PVT Calculation on Ptetroleum Fluids

7/27/2019 PVT Calculation on Ptetroleum Fluids

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1378 Znd. E n g . Chem. Res. 1992, 31, 378-1384

in dodecane-dilute nitric acid. J. Inorg. Nucl. Chem. 1977,39,

Yoshizuka, K.; Kondo, K.; Nakashio, F. Extraction equilibria ofCu(II),Zn(I1) and Co(I1)with N-8quinolylsulfonamide.J . Chem.Eng. Jpn . 1985,18,383-384.

Yoshizuka, K.; Kon do, K.; Nakashio,F. Effect of hydroph obicity ondistribution and interfacial adsorption equilibria ofN-8-quinolylsulfonamide. J . Chem. Eng. Jpn . 1986a, 19, 258-262.

Yoshizuka, K.; Kondo, K.; Nak ashio,F. Effect of interfacial reaction

1425-1430.on rates of extraction and strippingin memb rane extractor usinga hollow fiber. J . Chem. Eng. Jpn. 1986b,19, 312-318.

Yoshizuka, K.; Kondo,K.; Nakashio,F. Effect of hydrophobicity ofextractant on extraction kinetics of copper with N-8quinolyl-sulfonamide. J. Chem. Eng. Jpn . 1986c,19, 396-400.

Received f or review Jun e 12 , 1991Revised manuscript received January 21, 1992

Accepted February 20, 1992

PVT Calculations on Petroleum Reservoir Fluids Using Measured andEstimated Compositional Data for the Plus Fraction

Karen Schou Pedersen*CALSEP AIS, Lyngby Hovedgade 29, DK-2800 Lyngby, Denmark

Ann Lisbeth Blilie and Knut Kristian MeisingsetSTATOIL, Forus, N-4001 Stavanger, Norway

Molar com positionsto Cm are presented for 17 North Sea oil mixtures. The se extensive analyticaldata have bee n mad e available usinga high-temperature gas chrom atography technique.It is shownthat a simple exponen tial distributionfits th e C7+distribu tion ofall 17 oil mixtures very well. Becauseof thi s simple exp onential relation, i t is possible froma compositional analysis(to for example Clo+or C20+)o generate an extended com positionthat can be used to perform accuratePVT and phaseequilibrium calculations. The re appea rsto be little or no advantage ofhaving measu red compositionalanalyses beyond CzO+.

IntroductionTh e compositions of petroleum reservoir fluids are most

often reportedto C,+, CIW,or Cm an d in rare casesto CW(Pedersen et al., 1989a). T o be able to perform phaseequilibrium calculations (P V T calculations) on this kindof m ixtures, it is necessary to estimate t he m olar compo-sition of the plu s fraction. Th e final calculation resultsare very sensitive to t he molar distribution assumed forthe plus fraction. Pedersen e t al. (1985,198 9b) have ob-tained accurate P V T calculation results by using th eSoave-Redlich-Kwong (SR K) equation of state (Soave,1972) and assuming the following dependence of th e molefraction on carbon number:

(1 )

z, is the total mole fraction of componen ts withC, carbonatoms and A and B are constants. It has previously beenshown (Pedersen etal., 1984) th at this d istribution func-tion may be usedto represent reservoir fluid compositionsto a t least Clg.

With t he use of a high-temperature gas chromatography

technique , analytical data have now been m ade availableto CW+ or 17 North Se a oil mixtures. These dat a havemade it possible to check the validity of the distribu tionfunction expressed in eq 1, andto investigate whether thePVT-calculation accuracy can be improved by using ana-lytical dat a to CBocs compared to th e use of a distribu tionfunction for th e Cl0+, C20+ ,r C30+ raction.

Experimental DataThis pap er deals with 17 different reservoir fluids (gas

condensates and oils). The molar compositions of thereservoir fluids are determined from compositional a nal-yses of th e gas and liqu id phases resulting from a flash ofthe reservoir fluidto atmospheric conditionsor of the welltest separatorgas and liquid phases. In the la tter case the

z, = exp(A + BC,)

Ta b l e I. P l u s F r a c ti o n s of t h e S t a n d a r d M o l a rComDosi t ions for 15of t h e R e s e r v o i r F lu i d sof This S t u d s

