ice o

, G

ranspg, Be

Received 12 July 2005; received in revised form 8 April 2006; accepted 24 April 2006

been done on the rheological characterization of heavy oil/water and wax oil/water emulsions, canexhibit non-Newtonian behavior at low or moderatevolume fraction of dispersed phase, therefore some

Journal of Petroleum Science and Engine1. Introduction

Transportation of unprocessed or partly processedmixtures of oil and water is becoming more and morecommon in oil field developments, particularly in newoffshore oil fields. Prediction of the viscosity of oil/water emulsions is an important task for oil fielddevelopment and petroleum transportation (Johnsenand Rnningsen, 2003). A vast amount of research has

emulsions. However, most of them are based on lightoil and tap water, and these kinds of emulsions arealways Newtonian fluid and will exhibit some non-Newtonian behavior only if the volume fraction ofdispersed phase is very high and nearby the inversionpoint. So, most of the emulsion viscosity predictionmodels and correlations are related with volumefraction of dispersed phase only. Yet recently, it isunderstood that crude oil/water emulsions, particularlyAbstract

A new viscosity model for predicting non-Newtonian emulsions is proposed. Empirical and theoretical relationships aredeveloped to describe the apparent viscosity vs. water cut behavior of the water-in-crude oil emulsions. Based on Pal and Rhodesmodel [Pal, R., Rhodes, E., 1989. Viscosity/concentration relationships for emulsions. J. Rheol. 33 (7), 10211045] andexperimental data, an improved Pal and Rhodes model including the effective water cut theory and the relationship between non-Newtonian behavior and water cut is developed. In the new model, the effective water cut factor Ke has been divided into twofactors, Ke() and Ke(), to express the influence of the shear rate and the water cut on viscosity, respectively; and the factor Ke()is found to be power function of water cut. The proposed model can predict relative (apparent) viscosity of water-in-crude oilemulsions over the range of the maximum and minimum water cut. Validated with experimental data, 7 (1 heavy oil and 6 waxyoils) sets of water-in-crude oil emulsions in different water cut and shear rate, the result shows that the average deviation ofimproved model (8.9%) is smaller than the original model (27.1%). 2006 Elsevier B.V. All rights reserved.

Keywords: Crude oil; Emulsion; Non-Newtonian; Apparent viscosity; ExperimentApparent viscosity predwater-in-crud

Dou Dan

The Laboratory of Multiphase Flow in Oil & Gas Storage and T18 Fuxue Road, ChangpinCorresponding author. Tel.: +86 10 8973 3510; fax: +86 10 89733804.

E-mail address: doudan@sohu.com (D. Dan).

0920-4105/$ - see front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.petrol.2006.04.003tion of non-Newtonianil emulsions

ong Jing

ortation Engineering, China University of Petroleum (Beijing),ijing, 102249, PR China

ering 53 (2006) 113122www.elsevier.com/locate/petrolresearchers (Rnningsen, 1995; Guerrero et al., 1998;Pal and Rhodes, 1989; Masalova et al., 2003) provide

Sciennew emulsion viscosity prediction model including notonly volume fraction of dispersed phase but also shearrate.

In this paper, 7 sets of crude oil/mineralized wateremulsions with different water cut were prepared, andthe apparent viscosity of emulsions were measured atdifferent shear rate. Based on P&R (Pal and Rhodes,1989) model and experimental data, an improved P&Rmodel including relationship between non-Newtonianbehavior of emulsions and the water cut is developed topredict apparent (relative) viscosity of crude oil/wateremulsions; compared with the experimental data, theimproved P&R model agrees with the experimental databetter.

2. Existing emulsion viscosity prediction models

The viscosity of emulsions (e) is expected to beaffected by the following factors: (Johnsen andRnningsen, 2003; Pal, 1998): volume fraction ofdispersed phase (), viscosity of continuous phase (c),shear rate (), temperature (T), average droplet size (d)and size distribution, viscosity of dispersed phase (d),density of continuous phase (c), density of dispersedphase (d), nature and concentration of emulsifying agentsand presence of solids in addition to dispersed phase.

