Molecular Thermodynamics of Asphaltene Precipitation in Reservoir Fluids

8/18/2019 Molecular Thermodynamics of Asphaltene Precipitation in Reservoir Fluids

1/13

Molecular Thermodynamics of Asphaltene Precipitationin Reservoir Fluids

J ianzhongWu and J ohn M. PrausnitzD ept. of C hemical Engineering, U niversity of Ca lifornia, Berkeley, and

Chemical Sciences D ivision, La wrence B erkeley Nationa l La boratory, Berkeley, CA 94720

AbbasFiroozabadiR eservoir E ngineering R esearch Institute, P alo Alto, CA 94304

A pre ®iously described molecular-thermodynamic framework, based on colloid the -

ory, is used to correlate experimental asphaltene-precipitation data at high-temperature and pressure cond iti ons. I n thi s fram ework , asphaltenes and resins ar e represented by

pseudopure components, and all other components in a crude oil are presented by a

continuous medium that affects ®an der Waals attractions among asphaltene and resin

molecules. M odel parameters are e ®aluated systematically from a ®erage properties of

asphaltenes and resins i n crude oils, and from dispersion-force properties of the oi l

medium. Gi ®en the composition of the medium, and asphaltene and resin concentra -

tions, the molecular-thermodynamic model described here can be used to identify the

onset of asphaltene precipitation, and the total amount of precipitation at the gi ®en

operation conditions. Calculated results for the effects of oil composition and pressure

on asphaltene precipit ation are in good agreement wi th at least some experim ental mea -

surements f or four reser ®oir flui ds, includi ng Texaco, Shell, Weyburn, and Nort h-Sea

crude oi ls.

Introduction

Asphaltene precipitation is a perennial problem in produc-

tion and refining of crude oils. To avoid precipitation, it is

useful to know the solubility of asphaltenes in petroleum liq-

uids as a function of temperature, pressure, a nd liquid-phaseŽ .composition. In our ea rlier work Wu et a l., 1998 , a molecu-

lar-thermodynamic framework wa s developed to d escribe the

phase behavior of asphaltene-containing fluids. In this frame-

work, we represent asphaltenes by attractive hard spheres,resins by attractive hard-sphere chains, and all other compo-

nents by a continuous medium that affects interactions be-

tween aspha l teneaspha ltene, a spha ltene r esin, a n d

resinresin pairs. We consider explicitly associations between

asphaltene and asphaltene, and between asphaltene and

resin. The potential of mean force between asphaltene a nd

Correspondence concerning this article should be addressed to J. M. Prausnitz.

asphaltene, as well as that between asphaltene and resin, in-

cludes hard-sphere repulsion, van der Waals attraction, and

association. Ba sed on experimental evidence, we postulate

that, while asphaltene mo lecules can a ssociate themselves or

with resin chains, resin chains cannot associate with them-

selves. Resins, when associated with asphaltenes, stabilize as-

phaltenes, thereby reducing their tendency to precipitate. We

have shown that our molecular thermodynamic frameworkcan explain essentially all experimental observations for the

effects of temperature, pressure, and crude-oil composition

on asphaltene precipitation. In this work, we present a quan-

titative description of phase behavior based on the previously

described framework, and we illustrate its reduction to prac-

tice: once the model parameters are fixed with a few mea-

surements, our molecularthermodynamic framework can

predict semiquantitatively asphaltene precipitation at a vari-

ety of operating conditions.

J anuary2000 Vol.46, No. 1AIChE J ournal 197


2/13

We consider a crude oil containing a sphaltenes a nd resins.

Asphaltenes are represented by attractive hard spheres that

can associate with themselves, and resins are represented by

attractive hard-sphere chains that can associate with a s-

phaltenes, but not with themselves. Asphaltene molecules and

resin chains are dissolved in a continuous medium that af-

fects dispersion-force interactions among asphaltenes and

resin chains. The H elmholtz energy of the system is given by

an expression based on random-phase-approximation theory

Ž . Ž .RP A and on statistical-associated-fluid theory SAFTwithin the McMillan-Mayer description o f liquid solutions.

The H elmholtz energy A contains five contributions:

A s A i d q A h s q A ®d w q A assoc q A c hai n , 1Ž .

where superscript id stands for an ideal-gas mixture of as-

phaltenes and resin chains at system temperature, volume,

and molecular number densities; hs stands for the contribu-

tion from hard-sphere repulsion when resin chains are dis-

connected; ®dw stands for the contribution from van derŽ .Waals dispersion-force attractions; assoc stands for the

contribution from asphalteneasphaltene and asphaltene

resin associations; and chain stands for the entropic contri-bution to A from connectivity of resin chains.

The ideal-gas contribution to the Helmholtz energy takes

into account the translational kinetic energy of asphaltenes

and resin chains in the solution. It is given by

A i d 3s N ln y N , 2Ž .Ž .Ý i i i t

kT i s A , R

where k is the Boltzmann constant; T is absolute tempera-

ture; N and N are the number of asphaltene moleculesA R and resin chains; N s N q N is the tota l number oft A R molecules; s N rV and s N rV a re, respectively, theA A R R number densities of a sphaltene molecules and resin chains; V stands for volume; stands for the thermal wavelength ofi molecule i for i s A , asphaltene molecule, and for c s R ,

resin chain. Because depends only on temperature for ai given i , it cancels in phase-equilibrium calculations.

The contribution to the Helmholtz energy from hard-sphereŽinteractions among asphaltene and resin segments not resin

.chains is obtained from the equation of Mansoori et al.Ž .1971 :

h s 3A 2s s N y1 ln 1y Ž .t 32½kT 0 33 31 2 2

q q , 3Ž .2 5 1y Ž . 1y Ž .0 3 3 0 3

where N s is the number of asphaltene segments plus thet Ž . 2 n number of resin segments; s r6 Ý , n s0, 1, 2,n i s1 i i

3. When n s0, is a density; when n s3, is the packing0 3Ž .fraction. Subscripts i s1, 2 denote asphaltene segment 1

Ž .and resin segment 2 , respectively. Because we represent a s-phaltene molecules by attractive hard spheres, an a sphaltene

segment is identical to an a sphaltene molecule; thus we ha ve

s . H owever, because a resin chain contains several seg-A 1ments, s rl , where l stands for the number of seg-R 2 R R ments per resin chain. The segment diameter for component

i is denoted by .i The contribution to the Helmholtz energy from van der

Waals attractions among asphaltene and resin segments in aŽmedium is obtained from the RP A Ha nsen and McDonald,

