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RESIDENCE TIME DISTRIBUTIONS AND FLOW BEHAVIOUR

WITHIN PRIMARY CRUDE OILWATER SEPARATORSTREATING WELL-HEAD FLUIDS

M. J. H. SIMMONS1, E. KOMONIBO

2, B. J. AZZOPARDI

2and D. R. DICK

3

1Department of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham, UK2School of Chemical, Environmental and Mining Engineering, University of Nottingham, Nottingham, UK

3BP Exploration, Sunbury on Thames, UK

Within primary crude oil separators used by the oil industries, the residence time dis-tribution of both organic and aqueous phases has been obtained for the purpose offlow diagnostics. This paper describes the application of the Alternative Path

Model developed by Simmonset al.(2002) to give a quantitative description of the hydrodyn-

amics and mixing within several field separators. Parameters developed from the model areused to describe the degree of mixing within the vessels. The model shows that vessel per-formance is affected by the internal configuration (flow smoothing baffles and separationplates) and the primary separation duty (gasliquid or oilwater). The presence of bafflingis shown to reduce the turbulence within the flow for oilwater separation, but less so forgasoil separation, which had the overall effect of increasing mixing levels, perhaps due tothe buoyancy of the fast rising gas bubbles. The presence of secondary peaks on some ofthe measured residence time distributions indicates the presence of secondary flows withinthe main body of the separators. This was most noticeable when the differential velocitybetween the oil and water phases was high.

Keywords: multiphase flow; liquid liquid mixing; residence time distribution; crude oil waterseparators; gravity settling.

INTRODUCTION

Gravity separation of the mixture of fluids produced frompetroleum reservoirs is used to achieve a primary splitbetween the gas, oil, and water phases. This operation isnecessary since it is the usual practice to separate thephases before pumping to downstream process facilities.This is done in order to remove the water phase and alsoto prevent operational difficulties, such as the presence of

slug flow in the pipelines, which may occur. Since thevolume flow rates of the fluids produced are very large,the separation process is usually performed in a train ofhorizontal cylindrical vessels.

Recent trends in the design of offshore platforms and fluidseparation equipment are aimed at reducing costs by savingon space and weight, which creates considerable motivationfor the development of methods to improve separation effi-ciency. To achieve this, it is necessary to accelerate theseparation process. The major factors controlling the separ-ation of the phases are the settling and coalescence of drops

(Gerunda, 1981). Both of these processes can be acceleratedby augmenting the gravitational force, which has led todevelopment of centrifugal devices, such as hydrocyclonesand also electrostatic devices (Bailes and Larkai, 1981,1982). However, these methods do not have sufficient flexi-bility because adverse factors affect the operation of the sep-aration train. These factors include fluctuations in the flowrate, changes in the water cut (the volume fraction of

water) and the solids content, the flow pattern at the vesselinlet and variations in the physical properties of eachphase. For these reasons, the degree of separation obtainedbetween the phases, particularly for oil and water, can bepoor and high cross-entrainments are observed.

The most recent approaches have been directed towardsimproving the efficacy of gravity settlers. Effort has beenfocused upon the modification of the vessel internalseither by introducing structured packing or perforatedbaffle plates to promote coalescence and smooth the flowrespectively (Meon et al., 1993; Nilsen and Davies, 1996;Rowley and Davies, 1988; Simmons et al., 2002;Wilkinson et al., 2000).

Despite the many improvements made in the application

of computer modelling techniques such as computationalfluid dynamics (CFD) for multiphase flows (Hansen et al.,

Correspondence to: Dr M.J.H. Simmons, Department of Chemical Engin-eering, University of Birmingham, Edgbaston, Birmingham, B1S 2TT, UK.E-mail: [email protected]

1383

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1991; Mohamad Nor and Wilkinson, 1998; Rashad et al.,1997; Wilkinson and Waldie, 1994; Wilkinson et al.2000)these cannot be used to predict the flow field within theseparators a priori due to the highly complex multiphasehydrodynamics present. A particular problem experiencedin model validation is the varying physical properties ofthe phases in the separators due to the presence of contami-

nants. It is therefore necessary to complement any modellingwith flow visualization; however, this is impossible for fieldvessels since they operate under pressure and are constructedfrom steel. An alternative approach is to deduce the flowbehaviour by obtaining residence time distributions (RTD)for each phase. This approach has been used to yield quali-tative information on field vessels (Dick, 1997). Simmonset al. (2002) recently measured RTDs on a one-fifth scalemodel (pilot-scale) of a primary separator operated by BPOil on the Forties Oil Production Facility in the North Sea.This work introduced the Alternative Path Model (APM)as a means of developing quantitative parameters to describethe level of mixing.