The affecting factors are numerous and they caninfluence each other. For instance, a reduction oftemperature causes a remarkable increase in theviscosity of continuous phase; different shear ratesprovide different drop size and size distribution;furthermore people cannot explain the exact mechanismof emulsion viscosity. So, it is impossible to include allfactors in one single mechanism model.

A large number of viscosity equations and correla-tions have been proposed in the literatures. First,Einstein (1906) provided a viscosity prediction correla-tion of the dilute suspension system:

ge gc1 2:5/ 1The Einstein equation is valid only at dilute system

and the prediction results is incorrect when volumefraction of dispersed phase is over 2%, and then someexpanded versions of Eq. (1) are also suggested byBecher (1965) and Schramm (1992) to involve interac-tions between the droplets and the concentration rangeof the dispersed phase.

ge gc1 c1/ c2/2 c3/3 22 and 3 represent the interactions between the

114 D. Dan, G. Jing / Journal of Petroleumdroplets, and c1, c2 and c3 are coefficients.Based on Einstein equation similarly, Brinkman(1952) argued that the viscosity of emulsion withspherical surface droplets was given by:

ge gc1 /2:5 3

Eilers (1943) used bitumen emulsions and producedan empirical correlation for Newtonian behavior.

gr 1 1:25/=1 aE/ 2 4where 1.28

ScienSquires (1938) provide a modification form with asystem-dependent parameter A:

lngr A k/ 9After measuring eight different oils, covering a broadspectrum of oil types including a relatively heavy,biodegraded (21 API) oil, waxy oils and light waxy oils(3035 API), Rnningsen (1995) believes that both Aand k in Eq. (9) could be expressed as linear functions oftemperature and then proposed a set of correlations forestimation of relative viscosity of stable water-in-crudeoil emulsions:

lngr k1 k2T k3/ k4T/ 10where k1k4 are the shear rate-dependent coefficients. Itshould be noted that for there is not any system-dependent coefficient in Eq. (10), therefore Rnningsenmodel will give the same results for any oil/wateremulsion and will fail significantly for fluids which arevery different from the experimental oils.

Starting from the Taylor equation (Eq. (5)) and usingthe concept of effective medium, Phan-Thien and Pham(1997) developed another viscosity equation for con-centrated emulsions:

g2=5r2gr 5K2 5K

3=5 1 /1 11

where K is the ratio of dispersed phase viscosity tocontinuous phase viscosity.

K gdgc

12

Pal (2000) finds that the theoretical equation ofPhan-Thien and Pham (1997) under predicts therelative viscosity of concentrated emulsions by alarge amount, and discovers that the original modelsfail to account for the presence of surfactant in thesystem. Combing the Phan-Thien model and theeffective volume hypothesis, Pal (2000) suggests anew equation for predicting the relative viscosity ofconcentrated emulsions:

gr2gr 5K2 5K

3=2 1 K0/5=2 13

where K0 is a factor that takes into account thepresence of adsorbed surfactant on the surface of thedroplets, and it is a constant for a given system butmay vary from one emulsion system to another.

Recently, with the knowledge that the affecting

D. Dan, G. Jing / Journal of Petroleumfactors of emulsion viscosity are numerous and can berelated each other, some researchers try to correlatesome dimensionless numbers for viscosity prediction.

Be related to each other, some researcher (Pal, 1998)tried to take into account the effects of shear rate,average droplet size, droplet size distribution, viscosityof continuous phase, and viscosity of dispersed phase onthe viscosity of emulsions, and proposed the correla-tions with particle Reynolds number (NRe,p), volumefraction of dispersed phase, maximum packing concen-tration of dispersed phase (m) and intrinsic viscosity([]).

