UNSOLICITEDRECDAUG 13 i$85

IY(2Q36 sp,PUBLICATJOP4S

DJUSTMENT F C7+ -MOLECULAR WEIGHTS IN THE CHARACTERIZATIONOF PETROLEUM MIXTURES CONTAINING HEAVY HYDROCARBONS

.

Per Thomassen, STATOIL as., N-4001 Stavanger Norway.

*Karen Schou Pedersen, CALSEP A/S, Lyngby Hovedgade 29,DK-2800 Lyngby, Denmark.

Aage Fredenslund, Instituttet for Kemiteknik, DanmarksTekniske Hrajskole,DK-2800 Lyngby, Denmark.

ABSTRACT.

Deviations between measured and calculated phase equilibriumresults for oil and gas mixtures are usually accounted for bytuning the equation of state parameters. In this work it isshown that major improvements in the calculations of the phasebehavior of gas condensate mixtures can be obtained by takinginto consideration the inaccuracies in the measurements of themolecular weights of the plus-fractions.

*Author to whom correspondence should be addressed.

Copyright 1987 Society of Petroleum Engineers

This manuscript was provided to the Society of Petroleum Engineers for distributionand possible publication in an SPE journal. The materialis subject to correctionby the author(s). Permission tocopy is restricted toan abstract of not more tt,an300 words. Write SPE Publications Dept., P.O. Box 833836, Richardson, TX75083-3836 U.S.A. Telex 730989 SPEDAL.

INTRODUCTION .

SPE 1,936

An increasing part of the North Sea petroleum comes from gascondensate fields. Accurate predictions of the dew pointpressures are needed i11 reservoir and process plantsimulations. Pedersen et al. have presented a fullypredictive C,+ - characterization procedure (1) based on theSoave-Redlich- Kwong equation of state (2). The composition ofa plus-fraction is estimated by assuming a logarithmicdependence of the molar content of a given carbon numberfraction on the corresponding carbon number. In case of oilmixtures, slightly better results are obtained byextrapolating the true boiling point distillation curve to100% distilled off. Very accurate results are obtained foroil mixtures. Bubble point pressures are predicted to within4%. Larger deviations are however found for gas condensatemixtures. .23.~ dew point predictions are very sensitive tovariations in the C,+ - analyses. In most cases thegas/liquiciratios are underestimated at pressures slightlybelow the dew point pressure.

Tuning of equation of state parameters is commonly used inan attempt to account for deficiencies in the predictions ofthe phase behavior. As shown by Pedersen et al. (3) this canbe dangerous, in particular when the tuning is based onerroneous analy+ ~al i.ita.

WE

The composi t ional analyses used for oil and ga,smixtures aremost often given in wei.ght uni,ts. Conversion to molarcomposi tions requires knowled,ge of the mo 1ecular weight ofeach component and carbon number fraction. The experimentalinaccuracy on the determi,nation of the molecu,lar weights ofthe plus-fractions is of the order 5 lo%. Deviations in thatorder of magni t ude can

nsa

influence a cal ,culated dew pointpressure of a gas conde te mixture as much as 50 bar. Anobviou,s application of this fact is to use the molecularweight of the plus fraction as an adjustable pa,raneter.Adjustments within the experimenta1 uncertainty can e. beused to match a measured saturat point.

DATA,.

In this work simulation results are presented for 10 gascondensate mixtures and 2 oil mixtures. The c 7+ -fracti.onshave been split into carbon number fractions l For the gascondensate mixtures, the ana,lyses stops between

c1 o+ and c 20+c 30+

For the oi1 mixtures a na.lytical data are available up toThe simulated results are compared with reSults of con,stantmass expansion, constant Volume

se

depletion and differentialliberation experiments. The PVT-experi,ments are describedin (1b ).

RESULTS.

Dew point ca,lculations have been made forred

the 10 gascondensate mixtures. Calculated and measu results arepre:sented in t able 1. In ord,er to improve the dew pointcalculations I it was att,empted to treat the molecular weighof the plus fraction as an adjUstable parameter, ma,intainingthe measu weight composition Table 1 also shows theadjustmen,ts needed in the mo,lecular wei

redghts of the plus

fractions to get agre:ement with the measu dew point.

-3-

SPE 1403(3

The maximum adjustment required is 12 % (gas condensate 10).The molar compositions before and after this adjustment isshown in the Appendix.