~ ~~ ~~ ~ ~~

oil plus oil plus oil plusno. fraction no. fraction no. fraction

1 clot 6 G o + 11 ClOCc 3 0 t 7 cm 12 czo+

3 c 2 0 t 8 cm 13 c17t4 G o + 9 czot 16 G o +5 c20+ 10 G o t 17 CZOC

separator liquid is flashed to standard conditions beforethe analysis is performed. Th e molar composition to Cloof all samp les was determ ined by capillary gas chroma-tography. Fo r th e liquid samples at atmospheric condi-tions (in the following referredto as oils or stable oils) th eCIW compositionto Cm or to CN+ s usually determine dby T B P distillation (Osjord etal., 1985). Th e resultingmolar compositions are given in terms of carbon n umb erfractions,as described by Katz a nd Firoozab adi (1978).Acarb on numb er fraction , C,, consists ofall componentswith boiling points higher than th atof the n-alkane withn - 1 carbon atoms and lower tha nor equal to th at of then-alkane with n carbon atoms. Molecular weights arecalculated from the single-component distributionfor theC6-C g ractions an d measured for th e distillate fractions.Molar compositions determin ed in the described man nerare in th e following referred to a s stand ard molar com-positions. In Tab le I is shown a t what plus fraction thestan da rd molar composition stop s for the oil referred toin th e P V T calculations.

Th e extende d molar compositions to Cm presented inthis paper have been obtained using high-temperaturecapillary gas chromatography (GC) to analyze the stableoils (this technique is ofno interest for gas phases becausethe co nten t of CIWcompon ents is negligible). Th e appliedtechnique is similar to th at used by Curvers etal. (1989).The residue which does not pass through the high-tem-

0888-5885/92/2631-1378$03.00/0 0 1 9 9 2 A m e r i c a n C h e m i c a lSociety


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Ind. Eng. Chem. Res., Vol.31, No. 5, 1992 1379

Table 11. E xtended Molar Composition of Oil 1

compd fraction MW d c m 3mole p(15 "C , 1 a tm) ,

0.00130.00500.00470.00550.00620.01080.0050

0.01890.05340.08540.07040.06800.05510.05000.05580.05080.04660.03800.02670.02490.02140.02230.01710.01420.01630.01500.01250.01450.01330.01230.01150.01090.00900.00920.00790.00670.00700.00590.00490.00520.00460.00370.01590.01060.00740.00560.00410.00330.00270.00250.0029

16.030.144.158.158.172.172.1

86.290.9105.0117.7132.0148.0159.0172.0185.0197.0209.0227.0243.0254.0262.0281.0293.0307.0320.0333.0346.0361.0374.0381.0

+624.0

0.7490.7680.7930.8080.8150.8360.8500.8610.8730.8820.8730.8750.8850.9030.8980.8980.8990.9000.905

0.9070.9110.9150.920

+0.953

perature GC olumn was not qu antified an d therefore wasneglected. Th is residueusually amounts o 1-10 w t % ofthe total C3,,+ fraction.

In Tables I1 and I11 are shown the extended molarcompositions of oils1 and 2. Sta nd ard molar compositionsof t he reservoir fluids corresponding t o oils1 and 2 are

shown in Tables IV and V. They are determined bycombining oil and gas-phase compositionsas describedabove. Extend ed molar compositions for the15 remainingoils are contained in the supplementary material (seeparagraph a t end of pap er regarding suppleme ntary ma-terial).

PVT calculation results based on e xten ded molar com-positionsto CB oe ave been comp ared with those of usinga sta ndard molar composition to C l0+,C1,+, C20+,or Cmwith the constantsA and B in eq 1 determined from themole fraction and molecular weight of th e plus fraction.In ths comparative stud y the followingkinds of PVT datahave been used: satu ratio n point pressures (dew andbubble points); oi l densities in differential depletionstudies; gas-phase compressibility factors; separatorgas/oil

Table 111. Extend ed Mo lar ComDosition of Oil 2mole p(15 "C , 1 a tm) ,

compd fraction MW g/cm3o.Ooo1 30.10.00470.00580.01510.1680.01960.04370.0900

0.10710.0732-0.06230.05500.05140.04430.04800.03810.02820.03330.02340.02660.041770.01710.01480.01560.01130.01120.00970.01100.00730.00880.00650.00600.00620.00540.00450.00460.00380.00330.00340.00350.00210.00990.00640.00450.00310.00230.00180.00140.00120.0012

44.158.158.172.172.186.2

92.3105.9120.3133.0148.0163.0177.0190.0204.0217.0235.0248.0260.0269.0283.0298.0310.0322.0332.0351.0371.0382.0394.0

+612.0

0.7340.7560.7750.7890.7940.8060.8190.8320.8340.8440.8410.8470.8600.8740.8700.8720.8750.8770.8810.8860.8880.8950.898

+0.935

Table IV . Standard M olar Composition of ReservoirFluid 1

mole p(15 "C , 1 atm),compd fraction MW g/cm3

co2 0.010 00N2 0.004 03

C1 0.453 96c2 0.042 02c3 0.008 87i-C, 0.005 61c4 0.005 18i-C5 0.006 47Ck 0.002 94c, 0.010 11C, 0.028 78 91.7 0.742CB 0.041 14 105.0 0.768C9 0.033 22 117.6 0.794G o + 0.347 67 293.6 0.902

ratios. Th e employedPV T data are presented in thesection PVT Calculations.

