single-phase wax deposition experiments

1069r 2009 American Chemical Society pubs.acs.org/EF

Energy Fuels 2010, 24, 1069–1080 : DOI:10.1021/ef900920xPublished on Web 12/01/2009

Single-Phase Wax Deposition Experiments

Rainer Hoffmann* and Lene Amundsen

StatoilHydro ASA, Norway

Received August 25, 2009. Revised Manuscript Received November 5, 2009

The behavior of waxy crude oils in subsea production lines has been successfully investigated in a 2 in.deposition flow loop. A North Sea waxy gas condensate was used to investigate wax deposition inturbulent single-phase flow under different temperature and flow conditions. A reliable and accurateprocedure for determination of wax thickness and wax roughness from pressure drop, weight, and lasermeasurements has been developed. The laser technique is a new and promising method to measure thespatial distribution ofwax thickness, whichwas not captured by the traditional pressure drop andweighingmethods. These experiments have led to an increased understanding of the mechanisms of wax deposition,which is needed to developmore-accuratemodels based on physical effects. Thesemodels are then the basisfor a more accurate prediction of the rate of wax deposition in production lines. The main finding is thatmolecular diffusion is indeed the central mechanism that steers wax deposition but that an accuratequantitative description also needs to take thewax composition of the deposit and the effects of shear stressinto account. However, for higher oil temperatures it was found that the wax deposit’s structure changesfrom the well-known smooth homogeneous type to a new irregular, patchy type. This deposit cannot bedescribed by the traditional diffusion models. In addition, the experiments were used to confirm that thelaboratory-scale measurement techniques that are typically used to determine wax appearance tempera-ture do result in a temperature that coincides with the temperature where wax starts to deposit underrealistic flow conditions.

Introduction

Characterization of waxy oils and determination of deposi-tion rate in production pipes is crucial in concept developmentand engineering of new fields and for fields in operation.Waxdeposition can be an obstruction (show stopper) for develop-ment of new fields. For fields in operation, waxy oils can leadto reduction in oil production, increased operational costs,and HSE problems, and in some cases the pipeline can beplugged by either wax deposits or a stuck pig. For all of thewax control methods in use (pigging, pipeline insulation,heating) the rate of wax deposition needs to be known inadvance to choose and design the appropriate controlmethod.

To predict wax deposition, models are being used that takeinto account the properties of the gas condensate, the fluidflow, and the pipeline. From the various mechanisms thatwere discussed in the very first papers on pipeline wax depo-sition1 molecular diffusion is today considered to be thedominant one. Since field data from production pipelinesare difficult to obtain (due to nonconstant conditions andinsufficient instrumentation2) the only way to validate thebasic assumptions of a model is to perform experiments in aflow loop.

To this end a 2 in. flow loop was constructed at Statoil-Hydro Research Centre Porsgrunn where real waxy gas

condensate flows through a test section where a surroundingwater annulus simulates the conditions subsea. Several experi-mental campaigns were performed where the influence of theoil temperature, the cooling water temperature, and the flowrate were investigated. The measurements included severalindependent ways of determining the wax deposit thickness.In addition, the resulting deposit composition was also ana-lyzed to verify the assumption of somemodels that a constantporosity and a single diffusion equation is sufficient todescribe the deposition process.

These experiments are used to identify the main physicalmechanisms that have to be included in a wax depositionmodel. In a next step the aquired data will then be used toquantitatively verify available models and simulation tools.

Experimental Facilities

WaxDeposition Test Rig.The wax deposition test rig consistsof a flow loopwhere real crude oil or gas condensate is circulatedfrom a tank through the test section (see Figure 1). The testsection is 5.5 m long and is surrounded by an annulus that isflooded by a concurrent water flow. The temperatures of oil andwater can be adjusted separately in the interval of 5-70 �C sothat all kinds of temperature conditions (temperature andtemperature gradient) at the inner pipe wall can be set.

The tank volume is 4000 L and has been chosen so that waxdepletion during an experiment is not an issue. An example mayillustrate this: If the tank is only half-filled (2000 L) with a verylow wax-content oil (2.5%) there is 50 L of wax available. If anexperiment is runwhere a wax deposit of 3mm is built up (whichis a lot more than is usually obtained) about 2.7 L of wax are inthe deposit, so roughly 95% of the wax is still available in theflow.

The rig can operate with real crude oils and gas condensates atatmospheric pressure.Thepumpdelivers a flowrateof 3-30m3/h

*To whom correspondence should be addressed. E-mail: [email protected].(1) Burger, E. D.; Perkins, T. K.; Striegler, J. H. J. Pet. Technol. 1981,

36, 1075–1086.(2) Labes-Carrier, C.; Rønningsen, H. P.; Kolnes, J.; Leporcher, E.

Wax deposition in North Sea gas condensate and oil systems: Comparisonbetween operational experience and model prediction. SPE Annual Tech-nical Conference and Exhibition, San Antonio, Texas, 2002.

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Energy Fuels 2010, 24, 1069–1080 : DOI:10.1021/ef900920x Hoffmann and Amundsen

which is monitored by Coriolis flow meters (see Table 1). Thepiping consists of stainless steel with an inner diameter of 2 in.

The instrumentation for measuring wax thickness consists of:(1) Pressure drop measurement across the test section. Whenwax starts to deposit on the inner pipe wall of the test section theeffective diameter and wall roughness changes, which will resultin a change of the pressure drop. (2) Temperaturemeasurementsof the oil flow before and after the test section. Since wax acts asa thermal insulation the temperature difference across the testsection is a way of monitoring wax buildup. (3) A removablepart of the test section that can be used to visually inspect thewax deposit, to determine its weight by weighing it, and toretrieve wax sample for further lab analysis (GC, DSC, etc.).(4) A laser and a camera can be inserted into the rig to measurethe inner diameter and thus the deposit’s thickness optically.