.1986 :

®d w 2 2 U A V i j s , 4Ž .Ý Ý i j

kT 2 kT i s 1 j s 1

®d w Ž . 2 Ž .where U s4 H W r r dr with s q r2. In Eq .i j i j i j i j i j Ž .4, U rV is the mean-field average pair-dispersion energyi j

for all ij pairs, that is, for all pairs formed by asphaltene andŽresin segments in the oil medium U is similar to parameteri j

.a in the van der Waals equat ion of state fo r mixtures . Thei j ®d w Ž .potential of mean force, W r , due to dispersion interac-i j

Žtion between two segments in an oil medium is given by Wu.et al., 1998

H 1i m j ®d w W r sy , 5Ž . Ž .i j 2 0 0 6 r i j

where 0 is the segment number density of pure componenti i , that is, ‘‘pure’’ asphaltenes or ‘‘pure’’ resin segments; r is

the center-to-center distance between two segments; H isi m j the H amaker constant for the interaction of i with j when i

and j are immersed in medium m ; it is a pproximated byŽ .Israe lachvili, 1991 :

H s H 1r2 y H 1r2 H 1r2 y H 1r2 , 6Ž .Ž . Ž .i m j i m j m

where H , H , and H are the H amaker constants of pure i ,i j m pure j , and medium m . Equations 5 and 6 indicate that the

potential of mean force due to dispersion interactions de-

pends on the Hamaker constants of asphaltene, resin, and

the oil medium, as well a s on the number densities of ‘‘pure’’

asphaltene a nd resin segments.

Next, we consider asphalteneasphaltene and asphaltene

resin a ssociations. We assume tha t each asphaltene molecule

ha s N identical association sites, and each resin chain hasa only one association site. Asphaltene can associate with each

other, but resin chains can only associate with asphaltenes.ŽThe H elmholtz energy due to a ssociation is given by Cha p-

.man et al., 1990

A assoc 1y x s N X ln x q A ž /N kT 2t

1y x q X ln x q , 7Ž .R ž /2

where X an d X are, respectively, mole fractions of asphal-A R tene molecules and resin chains on a medium-free basis; x is the fraction of association sites at asphaltene molecules

J anuary2000 Vol.46, No. 1 AIChE J ournal198


3/13

that are not bonded; x is the fraction of association sites atresin chains that are not bonded. Fractions x and x are given by

y1 x s 1q N x q x 8Ž .Ž . A R

y1 x s 1q N x , 9Ž .Ž . A

where , are as before; the number densities of asphal-A R tene molecules and resin chains in the oil medium; ,

are given by

h s w x 3 s g exp rkT y1 10Ž . Ž . Ž .11 11 11

h s 3 s g exp rkT y1 , 11Ž . Ž .Ž .12 12 12

h s Ž .where g is the contact value of the pair correlationi j i j function in the hard-sphere mixture of asphaltene and resin

segments given by

3 1 i j 2h s g s qŽ .i j i j 1y q 1y Ž . Ž .3 i j 3

2 2 i j 2q2 , 12Ž .

3ž / q 1y Ž .i j 3 an d are parameters related to the square-well

widths for the association potentials. To reduce the number

of unknown parameters, we assume that they are identical

constants for associations between asphaltene and asphal-

tene, and between asphaltene and resin chain.

Finally, the contribution to the Helmholtz energy fromŽchain connectivity of resin segments is given by Cha pman et

.al., 1988 :

chainAh s s N 1y l ln g , 13Ž . Ž .Ž .R R 22 22

kT

h s Ž .where g is the contact value of the pair correlation22 22function between resin segments given by Eq. 12. Equation

13 takes into a ccount the difference in hard-sphere contribu-

tion of the Helmholtz energy between hard-sphere chains and

unconnected hard spheres.Ž .Ca lculations presented ea rlier Wu et al., 1998 showed that

the above molecular-thermodynamic framework can explain

essentially all observed experimental results for asphaltene

precipitation in crude o ils, that is, the ef fects of temperature,

pressure, and composition. To apply this framework to as-phaltene precipitation at reservoir conditions, we first need

to establish a reliable method to estimate required model pa-

rameters. Because asphaltene precipitation at reservoir con-

ditions is often accompanied by a vaporliquid equilibriumŽ .VLE , and because the Hamaker constant of the mediumdepends on its density and composition, we also need a reli-

able method for estimating liquid density and VLE for reser-

voir fluids. For this purpose, we use the volume-shifted

Peng-Robinson equation of state with an appropriate C q7

characterization method, as summarized in Appendix A. With

VLE and liquid density from the volume-shifted Peng-Robin-Žson equation of state, asphaltene precipitation liquidliquid

.equilibria can be calculated using the molecular thermody-namic model.

Molecular Parameters for AsphaltenePrecipitation

For quantitative applications, molecular parameters must

be estimated independently or from a few experimental datafor the particular system of interest. The model parameters

of our model include the diameter of the a sphaltene mo leculeŽ .segment and the diameter of resin segment ; the1 2number of segments per resin chain, l ; the Hamaker con-R stants for ‘‘pure’’ asphaltene, for ‘‘pure’’ resin, and for the oil

medium, H , H , H ; the asphaltene asphaltene associa-A R m tion energy ; the asphalteneresin association energy ;A A A Rthe number of association sites of each asphaltene molecule

N ; and the volume parameter in the SAF T equation. F ur-ther, to calculate the Hamaker constant between asphaltene

and resin pairs in a medium, we need to know the segment

densities of pure asphaltenes a nd pure resins. These proper-

ties are not readily obtained from typical asphaltene or

crude-oil characterizations.For phase-equilibrium calculations, we use average mo lec-

ular weights and densities for pure asphaltenes and resins.Ž .As discussed by Speight 1991, 1994 , the average molecular

weights of asphaltenes and resin chains are about M s2,000Aand M s800 Da, respectively. The mass density of a typicalR asphaltene is about d 0 s1200 kgrm3, close to that of theAheaviest hydrocarbons, and the ma ss density of a typical resin

0 3 Ž .is about d s1,000 kgrm Speight, 1991 . From the massR densities and molecular weights, we can calculate t he number

densities of pure asphaltenes and resin chains.