Eva lua t ion of Dis t r ibu t ion Func t ionTo test the ability of the distribution function shown


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1380 Ind . Eng. Chem. Res., Vol. 31,No. 5, 1992

Table V. Standard Molar Composition of Reservoir Fluid 2mole ~ ( 1 5C, 1 atm),

0 . 0 0 7

i

compd fractionN2 0.006 90

C l 0.470 60c2 0.056 90c3 0.043 90i- C4 0.009 50c4 0.024 20c5 0.014 60c6 0.022 60c7 0.039 30C8 0.045 20C9 0.032 30ClO 0.02300c11 0.020 30

c13 0.016 20c14 0.017 60C15 0.013 90c16 0.010 30

Cl8 0.008 50c19 0.009 70c 2 0 0.003 20

c22 0.005 30c23 0.004 40c24 0.00340c26 0.00480c2 6 0.003 90c27 0.003 10C28 0.003 0c29 0.002 40c30+ 0.029 40

COB 0.001 20

i-C5 0.01110

c12 0.018 80

c17 0.012 20

c21

0.008 00

. .MW

91.9105.2121.0133.0148.0163.0177.0190.0204.0217.0235.0248.0260.0269.4

282.5297.7310.1321.8332.4351.1370.8381.6393.7612.0

0.7350.7450.7840.7890.7940.8060.8190.8320.8340.8440.8410.8470.8600.874

0.8700.8720.8750.8770.8810.8860.8880.8950.8980.935

Table VI. Coefficient of Determination (r2) alculatedAssuming the Distribution Fun ction Expressed in Eq 1 fo rthe Composition of 17 Different Oil Mixtures

oil no. rz oil no. r2 oil no. P1 0.9873 7 0.9878 13 0.9432

2 0.9863 8 0.9842 14 0.98523 0.9852 9 0.9884 15 0.98654 0.9818 10 0.9924 16 0.98545 0.9764 11 0.9443 17 0.98946 0.9866 12 0.9949 av 0.9815

in eq 1 o represent the molar distributions of theC,+fractions of th e 17 oils, the coefficient of de term ination ,r2

has been calculate d for each mixture.In eq 2 x i and yi ar epaired values of observations a nd n is the nu mber of ob-servations. Assuming the distribution function of eq1, x iand yi are corresponding values of carbon number andmole fraction. Th e value of1.2wil llie between0 and 1 an dwill indicate how closely the equation consideredfits th eexperimental data. The closerP s to 1, the better thefit.

Th e final values forP for each of the17 oil mixtures areshown in Table VI. Th e average value of1.2 obtained usingthe distribution function of eq1 s 0.9815. I t is very closeto 1, and it can herefore be concludedthat eq 1 representsthe experimental molar distributions very closely.

In Figures 1-4 are shown experim entaland calculatedresults for the mole fraction versus carbon nu mb er for oils1-4. The squa res are experimental valuea for single carbonnum ber fractions, while th e crosses are based on da ta for

ii

. - -4 .00u

-

" 1- 8 0 0c- 1

0 . 0 0 20.00 40.00 60.00 80.00

C a r b o n N u m b e rFigure 1. Experimental ( 0 and X) and calculated molar distribu.tions of oil 1. The solid line is based on compositional data to CW,and the d ashed line is based on com positional data to Clo+.

0 . 0 0 2

i

i m

- ' 200 ' , I , , # , , , , I , , , , , , , , I , , , I , , , , I , , , / , / , , ,

0 00 20 00 40 00 6 0 0 0 8 0 00C a r b o n h u m b e r

Figure 2. Experimental (0 nd X) and calculated molar distribu-tions of oil 2. The solid line is based on compo sitional data to CM+,and the dashed line is based on compositional data to C30+.

0 0 0 -

c-

-12.000.00 20.00 40.00 60.00 80 00

Carbon N u m b e rFigure 3. Experimental (0 nd X) and calculated molar distribu-tions of oil 3. The solid line is based on compositional data to Cm,and the dashed line is based on compositional data to Cm.

groups of five fractio ns(Cdl*, Gem, etc.). Th e solid linerepresents the best fit from C, toC, according to eq 1.