Test Fluid. The used fluid for all experiments is a waxycondensate from the North Sea. The main properties of thisfluid are: (1) density Foil=809 kg/m3 at 20 �C; (2) cloud point(wax appearance temperature,WAT)TWAT≈ 30 �C, dependingon the measurement technique; (3) pour point TPP ≈ 1 �C;(4) wax content of ca. 4.5% using acetone precipitation techni-que (UOP Method 46-64); and (5) viscosity was measured ina rheometer (Physica MCR 301) at different shear rates (seeFigure 2)

Experimental Procedure. An important precondition for re-peatable stable experiments is a suitable experimental proce-dure. First, all wax in the rig is melted by running the rig at 60 �C(i.e., well above WAT) for at least 6 h. Then both oil and watertemperature Toil, Twater are set to the desired oil target tempera-ture. Flow rate versus pressure drop measurements are per-formed (see Figure 3) to verify that the pipe contains no waxdeposit prior to startup as expected and that all instrumentationis performing correctly. Then Twater is quickly set down to thetarget water temperature. Toil and Twater are kept within a rangeof 0.2 �Cof their target values and the flow rate within a range of0.1m3/hwithin its desired target value for the total experimentaltime. After the experiment is finished the pipe is drained, the testpipe is weighed, laser pictures are taken, and deposit samples arecollected for further analysis.

Wax Thickness Measurement Methods

Pressure Drop. One way of determining the wax depositbuildup is tomeasure the increase in pressure drop due to thedecrease of the pipe diameter. By using Haaland’s frictionfactor correlation3 a relationship for the inner diameterD of

the test section can be established that has to be solvednumerically

FðDÞ ¼ D5π2

8FoilQ2

Δp

L- 1:8 log10

6:9Dπηoil4QFoil

þ ε

3:7D

� �1:11 !0

@1A

-2

¼! 0

ð1Þwhere Δp is the pressure drop, Foil is the oil density, Q is theoil volume flow rate, L is the length of the differentialpressure measurement, ηoil is the viscosity of the fluid, andε is the roughness of the inner pipe wall.

The viscosity of the oil ηoil and the density Foil weredetermined for the relevant temperature interval using aPhysica MCR 301 rheometer and an Anton Paar densitymeter DMA 4500 M, respectively.

To determine the empty pipe diameter and roughness aseries of measurements were performed where the oil flowrate was varied across the possible operational range (Qmin=3 m3/h, Qmax = 30 m3/h), see Figure 3. Oil and watertemperature were both kept at 60 �C so that no precipitatedwax could disturb the measurements.

The measured data points were used for a nonlinear fitusing eq 1 to determine the diameter D and the roughness ε.The found diameter of 52.56 mm fits very well with thesuppliers specification of Dinner = 52.5 mm. The foundroughness of 0 m means that for the relevant turbulence

Figure 1. Wax deposition test rig layout.

Figure 2. Viscosity of test fluid at different shear rates.

Table 1. Instrumentation of Test Rig

mass flowdifferentialpressure temperature

instrument E&H CoriolisPromass 63 F

Rosemount3051 cd2

Rosemountk-element

accuracy (0.1% of reading (0.065% ofcalibrated range

(0.5 �C

range 0-31 m3/h 0-620 mbar -100 to 1300 �C

Figure 3. Determination of diameter and roughness from flow ratevariations.

(3) Haaland, S. E. J. Fluids Eng. 1983, 105, 89–90.

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regime (Remax=50 000) the wall roughness of the pipe is ofno significance. This does of course not imply that the sameassumption is valid for the wax deposit roughness. Thisroughness is unknown a priori and has to be determinedduring the deposition experiment.

To this end at regular intervals the oil flow rate was slightlyvaried as examplified in Figure 4: Starting from the standardflow rate (Qoil= 21 m3/h in Figure 4) the oil flow rate isadjusted in two steps ofΔQoil=1m3/h down toQoil=19m3/hand then in four steps up toQoil=23 m3/h for some minutes.The reasoning behind this is that small rate variations for ashort period of time will not unduly disturb the wax deposi-tion rate. However, by measuring the change in pressuredrop corresponding to the change in flow rate it is possible tofit diameter and roughness using eq 1. So the procedureshown in Figure 4 employs the same idea as used for anempty pipe (see Figure 3). The underlying assumption is thatthe wax thickness does not change significantly during theshort period of time it takes for performing the rate changes.As will be shown below, different experimental conditionscan result in very different wax deposit roughness.

Equation 1 is only valid for an isothermal flow, that is, forequal oil and water temperature. For the more realistic non-isothermal flow, the different wall temperature will lead to adifferent oil viscosity in the vicinity of the wall. This will inturn influence the fluid-wall drag forces and thus thepressure drop. Perry4 suggests a correction of the frictionfactor for non-isothermal flow depending on the ratio of theviscosity in the bulk flow ηb and the viscosity near the wall ηw

fnon-isothermal ¼ fisothermalηbηw

� �k

ð2Þ

The factor k in the exponent is 0.11 for cooling and 0.17 forheating according to Perry. To verify these numbers a seriesof experiments with a clean pipe were performed wheredifferent non-isothermal temperature combinations weremeasured. These were chosen so that no disturbing waxdeposition could occur since the temperatures were alwayskept well above WAT.

In a first series the water temperature was kept constant at60 �C while the oil temperature was varied between 30 and50 �C.The experimentwas repeated at two different flow rates

(Q=21 and 25 m3/h). Figure 5, left, shows the calculatedfactor k for the exponent in eq 2 according to the measuredpressure drop change compared to an isothermal flow. In asecond series the oil temperature was kept constant at 40 �Cwhile the water temperature was varied from 35 to 60 �C. Theresulting factor k is shown in Figure 5, right.