In this paper, experimental measurements of RTD madefor British Petroleum for a selection of field separators arepresented (Dick, 1997). The modelling approach describedby Simmons et al. (2002) is applied to obtain parametersthat are used to determine the relative levels of turbulenceand mixing. This information is used to assess the perform-ance of each separator with respect to the internal configur-ations and the operating parameters.

EXPERIMENTAL

Equipment

The RTD data was provided by British Petroleum (BP)

for several field primary separators. These separators areUla, Norway; Kinneil, UK; Milne Point, Alaska andMagnus, UK (Dick, 1997). Schematics of the vessels aregiven in Figure 1, which shows that the internals employedin each vessel vary considerably in sophistication. The Ulaand Magnus vessels might be described as the most basictype employed in this study (Figure 1a). They containa momentum breaker at the inlet to attempt to reduce theturbulence caused by the jet of liquid impacting on thefree surface of liquid within the vessel. A baffle is usedto separate the oil and water phases and the oil and wateroutlets are equipped with vortex breakers to prevententrainment of other phases due to vortices. A demister

pad is installed at the gas outlet to knock out any fine par-ticles of liquid. These vessels are used primarily for thethree-phase disengagement of gas, oil, and water.

The Milne Point vessel (Figure 1b) is somewhat morecomplex in configuration and also used for three-phase sep-aration. The risk of slugging, due to the configuration of thephases in the inlet pipework, has heavily influenced thedesign of the inlet section, where the feed passes downan expanding pipe through the length of the vessel inorder to dampen out any fluctuations in the flow. Thevessel is equipped with a perforated baffle downstream ofthe vessel inlet to attempt to smooth the flow through themain body of the vessel. Vane packs are installed to attemptto accelerate droplet coalescence. The outlet design is simi-

lar to that used applied to the Ula and Magnus vessels(Figure 1a) except that an elevated vortex breaker is used

instead of a baffle to separate the oil phase from thewater phase.

The Kinneil vessel, shown in Figure 1c, makes use ofa perforated baffle at the inlet combined with a cyclonic

inlet device that extends beneath the liquid surface in thevessel. The purpose of the perforated baffle is to smooththe flow through the vessel, as mentioned previously,while the cyclonic inlet device is present to assist in theknock out of the gas phase. Further smoothing baffles areinstalled along the length of the vessel to minimize thepossibility of formation of recirculation zones. Thisvessel differs from the others in that the main duty is theseparation of gas and liquid phases and only very smallamounts of water are present in the feed. All the othervessels are used primarily for oilwater separations.

Measurement Techniques

The significance of the distribution of residence timesin continuous flowing systems was first presented by

Figure 1. Schematic diagrams of the field separators.

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Danckwerts (1953) and a thorough explanation of theexperimental methodologies required to obtain RTDs isgiven in Levenspiel (1999). Critical to the determinationof the RTD is selection of an appropriate tracer. This isusually injected at the inlet of the flow system and by moni-toring of the concentration of the tracer at the system out-lets, the RTD may be obtained. Ingersoll (1951) discussed

the use of appropriate chemical tracers to investigate thehydraulic performance of separators. The measurement ofthe RTDs presented in this study involved the use of aradioactive tracer, Bromine-82, which was introducedinto the inlet process stream as an instantaneous pulse(Dick, 1997). Oil-soluble and water-soluble tracers wereused to enable monitoring of the individual passage ofthe oil and water phases via external scintillation detectorsmounted on the inlet and water/oil exit lines.

