Rheology of Heavy-Oil EmulsionsHussein Alboudwarej, Moin Muhammad, and Ardi Shahraki, Schlumberger; Sheila Dubey and Loek Vreenegoor,

Shell Global Solutions (US) Inc.; and Jamal Saleh, Shell International E&P

SummaryWater is invariably produced with crude oil. If there is enoughshear force when crude oil and produced water flow through theproduction path, stable emulsions may be formed. This scenariomay particularly be present during the production of heavy oils,where steam is used to reduce the viscosity of heavy oil, or in casesin which submersible pumps are used to artificially lift the pro-duced fluids. To efficiently design and operate heavy-oil produc-tion systems, knowledge of the realistic viscosities of the emulsi-fied heavy oil, under the actual production conditions, is necessary.This study is an attempt to investigate the effect of water content,pressure, and temperature (i.e., operating conditions on the viscos-ity of live heavy-oil emulsions).

Two heavy oil samples from South America were used for thisstudy. The stock tank oil (STO) samples were recombined with thecorresponding flash gases to reconstitute the original reservoir oilcompositions. Live oil/water emulsions were prepared in a con-centric cylinder shear cell using synthetic formation water, underpredetermined pressure, temperature, and shear conditions. Thestability of live emulsions was investigated using a fully visualpressure/volume/temperature (PVT) cell, while viscosities weremeasured using a precalibrated, high-pressure capillary viscom-eter. Viscosities were measured at least in three different flow ratesat the testing conditions. In addition to live-oil emulsion studies,the stability and droplet size distribution of STO emulsions werealso determined.

Experimental results indicated that the inversion point for theSTO emulsions was approximately 60% water cut (volume), andthe average droplet size was increasing with water content. For allmeasured cases, viscosities varied with temperature according toan Arrhenius relation, while viscosities did not indicate any varia-tion with flow rate (shear) within the range of tested flow rates.Measured viscosities also increased as pressure decreased belowthe bubblepoint of the sample as lighter hydrocarbon componentsevolved. The measured viscosities increased as much as 500%because of the presence of emulsions before a sharp drop in vis-cosity beyond the inversion point. The variation of viscosity withwater content for live emulsion samples indicated that the inver-sion point for live emulsions is similar to that of STO samples.

The experimental results are also used to analyze and evaluatethe performance of an ESP system when water cut increases andcauses emulsion in a well.

Introduction

As an oilfield ages, the rate of water production increases. Withenough shear force (e.g., flow through a downhole pump or a flowrestriction such as a choke valve or orifice), a stable emulsion canbe formed. Presence of inorganic solids such as sand, clay, andcorrosion products, together with surface-active materials such asasphaltenes and naphthenic acids, also enhance the stability ofemulsions (Kokal 2005). Because of the presence of these ele-ments, the occurrence of tight emulsions in the production facili-ties is quite common. In some cases, emulsions may also form inthe near-wellbore region, leading to emulsion blockage of porousmedia (Kokal et al. 2002).

In addition to formation blockage and general difficulty in theseparation of oil and water in production facilities, one of the maindrawbacks of emulsion formation is an increase in the apparentviscosity of the oil. Viscosity of water-in-oil emulsions increasesas the water cut increases before the so-called emulsion inversionpoint, beyond which the continuous phase changes to water (i.e.,water-in-oil emulsion switches to oil-in-water emulsion). It hasbeen shown that the viscosity of the water-in-oil emulsion mayincrease as much as one order of magnitude or even higher overthe viscosity of the dry oil (Singh et al. 2004). In oil-in-wateremulsions, viscosity decreases with an increase in water content.Therefore, the maximum apparent viscosity of emulsions occurs atthe emulsion inversion point (Szelag and Pauzder 2003).