The results show that the idea of correcting the frictionfactor by the viscosity ratio seems to work but that Perry’snumbers for the exponent are not applicable for our rig andfluid. Actually, the plots in Figure 5 seem to suggest that theexponent is not even constant for different temperaturecombinations. However, since the variation is not too largea fixed exponent of 0.07 was used for all further calculationsof wax thickness from pressure drop measurements. To givean idea of the sensitivity of the thickness calculation on the kexponent: Changing the k exponent by 0.01 will change thecalculated wax thickness by 0.7%.

Weight. An alternative way of determining the wax thick-ness is by measuring the weight increase of the pipe duringthe deposition. To this end the removable part of the testsection is weighed several times during an experiment.

From theweight difference compared to an empty pipe thewax thickness H can be calculated

H ¼ R-ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR2 -

mwax

FwaxπL

r

where R is the inner (empty) pipe radius, mwax is the mass ofdeposited wax, Fwax is the density of wax, and L is the lengthof the removable test section [m].

To determine wax deposition thickness by weighing it isnecessary to accurately determine the deposit’s density Fwax.This measurement is performed using a gas displacementpycnometer (Micromeritics AccuPyc 1330), which measuresthe volume of a sample, independent of its structure, bydetermining the volume of gas the sample displaces from thesample cell.

The measurement procedure is as follows (see Figure 5):The pressure in the sample cell Vcell and the expansion cellVexp is initially set to ambient pressure pa at ambient tem-perature Ta. Then the valve is closed and Vcell is filled withmeasurement gas (Helium) up to a pressure p1. The gasequation is

p1ðVcell -VsampÞ ¼ ncRTa

where Vsamp is the volume of the sample in the sample cell,Vcell is the volume of the sample cell, nc is the number ofmoles of gas in the sample cell, R is the universal gasconstant, and Ta is the ambient temperature.

The equation for the expansion is

paVexp ¼ neRTa

where ne is the number of moles of gas in the expansion cell.When the valve is opened the pressure is lowered to p2

p2ðVcell -Vsamp þVexpÞ ¼ ncRTa þ neRTa

This equation is used for the pycnometer measurement. Vcell

and Vexp are determined using calibration measurements.The pressures are determined using difference pressure mea-surements against ambient pressure. It is essential to keep thetemperatures in the sample and expansion cell constantduring the measurement.

A pycnometer measurement was performed on a waxdeposit sample from an experiment with Qoil=21 m3/h andtwo samples from an experiment with Qoil=5 m3/h. Both

Figure 4. Determination of wax deposit roughness by variation ofoil flow rate.

(4) Green, D. W.; Perry, R. H. Flow in Pipes and Channels, and Non-Isothermal Flow; McGraw-Hill Book Company, 1963.

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experiments had Toil=20 �C, Twater=10 �C and an experi-mental duration of 100 h. Because of the different flow rate,the deposits from the two experiments showed different waxcontents, which resulted in different deposit densities (seeTable 2). All samples were measured 10 times with resultingstandard deviations of less than 0.2%. The two samples fromthe experiment with Qoil=5 m3/h showed almost the sameresult (deviation of 0.3%).

Since the density difference between the two deposits fromlow and high flow rate experiments is below 2% it wasdecided to use a constant wax density of Fwax=891 kg/m3

for the evaluation of the weight measurements.Laser. Another deposit thickness measurement technique

that was tested is laser-based: A coaxial laser beam isdiverted by a 360� mirror toward the inner pipe wall, seeFigure 7, left. A camera mounted on the same mechanicsupport takes a picture of the pipe, including the projectedlaser beam, which will appear as a red circle, see Figure 7,right. The diameter of this circle will decrease with anincreasing deposit thickness.

To derive the pipe diameter from the captured picture aMatlab script is used (see Figure 8): First, the camera imageis read into Matlab. From the image center a number ofsearch rays is generated. Along each search ray the point ofmaximum light intensity is determined to define the circle’scoordinates. Some search rays will not return a result sincethe mechanic support will always hide a part of the laserbeam.

Using these coordinates a nonlinear best fit is used to findthe circle’s center coordinates and diameter. By comparison

with calibrationmeasurements for a series of clean pipeswithknown diameters the deposit thickness can be determined.The reason for using several calibration pipes with differentdiameters was that the fish-eye lense of the camera showssuch a large distortion that no simple linear relationshipbetween the diameter observed by the camera and the realdiameter could be used.

To test the reliability of the method, measurements wereperformed repeatedly first at the same position and after-ward at different positions in the pipe. The standard devia-tion of the determined diameter was around 0.1% (both forcomparing measurements at the same position and for com-paring measurements from different positions). A necessaryprecondition, however, is to reduce mechanic vibrations(e.g., due to operator movement in the vicinity of the rig)that can be carried over to the mechanic support of the laser.This leads to a blurred image, which makes precise imagerecognition impossible.

It was found that it is not necessary to change the analysisprocedure depending on the refraction index of the depositor its roughness. The main challenge that was found ismeasuring wax deposits with a high content of asphaltene.The resulting deposit tends to absorb a significant part of thered laser light so that determining the light circle on thecamera pictures can be difficult.

Temperature Difference.As the wax deposit builds up, theheat transfer between oil flow and cooling water decreasessince wax has a rather low thermal conductivity compared tosteel and therefore acts as a thermal insulator. If the thermalconductivity were known, the temperature drop of the oilflow in the test section could be used to calculate the waxthickness. However, measurements have shown that thethermal conductivity of wax deposits is highly dependenton the wax content. Since the wax content is also changingover time (aging effect) no reliable way of determing the waxthermal conductivity could be found yet. Therefore, the

Figure 5. Influence of non-isothermal flow.

Figure 6. Schematic of pycnometer.

Table 2. Oil and Deposit Density Measurements

samplewax

contentdensity(g/cm3)

standard deviation(g/cm3)

Qoil = 21 m3/h 33% 0.8996 0.0022Qoil = 5 m3/h, No. 1 18% 0.8859 0.0011Qoil = 5 m3/h, No. 2 18% 0.8827 0.0006

Figure 7. Laser-based thickness measurement;principle.