Constant mass expansion and constant volume depletion (lb)simulations were performed for the gas condensate mixtures.The Peneloux modification (4) of the SRK equation of state isused to calculate the phase densities. The relation betweenche SRK-volume, ~, and the Peneloux volume, V, is given by:

n

(1)

i=1where n is the number of components and xi and Ci are the

molar fraction and the volume correction, respectively ofcomponent i. For non-hydrocarbons and hydrocarbons < C, theexpression for c recommended in (4)-is used:

c= 0.40768(RTc/Pc)(0.29441 -ZRA) (2)

R is the gas constant, Tc is the critical temperature, Pcthe critical pressure and

RA is the Rackett compressibilityfactor (5). For C7+

- components Peneloux et al. recommend tocalculate c from a 5th degree polynomial in the carbonnumber. It is seen in (lb) that very inaccurate oil densitiesare calculated using this pr~ced.ure. In this work the c-v~lueof c,+ - components is calculated from the measured density atatmospheric pressure and 15 C.

-4-

In (1] the correlations of Kesler and Lee (6) are used forthe acentric factor, u, of the C,+ - fractions. The followingexpression is used for the C7+ - components lighter thanapproximately C15 (TBr < 0.8):

(II= (ln P~Br + al + a2/TBr +a~ in TBr

+ a4 Br ) / (a5 + a6/TBr +

a7 ln Br + a8 Br6,

Br is the reduced pressure PB/Pc, where PB is the pressureat which the boiling point

B was measured. The valuesrecommended in (6) for the coefficients of eq. (3)are listedin table 2. A parameter estimation was performed to determinethe optimum values of these coefficients. Binary interactioncoefficients of zero were used for all hydrocarbon -hydrocarbon interactions. The optimum values of thecoefficients a, in eq.1 (3) are given in tdble 2. Results ofdew point calculations on the gas condensate mixtlnes 1 - 10using this modified expression for the acentric factor arepresented in table 3.

Figs. 1- 5 present measured and calculated liquid dropout

curves. Calculated results are shown which are based on:

1. The characterization procedure of (1)

2. The characterization procedure of (1) where themolecular weights of the plus-fractions have beenadjusted to get agreement with the measured dew points

3. The characterization procedure of (1) where the modifiedw-expression for TBr < 0.8 is used and the molecularweights of the plus-fractions adjusted to get agreementwith the measured dew points

In figs 6 and 7 measured and calculated constant volumedepletion results for gas phases are shown. Fig 6 presentsthe molar fractions of methane in the liberated gas from gascondensate 8 and fig 7 the gas phase compressibility factorsof the gas from gas condensate 10. These results indicate thatthe adjustments of the molecular weights of the plus-fractionsand the modified w-expression have very little influence onthe calculated gas phase properties.

For the oil mixtures of this study bubble point pressureswhich deviate by -3.5% and 0.7% from the measured ones werecalculated using the characterization procedure of (1). If thec 7+ - molecular weights were adjusted by 19.3% and -2.1%,respectively, agreement was obtained between the measured andcalculated bubble points.

The results of table 3 reflect the influence on the dewpoint results of a reduction in the amount of analyticalinformation supplied to the program. Results are presentedwhere only the molar fraction, the specific gravity and themolecular weight of the total C7+

- fraction are used. Forthe two oil mixtures this reduction in the amount ofanalytical information gives bubble point pressures deviati::gby -0.93 and 4.2% from the measured ones. This means thatneither for the gas condensate mixtures nor for the oilmixtures it is necessary to have analytical data beyond C7+ inorder to describe the properties of the mixtures.

-6-

DISCUSSION+

The inaccuracy in the determination of the molecular weightof plus-fractions is of the order 5-10%. The results presentedin tables 1 and 3 show that deviations of that order ofmagnitude influeace the calculated dew points of gascondensate mixtures significantly. There is no systematicdeviation between the calculated and measured dew points oftable 1 (BIAS =

-0.2]. We therefore believe that thedeviations are mainly caused by inaccuracies in thedetermination of the molecular weights of the plus-fractionsand we find it justified to allow an adjustment of thesemolecular weights by up to lo%, maintaining constant weightcompositions. The results of figs 1-5 show that the liquiddropout curves are markedly improved when agreement with themeasured dew point is secured by adjusting the molecularweights of the plus-fractions. As seen in the Appendix themolar composition of gas condensate 10 still looks verysimilar to the original one after an adjustment of themolucular weight of the plus -fraction of 12%

Improved liquid dropout curves are obtained by modifying thecorrelation of Kesler and Lee for calculating the acentricfactors of components with a reduced boiling point below 0.8.This modification has only little influence on the calculatedsaturation pressures (table 3 and figs 6 and 7) and it can berecommended for general use.