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Ind. Eng. Chem. Res., Vol. 31,No. 5, 1992 1381

Table VII. Values of the Coefficients Enterinu into Eas 3-5coeff value coeff value

C1 1.6312 X lo2 d3 2.0846 x lo-*c2 8.6052 X 10 d4 -3.9872 X 103c3 4.3475 x 10-1 e1 7.4310 X lo-'c4 -1.8774 X lo 3 e2 4.8122 Xdl -1.3408 X lo-' e3 9.6707 X 10"d2 2.5019 e4 -3.7184 X 10"

The dashed line represents the d istribution function de-termined by eq l using only the sta ndard molar compo-sition and t he plus-fraction molecular weight.

The A and B param eters are determined from th e molefraction and th e molecular weight of th e plus fraction.Itis assumed th at th e dependen ce of th e molecular weightagainst carbon nu mbe r can be described by th e followingequation:

MW 14C, - 4 (3 )

PVT CalculationsVarious PVT properties have been measured for the 15

reservoir fluids of this stud y. Using theSRK quation inth e modified form suggested by Peneloux e tal. (1982), thas been investigated how closely the measuredPVTproperties can be predicted using standard m olar compo-sitions and using extended molar compositions. Th ecritical temperaturea a nd pressurea and the a centric factorsof the C7+ ractions are calculated using th e following re-lations (Ped ersen etal., 1989b):

T , = c lp + c2 In MW + c3MW + c,/MW (4)P, = dlp + d2p = d3/MW + d4/MW2 (5)

m = elp + ezMW+ e3p + e4MW2 (6)where the values of th e coefficients~ 1 - ~ 4 ,1-d4, and e1-e4are given in Table VI1 andm is the following functio n ofthe acentric factorw:

m = 0.480 + 1.5740 - 0.1760~ (7)Th e densities entering into eqs 4-7 are estim ated as de-scribed by Pedersen e tal. (1984). Th e molecular weightsare determined from eq3. When the extended molarcompositions are u sed, theC41-45 fraction is attributed th emolecular weight ofC43, he C46-50 raction is attrib ute dthe molecular weight of C48,etc. T he Cso+fraction isattributed the molecular weight ofCw.

Binary interac tion c oefficients of zero are assumed forthe hydrocarbon-hydrocarbon interactions while nonzerovalues are used for interactions with non-hydrocarbons(Pedersen e t al., 1989a). T he volume translation parameterentering into the Peneloux modification of theSR Kequation has, for defined components(N2,C02, 2-C,),

been determined as suggested by Peneloux. For C7+ om-ponents the volume translation param eter has been de-termined as the value whichfits the measured den sity ofth at fraction at standard conditions. Before thePVTcalculations are performed, some of theC,+ fractions aregrouped together. TwelveC7+ ractio ns of approxim atelyequal weight were used in t he final calculations.

Two parallel series ofPVT calculations have been per-formed with the purpose of investigating whether it ispossibleto improve the qu ality of th e calcu lations by usingextended compositional dat a insteadof standa rd compo-sitional data. In Table VI11 are shown measu red andcalculated saturatio n pressures for each of the15 reservoirfluids. Tab le IX shows results for experimental an d cal-culated single-stagegasloil ratios fo r 10 of the 15 reservoir

Table V I I I . Experimental and Calculated Saturation PointPressures of the Reservoir Fluids"

~~

fluid temp, expt, std comp, % ext comp, %no. "C ba r ba r dev bar de v

1 71.6 239.0 (b) 237.4 -0.7 224.7 -6.02 72.8 237.0 (b) 231.3 -2.4 214.8 -9.43 106.0 203.0 (b) 394.9 -2.0 381.7 -5.34 150.5 631.0 (d) 444.8 -29.5 557.1 -11.75 127.0 393.1 (b) 382.5 -2.7 376.6 -4.26 125.0 404.8 (b ) 394.4 -2.6 378.6 -6.5

7 90.0 223.5 (b) 211.5 -5.4 208.5 -6.78 77.0 101.0 (b ) 99.5 -1.5 97.2 -3.88 97.0 108.5 (b) 107.2 -1.2 106.6 -1.89 117.0 114.0 (b) 114.1 0.1 111.1 -2.59 130.0 379.0 (b) 386.4 2.0 383.7 1.2

10 112.0 244.5 (b) 228.2 -6.7 231.2 -5.411 84.0 190.9 (b) 215.0 13.2 182.5 -3.912 129.0 477.0 (d) 475.6 -0.3 473.2 -0.813 80.0 209.0 (d) 181.4 -13.2 205.9 -1.516 100.0 61.5 (b) 73.1 18.9 66.1 7.517 122.0 367.3 (b) 364.6 -0.7 375.9 2.3

90 ABS 6.1 4.7% BIA S -2.0 -3.4

"(b ), bubble point; (d ), dew point. % de v = 10 0 x (calculatedresult - experimental result)/experimental result.