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temperature dropwasmerely recorded to qualitatively checkthat it corresponds with the other measurements.

Similarly, water temperatures have been recorded sincethe temperature drop in oil should correspond to a tempera-ture increase in water. However, due to the higher heatcapacity of water the absolute temperature increase in wateris roughly a factor of two lower than the temperature drop inoil. This increases the measurement uncertainties withoutadding any additional information. Also, the water tempera-ture difference cannot be used to calculate the wax thicknesswithout precise information about the wax deposit’s heatconductivity.

Comparison ofMethods.All of the describedmethods havetheir specific advantages and disadvantages.

The pressure drop method can be performed online with-out interrupting the experiment and draining the rig. It istherefore the only method available that manages to recordthe development of the wax thickness over time. Unfortu-nately, this method is only available for single-phase flowsince the friction factor for multiphase flow is highly flowregime dependent and no correlations for the friction existfor multiphase flow that are as accurate as Haaland’scorrelation for single-phase flow.

The weighing of a small test section is a robust and reliablemethod provided that the wax density has been measuredappropriately and the test section has been completelydrained for remaining oil. It can obviously only be perfor-med when the experiment has been stopped and the rig fullydrained. Also the resulting wax thickness is an average overthe test section. If, for example, stratified oil-water flowexperiments were to be carried out, wax would only depositon the pipe wall in contact with the oil phase. This spatialvariation of the wax thickness cannot be captured by theweighing method.

The laser-based optical method can at present only becarried out when the experiment is interrupted and the testsection fully drained. In contrast to theweighingmethod, thelaser method should be able to detect also spatial variationsof the wax deposit. In a planned futuremodification the laserwill be changed from visible light to near-infrared at awavelength where oil is transparent it should also be possibleto carry out measurements without draining the test section.

Figure 9 shows a comparison of the results from the threemethods for a one-week experiment. The experiment wasinterrupted two times in-between (at t=23 and 92 h) to carryout weight and laser measurements in addition to measure-ments after the experiment was finished (t=190 h). As can beseen in Figure 9 the results from the threemethods show onlysmall deviations.

In this example the interruption of the experiment didnot lead to any problems. In some cases, however, the

dp measurements showed disruptions after restartingthe experiment, which is suspected to result from gasbubbles in the dp cell’s impulse lines. After several ofthese incidents it was concluded to only run uninterr-upted experiments. This results in smooth continuousdp curves but removes the possibility of obtaining depositsamples at different timesteps for investigating the changein the deposit’s composition (aging). If aging is to beinvestigated in more detail, a series of experiments withincreasing durations has to be carried out where eachexperiment runs uninterrupted. This is obviously a verytime-consuming method and was not pursued in thiscampaign.

Results for Constant Temperature Gradient

Motivation and Experimental Procedure. The standardassumption about the drivingmechanism for wax depositionis that a temperature gradient from the bulk flow toward thepipe wall causes a concentration gradient of dissolved wax(see e.g., refs 5-7). This concentration gradient determinesthe diffusion of waxmolecules leading to a change in the waxthickness h over time

dh

dt¼ D

dC

drð3Þ

Figure 8. Laser image evaluation.

Figure 9. Comparison of wax thickness measurement methods.

(5) Svendsen, J. A. AIChE J. 1993, 39, 1377–1388.(6) Matzain, A.Multiphase Flow Paraffin DepositionModeling; Ph.D.

Thesis, University of Tulsa, 1999.(7) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. AIChE J.

2000, 46, 1059–1074.

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where D is the diffusion coefficient and dC/dr the concen-tration gradient. This concentration gradient can be splitinto

dC

dr¼ dC

dT

dT

drð4Þ

where dC/dT represents the gradient of the wax solubilitycurve of the fluid and dT/dr is the temperature gradient nearthe pipe wall.

Tomeasure only the influence of the wax solubility curve aseries of experiments was run in the test rig where thetemperature gradient dT/dr was kept constant but the abso-lute temperature was varied. So, the first experiment had anoil temperature of Toil=10 �C and a cooling water tempera-ture ofTwater=5 �C, the next experiment hadToil=15 �CandTwater=10 �C, and so on.

In a first series of experiments, the oil temperature wasincreased for each experiment by 5 �C, starting atToil=10 �Cfor the first experiment. In the final experiment atToil=35 �Cno wax deposition was detected at all (measured by pressuredrop, weighing, and laser). The oil flow rate was keptconstant at high levelQoil=21 m3/h. In a second series someof the points were repeated at a low oil flow rateQoil=5m3/hto measure the influence of shear forces on the wax thicknessand the influence of the flow rate on the deposit’s compo-sition.

Wax Appearance Temperature (WAT) and Wax Solubility

Curve. Figure 10 shows the resulting wax thicknesses after50 h as a function of the wall temperature for two differentflow rates. The temperature difference between oil and cool-ing water was always 5 �C. The wall temperature shown inFigure 10 is the interface temperature between oil and steel atthe start of the experiment, that is, without any wax depo-sited. It was calculated by using the well-known equationsfor heat transfer in turbulent flow.8

First, the total heat transfer coefficient Utot from oil towater (for a clean pipe without wax deposit) is calculated

1

Utot¼ 1

hfilmoil

þ 1

hsteelþ 1

hfilmwater

ð5Þ

hsteel ¼ 2ksteel

Doil lnDoil þ 2dwax þ 2dsteel

Doil þ 2dwax

ð6Þ

hfilmwater¼ 0:023Re0:8waterPr

0:33water

kwater

Dwaterinner

hfilmoil¼ 0:023Re0:8oil Pr

0:33oil

koil

Doilð7Þ

Reoil ¼ FoilvoilDoil

ηoil

Proil ¼ cpoilηoilkoil

voil ¼ _moil

FD2oil

π

4

Rewater ¼ FwatervwaterDwatereff

ηwaterð8Þ

vwater ¼ 4 _mwater

FwaterπðD2waterouter

-D2waterinner

Þ ð9Þ

Dwatereff ¼

ðD2waterouter

þD2waterinner

Þ- ðD2waterouter

-D2waterinner

Þln

Dwaterouter

Dwaterinner

Dwaterouter -Dwaterinner

ð10ÞUsing this total heat transfer coefficient Utot and the heat

transfer coefficient hfilmoil, which describes the heat flow from

the bulk oil flow toward the inner pipe wall, the pipe walltemperature can be determined as