-7-

It is seen that it has only little influence on thecalculation results if the amount of analytical informationfor the C. -components is reduced to a minimum. This is a1+strong indication that the assumption of a logarithmicdependence of molar fraction against carbon number isreaso~lable.

CONCLUSION.

The results of phase equilibrium calculations on gascondensate mixtures can be markedly improved if theinaccuracies in the molecular weights of the plus -fractionsare taken into consideration by treating these molecularweights as adjustable parameters, maintaining constant weightcompositions. Deviations between measured and calculated dewpoints as large as 50 bar can be accounted for by anadjustment of this molecular weight of around 10%, i. e. anadjustment of the same order of magnitude as the experimentalinaccuracy on the determination of the molecular weight of aplus-fraction.

The liquid dropout calculations for gas condensates can befurther improved by a modification of the expression of Keslerand Lee for calculating the acentric factors of C7+-components with a reduced boiling point below 0.8. Thismodification has only little influence on the predictions ofother properties and is therefore generally applicable.Accurate phase equilibrium calculations do not require verydetailed analytical data. An accurate analysis up to C7+ isfor most purposes sufficient.

-8-

NOMENCLATURE .

al - a8c

kn

P

R

SG

T

v

x

z

Coefficients of eq. (3)Peneloux parameter of eq.(1 )Binary interaction coefficientNumber of componentsMolecular weightPressure

Gas constant

Specific gravityTemperature

Molar volumeMolar fractionCompressibility factor

Greek symbol

(l) Acentric factor

Subscripts

B Boiling pointc Critical property1 Component index

j Component indexr Reduced propertyRA Rackett

SPE 1036

REFERENCES .

1. Pedersen, K.S., P. Thomassen and Aa. Fredenslunda. IEC Process Des. Dev. 23, 163 (1984)b. ibid 23, 566 (1984)c. ibid 24, 948 (1985)

2. Soave, G.,Chem. Eng. Sci. 27, 1197 (1972)

3. Pedersen, K.S., P. Thomassen and Aa. Fredenslund,On theDangers of Tuning Equation of State Parameters, Presentedat the ACS National Meeting Miami Beach, Florida, April 1985

4. I?eneloux,A., E. Rauzy and R. Freze, Fluid Phase Equilibria 8, 7(1982)

5. Spencer, C.F. and R.P. Danner, J. Chem. Eng. Data 18, 230 (1973)

6. Kesler, ~4.G. and B. 1. Lee, Hydrocarbon Processing 55, 153 (1976)

TABLE 1.

Experimental and Calculated Dew Point ResultsCondensate mixtures. The calculations are basedon the characterization procedure of (l).

No Temp Exp Dew Pt Calc Dew Pt %Dev

for

.----

SPE 14056

10 Gas

Adjustment Plus-(c) (bar) (bar) (1) of MW (2) fraction

- - - -- - -- ----- -- - -- --- --- - -- - -- -- --- ---- - - - - --- -_---- ---- -- -- - - - . - -- . -- - .

.

1 96.6 282.0 311.6 10.5 -8.8 c 11+- - - -- ------ -- -- --- - -- - - . -- - - - -- -- - ---_-- -- . -_---- -- - -- -- __ .- _- - - - . _ - - - -

3 118.9 398.0 377.1 -5.3 8.3 c1 o+

4 119.7 394.0 369.7 -6.2 9.6 c lo+

5 150.3 381.5 396.3 3.9 -5.4 C20+- --- - -- -- - - -- - - - - --- - - - -- - - ------ --- --- --- ---- ------ _____ - _- - - - __ _ - -- - - .

6 154.1 385.5 410.2 6.4 -9.6 c 10+- - - - - - - - - --- --- - - - - --- ------ - - ---- - --- - - -_ -- ------ -- - --- - _ ~__ - - _ _ ___ _ - _ .

7 131.5 367.0 378.7 3.0 -9.0 c 20+

8 129.0 464.0 454.2 -2.1 5.6 c 20+- - - -- - -- - -- --- - - - - --- ---- - - - - ---- ----- - - -- - ----- ---- --- - __ - ___ - - - _ - _ __ _

9 136.1 386.4 375.6 -2.8 8.4 c 20+

10 148.9 542.5 493.5 -9.0 12.1c20t

---- ------_ ----- ------___ -___ _--------- -------- ----- -_-___ _-__--_______

%AAD 4.9 7.7

%BIAS -0.2 1.1

(1) All the analytical data are Used

(2) % adjustment needed in the molecular wei$hts ~f the plusfraction to get agreement with the measured dew pointsmaintaining the measured weight compositions

TABLE 2.