Since tracers were injected into the inlet stream as aninstantaneous pulse (Dirac delta function), the RTD of thevessel can be obtained from the outlet concentration distri-bution directly (Levenspiel, 1999). At the vessel outlet, the

outlet concentration at timet,c(t) is measured, wheret

0at the instance of tracer injection at the inlet. The exit age dis-tribution or residence time density function, E(t), is definedas the fraction of elements leaving with ages between tandtdt(Danckwerts, 1953). If the tracer is an instantaneouspulse,E(t) can be obtained by normalizing the exit concen-tration with respect to the area under the c(t) curve thus:

E(t) c(t)1

0 c(t) dt

(1)

Hence

10

E(t) 1 (2)

and it follows that

10

c(t) dtm

Q (3)

where m is the mass of tracer injected and Q is the volumetricflow rate of the organic or the aqueous phase. Since E(t) isnormalised, it is not necessary to know m, although if it isknown, the mass balance can be checked. The mean resi-

dence time (MRT), is given by (Levenspiel, 1999).

MRT

10

tE(t) dt (4)

Using

E(t) c(t)1

0 c(t) dt

(5)

we obtain

MRT1

0

tc(t) dt1

0 c(t) dt (6)

The upper limit in the integrals in the above equations can bereplaced by some finite time, T, beyond which no more tracercan be detected. It hence follows from Danckwerts (1953)that the MRT can also be found from

MRTA VA

Q(7)

where VA is the active vessel volume through which eachrespective phase flows.

Experimental Parameters

The RTD measurements were made for both oil and aqu-eous phases over a range of flow rates for the separatorsdescribed above. Operating parameters, vessel geometriesand MRTs calculated from both equations (6) and (7) aregiven in Table 1, together with heights of the gasoil andoilwater interfaces obtained from the interface level indi-cators installed on each vessel. The MRTs for either the

organic or aqueous phase obtained from equation (7)have been calculated using the measured volumetric flowrate and the volume of the vessel occupied by the respect-ive phase. The volume of each phase was determined bycalculating the cross-sectional area occupied by eachphase on the basis of the measured interface heights (illus-trated in Figure 2) and then multiplying by the vessel lengthto obtain a volume.

Table 1 shows that the values of MRT calculated viaboth methods are different. This indicates some form oferror in the experiments or model assumptions since, bycontinuity, the values should be the same. This can beattributed either to errors in the interface height measure-ments or blockage of the vessel active volume due to depo-

sition of solids or internals. These effects are illustrated bya fractional dimensionless volume, VD, in Table 1, whichrepresents the actual volume occupied by each phasebased on the measured MRT, V, divided by the volumeeach phase is assumed to occupy based on interfaceheight measurements, VA, that is,

VD MRT

MRTA

V=Q

VA=Q

V

VA(8)

MATHEMATICAL MODEL

Alternative Path Model (APM)

The APM is based on splitting the flow behaviour in thevessels into a series of zones and includes two alternativepaths for the fluid to travel that have different time con-stants. Possible velocity profiles in the vessel and flowzones are shown in Figure 3a. In the formulation of theAPM, the presence of the rag layer (the layer betweenthe two liquid phases containing one phase dispersed inthe other) is neglected. When systems are described inthis way, the model can be derived mathematically byusing transfer functions from Laplace Domain descrip-tions (Levenspiel, 1999; Luyben, 1990). A block diagramof the APM is given in Figure 3b.

The APM has six adjustable parameters for each phase:

. time constant in inlet mixing (CSTR) zone, t1;

. time constant of a stirred tank in each series, t2, t3;


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The parameters in the model were fitted to the experimen-tally determined exit age distributions,E(t), using the Sim-plex method. A full description of the application of theSimplex method to this problem is given by Komonibo(2002). A fixed value ofN 50 was used for both paths,

since the shape of the RTD becomes rapidly insensitiveto large N.

From these model parameters, it is possible to derive par-ameters that can be related to the hydrodynamics in thevessel. Following Danckwerts (1953), the time constantsobtained from the APM can be used to back-calculate thevolume of the tank occupied by the liquid. First, it is poss-

ible to calculate values of MRT for the organic and aqueousphases respectively,tmo,tmw. where o oil phase and w aqueous phase

tmo t1o fot2o (1fo)t3o (11)

tmw t1w fwt2w (1fw)t3w (12)

The total volume can then be calculated by multiplying bythe individual phase flow rates.