Twall ¼ Toil -Utot

hfilmoil

ðToil -TwaterÞ ð11Þ

Using this set of equations it is also easy to estimate the

temperature gradient at the pipe wall dTdr

�� which will be used

later on

dT

dr

�� ¼ hfilmoil

koilðToil -TwallÞ ð12Þ

Several interesting observations can be made from theseresults. One is that wax deposition was found to start some-where in the interval between 27.5 and 32.5 �C. It is instruc-tive to compare thisWATderived under real flow conditionswith the various small-scale lab tests that are used typically todetermine WAT: (1) DSC: As an oil sample cools below itscloud point wax crystals are formed. This results in a smallamount of heat being produced and therefore a slight rise inthe temperature of the sample. During a DSC analysis, theheat flow between two small aluminum pans is measuredvery accurately. One pan is empty and the other pan containsa small amount of oil. The DSC apparatus measures thedifference in the temperature of the two pans. As the waxappearance temperature is reached, the pan containing oilcools at a slightly slower rate than the empty pan, which is

Figure 10. Influence of wall temperature at constant temperaturegradient.

(8) Kays, W. M.; Crawford, M. E. Convective Heat and Mass Trans-fer; McGraw-Hill: New York, 1987.

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exhibited as an inflection in a cooling curve.9 For the fluidused here the WAT determined by DSC was 29( 1.5 �C. (2)NIR:TheNIRwaxonsetmethod is based on the observationthat there is a sharp increase in light absorption or attenuatinin the near-infrared region at the onset of wax crystallization.This is due to the formation of light-scatteringwax crystals.10

For the fluid used here the WAT determined by NIR was27( 1 �C. (3)Microscopy: The appearance of wax crystals isdetermined optically in a microscope using cross-polarizedlight.11 For the fluid used here the WAT determined bymicroscopy was 30( 1 �C. (4) Rheometer: The precipitationof wax results in a change of the fluid’s viscosity. The onset ofthis deviation can be detected using a statistical methoddescribed in ref 12. For the fluid used here the WATdetermined by rheometer was 31 ( 0.5 �C.

To summarize, it can be concluded that it is possible to usesmall-scale lab methods to determine a wax appearancetemperature that agrees well with the temperature at whichwax starts to deposit in a real flow loop. The small spread inthe resulting WAT for the various measurement techniquesis due to the different sensitivities of the techniques and doesnot necessarily reflect different physical conditions.

Another interesting application for the measured waxthicknesses is to check the validity of the assumption ofmolecular diffusion as the main mechanism that is steeringwax deposition (see eq 3). Since the temperature gradientdT/dr has been constant for all the experiments, the waxdeposition should follow the wax solubility curve. Figure 11shows a comparison of the measured wax thicknesses (atQoil

=21 m3/h) with the amount of wax that precipitated in aDSC instrument at comparable temperatures. The twocurves show a remarkable similarity, indicating that waxsolubility and thus also wax diffusion are indeed a majorparameter for wax deposition.

Wax Deposit Composition. To determine the compositionof the wax deposit, gas chromatography (Hewlett-Packard

6890A GC) is used. Figure 12 shows a comparison of thecomposition of the deposits that were retained from theexperiments at high flow rate (Q=21 m3/h). The figure alsoshows the composition of the waxy fluid. Compared to thefluid, the deposits show a significant peak ranging fromabout C25 to C45. This peak represents the accumulatedwaxy components in the deposit. Comparing the chromato-graphs of the deposits from different temperatures showsthat the wax peak size is growing significantly for highertemperatures and shifting its center toward heavier carbonfraction. This is in line with the visual observations of thedeposit where the wax layer for higher temperatures wasfound to be thinner (see Figure 10) but also harder than forlower temperatures. This growing hardness will probably bethe result of a combination of the two effects: the increase ofthe amount of wax in the deposit and the change of the waxcomposition toward heavier hydrocarbons.

The reason why the wax composition changes towardheavier hydrocarbons for higher temperatures is probablyrelated to the solubility of the various wax components. Forthe lower temperatures most of the heavier hydrocarbonshave already precipitated in the oil bulk flow. Since themostly accepted theory in the wax community is that waxdeposition is only possible by dissolved wax molecules butnot by precipitated wax crystals, these heavier hydrocarbonsare not available for wax deposition at lower temperatures.At higher temperatures where these heavier hydrocarbons

Figure 11. Comparison of wax deposition in rig with wax precipitation in DSC.

Figure 12.Comparison of wax deposit compositions (Q=21m3/h,Toil - Twater = 5 �C).

(9) Coutinho, J. A. P.; Goncalves, C.; Marrucjo, I. M.; Pauly, J.;Daridon, J.-L. Fluid Phase Equilib. 2005, 233, 28–33.(10) Leontaritis, K. J. Cloud point and wax deposition measurement

techniques. SPE International Symposium on Oilfield Chemistry, Houston,Texas, 2003.(11) Zougari, M. I.; Sopkow, T. Ind. Eng. Chem. Res. 2007, 46, 1360–

1368.(12) Sch€uller, R. B.; Tande, M.; Almøy, T.; Sæbø, S.; Hoffmann, R.;

Kallevik, H.; AmundsenAnnu. Trans. Nordic Rheol. Soc. 2009, 17, 191–197.