To a good approximation, the packing fraction of pure as-

phaltene, defined a s 3r6, lies between the minimum1 1Ž .packing fraction of a hard-sphere solid 0.55 and the high-

Ž .est liquid packing fraction of hard spheres 0.74 . U singthe molecular weight of a sphaltene, M s2,000 D a and massAdensity d 0 s1,200 kgrm3, we find that the diameter of anA

Ž .asphaltene molecule segment lies in a narrow range, 1.43 1.58 nm. In our calculations, we use s1.5 nm corre-1 1sponding to about the minimum asphaltene diameter re-

ported in the literature. Because asphaltene molecules

strongly bind with themselves in most solvents, experimental

measurements often tend to give the sizes of asphaltene ag-

gregates instead of asphaltene monomers.

To our best knowledge, no size information ha s been pub-

lished for resin chains. Because resin is a liquid at ambient

conditions, its packing fraction should be less than that of aŽ .hard-sphere solid at the fluidsolid phase transition 0.55 .

We assume that the diameter of a resin segment is about 0.5nm, and the number o f segments per chain is about 10. With

these parameters, and with molecular weight of resin, M sR 800 Da and mass density d 0 s1000 kgrm3, the packing frac-R tion of pure resin chain is 0.49, reasonable fo r a high-boiling

hydrocarbon. Provided that reasonable values are used, we

find that asphaltene-precipitation calculations are not sensi-

tive to resin-chain length and resin-segment diameter.

In principle, the Hamaker constant of a fluid can be calcu-

lated from its polarizability and dielectric permittivity using



4/13

Ž .Lifschitz theory of van der Waals forces Israelachvili, 1991 .However, polarizability and dielectric permittivity are often

not a vailable for components in a heavy reservoir oil. On the

other hand, the Hamaker constant of a fluid can be esti-

mated from interactions between individual pairs of ato ms or

groups that constitute the fluid. It has been suggested that

the Hamaker constants of hydrocarbons can be estimatedŽfrom van der Waals interaction between CH groups Israe-2

.lachvili, 1991 :

H s 2 B 2 14Ž .CH 2

where B is the London dispersion constant and is theCH 2number density of CH groups. For interaction between two2CH groups in vacuum, B f510y78 Jm6. Figure 1 shows2Hamaker constants estimated by Eq. 14 and results calcu-

lated from the Lifshitz theory of van der Waals forces. The

two methods agree remarkably well for normal alkanes. U s-

ing Eq. 14, we estimate the Hamaker constant of pure as-

phaltene H s1.32 10y19 J, and that for pure resin segments1H s9.06 10y20 J. Contributions of heteroelements to the2Hamaker constants of asphaltenes and resins are neglected.

In a realistic situation, the medium often contains lightcomponents such as CH , H S, CO , and N . The contribu-4 2 2 2tions of these components to the Hamaker constant of the

medium can be estimated fro m polarizability and first ion-0ization potential I . The London constants for light compo-

Ž .nents are obtained from Israelachvili, 1991

3 2I 0B s , 15Ž .

24 4 Ž .0

Žwhere is the electric permittivity of free space s8.8540 0y12 2 y1 y1.10 C J m . Table 1 gives calculated London con-

Figure 1. Hamaker constants of normal alkanes esti-mated from their densities.

Table1. London Constant B , Polarizability , and0FirstIonizationPotential I for Common Light

Componentsin CrudeOils

3 78 6 , A I , E v B 10 , J m0CH 2.59 12.51 10.14N 1.74 15.58 5.672H S 3.86 10.45 18.72CO 2.91 13.77 14.02

a nd I a re f rom CRC Handbook of Chemistr y and Physics , 76th ed. ,0 Ž .CR C P ress , New York 1995 .

stants, and I for CH , H S, CO , and N . The London0 4 2 2 2constants for CH is about twice that for the CH group in4 2the liquid state. All other components in the oil medium are

considered a s an assembly of CH groups. The overall2Hamaker constant of the oil medium is obtained from

H s 2 B , 16Ž .Ý Ým i j i j i j

where B s B B . Here subscripts i and j refer to CH ,'i j i j 4H S, CO , and N gases, and to the CH group in the liquid2 2 2 2state.

Because the effect of the oil medium on the potential of

mean fo rce between a sphaltenes and resin segments depends

only on its Hamaker constant, Eqs. 1416 imply that the

Hamaker constant of the oil medium can be determined by

its density and by concentrations of light components dis-

solved in the medium. To verify our assertion that it is pri-

marily the density that influences the effect of the medium

on asphaltene precipitation, we have considered asphaltene

precipitation in a crude oil diluted with 40 volume of solvent

per volume of crude oil. More than twenty solvents are con-

sidered, including n -alkanes, olefins, and cycloparaffins. As

shown in Figure 2, we find that the amount of asphalteneprecipitation is indeed primarily determined by the solventŽ .medium density. H ere the medium includes the asphalteneand resin-free crude oil and the diluent. B ecause of the large

dilution ratio, the density of solvent is essentially identical to

that of the medium. The experimental data used here wereŽ .reported by Mitchell and Speight 1973 . Figure 2 shows that

the amo unt of asphaltene precipitation is well correlated with

the density of the hydrocarbon solvent. B ecause the densities

of aromatics are higher than those of cycloparaffins, we ex-

pect no asphaltene precipitation when an aromatic diluent is

added , a s experimentally observed.

Remaining parameters are those related to the association

intera ctions of a sphaltenes a nd resins. As discussed by Speight

Ž .1994 , the association energies between asphaltene and as-phaltene, and between asphaltene and resin chains are in

Žthe range of normal hydrogen-bonding energy 540 kT ,0.T s298 K . Also, association between asphaltene and resin0

is usually stronger than that between asphaltene and asphal-

tene. B ecause the properties of different asphaltene- and

resin-containing crude oils are not identical, in general, the

remaining parameters must be obtained by fitting to a few

experimental data for a sphaltene precipitation; these a ssocia-

tion parameters may vary from one crude oil to another. To



5/13

Figure 2. Correlation between asphaltene yield and sol-vent density.

Ž .Experimental data from M itchell and Speight 1972 .

minimize further the number of unknown parameters, the

volume parameter o f the SAFT equation is fixed at s0.05,Ž .close to those reported by Huang and R adosz 1990 when

SAFT is applied to typical associating systems, including

alkanols, organic acids, and amines. Table 2 summarizes all

pre-fixed parameters.

