[16] www.akersolutions.com; Accessed September 30, 2010.[17] Kilpatrick, P.K. and Speicker, P.M. (2001) In Encyclopedic

Handbook of Emulsion Technology , edited by J. Sjo blom;New York: Marcel Dekker.

[18] Aske, N., Kallevik, H., and Sjo blom, J. (2002) J. Petrol. Sci.Eng. , 36: 117.

[19] Chiesa, M., Melheim, J.A., Hemmingsen, P.V., Hansen,E.B., and Hestad, . (2006) Sep. Purif. Technol. , 50: 267277.

[20] Less, S., Hannisdal, A., and Sjo blom, J. (2008) J. DispersionSci. Technol. , 29: 106114.

[21] Hemmingsen, P.V., Silset, A., Hannisdal, A., and Sjo blom, J.J. Dispersion Sci. Technol. , 26: 615.

[22] Hannisdal, A., Hemmingsen, P.V., Silset, A., and Sjoblom, J.(2007) J. Dispersion Sci. Technol. , 28 (4): 639652.

[23] Atten, P. (1993) J. Electrostatics , 30: 259270.[24] Beetge, J.H. and Horne, B.O. (2005) Chemical Demulsier

Development Based on Critical Electric Field Measurements,SPE 93325.

[25] Less, S. (2008) Ph.D. thesis, Norwegian University of Scienceand Technology, Trondheim, Norway.

[26] Lundgaard, L.E., Ingebrigtsen, S., and Atten, P. (2005) InEmulsion and Emulsion Stability ; 2nd ed. , edited by J.Sjo blom; New York: Taylor and Francis, chap. 15, 549592.

[27] Eow, J.S., Sharif, A.O., and Williams, T.J. (2001) Chem.Eng. , 84: 173192.

[28] Devulapalli, R. and Jones, F. (1999) J. Haz. Mater. , 70:

157170.[29] Urdahl, O., Wayth, N.J., Frdedal, H., Williams, T.J., and

Bailey, A.G. (2001) In Encyclopedia Handbook of EmulsionTechnology , edited by J. Sio blom; New York: MarcelDekker, chap. 28, 679694.

[30] Warren, K.W. and Sams, G.W. (2003) The Roles of Chemical Screening and Electrostatic Field Selection in Desalting;Houston, TX: NATCO Group, Inc.


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A P P E N D I X 1

C r u d e o i l c h a r a c t e r i s t i c s a n d r a w d a t a f r o m C E F e x p e r i m e n t s

C h e m i c a l c o m p o s i t i o n a

B u l k p r o p e r t i e s

I n t e r f a c i a l p r o p e r t i e s b

C E F a t 4 0

C m e a s u r e d

w i t h d i f f e r e n t d E

0 = d t

O i l

S a t u r a t e s

w t %

A r o m a t i c s

w t %

R e s i n s

w t %

A s p h .

w t %

T A N m g

K O H = g

M W

g = m o l

D e n s i t y 4 0

C

( g = c m

3 )

V i s c o s i t y

4 0 C ( c P )

V i s c o s i t y

6 0

C ( c P )