Table IX . Experimental and Calculated Single-Stage-FlashGas /Oil Ratios ( std m3 of Gas/std m3 of 0il)a

fluid temp, press., expt, std comp, % ext comp, %no . 'C bar m3/m3 m3/m3 dev m3/m3 dev

2 15.0 1.0 168.03 15.0 1.0 339.04 60.0 45.9 9900.06 15.0 1.0 210.07 15.0 1.0 148.29 15.0 1.0 188.6

11 23.0 1.0 51.612 36.0 52.0 898.013 32.0 60.7 18844.016 15.0 1.0 25.3

% AB S% BIAS

a % dev is defined in Table VIII.

163.2 -3.1324.0 -4.4

10196.0 3.0210.0 0.0150.6 1.6181.3 -3.951.4 -0.4

867.2 -3.416833.0 -10.7

24.9 -1.6

3.2-2.3

161.6329.0

9982.0208.9151.2181.150.3

867.916461.0

24.5

-4.0-2.90.8

-0.52.0

-4.0-2.5-3.4

-12.6-3.2

3.6-3.0

Table X. Experimental and Calculated Separator Gas/OilRatios of Reservoir Fluid No. 1 (std mJ of Gas/ma ofSeparator Oil)

temp, press., expt, std comp, % ext comp, %"C bar m3/m3 m3/m3 dev m3/m3 dev

55.4 69.7 63.8 66.2 3.8 64.3 0.8

64.2 1.0 7.8 9.8 25.6 10.2 30.867.9 55.4 21.8 20.5 -6.0 21.5 -1.4

% AB S% BIAS

"% dev is devined in Ta ble VIII.

11.8 11.07.8 10.0

Table XI. Experimental and Calculated Separa tor Gas/Oil

Ratios of Reservoir Fluid No. 7 (std ms of Gas/ma ofSeparator Oil)"temp , press., expt, std comp, % ext comp, %

"C bar m3/m3 m3/m3 dev m3/m3 dev81.1 70.0 98.8 94.7 -4.1 94.7 -4.177.8 26.0 26.3 25.9 -1.5 26.2 -0.472.2 8.0 12.8 12.8 0.0 12.9 0.868.9 1.9 7.0 10.5 50.0 10.6 51.4

% AB S% BIAS

13.9 14.211.1 11.9

% dev is defined in Table VIII.

fluids. Tables X and X I show experimental and calculatedmultistage separator gasloil ratios for the reservoir fluids1 and 7, respectively. In T ables XI1 and XI11 are shown


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1382 Ind. Eng. Chem. Rea., Vol.31, No. 5, 1992

Dir

1

0.00

o \0 ,

-

E 18 . 0 0r

-12.0.00.00 20.00 40.00 60.00 80.00

C a r b o n N u m b e rFig ure 4. Experimental(D and X) and calculated molar distribu-tions of oil 4. Th e solid line is based on compo sitional datato CW ,and th e dashed line is based on com positional datato CIM.

2. 0 -

Ta b l e XII. E x p e r i m e n t a l a n d C a l c u l a te d L i q u i d D e n s i ti e sof Reservoir Fluid No. at T = 71.6 OC (Di ffe ren t i a lLiberation Data)O

press., expt, std comp, % ext comp, %bar g/cm3 g/cm3 de v g/cm3 dev

239.0 0.761 0.774 1.7 0.769 1.1220.6 0.766 0.779 1.7 0.769 0.4191.5 0.774 0.788 1.8 0.779 0.6161.5 0.782 0.798 2.0 0.789 0.9131.7 0.790 0.80 8 2.3 0.800 1.3101 .5 0.799 0.819 2.5 0.811 1.571.7 0.809 0.830 2.6 0.822 1.631.5 0.822 0.845 2.8 0.838 1.9

% AB S 2.2 1.2% BIAS 2.2 1.2

"% dev is defined in Table V III.

experimental and calculated liquid-pha se densitiesof thereservoir fluids 1 and 3. Th e results are for differentialliberation experiments. In TablesXIV an d XV are shownmeasured and calculated gas-phase com pressibility ac torsof the reservoir fluids4 and 12 a t rather high pressures.