Coefficients of

SPE 15036

(3)

----- ----- ----- ___

eq

-------- ---- ---- ---- ---- ---- ---- ---- ---- ____ ---- ____ .

Coefficient Recommended in (7) This Work--------------------------------------------------------------________

al 5.92714 5.77881------------------------------------------------------------__________

a2 6.09648 6.05615----------------------------------------------------__________________

a3 I.28862 1.37882----------------------------------------------------_____________-----

34 0.169347 0.173914-------------------------_________________----------___________-----___

a5 15.2518 15.5523-----------------------------------------------------------___________

6 - 15.6875 - 15.7915----- ----- ----- _____ ----- ________ _______ ----- ------ ----- ----- ________ -

7 13.4721 - 12.7855----- ----- ----- ------ _____ _____ ----- ----- _____ ----- ----- ________ ----- _

a8 0.43577 0.43487----- -------- ----- ------ __________ ----- ----- ------ ------ ------ _____ ___

SPE 1$036

TABLE 3.

Experimental and Calculated Dew Point Results for the 10 GasCondensate mixtures of Appendix A. The coefficients of table 2are used in the omega-correlation of eq. (3)

No Temp Exp Dew Pt Calc Dew Pt %Dev Calc Dew Pt %Dev Adjustment(c) (bar) (bar) (1) (bar) (2)

1 96.6 282.0 301.2 6.8 296.2 5.0 -5.7--- -. - - ---- - ------ - - --- --- -- ---- - - ___ -_ - - - --- -- - -- _ - - ______ . - -- __ _ _ _ _ . .

2 93.8 235.0 225.7 -4.0 237.7 1.1 -13.5

3 118.9 398.0 374.7 -5.9 369.3 7.2 8.3

4 119.7 394.0 364.8 -7.4 370.2 6.1 3.8- - -- ---- ---- - - ---- -- ---- - -- -- - -- -- --- - -- ----- ---- - - - - _ - -- - - __ . _ - _ _ _ _ - .

5 150.3 381.5 392.5 2.9 390.5 2.4 -3.5

6 154.1 385.5 409.7 6.3 406.5 5.4 -7.4

7 131.5 367.0 373.8 1.9 388.8 6.0 -4.1

8 129.0 464.0 460.6 -0.7 444.3 4.2 1.7-- - - - - -- - -- _- - -- - _- ______ - - _____ -- - -- -- - - - ___ -_ - - - - -- - - _____ _____ _ _ _ _ .,

9 136.1 386.4 379.7 -1.7 364.5 5.7 5.1---- ---- ---- ---- ------- _______ ---- ---- ---- ---- ---- ---- ---- ---- ____ ----

10 148.9 542.5 497.6 -8.3 491.9 9.3 9.5

----- ----- ----- ----- ------ ----- ----- ----- ----- ----- ----- -------- _____ _

%AAD 4.6 5.2 6.9----- ----- ----- ----- ----- ----- ------ ----- ----- ----- ----- ----- _____ ____

%BIAS -1.0 1.3 0.0----- ----- ----- ----- ------ ----- ----- ----- ----- ----- ----- ----- _____ ----

(1) All the analytical data are used

I

(2) The C7+ - characterization is based on the analyticalinformation available for the total C7+ - fraction only

(3) % adjustment needed in the molecular weight of the plusfraction to get agreement with the measured dew points .maintaining the measured weight compositions. All theavailable analytical data are used i.e. the plus-fractionsare those listed in table 1

APPENDIX

MEASURED MOLAR COMPOSITION OF GAS CONDENSATE 10

COMPONENT

N2

C02

cl

C2

C3

IC4

C4

IC5

C5

C6

C7

C8

C9

cl o

cl 1

cl 2

cl 3

cl 4

cl 5

Cl 6

c1 7

Cl 8

cl 9

C20+

MOLE%

.39

3.47

80.17

6.28

2.75

. 43

.88

.31

.35

.54

.72

.88

l 55

.33

.24

.20

.21

.18

.15

.11

. 12

.03

.06

.57

MOLECULAR DENSITY AT 15 C

WEIGHT (G/cM3)

95.106.118.:32.149.