In a ny crude oil, there is a broa d distribution of asphaltene

molecular weight. In this model, we assume that asphaltene

components in a crude oil can be represented by a single

pseudocomponent. The average molecular weight of as-

phaltenes appears to be a sensitive para meter in any thermo-dynamic model for correlation asphaltene precipitation be-

cause it is directly related to the molar concentration of as-

phaltenes. U nfortunately, most experiments report only the

weight percent of asphaltenes. To convert weight percent to

mole concentration, an average molecular weight is required.

Most earlier literature reported a high value of averageŽ .molecular weight 5000 Da for asphaltenes because the

measurements were carried out in aromatic solvents. Based

on vapor-pressure osmometry experiments in pyridine sol-Ž .vents, Speight 1994 concluded that the average molecular

weight of a sphaltenes is abo ut 2000500. However, some veryŽ .recent results after this work was completed from gel-per-

Žmeation-chromatography measurements Pan and Firooz-

.abadi, 1998b; Nalwaya et al., 1999; Artok et al., 1999 inŽ .CH Cl or THF solvents give much lower about 700 Da2 2

number-average molecular weights. Our use of 2,000 Da is

nevertheless valid because asphaltenes exist as oligomers

rather than monomers in a crude oil. If a smaller average

molecular weight is used, the association ability amongŽmonomers should be increased correspondingly compared to

.that for a larger monomer such that asphaltenes have a dis-tribution of large oligomers. In addition, if the molecular

weight of the monomer is reduced, the molecular size of the

monomer must be reduced accordingly. Because association

between asphaltene molecules is not well understood, and

because asphaltenes are known to exist a s large aggregates in

a crude oil, it is not unreasonable to assume an effective as-

phaltene unit that is larger than tha t corresponding to a more

reactive ‘‘real’’monomer. After the a verage molecular weight

of asphaltenes is fixed, there is not much room to adjust the

monomer size, because both the packing fraction and the

density of asphaltene do not vary much with respect to the

source of crude oil or solution conditions.Ha maker constants of asphaltene, resin, and the medium

affect dispersion interactions among asphaltene and resin

molecules; these parameters are not as sensitive as associa-

tion parameters. As shown in Figure 2, however, as the den-Ž .sity of the medium solvent increases, the dispersion interac-

tion amo ng asphaltene a nd resin molecules falls, producing a

dramatic decrease in the total amount of asphaltene precipi-

tation. Our para meters for resins are less justified tha n those

for a sphaltene. Although the parameters given in Table 2 a re

obtained by reasonable assumptions, it is clear that further

work on the optimization of these parameters is required.

R egrettably, such opt imizat ion requires a substant ia l

database.

Asphaltene Precipitation in Crude Oils

We have calculated asphaltene precipitation equilibria for

a few crude oils at high-temperature and high-pressure con-Žditions. These crude oils include S hell oil Hirschberg et al.,

. Ž . Ž1984 , Texaco oil B urke et al., 1990 , Weyburn oil Sirvastava. Ž .et a l., 1995 , and North-Sea o il Fotland et al., 1997 . Table 3

summarizes asphaltene and resin contents and light-compo-

nent compositions of the reservoir fluids used in our calcula-

tions.

When two liquid phases coexist at equilibrium, the chemi-

cal potential for each component is the same in both phases:

s 17Ž .A A

s

18Ž .R R

where

an d

represent two equilibrated phases. In addition,

MacMillan-Mayer theory requires that the o smotic pressures

for the two equilibrated phases must be equal,

P s P

, 19Ž .

where P denotes osmotic pressure. Both chemical potentials

and osmotic pressure can be obtained from Helmholtz en-

Table2. Independently EstimatedMolecularParameters

Asphalt ene R e sin Chain

Molecular weight, D a 2,000 8003Ma ss density, kgrm 1,200 1,000

Number of segments 1 10

Segment diameter, A 15 520H amaker constant, 10 , J 13.2 9.06

SAFT -parameter 0.05 0.05



6/13

Table3. Characterization Data for Reservoir FluidsUsedin theCalculations

Texaco R eservoir Shell Tank Oil Weyburn Oil North-Sea OilH CG Oil 1 Oil 2 Sep. Oil Sep. G as

mol % mol % mol % mol % mol % mol % mol %

N 3.17 0.57 0.51 C 0.1 N 0.96 N 0 2.3572 1 2 2CO 17.76 2.46 1.42 C 0.48 CO 0.58 CO 0 0.4262 2 2 2C 30.33 36.37 6.04 C 2.05 H S 0.3 C 8.365 67.4961 3 2 1C 26.92 3.47 7.00 i -C 0.88 C 4.49 C 4.848 12.7932 4 1 2C 13.09 4.05 6.86 n -C 3.16 C 2.99 C 7.888 9.7333 4 2 3i -C 1.26 0.59 0.83 i -C 1.93 C 4.75 i -C 1.486 1.215

4 5 3 4n -C 4.66 1.34 3.35 n -C 2.58 i -C 0.81 n -C 5.586 3.0274 5 4 4i -C 0.77 0.74 0.70 C 4.32 n -C 1.92 i -C 2.201 0.8155 6 4 5

qn -C 1.26 0.83 3.46 C 84.5 i -C 1.27 n -C 3.263 0.7615 7 5 5C 0.78 1.62 3.16 n -C 2.19 C 4.53 0.6196 5 6

q q qC 0.00 47.96 66.67 C 79.74 C 61.833 0.7587 6 7

Ž .q qM , D a 329 281 250 C 230 218C 6Ž .q qC densi ty, grml 0.96 0.90 0.96 C 0.870 0.837 6

wt. % asphaltene 16.8 9 3.9 4.7 0.9wt. % resin 21.5 12.25 14.1 8.51 2.8

HCG refers to hydrocarbon gas.