One of the field implications of emulsion inversion and emul-sion viscosity is the transportation of heavy oil-in-water emulsions.It has been shown that under certain conditions, the viscosity ofthe heavy oil-in-water emulsion is considerably lower than theheavy oil (Nunez et al. 2000). Because water production is gen-erally increasing with the life span of the oil production field, itis also very important to have an accurate measure of the emul-sion inversion point and viscosity for optimum pipeline and facil-ity design.

The majority of experimental work on the emulsion stabilityand viscosity measurements is performed for STO samples. How-ever, dissolved gases affect the viscosity of oil and the correspond-ing emulsions. For optimum design and operation of the oilfieldproduction facilities, knowledge of live-oil emulsion properties isrequired. In the present work, stability and viscosity of two SouthAmerican live heavy-oil emulsions were studied. Live-oil emul-sions were prepared in a shear cell and analyzed in a visual PVTcell for stability and in a capillary viscometer for viscosity mea-surement. The information from this study may be used for bothfacility-pipeline and artificial lift system design.

The study of the performance of ESP systems indicates thatunder these conditions, a given system will not be able to provideoptimum performance if the water cut increases from 0 to 50%.For a system operating on unchanging parameters, the rate ofproduction will decrease drastically because of the scale of in-crease in emulsion viscosity with water cut.

ExperimentalTwo South American live-oil samples were used for this study.The STO samples were recombined with 5-component syntheticgas mixtures to reconstitute the reservoir fluid compositions. Therecombined samples were conditioned at reservoir pressure andtemperature for a period of 5 days. The recombined samples werethen analyzed for composition and physical properties, as shown inTables 1 and 2 for Oil A and Oil B, respectively.

To prepare emulsions, water samples with similar compositionsto reservoir waters were used. Compositions of formation watersamples are provided in Table 3. Note that Water A and B cor-respond to Oil A and Oil B, respectively. A high-pressure shearcell was used to prepare live emulsions. The device is a Taylor-Couette flow device in which the annulus between the two con-centric cylinders is used to provide the shear environment for thefluid. It is rated to pressures up to 7,000 psia, temperatures up to390°F, and rotational frequencies (through a magnetic coupling)up to 100 Hz. The operation of the shear cell is controlled auto-matically to maintain operating conditions. To form emulsions, theshear cell is first filled with a water sample, and then pressurizedand heated up to the desired set points. Water is then displacedunder live conditions with the oil sample until desired water/oilvolume ratio is achieved. The rotational speed in the cell then

Copyright © 2007 Society of Petroleum Engineers

This paper (SPE 97886) was accepted for presentation at the 2005 SPE/PS-CIM/CHOAInternational Thermal Operations and Heavy Oil Symposium, Alberta, 1–3 November. Origi-nal manuscript received for review 26 August 2005. Revised manuscript received 3 January2007. Paper peer approved 8 February 2007.

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emulsifies the water under provided shear condition. After shear-ing the mixture for the desired period of time, the cell content isdisplaced with an inert gas isothermally and isobarically to asample cylinder equipped with an internal mixing ring. The emul-sion cylinder is maintained under the same pressure and tempera-ture and a continuous rocking condition. Emulsion samples aretransferred to a visual PVT cell for stability analysis and to acapillary viscometer for viscosity measurement as needed. Table 4summarizes the conditions under which different emulsions wereprepared. Note that the water cut (%vol) is defined as the volumeof water over the total volume expressed as percentage.

Stability analyses for STO samples were performed usingbottle tests; however, for live emulsion samples, a fully visual PVTcell was used. Live emulsion samples were transferred from asample cylinder (with mixing ring) to the PVT cell. The magneticcoupling in the PVT cell was turned off to eliminate any furthershearing of the sample. For live emulsion samples, only stability of85% water-cut samples were tested.