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are still in solution they start to contribute significantly to thewax deposit. The reason why the wax composition at thesehigher temperatures no longer includes the same amount oflighter hydrocarbons must be due to the fact that at thesetemperatures the wall temperature is so high that the lighterheavycarbons cannot form wax crystals at the pipe wall. Tosummarize, the condition for a certain carbon fraction toparticipate in the deposition process is that it needs to be insolution at the bulk temperature but it also needs to crystal-lize at the wall temperature.

As can be seen from the chromatographs that the depositfound on the inner pipe never consists entirely of wax but isalways a combination of wax and oil, where oil is entrappedin the wax network. The amount of oil in the deposit is oftencalled porosity (P) in the literature and is an importantparameter since the included oil will increase the thicknessof the deposit compared to a hypothetical deposit consistingonly of wax. Typically, wax deposition models enhance thebasic diffusion eq 3 by including the porosity13

dh

dt¼ 1

1-PDdC

drð13Þ

To test these models against the experimental data it istherefore important to define the amount of oil/wax in thedeposit. The method used here is based on the deposit’s GCdata. Figure 13 shows a typical chromatogram of a waxdeposit.

The peak including the wax components starts at C24 (seeFigure 13), where the measured weight fractions start todeviate from the exponential decline typically seen in wax-free oils. The problem is to define which amount ofthe components heavier than C24 are due to the wax inthe deposit and which of them are due to the included oil inthe deposit. The method used here is to fit an exponentiallydeclining curve based on themeasurements fromC10 toC20,that is, in a region where no wax components should occur.This curve is assumed to describe the pure oil. Only the areaabove this curve (marked dark gray in Figure 13) is assumedto include wax. So the wax content of a deposit is calculatedby integrating the area between the wax peak and theexponential fit.

Figure 14 shows the resulting wax content for the depositsfrom variouswall temperatures at low and high flow rate. All

experiments were run at 5 days except the one forTwall=17.5�C and Qoil = 5 m3/h, which was run for 11 days. Theconclusions that can be drawn from the results shown inFigure 14 are: (1) Wax content increases for deposits ob-tained at higher wall temperatures. (2)Wax content is higherfor higher flow rates. (3)Wax content is increasing with time.Thewax content forTwall=17.5 �CandQoil=5m3/h is higherthan the next one at Twall = 22.5 �C due to the longerexperimental runtime.

The higher wax content coincides with the observation ofharder wax deposit for all three cases (higher wall tempera-ture, higher flow rate, and longer experimental runtime).

Some of the experiments were repeated and the differenceof the measured wax content for equal experimental condi-tions was found to be below 5%.

Results for Constant Cooling Temperature

Experimental Procedure. In a real subsea application thecooling medium of the pipeline (i.e., seawater and sea bed)has approximately constant temperature, whereas the fluidin the pipeline typically starts at high temperatures and iscooled down in the pipeline until it reaches the same tem-perature as the surrounding seawater.

Therefore, a second series of experiments was run withconstant cooling temperature Twater=10 �C, which is thelowest cooling temperature that can be kept stable in the rigduring summer times and various oil temperatures, rangingfrom Toil=15 �C up to Toil=50 �C. At Toil=50 �C theresulting wall temperature is around 30 �C where waxdeposition was found to cease in the previous serious ofexperiments (see Figure 10). The oil flow rate was keptconstant atQoil=21m3/h for all experiments.Unfortunately,no wax content measurements are available for these experi-ments.

WaxStructure.Figure 15 shows the pressure drop increaseover time for the various experiments. Unfortunately, it isnot possible to show the wax thickness for each experimentssince some of the experiments showed highly irregulardeposits (see below) that make the calculation of wax thick-ness from pressure drop impossible. For each experimentthe oil bulk flow temperature Toil and the inner pipewall temperature Twall are specified in Figure 15. Twall is

Figure 13. Definition of wax content from GC results.

Figure 14.Deposit wax content depending on wall temperature andflow rate.

(13) Hovden, L.; Rønningsen, H. P.; Xu, Z. G.; Labes-Carrier, C.;Rydahl, A. Pipeline Wax Deposition Models and Model for Removal ofWaxbyPigging:Comparison betweenModelPredictions andOperationalExperience; Multiphase Technology: Banff, Canada, 2004.

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calculated for the start of the experiment where no wax wasyet deposited, that is, at the interface of oil and steel.

Several observations can be made from Figure 15: (1)Pressure drop (and thus wax thickness) increases fastest forthe lowest wall temperatures. This is consistent with thesolubility curve that shows the highest gradient in this lowtemperature region. One exception is the curve for Toil =20 �C,Twall=14.4 �C:This curve rises faster at the start of theexperiment than any other curve, including the one withlower wall temperature (Toil=15 �C, Twall=12.1 �C). Thiscan be partly explained by not only looking at the solubilitycurve but also at the total concentration gradient dC/dr=(dC/dT)/(dT/dr). This is plotted in Figure 16 and shows aclear peak at aboutTwall≈ 17 �C.This curve has been derivedbymultiplying the gradient of the solubility curve (measuredin the DSC) by the temperature gradient at the inner pipe

wall dTdr

��. The innerwall temperatureTwall and the temperature

gradient at the inner wall dTdr

�� are calculated by eqs 11 and 12,

respectively. (2) The curve for Toil=25 �C, Twall=16.8 �Cshows instabilities for t > 100 h, which was caused bynonstable experimental conditions (the experiment wasstopped several times to obtain deposit samples). (3) The

curves for oil temperatures up to Toil = 30 �C show acontinuous rising trend with no sign of reaching an asymp-totic state. In contrast to this, the curve for Toil=40 �C, Twall

=24.7 �C becomes asymptotic for t > 100 h. However, thefluctuations of the pressure drop are much higher here thanthose that are usually observed. When the deposit wasinspected visually after the experiment was finished itshowed a very different structure then is usually observed.Figure 17 shows a comparison of the wax that was depo-sited at Toil=20 �C, which was smooth and homogeneous,and the one that was deposited at Toil=40 �C. This waxshowed a highly irregular structure where spots of wax withdiameters of some millimeters were surrounded by areas ofbare steel.