Measured according to the standard ASTM method.

ergy A a s given in Eq . 1

A s 20Ž .A ž / N A T , V , N R

A s 21Ž .R ž / N R T , V , N A

AP sy , 22Ž .ž / V T , N , N A R

where N an d N are the number of asphaltene moleculesA R and resin chains, respectively; V is total volume and T is

temperature. Pha se equilibria are calculated using Eq s. 1719

coupled with three material-balance equations:

N

q N

s N 0 23Ž .A A A

N

q N

s N 0 24Ž .R R R

N

q N

s N 0 , 25Ž .m m m

where superscript 0 indicates before phase separation; N ism the tota l number of medium molecules. B ecause it is difficult

to predict accurately the density of a heavy crude oil, and the

change in tota l volume usually is small after phase separa-

tion, we replace Eq. 25 with V qV

sV 0, where V

and V

are total volumes in phase

and phase

, respectively; V 0 is

the total volume before phase separation. G iven tempera-ture, total volume, and the total numbers of a sphaltene and

resin mo lecules, from E qs. 1719, E qs. 23 and 24, a nd V q

V

sV 0 , we can obtain N , N

, N

, N

, V

, and V

usingA R A R

the Brandt algorithm for a set of nonlinear equations withŽinitial guesses provided by phase-stability analysis Michel-

.sen, 1982; Wasylkiewicz et al., 1996 .The onset of asphaltene precipitation is found through

global-phase-stability analysis using the G ibbs-tangent-planeŽ .method Wasylkiewicz et a l., 1996 . Either simulated anneal-

ing or simplex algorithm is used to search for the global mini-

Žmum of the tangent-plane distance Pan and Firoozabadi,.1998a .When a n a sphaltene-containing crude oil is in contact with

a gas phase, we need to find the composition of the oil

medium, as well as the asphaltene and resin concentrations

of the crude-oil phase from the vaporliquid eq uilibrium. For

this purpose, we use the volume-shifted PREOS. Binary pa-

rameters k for interactions among the light components arei j Ž .obtained from Katz and Firoozabadi 1978 . For interactions

among heavy hydrocarbons, we use the C hueh-Pra usnitz cor-Ž .relation 1967 :

1r6 1r62V V c c i j

k s1y , 26Ž .i j 1r3 1r3V qV

ž /c c i j

where V is critical volume estimated from Twu’s correlationc Ž .1984 ; is a parameter independent of the heavyheavy ij pair, fixed by one experimental bubble-point pressure mea-

surement.

Texaco crude oils

Ž .B urke et al. 1990 reported experimental asphaltene-pre-cipitation data for mixtures containing crude o il and scrubber

Ž .gas 85 mol % CO q15 mol % H S , a nd for mixtures con-2 2taining crude oil and hydrocarbon gas. Burke and coworkers

were concerned with the effect of pressure and composition

on precipitate formation at elevated temperatures.The crude oils investigated in these experiments a re in

equilibrium with a gas phase. To find the composition of as-

phaltene-containing crude oil, we first apply the volume-

shifted Peng-Robinson equation of state for vaporliquid

equilibrium calculations. Figure 3 illustrates predicted a nd

measured saturation pressures for mixtures of Texaco oil 2

and hydrocarbon gas at 376.6 K. For this mixture, the -

parameter in Eq. 26 is 0.66, obtained from the experimental

bubble-point pressure of this o il at reservoir conditions.



7/13

Figure 3. Saturation pressures for mixtures of TexacoOil 2 and hydrocarbon gas at 376.6 K.

Agreement between calculated and experimental results for

the saturation pressure is excellent.

To calculate asphaltene precipitation of the crude-oil phase

at various temperatures and oil compositions, we use esti-

mated association parameters N s 6, rkT s 5, anda A A 0Ž . Ž rkT s10 T s298 K , as discussed previously Wu etA R 0 0

.al., 1998 . Because the experimental data scatter widely, thereis no advantage in further refinement of these molecular pa-

rameters. However, because the resin contents are not re-

ported for the Texaco crude oils used here, we fix the resin

content by a djusting the calculated amount of asphaltene

precipitation with one experimental measurement for each

crude oil. The ‘‘fitted’’ resin content may not be identical to

Figure 4. Asphaltene precipitation for Texaco Oil 1 incontact with scrubber gas.T s 373 K, P s 20.9 MPa ; points are mea surements by Burke

Ž .et al . 1990 ; l ines are calculated.

Figure 5. Effect of pressure on asphaltene precipitationfor Texaco oil 1 at 373 K.Saturat ion pressure s 20.3 MPa ; points are measurements by

Ž .Burke et al . 1990 ; l ines are calculated.

that actually present in the crude oil. The fitted weight per-

cents of resins of two Texaco oils are also listed in Table 3.

Figure 4 shows asphaltene precipitation from mixtures of

Texaco oil 1 and a scrubber gas at 373 K and 20.9 MPa. At

the conditions shown in this plot, the applied pressure is lower

than the saturation pressures of the mixtures; therefore, the

crude oil is in contact with a gas phase. Figure 4 presents the

amount of asphaltene in both the asphaltene-rich liquid phase

and in the solvent-rich phase after asphaltene precipitation.

Due to experimental uncertainties, measured amounts of as-

phaltenes in the two equilibrated liquid phases do not satisfy

material balances. B oth experiment and calculated results

show that the amount of asphaltene precipitated falls slightly

as the overall concentration of the scrubber gas rises. Thedecline in the amount of asphaltene precipitation is because

the liquid density of the oil medium increases as more scrub-

ber gas dissolves in the crude oil at the prevailing tempera-

ture a nd pressure. Our calculated results agree reasonably

well with the experimental measurements.

Figure 5 shows the ef fect of pressure on a sphaltene precip-

itation for the same crude oil as that discussed in Figure 4.

Because we have fixed all model parameters and resin con-

tent, no additional adjustable parameters are used in these

calculations. The saturation pressure of the crude oil is about

200 bar. Both experiment and our theory show a weak non-

monotonic pressure effect on the amount of asphaltene pre-

cipitation. This nonmonotonic effect is related to the satura-

tion pressure of the mixture. When the applied pressure islower than the saturation pressure of the mixture, an in-

crease in pressure dissolves more gas, causing more asphal-

tene precipitation; on the other hand, when the pressure is

higher than the saturation pressure, the density of the medium

increases with applied pressure. The amount of asphaltene

precipitation decreases as the density of the medium rises.

Our calculations agree reasonably well with measurements

over the pressure interval studied in the experiments. Figures

4 and 5 suggest that, once model parameters are fixed using



8/13

Figure 6. Asphaltene precipitation in Texaco Oil 2 byadding hydrocarbon gas at 376.6 K and 3.55MPa.All mixtures are below saturation pressure; points are mea-

Ž .surements by Burke et al . 1990 ; l ines are calculated.

some experimental data at a fixed condition, our framework

can predict the a mount of asphaltene precipitation at other

conditions.