A capillary viscometer rated to 10,000 psia and 374°F was usedfor viscosity measurements. The capillary viscometer consists oftwo, high-pressure cylinders (32 ml each) connected to a 10-ft-long and 0.03-in. diameter capillary coil. A differential pressuretransducer is used to monitor the pressure drop across the capillarycoil. The fluid sample is pumped from one cylinder to the otherthrough the capillary coil by an opposed pump. From the measuredfluid-flow rate and pressure drop, the viscosity can be determinedusing the Hagen-Poiseuille relationship for laminar flow in tubes,namely

� =�p

Q �� r4

8 L � =�p

Qk, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

where � is the fluid apparent viscosity; �p is the pressure dropacross the capillary tube of length, L, and an internal radius r; andQ is the volumetric flow rate. The tube constant k is determined bycalibrating the viscometer using standards of known viscosity attest pressures and temperature. Note that the maximum Reynoldsnumber for this study corresponding to the highest flow rate andthe lowest viscosity was approximately 25, indicating a fully lami-nar flow. Shear stress at the wall can be calculated as

� =�p D

4 L, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

in which D is the internal diameter of the capillary tube, L is thelength of capillary tube, and �p is the pressure drop across thecapillary tube. Shear rate at the wall may be calculated as

� =�

�, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

in which � and � are wall shear stress and fluid apparent viscosity.

Results and DiscussionSTO Emulsion Preparation and Stability Analysis. STO emul-sions were prepared for both Oil A and Oil B samples to determinethe emulsion inversion points. The significance of the inversionpoint is that generally, emulsions show the maximum viscosity ator near the inversion point. Also, the STO inversion points maygive an idea about the corresponding live-oil emulsion inversion

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points. STO emulsions were prepared by simply adding propervolume ratio of oil and formation water, and hand-shaking themixture intermittently for at least half an hour. In all cases, both oiland water had been equilibrated at 130 °F before mixing. Noestimate of applied shear rate is available. The samples were keptat the same temperature for at least 18 to 20 hours before anyphotomicrographs were taken. For the cases of 85% volume watercuts, both Oil A and Oil B sample emulsions were unstable, and oiland water started segregating instantaneously.

Fig. 1 shows the results of stability bottle tests for STO Oil Aemulsion samples with water cuts of 10, 50, 62, and 85% volume,respectively. The 50% water-cut emulsion was stable at least for18 to 24 hours, whereas the 62% volume water-cut emulsionshowed signs of oil/water segregation after a few hours. The in-version point for STO Oil A emulsions samples is estimated to be60±5% volume water cut. Fig. 2 shows the stability results forSTO Oil B emulsion samples with water cuts of 50, 70, and 85%volume, respectively. Both 70 and 85% volume water cuts showedinstantaneous segregation of oil and water, indicating unstableemulsions. The inversion point for STO Oil B emulsion samples isestimated to be 65±5% volume water cut.

Live Emulsion Preparation and Stability Analysis. Table 4shows the conditions at which live emulsions were prepared in theshear cell. The difference in the applied shear rates for the Oil Aemulsion samples is caused by the viscosity of the samples and therotational speed. For 10 and 85% volume water contents, viscosityis lower than the case of 50% volume water content, and rotational

speed is higher. A combination of lower rotational speed (i.e.,decoupling at higher rotational speed than 70 Hz) and higher vis-cosity leads to a lower shear rate environment for the case of 50%volume water content emulsion sample. Stability analysis was onlyperformed on 85% water cut emulsions for both Oil A and Oil Bsamples. Water separation could be observed as soon as the emul-sion sample was transferred from shear cell to the visual PVT cell(in less than 15 minutes). Fig. 3 shows the segregated water and oilin a visual PVT cell under the same conditions. Note that for thecase of Oil B, oil is partially adhered to the glass surface and doesnot allow clear observation. The 85% water-cut emulsions wereunstable even in the presence of shear from PVT cell magneticstirrer. No image analysis was performed on the 85% water-cutemulsions, because both STO and live emulsions were unstableand could not be used for viscosity testing. No stability analysiswas performed on other live emulsions.