I F T

6 0

C m

N = m

E 6 0 C

m N = m

0 . 0 0 2 k V =

c m s

1

k V = c m

0 . 0 0 4 k V =

c m s

1

k V = c m

0 . 0 0 8 k V =

c m s

1

k V = c m

0 . 0 2 k V =

c m s

1

k V = c m

0 . 0 4 k V =

c m s

1

k V = c m

1

3 3 . 1

4 6 . 0

1 8 . 8

1 . 2

4 . 2

3 6 8

0 . 9 5

2 7 6

8 0

1 0 . 4

1 9

1 . 4

1 . 7

1 . 9

2 . 3

2 . 8

2

4 3 . 5

4 1 . 1

1 2 . 6

1 . 9

0 . 6

2 7 8

0 . 8 8

1 8

9

1 8 . 3

1 7

0 . 7

0 . 9

1 . 2

1 . 5

1 . 6

3

3 0 . 6

4 3 . 3

2 0 . 9

5 . 0

1 . 3

3 4 3

0 . 9 3

1 1 8

4 3

2 1 . 3

7

2 . 2

2 . 5

2 . 8

3 . 4

3 . 9

4

3 5 . 2

3 0 . 1

2 2 . 1

3 . 1

2 . 3

5 3 6

0 . 9 5

2 2 8 6

5 1 5

1 6 . 9

8

2 . 8

3 . 0

3 . 3

4 . 0

4 . 0

5

5 2 . 2

3 6 . 0

1 0 . 4

1 . 2

0 . 0

2 4 6

0 . 8 5

9

4

1 2 . 0

1 8

0 . 3

0 . 5

0 . 5

0 . 6

0 . 6

6

2 6 . 0

3 8 . 0

2 0 . 5

2 . 8

7 . 5

4 2 9

0 . 9 8

2 2 6 9

4 6 4

1 0 . 2

2 0

2 . 7

3 . 3

3 . 5

4 . 0

4 . 0

7

4 6 . 6

3 7 . 6

1 4 . 0

1 . 7

1 . 4

3 0 9

0 . 9 0

3 6

1 7

1 7 . 4

1 0

0 . 8

1 . 0

1 . 4

1 . 8

2 . 1

8

3 2 . 8

3 7 . 2

1 6 . 8

1 2 . 9

1 . 1

4 7 3

0 . 9 6

5 4 1 8

1 0 3 1

1 8 . 8

6

3 . 9

4 . 0

4 . 0

4 . 0

4 . 0

9

5 1 . 3

3 7 . 5

9 . 8

1 . 2

0 . 0

2 6 8

0 . 8 6

1 3

6

1 7 . 9

1 4

0 . 6

1 . 2

1 . 5

1 . 9

2 . 1

1 0

4 7 . 5

4 0 . 1

1 1 . 5

0 . 8

2 . 9

3 1 9

0 . 9 1

4 9

2 0

1 1 . 1

1 2

0 . 8

1 . 2

1 . 4

1 . 7

1 . 9

1 1

5 2 . 3

3 9 . 4

7 . 2

0 . 6

2 . 9

2 4 2

0 . 8 7

1 1

5

1 4 . 9

1 2

0 . 3

0 . 4

0 . 5

0 . 5

0 . 8

1 2

3 6 . 5

4 7 . 4

1 1 . 6

3 . 9

0 . 4

3 3 8

0 . 9 3

1 0 9

4 0

1 3 . 4

7

0 . 8

0 . 9

1 . 2

1 . 7

2 . 0

1 3

3 2 . 8

3 3 . 2

2 8 . 5

4 . 3

5 . 2

5 2 7

0 . 9 8

2 3 3 9 7

2 8 8 0

1 0 . 7

1 2

4 . 0

4 . 0

4 . 0

4 . 0

4 . 0

1 4

5 7 . 3

3 3 . 4

8 . 2

1 . 0

0 . 4

2 6 3

0 . 8 7

1 3

7

1 5 . 3

1 8

0 . 0

n . a .