Vtotal Qotmo Qwtmw (13)

The total size of the inlet mixing zone, Vmix can be esti-

mated similarly.

Vmix Qot1o Qwt1w (14)

Figure 2. Illustration of volume occupied by each phase.

Figure 3. (a) Possible flow zones within separator; (b) block diagram of Alternative Path Model (APM).



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The Fractional Mixed Volume,D, is defined as the frac-tional amount of the vessel active volume occupied by tur-bulent mixing at the inlet, that is,

D Vmix

Vtotal(15)

Values of fractional mixed volume close to unity indicatehigh turbulence within the vessel, which would impedesettling. Values close to zero indicate a plug-like flow. Ifit is assumed that the mixing zone occupies the totalvolume of the vessel up to a certain point, after whichthere is a distinct water oil interface, then it can besimply derived that

Dlmix

l (16)

where lmix is the length of the mixing zone and l is theactive length of the vessel.

As described later, a feature noticeable on several of theexit age distributions produced was the presence of a sec-ondary peak. A secondary peak number, F, is proposedthat can be calculated from parameters in the APM.

F f t3

t21

(17)

For full details of the physical basis of the model and thedevelopment of the model parameters, the reader is directedto the paper of Simmons et al. (2002).

RESULTS AND DISCUSSIONTable 1 shows the values of MRT calculated from

equations (6) and (7) and fractional dimensionlessvolume, VD. For the Kinneil and Magnus vessels, thevalues of VD are close to unity, which indicates accuratemeasurement of interface height and an absence ofblockages within the vessels. However, this is not thecase for the Milne Point and Ula vessels where VDdeviatesboth above and below unity. For the Milne Point vessel, VDis below unity for the organic phase and above unity for theaqueous phase. This would seem to indicate a systemicunderprediction of the height of the oilwater interface,since the measured MRT of the oil and aqueous phases

are respectively shorter and longer than expected. Interfaceheight measurements are known to be prone to error due tothe presence of a rag layer between the oil and water phasesand this effect, although not measured, may be attributable.This is also the case for the Ula vessel (Expt. 14), althoughhere the effect is even more marked. This result raises animportant and sometimes neglected issue in the control ofsuch separators, since the calculation of MRT for eachphase is commonly done by plant operators on the basisof interface height information. On the basis of this data,this can lead to errors of up to 100% (Expt. 15), with con-sequences for the separation efficiency.

Examples of the exit age distributions produced for bothorganic and aqueous phases for the Milne Point vessel are

given in Figure 4. The injection of tracer at the vessel inletcorresponds to time 0 on the x-axis for all these plots

(Figures 46). The shape of the exit age distribution issimilar for both phases: after a short delay, there is arapid rise to a sharp peak, followed by a slower decayand a long tail. This is particularly noticeable for the aqu-eous phase. The exact length of the tail is generally difficultto predict because of noise in the experimental data. How-ever, in this case there is clearly no offset between the final

and end values of the exit age distribution indicating thatthe entire tracer had exited. A shoulder (indicated onFigure 4b), or secondary peak is observable for the aqueousphase indicating later release of tracer possibly due to asecondary flow or dead zone somewhere in the vessel.The fitted APM curves show a good agreement, althoughthere are some small discrepancies near the tail of the dis-tribution. A check on the fit of the APM may be made bycomparing the measured MRT of each phase with themean residence times obtained from the model, tmo andtmw. The agreement between these parameters was within10% for all experiments, indicating that the fit was ade-quate within experimental accuracy.

Figures 5 and 6 show examples of the exit age distri-

butions produced from the Magnus and Ula vessels. Theshapes of the curves are qualitatively very similar to

Figure 4. Comparison of exit age distributions with APM for Expt. 1,Milne Point vessel: (a) organic phase; (b) aqueous phase.


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those observed in Figure 4 except that no secondary peaksare observed for the Magnus vessel. There is similar goodagreement with the APM. The qualitative similarity

between the distributions produced from different vesselshighlights clearly the need for a modelling approach,since the model parameters allow subtle differencesbetween the E(t) curves to be identified.