To investigate water droplet size distribution in emulsions, asubsample of the live emulsions was flashed from the correspond-ing emulsion cylinders to ambient conditions. The samples werethen analyzed under a microscope, and photomicrographs for eachemulsion were analyzed using image analysis software. Figs. 4and 6 show the photomicrographs of emulsions for the Oil A andOil B samples, respectively. Figs. 5 and 7 depict the correspond-ing droplet size distribution for the same images. Note that theresolution of the images is approximately 1 micron, and numberfrequency for droplets smaller than 1 micron is merely a calculatednumber and may not represent the actual droplets. For Oil A emul-sions, the droplet size distribution for both 10 and 50% water cut

Fig. 2—Stability of Oil B (STO) at 130°F.Fig. 1—Stability of Oil A (STO) at 130°F.

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are very similar, and only the number frequency in the 50% watercut is slightly higher. For Oil B, there is a slight shift in the dropletsize distribution of 50 and 60% emulsions compared to the 15%emulsion. Comparing the 50 and 60% emulsions of Oil B, it seemsthat 50% emulsion has a higher-number frequency of smaller drop-lets, while the 60% emulsion has a higher number of larger drop-lets. Note also that for 60% water cut, droplet size distributionsuggests the existence of another size mode, thus a near bimodaldistribution [e.g., partially unstable emulsions (Salager et al.2000)]. The viscosity measurements for the same oil at 60% watercut also shows a partially unstable system.

Viscosity Measurements. The viscosities of the neat Oil A andOil B samples, together with their corresponding emulsions, weredetermined using a capillary viscometer. Measured viscosities forboth dry Oil A and Oil B samples, at various pressures, are shownin Fig. 8. Data follow an Arrhenius-type temperature trend, at leastfor the measured range of temperature. Also, the neat oil viscosi-ties decrease as the amount of solution gas increases with increas-ing pressure. The viscosity of each sample was measured at leastat three different volumetric flow rates (shear rates), and the re-ported viscosity values are the arithmetic average of measuredviscosities for each sample. There was no significant variation ofviscosity with shear rate. Tables 5 and 6 show the range of appliedshear rates (s−1) for each measured viscosity point. The standarddeviation of viscosity with shear rate varied between 0.1 and 1.4%for Oil A and between 0.02 and 1.4% for Oil B. The overallaverage standard deviations of measured viscosities over the rangeof shear rate were 0.5 and 0.4% for Oil A and Oil B, respectively.

In all cases, reducing pressure below the bubblepoint (and sepa-ration of lighter hydrocarbon components) increased the measuredviscosities for both neat oils and emulsions, as expected. At thesame time, an increase in water content of emulsions (up to andnear inversion point) increased the viscosities (Fig. 9). For the case

Fig. 3—Stability of live 85% water-cut live emulsions of Oil Aand Oil B.

Fig. 4—Photomicrographs of Oil A live emulsions (sampleflashed to ambient conditions).

Fig. 5—Droplet size distribution of Oil A live emulsions (sampleflashed to ambient conditions).

Fig. 6—Photomicrographs of Oil B live emulsions (sampleflashed to ambient conditions).

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of the Oil A sample, viscosities increased up to 30% for 50%water-cut emulsions at 40°F, and viscosity variation was moresensitive to pressure than to water content. In comparison, theviscosity of Oil B emulsions showed higher variation with watercontent than with pressure. For the case of Oil B emulsions, vis-cosities increased more than 5 times at 50% water cut and 40°F.For Oil B at 60% water cut, the viscosity dropped drasticallycompared to the 50% water cut. This behavior might be an indi-cation that the emulsions were beyond the inversion point.