0 . 4

0 . 5

0 . 6

1 5

3 5 . 8

4 1 . 3

1 8 . 2

4 . 6

3 . 4

4 3 6

0 . 9 4

5 0 5

1 5 1

1 7 . 2

7

2 . 1

2 . 9

3 . 7

4 . 0

4 . 0

1 6

3 8 . 2

4 3 . 6

1 4 . 1

3 . 8

0 . 6

3 3 5

0 . 9 2

8 1

3 3

1 4 . 0

7

0 . 8

0 . 9

1 . 0

1 . 4

1 . 7

1 7

5 1 . 5

4 1 . 3

7 . 0

0 . 2

1 . 8

2 6 8

0 . 8 9

1 6

8

1 1 . 4

2 5

0 . 7

0 . 9

1 . 2

1 . 4

1 . 7

1 8

2 6 . 2

4 1 . 5

2 1 . 9

1 0 . 2

3 . 7

4 3 5

0 . 9 7

2 4 9 7

5 2 8

1 1 . 0

7

1 . 9

2 . 4

2 . 8

3 . 3

4 . 0

1 9

5 7 . 2

3 4 . 0

8 . 1

0 . 2

0 . 2

2 3 5

0 . 8 5

8

3

1 6 . 1

1 1

0 . 2

0 . 5

0 . 6

0 . 7

0 . 9

2 0

2 5 . 9

5 3 . 1

1 1 . 5

5 . 4

0 . 0

2 9 5

0 . 9 1

3 3

1 4

1 6 . 2

1 9

1 . 4

1 . 6

1 . 9

2 . 5

3 . 0

2 1

4 2 . 9

4 2 . 1

1 3 . 9

0 . 6

2 . 5

3 7 4

0 . 9 2

1 3 8

4 8

1 2 . 4

2 3

1 . 1

1 . 3

1 . 4

1 . 8

2 . 1

2 2

4 0 . 3

4 1 . 0

1 5 . 6

2 . 8

1 . 7

3 4 5

0 . 9 2

1 0 4

4 0

1 7 . 8

9

1 . 7

1 . 9

2 . 1

2 . 4

3 . 0

2 3

5 7 . 9

3 4 . 8

6 . 7

0 . 2

0 . 7

2 4 7

0 . 8 7

1 1

6

8 . 3

1 7

0 . 1

0 . 1

0 . 1

0 . 2

0 . 3

2 4

5 6 . 1

3 7 . 6

6 . 2

0 . 1

0 . 9

2 2 7

0 . 8 8

1 2

6

1 0 . 9

3 2

0 . 2

0 . 2

0 . 3

0 . 4

0 . 4

2 5

4 3 . 8

3 8 . 4

1 5 . 0

2 . 3

2 . 2

3 3 4

0 . 9 2

8 2

3 1

1 6 . 5

1 6

1 . 1

1 . 4

1 . 9

2 . 3

2 . 4

2 6

6 3 . 7

2 8 . 6

6 . 3

0 . 3

0 . 5

2 0 4

0 . 8 4

5

2

1 2 . 9

1 7

0 . 6

0 . 7

0 . 8

0 . 9

0 . 9

2 7

3 9 . 0

3 9 . 2

1 8 . 4

3 . 4

2 . 5

3 6 6

0 . 9 4

2 2 5

7 2

1 4 . 4

1 4

1 . 4

1 . 7

2 . 1

2 . 4

2 . 9

2 8

4 1 . 2

4 5 . 0

1 0 . 6

2 . 2

0 . 0

3 3 1

0 . 9 0

3 6

1 6

2 3 . 9

1 4

1 . 2

1 . 7

2 . 3

3 . 0

3 . 5

2 9

3 9 . 9

3 9 . 7

1 4 . 3

6 . 2

0 . 8

3 4 5

0 . 9 0

6 9

2 9

2 3 . 2

1 5

2 . 1

2 . 4

2 . 9

3 . 5

3 . 9

3 0

5 8 . 4

3 0 . 7

7 . 6

3 . 3

1 . 9

2 7 0

0 . 8 6

1 0

5

5 . 1

1 5

1 . 6

1 . 8

2 . 2

2 . 4

2 . 8

a A n a l y t i c a l m e t h o d e x p l a i n e d b y H a n n i s d a l e t a l . [ 2

2 ]

b E q u i l i b r i u m i n t e r f a c i a l t e n s i o n a n d e l a s t i c m o d u l u s E . A n a l y t i c a l m e t h o d i s e x p l a i n e d b y H a n n i s d a l e t a l . [ 3

7 ]

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