The presence of secondary peaks on the exit age distri-butions may be due to the presence of secondary flows.Nilsen and Davies (1996) and Simmons et al.(2002) postu-lated that these flows may be caused by high differentialvelocities between the phases (Figure 3a). Recirculationzones then develop, retarding the release of one or moreof the phases. Hence, a greater amount of secondarypeaks would be expected at higher differential velocities.For the Milne Point vessel, there is a general increase in

the secondary peak number, F, with increasing differentialvelocity, as shown in Table 1 and Figure 7. Insufficientexperimental data are available to compare trends in theother vessels. The presence of a rag layer may also causesimilar effects and this needs further investigation.

The variation of fractional mixed volume with water cutis shown in Figure 8. Since the minimization of mixing andturbulence would be expected to ease the separation of thephases, this parameter can be used as a measure of the sep-aration efficiency of the vessels. Upon examination of thevalues, fractional mixed volumes for Ula and Magnus areapproximately between 0.5 and 0.8. Values for MilnePoint are approximately 0.3. This suggests that the con-siderably more sophisticated internals of the Milne Point

vessel are having a desirable effect in reducing the overallturbulence in the vessel and also demonstrates that this

parameter can be used to characterize the relative levelsof turbulent mixing. Another important factor is thevessel L/d ratio. The Milne Point vessel has a high L/dof nearly 7, hence the flow has more length over whichthe flow can stabilize compared with the other vessels,which have L/d ratios from 2.8 to 4. This longer designis advantageous. The values of fractional mixed volume(Table 1) obtained for the Kinneil Separator are veryhigh, approximately 0.70.9. This shows that there is still

Figure 5. Comparison of exit age distributions with APM for Expt. 12,Magnus vessel: (a) organic phase; (b) aqueous phase.

Figure 7. Variation of secondary peak number, F, with differential phasevelocity for Milne Point vessel.

Figure 6.Comparison of exit age distributions with APM for Expt. 14, Ulavessel: (a) organic phase; (b) aqueous phase.



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considerable mixing in the liquid phase despite internal baf-fling. This could be due to the rapid rise of bubbles of gas inthe oil, driven by buoyancy effects arising from large den-sity differences between the gas and oil phases since thisvessel is used primarily for gasoil separation.

CONCLUSIONS

The alternative path model (APM) has been applied toobtain parameters describing the hydrodynamics and separ-ation performance of field separators from residence timedistribution (RTD) data. The model was fitted to the exper-imental exit age distributions using the Simplex method

and good agreement was obtained. For one of the vesselsused, the secondary peak number, F (an indication of thepresence of dead zones and re-circulatory effects) wasfound to generally increase with increasing differential vel-ocity between the organic and aqueous phases. Values offractional mixed volume,D, are lowest for vessels contain-ing baffles at the inlet and down the body of the vessel tosmooth the flow and lower turbulence. A long vessel, thatis, high L/d, is advantageous. The effect of the baffles isreduced for gas oil separation, perhaps due to the presenceof rapidly rising disengaging gas bubbles, which act toincrease the local turbulence.

NOMENCLATUREc concentration, kg m23

d vessel diameter, mD fractional mixed volumeE exit age distribution

f flow fraction through each pathF secondary peak number

L vessel length, mlmix length of mixing zone, mm mass of injected tracer, kg

MRT measured mean residence time, sMRTA mean residence time (volume/volume flowrate), sN number of stirred tanks in each pathQ volume flowrate, m3 s21

t time, sV phase volume, m3

VA phase volume based on interface height measurements, m3

VD dimensionless volume

Greek symbolst time constant, s

Subscriptso organic phasew aqueous phase

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ACKNOWLEDGEMENTS

M.J.H. Simmons would like to acknowledge funding by the Schoolof Chemical, Environmental and Mining Engineering, University ofNottingham, and BP Exploration

The manuscript was received 10 November 2003, and accepted forpublication after revision 14 July 2004.

Figure 8. Variation of fractional mixed volume, D, with water cut.


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