Comparison of Emulsion Viscosity Correlations. Four single-parameter correlations were chosen for the comparison. Taylor’s(1932) and Vand’s (1948) correlations were used as the pioneerand most commonly referred correlations. The correlations of Ron-ningsen (1995) and Yaron and Gal-Or (1972) were chosen basedon two separate performance studies (Johnsen and Ronningsen2003; Pal 2001). Although multiple-parameter correlations areavailable for more accurate prediction of emulsion viscosities, thesingle-parameter equations were chosen for the sake of simplicity.Multiple-parameter viscosity correlations need experimental datafor tuning purposes. The emulsion viscosity data may not be avail-able a priori. Details of the correlations are provided in the Ap-pendix.

Figs. 10 and 11 depict the results of such a comparison for OilA and Oil B, respectively. The emulsion viscosities for Oil A werebest predicted with Taylor’s correlation with an absolute averageerror of 13%; Oil B emulsion viscosities were best predicted by thecorrelation of Yaron and Gal-Or with an average absolute error of21%. Note that only emulsion viscosity data were considered in theerror analysis. For Oil A, single-parameter correlations tend tooverpredict the viscosity of emulsions, while for Oil B, no par-ticular trend could be distinguished. This comparison between theselected correlations, although limited to single-parameter corre-lations, shows that the predicted viscosity of emulsions with no apriori measurement may be largely inaccurate.

Case Study

An ESP system performance analysis under these experimentalresults was conducted. For this analysis, the measured data for OilB at 2,000 psia and 70°F is used. The measured data under theconditions was used to calibrate the calculated viscosity. The in-formation and data for the reservoir and the well are presented inTable 7 and Fig. 12.

Fig. 13 displays the well performance curves for oil (with noemulsion). For this case, the flowing bottomhole pressure (FBHP)was 511 psia. For the flow rate, a pressure of 1,076 psia is requiredto lift the fluid to the surface. This difference in pressure clearlyindicates that the well requires artificial lift to produce 950 B/D ofliquid, and an ESP system is the most suitable candidate for thissituation. To achieve this flow rate, an additional 565 psi of pres-sure is required. The pressure profile (pressure gradient) plot, seenin Fig. 14, summarizes the available and required lift pressures.

The change in water cut that changes the viscosity affects thewhole system twofold.

First, increase in viscosity drastically changes the tubing per-formance. Achieving the same rate requires much higher pressureto lift the fluid to the surface when water cut is increased. Thechange in profile is shown in Fig. 14, and the friction componentthat bears the effect of the viscosity is shown in Fig. 15.

Second, the viscosity affects the performance of the pump. Asthe viscosity increases, the efficiency of the pump decreases andrequires more stages to produce the same flow rate. Table 8 showsthat the number of stages, and required power increases drasticallyas water cut increases. The table also shows that the head factor foreach stage decreases and the power factor increases. The lower thehead correction factor, the less head or lift will be provided. On theother hand, the higher the power factor, the more power will berequired by the pump to operate and lift the same rate (thesefactors are 1.0 for water). Therefore, the pump provides less heador lift and requires more power (e.g., a larger motor) as emulsionviscosity increases. This increase indicates that if the increase inwater cut is expected, the system should be designed for approxi-mately the inversion point that causes the highest viscosity. Asemulsion viscosity increases with the water cut, more lift is re-quired to move the fluid to the surface, and also the increase inviscosity reduces the efficiency of the pump. In Table 9, the bestefficiency rate of the pump decreases as the viscosity increases.

In this analysis, the number of stages required to continueproducing the same rate was determined. In actual practice, if thenumber of stages is set, then the production rate will decrease aswater cut increases, as expected.

Fig. 8—Viscosities of Oil A and Oil B (no water). Triangles for100 psia, circles for 1,000 psia, diamonds for 2,000 psia, andsquares for 3,000 psia.

Fig. 7—Droplet size distribution of Oil B live emulsions (sampleflashed to ambient conditions).