Liquid dropo ut curvesof mixtures 4, 12, and 13 areshown in Figures5-7. Th e results for mixtures4 and 12are fo r constant mass expansion experiments while the

Ta b l e XIII. E x p e r i m e n t a l a n d C a l c u l a t e d L i q u i d D e n s i ti e sof Reservo i r F lu id No. at T = 106 OC (Different ia lL ibe ra t ion Da ta ) "

press.,ba r

352.4302.8246.0176.7101.7

30.23.9

% AB S% BIAS

expt ,g/cm30.6190.6420.6660.6930.724

0.7580.791

std comp,

0.6290.6530.6790.7100.746

0.7860.813

g/cm3%

de v1.61.72.02.53.0

3.72.8

2.42.4

ext comp,g/cm30.6160.6420.6690.7020.740

0.7810.809

%de v-0.50.00.51.32.2

3.02.3

1.41.1


Ta b l e XIV. E x p e r i m e n t a l a n d C a l c u l a te d G a s - P h a s eCompress ib i l it y Fac to r s o f Rese rvo i r F lu idNo. a t T =150.5 OC"

Dress.. bar exDt st d comD % dev ext comD % de v899.7852.7797.9754.3698.7

651.1638.6631.0

% A B S% BIAS

1.542 1 1.5727 2.01.4940 1.5268 2.21.4331 1.4736 2.81.388 9 1.4314 3.11.3315 1.3779 3.5

1.2841 1.3325 3.81.2706 1.3207 3.91.2627 1.3135 4.0

3.23.2

1.57341.52761.47431.43201.3785

1.33301.32121.3140

2.02.22.93.13.5

3.84.04.1

3.23.2


Ta b l e XV. E x p e r i m e n t a l a n d C a l c u l a t e d G a s - P h a s eCompress ib i l i ty Fac to r s o f Rese rvo i r F lu idNo. 12 at T =159 "C"

press., bar expt std comp % dev ext comp % de v598.0 1.409 1.414 0.4558.5 1.343 1.352 0.7548.6 1.324 1.336 0.9536.7 1.306 1.317 0.8

509.1 1.261 1.274 1.0489.7 1.230 1.243 1.0477.0 1.208 1.223 1.2

% AB S% BIAS

a % dev is devined in Table V III.

3 0 . 0 11

0.90.9

1.414 0.41.351 0.71.336 0.91.317 0.8

1.273 0.91.242 1.01.222 1. 2

0.80.8

- 2 5 0

ER

15 3

v

0

33

1

, , , , , , , , , , , , , Yk,0 - 13 '00 200 30 0 600 530

'cessure ( b a r )

F i g u r e 6. Measured (0 ) and calculated liquid dropout curves formixture 12 a t T = 12 9 OC. Th e solid line shows calculation resultsbased on standard com positionaldata, and the dashed line shows theresults of using extended co mpositional data.

results for mixture13 are for a c onstant volume d epletionexperiment.


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Ind. Eng. Chem. Res., Vol.31, No. 5, 1992 1383

sities using sta nda rd molar compositions a re fairly closeto those obtainedusing extended molar compositions.Thiswa s to be expected. Gas/oil ratios are not very sensitiveto th e details of th e molar distribution assumed for theheavy end.

For mixtures4 and 13 th e calculation accuracy for theliquid dropou t curves can be improved by using extend edmolar compositions instead of standard molar composi-tions. For mixture 12 there is almost no difference betweenthe results obtained using standard a nd extend ed molarcompositions. As already mentioned , the sta ndar d molarcompositions for m ixtures4 and 13 stop at Clo+while formixture 12 a stan da rd molar composition is available toCZW This is another indication that it is essentialto havea molar compositionto Cm+. Analytical dat a in additionto that do no t markedly influence the calculation accuracy.

ConclusionWith the use of experimen tal molar compositionsto Cw

for 17 different No rth Sea reservoir fluids, it has beenshown that a simple exponential distribution functionfitsth e plus fractio n of reservoir fluids very well. By com-paring PVT predictions based on compositional analysesto CIW, o C W , nd to CW, t is shown that compositionaldata are needed toCZO+o accurately determine th e pa-rameters of the exponential distribution. The re appearsto be little or no advantage of having measured compo-sitional analyses beyondCzo+.

Nomencla ture

A = constant defined in eq1ABS = average absolu te deviationB = constant defined in eq1BIAS = average deviationc1-c4 = coefficients defined in eq3 and in Table VI1dl-d4 = coefficients defined in eq4 and in Table VI1e1-e4 = coefficients defined in eq5 and in Table VI1C, = carbon numberMW = molecular weightm = function of th e ace ntric factor defined in eq6n = number of observationsP, = critical pressurer2 = correlation coefficientTBP = true boiling pointT, = critical temperature.xi = x-value of ith observationyi = y-value of ith observationz, = total mole fraction of com ponents withC, carbon atoms% dev = percent deviation

Greek Symbolsw = acentric factorp = density in g/cm3 at15 O C and 1 atm

c

a

2 0 . 3 y\

\ \ = ,0. 0 1 ' , I '0 100 200

P r e s s u r e (ba r )

Figure 7. Measured (0 ) nd ca lculated liquid dropout curves formixture 13 at T = 80 "C. The so lid line shows calculation resultsbased on standard compositional data, and the dashed line shows theresults of using extended compositional data.