Determination of the hydraulic roughness of this depositby flow rate variation (see Figure 3) showed a roughnessaround 40 μm, whereas the smooth deposits that are usuallyobtained show a roughness below 5 μm. The experiment atToil=40 �Cwas repeated to ensure the validity of the results.More experiments were carried out with variation of the oiland water temperature to find out more about the onset ofthis different type of deposit. It seemed like that there is agradual onset of this phenomenon for high oil temperaturesToil > 30 �C (i.e., Toil ≈ TWAT) and high oil-water tem-perature differences Toil - Twater > 20 �C.

A possible explanation for this deposit structure is that atthe high wall temperatures the adhesion force between thewax layer and the steel pipe is so low that wax is periodicallyremoved from the pipe wall due to the turbulent shear force.That means that the overall amount of wax stays constantover time but that the actual topology changes constantly.That would also explain the high fluctuation in the pressuredrop measurements.

A conclusion of this observation is of course that theclassical diffusion-based models are not suitable to representthis type of deposition. So, care has to be taken whenperforming a simulation of a real subsea production pipelineon how the simulation results for the first kilometers afterWAT has been passed are evaluated. A classical mole-cular diffusion-based model will probably overestimatewax deposition in this region.

Results for Varying Oil Flow Rate

Motivation. Since the results shown above indicated a signi-ficant influence of the oil flow rate (see Figures 10 and 12)a separate series of experiments was run where the oil flow ratewas varied from 5 to 25 m3/h . This corresponds to a variationof the shear stress τ from 5 to 89 Pa.

τ ¼ 1

2f Foilv

2oil

where f=0.315Re-0.25 is the Blasius friction factor,14 Foil is theoil density, and voil is the oil velocity. The shear rate dv/dy variesfrom 444 to 7420 s-1.

dv

dy¼ 1

8fv2oil

Foilηoil

where ηoil is the oil viscosity. The temperatures of oiland water were kept constant at Toil=20 �C and Twater=10�C. Due to the varying flow rate, the inner steel wall tempera-ture Twall, calculated by eq 11, varies from 12.2 to 15.2 �C.

Figure 15. Influence of oil temperature at constant cooling tempe-rature.

Figure 16. Concentration gradient as a function of temperature.

(14) Blasius, H. Z. Ver. Dtsch. Ing. 1912, 56, 639–643.

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Wax Deposition Thickness. Figure 18 shows the resultingwax thickness for the experiments with varying oil flow rate.A clear trend is visible that indicates thinner wax deposits forincreasing flow rates, confirming the findings shown alreadyin Figure 10.

The problem is that this behavior cannot be explainedby a diffusion model. Figure 19 compares the measuredwax thickness after 50 h for the various flow rates withthe calculated concentration gradient dC/dr=(dC/dT)/(dT/dr), which is the steering factor in a diffusion model(see Section ). As can be seen in Figure 19, the concentrationgradient increases with increasing flow rate whereas themeasured deposit thickness decreases.

The main reason is that the temperature gradient in the

vicinity of the inner pipe wall dTdr

��Twall

is given by

dT

dr

��Twall

¼ hoil

kwaxðToil -TwallÞ

where hoil is the inner convective heat transfer coefficient,kwax is the heat conductivity for the wax layer, Toil is thetemperature of the oil in the bulk flow, and Twall the oil/wallinterface temperature. The heat transfer coefficient can be

approximated by the Colburn analogy15

hoil ¼ 0:023Re0:8oil Pr0:33oil

koil

Doil

where Reoil is the Reynolds number of the turbulent oil flow,Proil is the Prandtl number of the oil, koil is the heatconductivity of the oil, and Doil the diameter of the oil pipe.The dependence on the Reynolds number explains why theheat transfer coefficient rises with increasing flow rate andthus in turn also the temperature gradient and the concen-tration gradient.

A pure diffusion-based model can therefore not explainthe decreasing wax thickness for increasing flow rates. Twoadditional effects are necessary to explain this behavior: thedifferent wax content in the deposit and the effect of increas-ing shear stress.

The wax content’s deposit changes significantly for differ-ent flow rates. Higher flow rates result in a higher waxcontent, leading to a more compact wax deposit. To modelthis behavior an additional set of equations needs to beintroduced that describes the (time-changing) wax contentof the deposit.16 To visualize the amount of the effect,Figure 19 shows also the calculated thickness of pure wax

Figure 17. Comparison of smooth (Toil = 20 �C) and rough (Toil = 40 �C) deposit.

Figure 18.Deposit thickness depending on flow rate (Toil = 20 �C,Twater = 10 �C).

Table 3. Deposit Thickness Depending on Flow Rate (Toil = 20 �C,Twater = 10 �C, t = 65 h)

flow rate Qoil (m3/h) deposit thickness (mm)

5 1.5510 0.9215 0.7521 0.6225 0.53

Figure 19. Comparison of wax thickness with concentrationgradient.

(15) Chilton, T. H.; Colburn, A. P. Ind. Eng. Chem. Res. 1934, 26,1183–1187.

(16) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. R.Agingand Morphological Evolution of Wax-Oil Gels During Externally CooledFlow Through Pipes. Second International Conference in Petroleum PhaseBehaviour and Fouling, Copenhagen, Denmark, 2000.

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by multiplying the total deposit thickness with the measuredwax content of the deposit. This shows that for the flow rateincrease from 5 to 10 m3/h the pure wax thickness doesindeed increase according to the increasing concentrationgradient. For even higher flow rates, however, the pure waxthickness starts to decrease again. The assumption is that thisis mainly an effect of the increasing shear stress at the fluid-deposit interphase.