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ConclusionsViscosities of live recombined Oil A and Oil B samples and theirdifferent water-cut emulsions were measured using a capillary vis-cometer. Experimental results indicated that for all measuredcases, viscosities varied with temperature according to an Arrhe-nius relation, while viscosities did not indicate any variation withinthe range of tested flow rates, suggesting that fluids are Newto-nian. Measured viscosities also increased as pressure decreasedbelow the bubblepoint of the sample, inline with the amount ofdissolved gases. Viscosity measurements for dry oil and emulsionsof Oil A samples indicated that emulsion viscosities have in-creased by 30%, while for the case of Oil B samples, the increasein the emulsion viscosities was as high as 500%.

Regarding emulsion stabilities, the bench top bottle tests indi-cated that the inversion point for STO Oil A emulsions was ap-proximately 60±5% volume water cut, and, for STO Oil B emul-sions, was approximately 65±5% volume water cut. For live-oilsamples, the stability of only 85% volume water cut for both OilA and Oil B samples was tested, and both emulsion samples wereunstable. A systematic study to determine the inversion point oflive-oil emulsions was not performed. However, the viscosity mea-surements for the Oil A sample suggest that the inversion pointmay be approximately 55±5% volume water cut at the tested con-ditions (10% volume water cut lower than that of the STO sample).A more definitive experimental scope of work is required to de-termine the inversion point for the live emulsion samples.

Comparison between four emulsion viscosity single-parametercorrelations and measured viscosities indicated that the absoluteaverage error in the predicted emulsions viscosities could be ashigh as 200% for the tested fluids, as shown in Table 9. Single-parameter emulsion viscosity correlations should only be usedwith an expectation of large errors.

If higher water cut is expected during the lifespan of the ESPsystem operation, the performance of the ESP should be consid-ered very carefully. As the results show, either the system shouldbe designed for the worst-case scenario, which is the inversionpoint, or change in the ESP system should be considered at dif-ferent stages of the well’s life as water cut increases. But theseevaluations require reliable data for the emulsion viscosity of thefluid.

NomenclatureD � internal diameter of capillary tube

k1–k4 � constants in Eq. A-4K � dispersed-phase viscosity/continuous-phase viscosityL � length of capillary tubeQ � volumetric flow rater � internal radius of capillary tubeT � temperature� � shear rate

�p � differential pressure� � volume% water cut in Eq. A-4� � apparent emulsion viscosity

�c � continuous phase viscosity�r � relative viscosity defined in Eq. A-1

� � shear stress� � volume fraction of dispersed phase

AcknowledgmentThe authors wish to thank Schlumberger and Shell Global Solu-tions (U.S.) Inc. for permission to publish this work. The authorswould also like to thank Craig Borman, Trevor Lockyer, RobFisher, and Abdulai Dawodu for performing experimental work.

ReferencesJohnsen, E.E. and Ronningsen, H.P. 2003. Viscosity of ‘Live’ Water-in-Oil

Emulsions: Experimental Work and Validation of Correlations. Jour-nal of Petroleum Science and Engineering 38: 23–36.

Kokal, S. 2005. Crude-Oil Emulsions: A State-of-the-Art Review. SPEPF20 (1): 5–13. SPE-77497-PA. DOI: 10.2118/77497-PA.

Fig. 9—Viscosities of Oil A and Oil B and correspond-ing emulsions.

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Kokal, S. et al. 2002. Productivity Decline in Oil Wells Related to As-phaltene Precipitation and Emulsion Blocks. Paper SPE 77767 pre-sented at the SPE Annual Technical Conference and Exhibition, SanAntonio, Texas, 29 September–2 October. DOI: 10.2118/77767-MS.

Nunez, G.A., Sanchez, G., Gutierrez, X., Silva, F., Dalas, C., and Rivas, H.2000. Rheological behavior of concentrated bitumen in water emul-sions. Langmuir 16 (16): 6497–6502.

Pal, R. 2001. Single-Parameter and Two-Parameter Rheological Equationsof State for Nondilute Emulsions. Industrial and Engineering Chem-istry Research 40: 5666–5674.