For concentrated emulsions:

/1=2m 1 g1=g/mr A0 A1log10NRe;p A2log10NRe;p2 14

For lower concentrations:

/1=2m 1 g1=gr A0 A1log10NRe;p 15where intrinsic viscosity:

g 2:5 K 0:4K 1

16

3. Development of new viscosity prediction model

Water-in-crude oil emulsions can exhibit non-New-tonian behavior in lower water cut (if water is thedispersed phase, water cut means the volume fraction ofwater). But most of the existing viscosity predictionmodels for emulsions are restricted to Newtonianemulsions; only Pal and Rhodes (1989) model andRnningsen (1995) model take account for effects ofshear rate. However Rnningsen (1995) model is anexperiential model and it is hard to suit differentemulsion systems. Thus, the objective of this section isto develop theoretically viscosity equation based on Paland Rhodes (1989) for non-Newtonian emulsions.

First, let us review the concept of effective dispersedphase volume briefly: the true volume of dispersedphase droplets plus some volume of continuous phaseadhesion to dispersed phase droplets. There are twokinds of effects that can make continuous phaseadhesion to dispersed phase droplets. One of them ishydration effect: there are much of emulsifiers existingin a water-in-crude oil emulsion system and due to theattractive forces on the continuous phase molecules byemulsifiers' molecules (adsorbed on the droplet sur-face), a significant amount of the continuous phaseassociates itself with the dispersed phase droplet. The

115ce and Engineering 53 (2006) 113122other is floc effect: the cause of flocculation lies in the

116 D. Dan, G. Jing / Journal of Petroleum Science and Engineering 53 (2006) 113122van der Waals' attractive forces present between theparticles, and when a floc of particles is formed, itimmobilizes a significant amount of the continuousphase within itself. The hydration effect and floc effectcan make the effective volume of dispersed phase of anon-Newtonian emulsion higher than its true volume.Consequently, the viscosity of non-Newtonian emul-sions is higher than those of the Newtonian emulsions atthe same true concentration (Schramm, 1983; Pal andRhodes, 1989).

We assume that the effective volume of dispersedphase Ve is related to the true volume of disperseddroplets V0 as:

Ve KeV0 17where Ke is a system-dependent factor that takes intoaccount the effect of hydration and floc. Ke is a functionof shear rate and true volume fraction of disperse phase.

Ke f g;/ 18

In terms of the volume fraction of disperse phase, Eq.(18) can be written as:

/e Ke/ 19where e is the effective volume fraction and is thetrue volume fraction of dispersed phase.

Let us now consider a concentrated emulsion withthe true volume fraction of dispersed phase . Thisemulsion can be prepared by the following steps:successively adding minute amounts of the dispersedphase (Vd) into the pure continuous phase until theobject volume fraction dispersed phase is reached. Atstage (i) in the process of dispersed phase addition, letthe total volume of emulsion is Vt; the effective volumeof dispersed phase is Ve and the effective dispersedphase viscosity of emulsion is . Upon addition of Vdto the stage (i) emulsion, the stage (i+1) is reachedwhere the effective dispersed phase volume is Ve+Ve,the total volume of emulsion is Vt +Vd, and theemulsion viscosity is +. According to the effectivemedium theory, the emulsion in stage (i) surrounding thenew droplets added at stage (i+1) can be regarded as thecontinuous phase, therefore from stage (i) to stage (i+1)can be regarded as a process of addition minutedispersed phase to continuous phase. Then we canapply the Einstein equation (Eq. (1)) to calculate theviscosity of the emulsion in stage (i+1):

DVe g Dg g 1 2:5Vt DVd 20The change in the effective volume fraction ofdispersed phase (e) is:

D/e Ve DVeVt DVd /e 21

where e is the effective volume fraction of dispersedphase at stage (i) and can be written as:

/e VeVt

22

Substituting Eq. (22) to Eq. (21) and assumingVeVd, we can get:

D/e DVe1 /eVt DVd 23

Substituting Eq. (23) to Eq. (20), we obtain:

Dgg

2:5 D/e1 /e

24

From Eq. (19) and Eq. (24),

Dgg

2:5 KeD/1 Ke/ 25

Integrating the above equation with the limits cwhen 0, and when , the following newviscosity equation for non-Newtonian emulsions isobtained:

gr 1 Ke/25: 26

The non-Newtonian factor Ke can be calculated by:

Keg;/ KegKe/ 27Among Eq. (27), factor Ke() represents the effect of

hydration and floc, is a function of shear rate; and therelationship between Ke() and shear-rate () can bedetermined by the experimental relationship betweenrelative viscosity (r) and shear rate () at the highestvolume fraction of dispersed phase (). Another factorKe() represents the effect of the volume fraction ofdispersed phase: it means that the emulsions exhibitdifferent non-Newtonian behavior at different volumefraction of dispersed phase, and the non-Newtonianbehavior factor Ke() is a function of volume fraction ofdispersed phase ().

From Eqs. (26) and (27), we can obtain:

Ke / Keg;/Keg 1 g0:4r g;/

/1 g0:4g;/max

28

r/max

Therefore we can get two points in the function Ke(), when =max:

Ke/max Keg;/j//maxKegj//max

1 29

when =min:

Ke/min Keg;/j//minKegj//max

1 g0:4r g;/min

/min1 g0:4r g;/max

/max

30

Then if one knows the form of the function Ke() andtwo experimental apparent viscosity values of water-in-crude oil emulsion at two volume fraction of dispersedphase (maximum and minimum) in one shear rate, theactual Ke() value can be determined; and the

relative viscosity (r) and shear rate () at the highestvolume fraction of dispersed phase (max). Consequent-ly we get the factor K and we can predict apparent(relative) viscosity value of water-in-crude oil emulsionsin dispersed phase volume fraction between maximumand minimum value we have measured and under anyshear rate with the improved P&R model (Eq. (26)).

4. Experimental

To justify the validation of the improved P&R model,7 sets of water-in-crude oil emulsion from different oilfields are presented. The samples directly come from oilwells and were processed by an electricity separator toget pure oil and mineralized water.

The crude oil and water were mixed at differenttemperature (heavy oil at 60 C and waxy oil at 30 C)by the IKA RW20DZM.N stirrer lasted for 10 min indifferent volume fraction of dispersed phase, and theapparent viscosity was measured by HAKKE RV20viscometer. All of the emulsions are water-in-crude oiltype.

The viscosities of crude oils are listed in Table 1.Sample 1# is heavy oil and the processing temper-

Table 1Summary the viscosity of crude oil samples

Crude oil samples

1# 2# 3# 4# 5# 6# 7#

Viscosity (mPa s) 534.0 137.6 52.9 46.3 101.4 112.7 59.6

117D. Dan, G. Jing / Journal of Petroleum Science and Engineering 53 (2006) 113122relationship between Ke() and shear-rate () can bedetermined by the experimental relationship betweenFig. 1. Experimental verification of theature is 60 C; samples 2#7# are waxy oil and theprocessing temperature is 30 C.form of the function Ke() vs. .

5. Results and discussion

5.1. Form of the function Ke()

Based on Eq. (28), calculating the experimental Ke() data of different oil samples in every shear rate anddispersed phase volume fraction, compared the resultswith the power function curve fitting from the twopoints Ke(max) and Ke(min). Fig. 1 shows: in differentshear rate, where the experimental data of Ke() and are factors and can be obtained by the power functionrelationship.

Ke/ a/b 31where a and b are factors that they can be get by powerfunction curve fitting from two points.

P&R (1989) model takes account of the non-Newtonian behavior of emulsions only, but theimproved P&R model includes the characterizationthat the non-Newtonian behavior of water-in-crude oilemulsions changes with the volume fraction of dis-persed phase farther. During the measuring andcalculating processes, the P&R model and the improvedP&R model are basically the same except the latter

needs a set of apparent viscosity when =min. It is tobe noted that the emulsions are often Newtonian fluidwhen =min. Then the apparent (relative) viscosity ofwater-in-crude oil emulsions in any temperature, shearrate and dispersed phase volume fraction between thelowest and the highest value could be predicted whenone knows the viscositytemperature relationship ofpure oil, a set of apparent viscosityshear raterelationship in the highest dispersed phase volumefraction and the viscosity in the lowest dispersed phasevolume fraction.