Figure 6 presents predicted and measured percent of as-

phaltene precipitation for mixtures of Texaco oil 2 and hy-

drocarbon gas at a given temperature a nd pressure. The com-

position of the hydrocarbon gas is also given in Table 3. The

same set of model parameters is used for this oil; the resin

content fo r this crude oil is aga in fixed using one experimen-

tal measurement for asphaltene precipitation. When the ap-

plied pressure is below the saturation pressures of the oilga s

mixtures, the amount of asphaltene precipitation is insensi-

tive to the overall concentration of the hydrocarbon gas, asindicated both by calculation and by experiment. However,

Ž .more asphaltenes are precipitated at very high 70% hy-drocarbon gas content, as shown by calculation and by ex-

periment. Different from the effect of scrubber gas on as-Ž .phaltene precipitation as shown in Figure 4 , the density of

the oil medium decreases monotonically as more hydrocar-

bon ga s dissolves in the crude oil.

Shell tank oil

Ž .Hirschberg et al. 1984 measured the pressure at the onsetof asphaltene precipitation for a Shell crude oil in contact

with propane. At a given temperature, propane solubility in-

creases with pressure, lead ing to asphaltene precipitation. Inthis calculation, we first compute the solubility of propane

and the liquid density of tank oil 1. We use the volume-Žshifted Peng-Robinson equation of state with k s0 where i i j

.and j refer to heavy components because no measured bub-ble-point pressure is available. Then, our molecularthermo-

dynamic model is used to calculate the pressure at the onset

of a sphaltene precipitation. The concentration of resin is ob-

tained from the content of asphalt that is understood to be

the combination of a sphaltene and resin. The onset pressure

was det ermined by ta ngent-plane stability a nalysis of t he sys-Ž .tem Pa n and Firooza badi, 1998a . Figure 7 shows calculated

and measured pressures at the onset of asphaltene precipita-

tion for tank oil 1 in contact with propane. In this calcula-

tion, the number of a ssociation sites per asphaltene mo lecule

is again equal to 6, but association energy parameters are

obtained by fitting to the experimental onset-pressure data,

rkT s5.26 and rkT s7.92, where T s298 K. TheA A 0 A R 0 0same set of parameters was then used to predict the onset of

asphaltene precipitation for a mixture of ta nk oil 1 and nor-mal decane in contact with propane at different tempera-

tures. Figure 7 also shows predicted a nd measured pressures

at the onset of asphaltene precipitation for the mixture of

tank oil 1 and normal decane in contact with propane. For

this Shell tank oil, agreement between predicted and experi-

mental results is reasonably good. In this example, several

experimental points are neglected in Figure 7 because one

point is a duplicate, and because at low temperature, wax

precipitation wa s expected as indicated by the original au-

thors.

Weybur n reser ©oir oil

Ž .Sirvastava et al. 1995 have investigated the effect of aCO -miscible displacement process on asphaltene precipita-2tion for Weyburn reservoir oils. In the experiments, different

amounts of CO and Weyburn reservoir fluid were mixed by2application of high pressure. After precipitation equilibrium,

the amount of asphaltene precipitated was measured by quickŽ .release of the applied pressure; Sirvastava et a l. 1995 as-

sumed that asphaltenes do not redissolve during the quick

pressure-release process.

Figure 7. Effectof temperature on the pressure atonsetof asphaltene precipitation by injection of propane for two Shell reservoir fluids.

Ž .Points are exper imenta l da ta by H irschberg e t a l . 1984 ;lines are calculated.



9/13

Figure 8. Effect of CO injection on asphaltene precipi-2

tation for Weyburn oil at 16 MPa and 332 K.Ž .Po ints are measurements by Sirvastava et al . 1995 ; l ine is

calculated.

When pressure is lower than the saturation pressure, CO 2solubility is calculated from the volume-shifted Peng-Robin-

son equation of state with s2.1 and k s0.095 for intera c-i j tions between CO and heavy components. Here k and 2 i j are obtained by fitting to measured saturation pressures of

this crude oil a t various temperatures. Figure 8 shows calcu-

lated and measured fractions of asphaltene precipitated at

different CO concentrations. In this calculation, we find that2three a ssociation sites per asphaltene molecule gives the best

fit of experimental results. Associated energy parametersŽ . rkT s12.5 and rkT s9.77 T s298 K a re ob-A A 0 A R 0 0

tained by fitting the experimental asphaltene-precipitation

data. From the volume-shifted Peng-Robinson equation of

state, we find that the liquid density of the oil medium in-

creases as more CO dissolves in the crude oil. Both experi-2ment and calculation indicate that the solubility of asphal-

tene in the oil declines as the content of CO in the crude oil2rises. If any standard solubility model were used for this ex-

ample, an increase in asphaltene precipitation with rising CO 2concentration would be expected because, as CO concentra-2tion rises, the solubility parameter of the medium becomes

closer to that of asphaltene. Our calculations, in agreement

with experiment, show the opposite trend that follows from

enhanced resin solubility in the medium. Because resin now is ‘‘more comfortable’’ in the medium, the tendency of resin

to a ssociate with asphaltene declines. As a result, asphaltene

is destabilized and precipitates.

North-Sea crude oil

Ž .Fotland et a l. 1997 investigated the effect of oil composi-tion on the o nset pressure of asphaltene precipitation f or dif-

ferent North-Sea crude oil mixtures, made from mixing vari-

ous ratios of separator oil and separator gas. Separator oil

and separator gas are, respectively, the liquid a nd gas frac-

tions of the reservoir oil flashed a t ambient conditions. For

the crude oil used here, the a verage C q ma ss density that is7used in our C q characterization is not reported in the oil-7characterization data. Thus, we first estimated the average

C q mass density by adjusting the reported density of the7separator oil at 20 MPa and 365 K using the volume-shifted

Peng-Robinson equation of state. Parameter of E q. 26 was

set at 1.42, ba sed on the mea sured bubble-point pressure fo rthe reservoir oil. Figure 9 compares predicted and measured

saturation pressures and liquid densities for mixtures of the

North-Sea separator oil and separator gas at 365 K. The liq-

uid densities were not measured at the saturation pressure;Ž .instead, they were measured at constant pressure 320 bar ,

higher than the saturation pressures of all the mixtures. As

found in other examples, the volume-shifted Peng-Robinson

equat ion of state provides reliable predictions for liquid den-

sities. The volume-shifted equation does not affect calcula-

tion of the saturation pressure.