Ronningsen, H.P. 1995. Correlations for Predicting Viscosity of W/OEmulsions Based on North Sea Crude Oils. Paper SPE 28968 presentedat the SPE International Symposium on Oilfield Chemistry, San An-tonio, Texas, 14–17 February. DOI: 10.2118/28968-MS.

Salager, J-L., Marquez, L., Pena, A.A., Rondon, M., Silva, F., and Tyrode,E. 2000. Current Phenomenological Know-How and Modeling ofEmulsion Inversion. Industrial and Engineering Chemistry Research39: 2665–2676.

Singh, P., Thomason, W.H., Gharfeh, S., Nathanson, L.D., and Blumer,D.J. 2004. Flow Properties of Alaskan Heavy-Oil Emulsions. PaperSPE 90627 presented at the SPE Annual Technical Conference andExhibition, Houston, 26–29 September. DOI: 10.2118/90627-MS.

Szelag, H. and Pauzder, B. 2003. Rheological properties of emulsionsstabilized by acylglycerol emulsifiers modified with sodium carboxy-lates. Colloids And Surfaces A—Physicochemical And Engineering As-pects 219 (1–3): 87–95.

Taylor, G.I. 1932. The Viscosity of Fluid Containing Small Drops ofAnother Fluid. Proceedings of Royal Society A 138: 41–48.

Vand, V. 1948. Journal of Physics and Colloidal Chemistry 52: 217.

Yaron, I. and Gal-Or, B. 1972. On Viscous Flow and Effective Viscosityof Concentrated Suspensions and Emulsions. Rheologica Acta 11:241–252.

AppendixIn the following equations, the relative viscosity is defined as:

�r =�

�c, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-1)

in which �r is the relative viscosity, � is the emulsion apparentviscosity, and �c is the continuous-phase viscosity.

The celebrated Taylor equation for the relative viscosity of verydilute emulsions of nearly spherical noncolloidal droplets is:

�r = 1 + �5K + 2

2K + 2��, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-2)

in which K is the viscosity ratio of dispersed phase to continuousphase, and � is the dispersed-phase volume fraction.

Vand’s correlation is a theoretically based exponential functionin the form of

�r = exp� 2.5�

1 − 0.609��, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-3)

in which � is the volumetric concentration of dispersed phase.Variations of Vand’s equation have been used. The most commonmodification is to replace 0.609 with a constant that can be deter-mined by fitting experimental data.

Ronningsen correlation is represented as

ln �r = k1 + k2T + k3� + k4T�, . . . . . . . . . . . . . . . . . . . . . . . (A-4)

Fig. 10—Comparison between measured and calculated emul-sion viscosities for Oil A.

Fig. 11—Comparison between measured and calculated emul-sion viscosities for Oil B.

Fig. 12—Well trajectory.

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in which k1 to k4 are constants that have been determined at dif-ferent shear rates (30, 100, and 500 s−1) and based on a set of NorthSea oil database, T is temperature (°C), and � is the volume per-cent water cut. The constants for 500 s−1 are: k1�−0.06671,k2�−0.000775, k3�0.03484, k4�0.00005. At constant tempera-ture, Eq. A-3 reduces to a single-parameter equation.

Yaron and Gal-Or’s analysis gives the following correlation forthe relative viscosity of concentrated emulsions:

�r = 1

+ � 5.5�4�7�3 + 10 − �84�11��2�3 + �4�K��1 − �7�3��

10�1 − �10�3� − 25��1 − �4�3� + �10�K��1 − ���1 − �7�3���,

. . . . . . . . . . . . . . . . . . . . . . . . (A-5)

in which K is the viscosity ratio of dispersed phase to continuousphase, and � is the dispersed-phase volume fraction.