5.2. Comparison between experimental data andemulsion viscosity models

In Table 2, the experimental relative viscosities of 1#

(heavy oil) sample are presented along withcorresponding values predicted by P&R model andimproved P&R model. For heavy oil/water emulsion,the maximum and average deviations of P&R model are24.28% and 8.20% but 15.35% and 3.75% for theimproved P&R model. Compared with P&R model, theprediction results of the improved P&R model are inmost agreement with experimental data especially for

el and

Sh

15

1191

011111

32217263383244

14

118 D. Dan, G. Jing / Journal of Petroleum Science and Engineering 53 (2006) 113122Table 2Comparison of experimental data with prediction values by P&R mod

Water cut

0.1 Experimental relative viscosityP&R model Relative viscosity

Deviation (%)Improved P&R mode Relative viscosity

Deviation (%)0.2 Experimental relative viscosity

P&R model Relative viscosityDeviation (%)

Improved P&R mode Relative viscosityDeviation (%)

0.3 Experimental relative viscosityP&R model Relative viscosity

Deviation (%)Improved P&R mode Relative viscosity

Deviation (%)0.35 Experimental relative viscosity

P&R model Relative viscosityDeviation (%)

Improved P&R mode Relative viscosityDeviation (%)

0.4 Experimental relative viscosityP&R model Relative viscosity

Deviation (%)Improved P&R mode Relative viscosityDeviation (%) 1improved P&R model of 1# (heavy oil) sample (60 C)

ear rate (s1)

25 40 60 90

.23 1.23 1.23 1.23 1.23

.35 1.34 1.33 1.31 1.29

.76 9.18 8.31 7.16 5.48

.23 1.22 1.21 1.21 1.19

.14 0.50 1.03 1.73 2.77

.70 1.70 1.70 1.70 1.70

.89 1.86 1.83 1.79 1.72

.04 9.69 7.71 5.15 1.46

.64 1.62 1.60 1.57 1.53

.75 4.63 5.93 7.63 10.09

.38 2.34 2.18 2.11 1.92

.79 2.73 2.65 2.54 2.39

.01 16.86 21.27 20.45 24.28

.55 2.50 2.43 2.34 2.22

.87 6.98 11.39 11.11 15.35

.21 3.09 3.05 2.94 2.86

.48 3.39 3.25 3.09 2.86

.46 9.73 6.56 4.95 0.10

.29 3.21 3.09 2.94 2.73

.65 4.00 1.22 0.03 4.45

.49 4.24 4.06 3.82 3.49

.43 4.28 4.07 3.81 3.47

.34 1.07 0.25 0.07 0.58

.43 4.28 4.07 3.81 3.47.34 1.06 0.25 0.07 0.58

Table 3Comparison of experimental data with prediction values by P&R model and improved P&R model of 2#7# (waxy oil) samples

Samplesnumber

Watercut

Shear rate 200 (s1) Shear rate 400 (s1) Shear rate 600 (s1)

Exp.relativeviscosity

ImprovedP&R mode

Deviation(%)

P&Rmode

Deviation(%)

Exp.relativeviscosity

ImprovedP&R mode

Deviation(%)

P&Rmode

Deviation(%)

Exp.relativeviscosity

ImprovedP&R mode

Deviation(%)

P&Rmode

Deviation(%)