These effects of increasing shear stress at increasing flowrates have often been discussed in the literature.17-20 Thepossible explanations are either that the increasing shearstress makes it more difficult for new wax molecules toadhere to the already existing wax deposit or that the shearstress removes parts of the already deposited wax. Noconclusion has been reached yet on the dominant mecha-nism and therefore no suitable model is available to incor-porate these effects in a prediction tool. It should also benoted that shear stress is highly dominant on the pipediameter, so to reach a better understanding it wouldalso be necessary to perform experiments with test pipes ofdifferent diameters.

Wax Deposition Composition. The change in wax contentin the wax deposit for varying flow rates is clearly reflected inthe changing composition from the samples taken after eachexperiment (see Figure 20). The area under the wax peak isincreasing with increasing flow rates, which explains theharder and thinner deposit. Only the curves for Qoil= 15and 21 m3/h seem to be almost equal, but this is due to thefact that the experiment at 21 m3/h had to be stopped after100 h whereas all the other experiments were run for about140 h. So the assumption is that, if the 21 m3/h experimenthad been allowed to run further on, the aging effect wouldhave increased its wax peak accordingly.

The discontinuity of the gas chromatography curves inFigure 20 at around C50 is due to the used measurementtechnique. To performmeasurements of solid deposits inGCit is necessary to dilute the deposit 1:100. A side effect is thatthe heavier hydrocarbons are no longer detectable with anacceptable accuracy.

Since the temperature conditions for all experiments werekept constant, the wax peak in the composition of the waxsamples is almost at the same carbon number for all experi-ments. Only a slight shift toward lower carbon numbers canbe detected for the wax peak at the lowest flow rate (Qoil=5m3/h). The explanation for this is that the oil/steel interfacetemperature depends on the oil’s convective heat transfercoefficient. For the lowest flow rate this results in a signifi-cantly lowerwall temperature (Twall=11.9 �CforQoil=5m3/h)than for thehigher flow rates (Twall=14.4 �CforQoil=21m3/h).This lower wall temperature leads to a wax peak at lowercarbon numbers (see Figure 12).

Conclusions and Outlook

The wax deposition experiments in the flow loop usingNorth Sea gas condensate showed that it is possible to obtainstable repeatable data on both wax deposit thickness andcomposition. The results were confirmed by repetition of theexperiments and the wax thickness measured by three inde-pendent measurement techniques (pressure drop, weight, andlaser). The laser measurement technique is a new techniquethat will also be very valuable when continuing with multi-phase experiments, as it can also measure the spatial distribu-tion along the circumference.

One important result from these flow loop experiments is toshow that theWAT value that is measured using various small-scale labmeasurement techniques is indeed representative for thetemperature where wax starts to deposit in a real turbulent flow.

Another conclusion from the experimental results is that,indeed, molecular diffusion seems to be the dominant me-chanism for wax deposition for most of the temperaturesstudied. So any model that attempts to describe the processwill have to use a diffusion equation as the main buildingblock. However, the results from different flow rates anddifferent experimental runtimes also showed clearly that thewax content cannot be consideredas an independent, constantparameter. So a useful model will also have to include a set ofequations describing the wax content or even needs to becompositional, that is, to treat the various wax componentsindependently. In addition there is the open issue of modelingthe effect of shear stripping. Currently there is nomodel basedon first-principles available so this will probably have toremain an empirical term as in ref 6.

However, for certain temperature conditions (high oil tem-perature and low wall temperature) a new type of depositstructure was found that was rough and irregular comparedto the otherwise smooth and homogeneous deposits. This newtype of deposit cannot be describedby a diffusion-basedmodel.

Having managed to acquire high-quality reliable data anatural next step will be to test available wax depositionsimulation tools like Olga2,21 or theMichigan wax depositionmodel22 against these data.

Figure 20.Deposit compositiondependingon flowrate (Toil=20 �C,Twater = 10 �C).

(17) Hernandez, O. C.; Sarica, C.Effect of FlowRegime, TemperatureGradient and Shear Stripping in Single-Phase Paraffin Deposition. 11thInternational Conference Multiphase '03, San Remo, Italy, 2003.(18) Matzain, A.; Zhang, H.-Q.; Volk, M.; Redus, C. L.; Brill, J. P.;

Apte, M. S.; Creek, J. L. Multiphase flow wax deposition model.Engineering Technology Conference on Energy, New Orleans, Louisiana,2000.(19) Venkatesan, R. The Deposition and Rheology of Organic Gels;

Ph.D. Thesis, University of Michigan, 2004.(20) Singh, P.GelDeposition onCold Surfaces; Ph.D. Thesis, University

of Michigan, 2000.

(21) Rygg, O. B.; Rydahl, A.K.; Rønningsen,H. P.Wax deposition inoffshore pipeline systems. BHRG Multiphase Technology Conference,1998.

(22) Singh, P.; Venkatesan, R.; Fogler, H. S.; Nagarajan, N. R.AIChE J. 2001, 47, 6–18.

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Regarding the next experimental campaign, several possi-ble routes are open: (1) One option is to repeat parts of theexperiments with a different crude oil to avoid drawing allconclusions froma single fluid. Preferrably, a heavier crude oilshould be used that also shows a higher pour point so thatgelling effects will be more visible when operating at lowtemperatures. (2) A series of experiments with identicaltemperatures and flow rates but different runtimes shouldbe carried out to gather more-reliable data on the effect ofaging. (3) By repeating someof the experimentswith anew testsection at a different diameter, the effect of shear stripping

could be investigated in more detail. Since production pipe-lines usually have considerably larger diameters than thetypical 2 in. that is used for flow loops it is especially importantto learn about the scale-up laws that apply to wax depositionmodels. (4) Also, since most production streams consist notonlyof single-phase oil flowbut contain alsowater and/or gas,the test rig will be modified so that two-phase flow experi-ments using oil and water mixtures can also be performed.This will open up a whole new set of parameters since the flowregime (stratified-wavy, dispersed, etc.) will have considerableinfluence on the wax deposition.

single-phase wax deposition experiments

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