Figure 10 shows the pressure at the onset of asphaltene

precipitation a s a function of the separator-gas concentration

for the North-Sea crude oil at 365 K. We find that three a sso-

ciation sites for each a sphaltene molecule gives the best f it ofexperimental results for this oil. The association-energy pa-

rameters for asphaltene-asphaltene and for a sphaltene-resin,Ž . rkT s8.35 a nd rkT s7.49 T s298 K a re ob-A A 0 A R 0 0

tained by fitting the experimental data of asphaltene precipi-

tation. As more separator gas dissolves in the crude oil, the

Ha maker constant of the medium declines, leading to addi-

tional attraction between asphaltene molecules. As a result,

the onset pressure increases nearly linearly with the mole

fraction of separator gas in the oil.

Figure 9. Calculated and measured saturation pres-sure, and density of mixtures of separator oiland separator gas of the North-Sea oil at 365K.

Ž .Points are exper imenta l da ta by Fot land e t a l . 1997 ; l inesare calculated.



10/13

Figure 10. Calculated and experimental pressure at on-

set of asphaltene precipitation for North-Seaoils at 365 K.

Ž .Po ints are experimental data b y Fotland et al . 1997 ; l ineis calculated.

Fotland et al. also reported experimental data on asphal-

tene precipitation for the same crude oil at 333 K. They found

that temperature has essentially no effect on the pressure at

the onset of a sphaltene precipitation, a nd on t he bubble-point

pressure of the crude oil. It is difficult for us to interpret

these results. Our model predicts that the onset pressure is

sensitive to temperature changes, because a change in tem-

perature not only affects interactions among asphaltenes and

resins, but also changes the equilibrium composition of the

asphaltene-containing liquid phase.

Conclusions

The effect of the oil medium on asphaltene precipitation is

determined only by its Hamaker constant as obtained from

the oil’s density and from the concentration of light compo-

nents in the o il. At reservoir conditions when the crude oil is

in equilibrium with light-component gases, the properties of

the medium, and the contents of asphaltene and resin in the

oil phase ca n be reliably calculated using the volume-shifted

PREOS with an appropriate C q characterization procedure7and with suitable binary interaction parameters. In general,

because the asphaltene content in the oil is not large, asphal-

tene precipitation do es not significantly a ffect o il-vapor equi-libria.

The molecularthermodynamic model discussed here has

been tested with experimental data for a few reservoir fluids

to describe the effects of pressure and oil composition on

asphaltene precipitation. This model can be applied to iden-Ž .tify 1 the operation conditions at the onset of asphaltene

Ž .precipitation, and 2 the amount of precipitation under vari-ous reservoir conditions. Most parameters in our model can

be estimated independently from average properties of as-

phaltenes and resins. The parameters related to association

interactions, N , , and , are confined within physicallya A A A R meaningful lower and upper limits. However, because calcu-

lated results are often sensitive to these parameters, and be-

cause asphaltenes and resins in crude oils differ from one

crude oil to a nother, in typical cases, they must be correlated

with some experimental data for the particular crude oil of

interest. For the North Sea crude oil, the effect of tempera-

ture req uires further study to a chieve clarification.

Acknowledgments

This work was supported, in part, by the Director, Office of En-ergy Research, Office of Basic Energy Sciences, Chemical SciencesD ivision of the U .S. Department of E nergy under C ontract No. DE -AC03-76SF00098. For initial support, w e are gratef ul to the U niver-sity of Ca lifornia Energy Institute.

Literature Cited

Alexander, G . L., A. L. Creagh, and J. M. P rausnitz, ‘‘Phase Eq uilib-ria for High-Bo iling Fo ssil-Fuel D istillates. 1. Cha racterization,’’

Ž .I nd . Eng . Chem . Fundam ., 24, 301 1985 .Artok, L., Y. Su, Y. Hirose, M. Hosokawa, S. Murata, and M. No-

mura, ‘‘Structure and Rea ctivity of Petroleum-D erived Asphal-Ž .tene,’’ Energy Fuels , 13, 287 1999 .

Burke, N. E., R. E. Hobbs, and S. F. Kashou, ‘‘Measurement andModeling of Asphaltene Precipitation,’’ J . Pet . Technol ., 42, 1440Ž .1990 .

Chapman, W. G ., G . Jackson, and K. E. G ubbins, ‘‘Phase Equilibriaof Associating Fluids, Chain Molecules with Multiple Bonding

Ž .Sites,’’ M ol . Phys ., 65, 1057 1988 .Chapman, W. G., K. E . G ubbins, G . Jackson, and M. Radosz, ‘‘New

Reference Equation of State for Associating Liquids,’’ I nd . Eng .Ž .Chem . Res ., 29, 1709 1990 .

Chueh, P. L., and J. M. Prausnitz, ‘‘Vapor-Liquid Equiibria at HighPressures: Calculation of Partial Molar Volume in Non-Polar Liq-

Ž .uid Mixtures,’’ AIChE J., 13, 1107 1967 .Cotterman, R. L., and J. M. Prausnitz, ‘‘Flash Calculations for Con-

tinuous or Semi-Continuous Mixtures using Equation of State,’’ I nd .Ž .En g . Chem . Pr ocess Des . D e ®., 24, 434 1985 .

Fotland, P., H. Anfinsen, H. Foerdedal, and H. P. Hjermstad, ‘‘ThePhase D iagrams of Asphaltenes: Experimental Technique, R esults

and M odeling on Some North Sea Crude O ils,’’ Symposium on theChemistry of the Asphaltene and Related Substances, Cancun,

Ž .Mexico 1997 .Hansen, J. P., and I. R . McDonald, Theory of Simple L iquids , 2nd ed.,

Ž .Academic Press, San D iego 1986 .Hirschberg, A., L. N. J . de Jong, B. A. Schipper, and J. G . Meyers,

‘‘Influence of Temperature and Pressure on Asphaltene Floccula-Ž .tion,’’ SPE J ., 283 1984 .

Ho ng, S. G, K . A. G reen, and K. D . Luks, ‘‘Solubility and Volumet-ric Behavior of Methane and Carbon Dioxide Plus C q Pseudo-7

Ž .components of an O il,’’ Fluid Phase Equilibria , 95, 267 1994 .Huang, S. H ., and M. Radosz, ‘‘Equation of State for Small, Large,

Polydisperse and Associating Molecules,’’ I nd . En g . Chem . Res .,Ž .29, 2284 1990 .