2# 0.1 1.42 1.45 2.21 1.30 8.46 1.42 1.42 0.29 1.28 9.47 1.42 1.39 1.58 1.27 10.460.2 2.29 2.00 12.87 1.73 24.31 2.29 1.92 15.86 1.69 25.96 2.28 1.85 18.79 1.65 27.640.3 3.82 2.78 27.15 2.41 36.87 3.14 2.62 16.66 2.31 26.52 2.81 2.47 11.91 2.22 21.040.4 4.61 3.97 13.79 3.52 23.60 4.05 3.64 10.07 3.30 18.63 3.76 3.35 10.81 3.09 17.690.5 6.50 5.89 9.28 5.50 15.34 5.48 5.23 4.58 4.99 8.87 4.96 4.66 5.99 4.55 8.280.6 9.37 9.24 1.33 9.48 1.17 7.65 7.83 2.43 8.21 7.36 6.79 6.71 1.23 7.17 5.56

3# 0.1 5.48 5.43 0.79 1.73 68.43 5.00 4.94 1.21 1.69 66.26 4.74 4.51 4.95 1.65 65.260.2 7.83 7.43 5.13 3.49 55.46 6.84 6.59 3.75 3.27 52.19 6.32 5.87 7.16 3.07 51.400.3 9.40 9.29 1.16 9.29 1.12 7.90 8.07 2.16 8.07 2.20 7.14 7.07 1.01 7.07 0.97

4# 0.1 2.20 2.19 0.41 1.31 40.51 2.20 2.08 5.46 1.29 41.42 2.19 1.97 10.20 1.27 42.340.2 2.60 2.98 14.89 1.77 31.94 2.58 2.76 6.64 1.70 34.14 2.58 2.55 0.96 1.64 36.340.3 3.18 3.83 20.57 2.49 21.77 3.09 3.46 12.11 2.33 24.41 3.04 3.14 3.41 2.19 27.720.4 4.41 4.80 8.66 3.69 16.29 3.95 4.24 7.22 3.35 15.24 3.70 3.76 1.63 3.05 17.720.5 5.99 5.92 1.18 5.92 1.18 5.00 5.11 2.25 5.11 2.24 4.49 4.45 1.06 4.45 1.06

5# 0.1 2.17 1.95 10.03 1.36 37.26 1.88 1.89 0.51 1.34 28.65 1.73 1.83 5.89 1.32 23.490.2 2.56 2.89 13.10 1.93 24.46 2.28 2.74 20.36 1.87 17.73 2.13 2.60 22.19 1.82 14.590.3 3.51 4.17 18.69 2.91 17.10 3.03 3.85 27.33 2.76 8.93 2.77 3.57 28.75 2.61 5.820.4 4.45 5.99 34.56 4.74 6.64 3.56 5.39 51.14 4.35 21.96 3.13 4.87 55.50 3.99 27.590.5 8.82 8.72 1.08 8.72 1.10 7.43 7.59 2.18 7.59 2.16 6.73 6.66 0.95 6.66 0.97

6# 0.1 3.25 3.50 7.87 1.45 55.41 3.06 3.12 1.83 1.41 54.07 2.96 2.79 5.68 1.37 53.810.2 3.55 3.68 3.83 2.24 36.87 3.21 3.26 1.61 2.09 34.83 3.03 2.90 4.07 1.96 35.350.3 3.84 3.80 1.01 3.80 1.02 3.29 3.35 1.97 3.35 1.96 3.00 2.97 0.92 2.97 0.92

7# 0.1 4.55 4.39 3.41 1.45 68.10 4.15 4.17 0.43 1.44 65.43 3.94 3.96 0.66 1.42 63.910.2 6.66 6.94 4.19 2.25 66.25 5.98 6.44 7.66 2.19 63.33 5.61 5.98 6.62 2.14 61.890.3 8.42 10.00 18.77 3.82 54.61 7.74 9.08 17.30 3.65 52.84 7.37 8.27 12.28 3.49 52.640.4 12.64 13.86 9.69 7.50 40.66 10.86 12.32 13.37 6.93 36.23 9.94 11.00 10.63 6.41 35.490.5 19.15 18.88 1.45 18.94 1.11 16.08 16.38 1.92 16.44 2.24 14.51 14.33 1.24 14.37 0.96

119D.Dan,

G.Jing

/Journal

ofPetroleum

Scienceand

Engineering

53(2006)

113122

the non-Newtonian emulsions in moderate and highvolume fraction of dispersed phase.