163.175.194.

203.217.235.247.

255.

396.

.7432

.7612

.7786

.7869

.7883

.7980

.8195

.8307

.8332

.3383

.8360

.8415

.8520

.8673

COMPONENT

N2

co 2

cl

C2

C3

IC4

C4

IC5

C5

C6

C7

C8

C9

cl o

cl 1

C12

cl 3

cl 4

cl 5

Cl 6

cl )Cl 8

cl 9

C20+

MOLE%

*39

3.47

80.22

3.28

2.75

.43

.88

.31

.35

.54

. 72

.88

.55

.33

.24

.20

.21

.18

.15

.11

.12

.09

.08

.51

MOLECU LAR DENSITY AT 15 cWEIGHT

96.

106.

116.

132.

149.

163.

175.

194.

203.

217.

235.

247.

255.

444.

G / CM 3)

.743

.761

.779

.787

.788

.799

.820

.831

.833

.833

.836

.842

.852

.867

o0

w

o0

0

No00

wo00

&o

0

Vol% Liquid

o yo 0

of

t

y

lx //

x / ,/,/

//

I?oint

b,

0

Volume

m,

m,

0 0

x.

\

\ \\\ x

-Al-

,/w(D!24

I;xI i

1

. .

u.cmrt

o,

0

U-Io*

o

1-

0

1-

Ul00

N000

5Nw(D (n0In,mc 0n(D

SPEW376

Vol% Liquid of Dew Point Volume

p N b#

e ml , p o0

*o 0 0 0 0

~--- -I

III I_ IIIlx-. - .I

I

I

L__I

I-- -

I

. ,____ ____

rIII

__J_______[x .,\

\~

I

. ..

I

IIII

Ii11---- ... .-

11

II.

y

I

I___i._.._..__

.__.

.

..

- . .-. ..__

\. . .... .

I

I...

t

.-

.. .

.- . .--

I%l-.,N

. ---- ., ..- - -, .-. .

vol% ~lqula or Dew Point volume

1-h

p

D

o.po o 0 0

. . ---- ------

---__-,._.___T_..- .. - ..-

1 II

. ----

H-1:i

DCL

u.cml-r0Q

1II III 1

Ii

. x ii-r0

I!-L -. . .- .--. -

Ii QJnJt P-I-hP.I

II

iI

I

I \\ II

I\I

..-

i----

I

I

- .. ----- ..--- . .-J.

1-OJ(-F

ItI r-, lxII

IHl 1~ i a0

!Ic!LoII

L. _____ .. ---- .-- ._ ~_..__ ,- . . . . .------ ;-

---l--Y---- ----- ---Ii / i1!1 / /!

I i / /

I

II

1L.-_.__._.. _-_._-.- ,----.L---- ..-_......i_ .. . . i

GVol% Liquid in % of Dew Point Volume

P w;

My

Np y

o 0 0 0p

o

r-- . ....~.. .-------- , ---- -. - -. ________I ~_ ,-...-- 1I I I

oI

II I I iIII

A!\iik... . . .. J _._.__. -.,-----n-._? .1 _x\._ ._..-z; \ /YIDo x I.-_. . J.- ..-- ..- .

I

I[

i-h\;

\\Xj

I

\

!.-\\[1

M0G,

.-. .-._, ._._ .____

I -x-.. .

c1

0l-h_L._-.. ---4 .-~= ..

0c

w

000

N0a

0

u000

k00

W

:

0

mc100

Vol% Liquid of Dew Point Volume

p p b p* p i io 0 0 0 0

.

0

x/

/

7 //

II

i

I lx

$ 0m

I x

\

x

,1II

x

2

Mel% Methane in the Gas Phase

0b

.

00,0

Ill0p0

(lJ

:,

(3

b000

0

u-l0p0

Ln

i

.

..

II

. _

//

mpo

.

1; I x5sQ191w @lI-41!21l-- (-)fDrtQIO

Ii

m

-&_._.

>

.

-+$

Ix

I~

_..__L._-._

. _____

. -______

m(nso

I-J.03

m(Q(n!=1-rrm

nDIn

z0.a)

ElII

-.

o

0

00

0

Nc1,-

0

:00

k00

Ln00

0

0-l000

tiasPnase compressibility Factor

1- 1-* -. ,

0 0 1- N

/7x

1----L

.

!1~1d%

SClcllaOS-TXSLsunJm

u.cUY