Discussion of the R e s u l t sTh e parameter regression clearly indicates tha t th eas-

sumption of an exponential molar distribution againstcarbon number is reasonable. It must therefore be ex-pected th at it is possibleto perform accuratePVT calcu-lations using a less extensive compositional analysis th anthat provided using the high-temperature gas chroma-tography technique . In Figures1-4 are shown molardistributions which are based on regressionsto analyticaldata to CBotogethe r with estimated distributio ns forCIw,CW, r CW fractions where the estimations are based oneq 1 and the A and B values determ ined from the molefraction and t he molecular weight of the p lus fraction ofth e stan dar d molar composition. For oils1 and 3 themeasured and the estimated molar distributions are inclose agreem ent. For oils 2 and 4 there is some deviation.This deviation must be expectedto be less important for

mixture 2 than for mixture 4 because a stan dard molarcomposition to C30+ is available for the latter mixture.When the reservoir fluid saturationpoints calculated on

the basis of standard molar compositions are comparedwith those calculated on the basisof extended molarcompositions (Ta bleVI), it is seen that the results obtainedfor fluids4,11,13, an d 16 using stand ard compositions areof a somewhat lower quality than the results obtained withextended molar compositions. For three of these m ixtures(4, 11, and 16) the sta ndard compositional da ta stop atCIW. For the last one (mixture13) the compositional dat astop at C1,+ an d no molecular weight is available for theC1,+ fraction. This indicates th at an analysis must beavailable at leastto CZ0+o achieve the best possible ac-curacy in th ePV T calculations. For the remaining mix-tures where a stand ard c ornpositional analysisis availableto Cm+ r to C3,,+, he saturation point predictions basedon stan dard molar compositions are generally betterthanthose based on extended molar compositions. The reasonfor this is probably th at the correlations usedto calculatethe equation of state parameters have been optimizedagainst standa rd compositional data. The small errorswhich are introduced via the distribution function areaccounted for by the choice of equation of state para me-ters. Anoth er potential reason for the differences in cal-culation results could be th at th eCm+fraction is under-estimated in the high-temperature GC results because theresidue which does not pass through th e column is ne-glected.

The results obtained for gas/oil ratios and phase d en-

Sup plem enta ry Ma terial Available: TablesA1-A15listing ex tended molar com positions of oils3-17 (29 pages).Ordering information is given on any current masthead page.

L i t e r a t u r e C i t edCurvers, J.; van den Engel, P. Gas Chromatographic Method for

Simulated Distillation up to a Boiling Point of 750 "C UsingTemperature Programmed Injection and High TemperatureFused Silica Wide-Bore Columns. J . High Resolut. Chromutoar.-1989, 12, 16.

Katz. D. L.: and Firoozabadi. A. Predictinn Phase Behavior of Con-densate crude Oil Systems Using Methane Interaction Coeffi-cients. J . Pet . Technol. 1978, 20, 1649.

Osjord, E. H.; Rmningsen, H. P.; Tau, L. Distribution of Weight,Density a nd M olecular Weight in Crude Oil Derived from Com-puterized Capillary GC A nalysis. J . High Resolut. Chromatogr.


7/7

1384 Ind . E n g . C h e m . Res. 1 9 9 2 , 3 1 , 1384-1391

Chroamtogr. Commun. 1985,8,684.Pedersen, K.; Thomassen, P.; Freden slund,Aa. Thermod ynamics of

Petroleum M ixtures Containing Heavy Hydrocarbons.1. PhaseEnvelope Calculations by Use of the Soave-Redlich-KwongEquation of State Ind. Eng. Chem . Process D es. Dev. 1984,23,163.

Pedersen,K. .; homassen, P.; Fredenslund, Aa. Thermodynam icsof Petroleum M ixtures Containing Heavy Hyd rocarbons.3. Ef -ficient Flash Calculation Procedures Using th e SR K Eq uation ofState. Ind. Eng. C hem. Process Des. Dev. 1985, 4, 948.