Deviation 100 prediction value experimental value= experimental value

Average Deviations 100Xni1

jDeviationsj=n

In Table 3 and Fig. 2, the experimental relativeviscosities of 2#7#(waxy oil) samples are presented

along with corresponding values predicted by P&Rmodel and improved P&R model.

In Table 3 and Fig. 2, the physical properties ofwater-in-crude oil emulsions are much different, theviscosities of pure oil (30) are from 46.3 mPa s to137.6 mPa s; the apparent viscosities of emulsions arefrom 101.8 mPa s to 1288.8 mPa s and the relativeviscosities of emulsions are from 1.42 to 19.15. Figs. 3and 4 shows a comparison between experimental valuesand predicted values by P&R model and improved P&Rmodel at different shear rate and water cut. The averagerelative deviation of P&R model is 27.81% but decreaseto 8.9% when improved P&R model are applied.

120 D. Dan, G. Jing / Journal of Petroleum Science and Engineering 53 (2006) 113122# #Fig. 2. Experimental data for 2 7 samples compared to corresponding remodel.lative viscosities predicted by using P&R model and improved P&R

It should be noted that water-in-crude oil emulsionsare often Newtonian fluids at low water cut, but theexact value of at which non-Newtonian emulsionsinverse to Newtonian emulsions cannot be predicted.Therefore one has to consider the whole range of watercut to be non-Newtonian fluids just as P&R model,although, the predicted results of the improved P&Rmodel for non-Newtonian emulsions is very acceptable(the maximum deviation is less than 10%).

So many factors may affect the formation of stablecrude oilwater emulsions. Different oilwater systemmay reach different maximum water cut; even the sameoilwater can reach different max water cut by differentpreparation conditions, these conditions includes system

much more precision than P&R model.

Acknowledgements

Financial support from the National Nature Sciencefundamentals; the authors are grateful to Jilin oilcompany and Bohai oil company to provided thesamples; and the experimental help from Zhao Yongand Guan Wei are also appreciated.

References

Becher, P., 1965. Emulsions and Practice, 2nd ed. Reinhold Pub.Corp., New York.

D. Dan, G. Jing / Journal of Petroleum Scientemperature, wet ability of vessel, the way of addingdispersion phase(mixed totally or adding water step bystep), stirring speed and so on. Therefore, in petroleumengineering, the following methods are always acceptedto determine the proper preparation conditions. For thefirst, the viscosity between the prepared emulsion andthe field emulsion sample are compared; for the second,the size distributions of dispersion phase between thetwo systems are compared. Then the most resembleprepared condition is selected. As a result, themaximum water cut value of a kind of crude oilwater system must be determined by certain preparationconditions, and the minimum water cut can be chosenby practical needs.

Finally, it is recommended that the improved P&Rmodel should not be applied for water cut very closeto inverse point, because the rigid high dispersedphase fraction will cause some abnormal phenomenasuch as collision and distortion of the dispersed phasedroplets, and that would make the rheologicalcharacterization of emulsions more complex. Theviscosity prediction model for emulsions near theFig. 3. Comparison between the experimental data with the P&Rmodel.inverse point needs farther experimental and theoret-ical research.

6. Conclusions

Water-in-light oil emulsions are often Newtonianfluids and they would show some non-Newtonianbehaviors only close to inverse point. However, water-in-crude oil, especially water-in-heavy oil and water-in-waxy oil emulsions, show strong non-Newtonianbehavior at lower water cut.

P&R model takes account of the non-Newtonianbehavior of emulsions, and the improved P&R modelincludes the characterization that the non-Newtonianbehavior of water-in-crude oil emulsions changes withthe volume fraction of dispersed phase farther.

The non-Newtonian property of water-in-crude oilemulsion is related with water cut, and power functionmatches this relationship best.

Comparison between experimental and predicteddata argues that the improved P&R model can provide

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