Hussein Alboudwarej is a senior research project engineer withSchlumberger at DBR Technology Center, Edmonton. The fo-cus of his research is on wax and asphaltene flow assuranceand the rheology of waxy and heavy crude oils. His researchinterests also include development of experimental tech-niques and tools for complex phase behavior and flow assur-ance studies. Before his graduate studies, he worked for the

National Iranian Oil Company (NIOC) at both onshore andoffshore production fields as a process/production engineer.He holds PhD and an MSc degrees from the University of Cal-gary, and a BS degree from the Abadan Institute of Technol-ogy, all in chemical engineering. Moin Muhammad is Managerof the DBR Technology Center with Schlumberger in Edmon-ton, Canada. He has more than 12 years of operational, re-search, and management experience in reservoir fluid prop-erties, flow assurance, and business development-related po-sitions (Canada and U.S.). Moin holds an MS degree from theUniversity of Alberta, Canada and a BS degree from PunjabUniversity, Pakistan, both in chemical engineering. Ardeshir(Ardi) Shahraki is a senior production engineer with Schlum-berger in the Artificial Lift segment at Schlumberger ReservoirCompletions campus in Rosharon, Texas. He has been withSchlumberger since 2002. He previously worked for IHS Energyas a principal engineer/project manager. His interests includemultiphase fluid flow, well-system analysis, and modeling andpredicting the performance of artificial lift systems for the de-sign and diagnostics of systems. He holds BS and MS degrees inpetroleum engineering from the University of Louisiana atLafayette, and a PhD degree in petroleum engineering fromNew Mexico Tech. Sheila Dubey is a senior staff research en-gineer at Shell Global Solutions (U.S.) Inc. at the WesthollowTechnology Center in Houston and has been with Shell OilCompany for 27 years. She is currently the U.S. team lead forScale Emulsions Rheology Foam (SERF) in Flow Assurance. Shebrings significant experience to these areas of flow assurancebecause of her background in physical organic chemistry,analytical chemistry, chemical engineering, and strong prac-tical laboratory skills in the areas of E&P, chemicals, and refin-ing. Her interests also include EOR and asphaltenes. She holdsan MS degree from MUN in Newfoundland and a PhD degreefrom the University of Calgary, both in chemistry, as well as anMS degree in chemical engineering from the University of Tulsa.Loek Vreenegoor joined Shell in 1990, working at the Shell Re-search and Technology Center Amsterdam (SRTCA) in TheNetherlands with a focus on R&D and Technical Services. Hestarted in the area of polymer processing, then becoming in-volved in modeling and computational fluid dynamics (CFD)of viscoelastic flows. After a 1-year assignment at WesthollowTechnology Center (WTC) in Houston, where he worked on 3DCFD of degrading polymers and multiphase flow, he returnedto SRTCA as the team leader in multiphase flow and became

Fig. 13—Inflow and outflow curves for 0% water cut.Fig. 14—Pressure profile for different water cuts, at 950 B/D.

Fig. 15—Friction component of pressure profile for 15 and 50%water cut and 950 B/D.

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involved in three-phase flow modeling and slug mitigation. Hethen joined the Flow Assurance group, working out of Amster-dam and Houston. Managerial responsibilities were combinedwith providing technical support, both in the design and op-erational phase of upstream projects, varying from the OrmenLange deepwater gas/condensate development in Norwayto plugged flow lines in the Gulf of Mexico to heavy oil devel-opments off the coast of Brazil. Vreenegoor holds a cum laudedegree obtained at the Applied Mathematics Faculty of the

Delft University of Technology, and he completed his PhD thesison the mathematical modeling of two-phase bubbly flows onthe same faculty. Jamal Saleh has been a senior process/flowassurance engineer with Shell International Exploration & Pro-duction since 2002. Before joining Shell, Jamal worked as asenior flow assurance engineer at Intec Engineering for 2 yearsand a process simulation engineer at Epcon International for 4years. He holds a PhD degree in chemical engineering fromLamar University.

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