Pedersen, K.S.; Fredenslund, Aa.; Thom assen,P. Properties of Oils

and Natural Gases; Gulf: 1989a.Pedersen, K.S.; Thom aasen, P.; Frede nslund , Aa. Characterization

of Gas Condensate Mixtures. Adv. Thermodyn. 1989b, , 137.Peneloux, A.; R auzy, E.; Freze, R. A Consistent Correction for Red-

lich-Kwong-Soave Volumes. Fluid Phase Equilib. 1982,8, .Soave,G. Equilibrium Constants from a Modified Redlich-Kwong

Equation of State. Chem. Eng. Sci. 1972,27,1197.

Received for reviewJu ly 17, 1991Revised manuscript received November 11, 1991

Accepted Februa ry 19,1992

Local Heat Transfer in a Mixing Vessel Using Heat Flux Sensors

S e u n g j o o H a a m and R o b e r t S . B r o d k e y *Depa rtmen t of Chemical Engineering, Th e Ohio State University, 140 We st 19th Avenue,Columbu s, Ohio 43210-1180

J u l i a n B. FasanotChemineer Inc., P.O. Box 1123, Dayton, Ohio 45401

A rapid, computer based , local heat-transfe r sensor system has been developed. Th e concept wasto provide a quick, accurate,and efficient techniqu e for th e determ inatio n of process side heat-transfercoefficient models through t he u se of he at flux sensorsand PC dat a acquisi tion. Th e system hasbeen thoroughly tested. System noise and typical sensor variation with time have been studied;however, only part of th e noise is real: the rema inder is associated and correlatable with specificphysical phe nomen a (vortical motions) th at occur in the m ixing vessel.A detailed study of thevariation of t he local coefficientsas a function ofangular position relativeto the baffles is presented.Th e influence due to th e presence of baffles canbe seen and explained. Some typical results aregiven to illustrate th e effect of th e prim ary variable, Reynolds num ber. Th e relative level of effectsfrom other design variables are presented.

In t roduc t ionHe at transfer in agitated vessels is a common operation

in chemical processing. Th e rate of hea t transfer during

mixing of liquids depe nds on the type of th e ag itator, thedesign of the vessel, and processing conditions. In thisresearch, the h eat transfer a t the wall of an a gitated vesselwith a dished bottom and four baffles was investigated.Thre e well-known impeller types were studied. Th e con-tents (water) of the vessel were slowly cooled by naturalconvection from the outer surface and small local coolingexchang ers located directly under the sensors. Th eheat-transfer me asurements were made by M icro-Foil hea tflux sensors tha t are placed on the inside surface of th evessel. The se sensors exhibit a potential directly pro-portional to the heat flux and are calibrated by the m an-ufacturer. Th us, process side heat-transfer coefficientswere determ ined. Determining heat-transfer Coefficientsby conventional thermocouple an d heat balance techniqueis ardu ous and tim e consuming. Th e use of the therm o-phile style hea t flux sensor to measure the heat flux an dtemperature of the wall would be a useful and a viablemeans of making po int to point local mea surem ents.Fordata acquisition, MetraByte's DAS-8 data acquisitionsystem was used. Two BASIC programs were developedfor data acquisition and determination of the h ea t- tr ad ercoefficients and o ther imp ortan t values. Th e goal of thisresearch was t o create a quick, accurate, and efficientsystem for the determinationof process side local heat-transfer co efficients throu gh the use of hea t flux sensorsan d a PC based d ata acquisition system.

'Technical Director.

O88S-5885/92/263~-1384$03.O0O

Li te ra tu re ReviewHeat transfer in an agitated vessel is definedas

q = UiAi(To- Ti) (1)where Vi = the overall heat-transfer coefficient,Ai = th eheat-transfer area,To = temp eratu re of the heat-transferfluid, an d Ti = temperature of the process fluid.

If fouling factors are negligible, the overall heat-transfercoefficient can be described in te rms of three sep aratedheat-transfer resistances:

Ui = 1/ [ (1 /hJ + (b /kw)(Ai /Aw) + ( l /hJ(Ai/AJl(2)

See, for example, Chem ineerCo. (1985), hapman andHolland (1965a,b), and Po ggeem ann e t al. (1980). In eq2, th e first term is the inside film coefficient, hi, tha t is onthe process liquid side of the surface. Th e second termis the conduction through th e wall, and the third term isthe outside film coefficient.

Dimens iona l Analys i s fo r Hea t -Transfe rCoeffi-cient. The insideor process side heat-transfer coefficientcan be defined from the heat flow,Q, heat-transfer area,Ai, and the tem pera ture difference between th e inside walland the bulk of the fluid, ATi:

hi Q Ai( ATi) (3)

Th e heat flow,q , can be determined from the tem peraturegradient a t th e inside wall of th e vessel:

0 1992 American Chemical Society

PVT Calculation on Ptetroleum Fluids

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