Israelachvili, J., Intermolecular & Surface Forces , Academic Press,Ž .London 1991 .

Katz, D. L., and A. Firoozabadi, ‘‘Predicting Phase Behavior of Con-

densaterCrude-Oil Systems U sing Methane Interaction Coeffi-Ž .cients,’’ J . Pet . Technol ., 1649 1978 .

Kokal, S. L., and S. G . Sayegh, ‘‘G as-Saturated Bitumen D ensityPredictions Using the Volume Translated Peng-Robinson Equa-

Ž .tion of State,’’ J . Can . Pet . Technol ., 29, 77 1990 .Mansoori, G . A., N. F. Carnahan, K . E. Starling, and T. W. Leland,

‘‘Equilibrium Thermodynamic Properties of the Mixture of HardŽ .Spheres,’’ J . Chem . Phys ., 54, 1523 1971 .

Michelsen, M. L., ‘‘The Isothermal Flash Problem. I. Stability,’’ Fluid Ž .Phase Equilibria , 9, 1 1982 .

Mitchell, D . L., and J. G . Speight, ‘‘The Solubility of Asphaltenes inŽ .Hydrocarbon Solvents,’’ Fuel , 53, 149 1973 .



11/13

Nalwaya, V., V. Tangtayakom, P. Piumsomboon, and S. Fogler,‘‘Studies on Asphaltenes Through Analysis of P olar Fractio ns,’’ I nd .

Ž .En g . Chem . Res ., 38, 964 1999 .Pan, H. Q., and A. Firoozabadi, ‘‘Complex Multiphase Equilibrium

Ca lculations by Direct Minimization of G ibbs Free Energy by U seŽ .of Simulated Annealing,’’ SPE Reser ®oir E ®al . En g ., 36 1998a .

Pan, H. Q., and A. Firoozabadi, ‘‘Thermodynamic M icellizationModel for Asphaltene Aggregation and Precipitation in Petroleum

Ž .Fluids,’’ SPE Prod . Facil ., 13, 118 1998b .Peneloux, A., E. Ra uzy, and R . Freze, ‘‘A Consistent C orrelation for

Ž .Redlich-Kwong-Soave Volumes,’’ Fluid Phase Equilibria , 8, 7 1982 .

Peng, D . Y ., and D . B . R obinson, ‘‘A New Two-Constant Eq uationŽ .of State,’’ I nd . En g . Chem . Fundam ., 15, 59 1976 .Rackett, H. G ., ‘‘Equation of State for Saturated Liquid,’’ J . Chem .

Ž .En g . Data , 15, 514 1970 .Reid, R. C ., J. M. P rausnitz, and B . E. P oling, Properties of G ases and

Ž .Liquids , 4th ed., McGra w-Hill, New York 1986 .Schreiber, D . R ., and K. S. P itzer, ‘‘Equation o f State in the Acentric

Ž .Factor System,’’ Fluid Phase Equilibria , 46, 113 1989 .Sirvastava, R . K., S. S. H ung, S. G . D yer, and F. M. M ourits, ‘‘Quan-

tification of Asphaltene Flocculation D uring Miscible CO Flood-2Ž .ing in the Weyburn Reservoir,’’ J . C an . Pet . Technol ., 34, 31 1995 .

Speight, J . G ., The Chemistry and T echnology of Petroleum , Dekker,Ž .New York 1991 .

Speight, J . G ., ‘‘The M olecular Nature o f P etroleum Asphaltenes,’’Ž .Arab . J . Sci . Eng ., 19, 335 1994 .

Twu, C. H., ‘‘An Internally C onsistent C orrelation for Predicting theCritical Properties and M olecular Weights of Petroleum and Coa l-

Ž .Tar Liquids,’’ Fluid Phase Equilibria , 16, 137 1984 .Wasylkiewicz, S. K., L. N. Sridhar, M. F. Doherty, and M. F. Ma-

lone, ‘‘Global Stability Analysis and Ca lculation o f L iquid-LiquidEquilibrium in Multicomponent Mixtures,’’ I nd . En g . Chem . Res .,

Ž .35, 1395 1996 .Whitson, C. H., T. F. Anderson, a nd I . Soreide, ‘‘Application of the-D istribution M odel to Mo lecular Weight and B oiling Point D ata

Ž .for P etroleum Fractions,’’ Chem . En g . Commun ., 96, 259 1990 .Wu, J ., J . M. Prausnitz, and A. Firoozabadi, ‘‘Molecular Thermody-

namic Framework for Asphaltene-Oil Equilibria,’’ AIChE J., 44,Ž .1188 1998 .

( )Appendix A: Vapor-Liquid Equilibria VLE andLiquid-Density Calculations UsingtheVolume-Shifted Peng-Robinson Equation of State

( )PREOSŽ .We use the PR EOS Peng and R obinson, 1976 to calcu-

late VLE of reservoir fluids. To include heavy hydrocarbons,

we describe a C q characterization procedure for the heavy7end of a crude oil in Appendix B. With suitable binary inter-

Ž .action parameters k and reasonable critical properties ofi j C q pseudocomponents, the PR EO S provides a good de-7scription of vaporliquid eq uilibria f or reservoir fluids.

Ž .For liquid-density calculations, P eneloux et al. 1982 pro-posed the volume-shifted equation-of-state method. They as-

sume that for a pure component at a temperature below its

critical point, the difference between the experimental liquid

molar volume and that predicted by the PR EO S is indepen-

dent of pressure. This difference can be estimated at satu-

Ž .rated conditions using R ackett’s equation R ackett, 1970 . Attemperatures exceeding critical, the volume offset depends

only on the critical compressibility factor. The liquid molar

volume at an arbitrary pressure and temperature is obtained

by making a correction to that calculated from the PREOS

by a volume-offset calculated at the saturation pressure. For

pure components at saturation conditions, the volume-shifted

method gives the same results as those of R ackett’s equation.

For mixtures, the o verall shifted-volume eq uation is obtained

by linear combination of t he shifts for pure components. The

Figure A1. Comparison between volume-shifted andoriginal PREOS for prediction of liquid mo-

(lar volume of two reservoir fluids CutA and

)Cut B at 360.9 K.Solid lines are calculated using the volume-shifted PR EO S;

dashed lines are calculated using the original PR EOS;Ž .points are experimental data by H ong et al . 1994 .

volume-shifted method has been successfully applied to cal-Žculate the densities of gas-saturated bitumen Kokal and

.Sayegh, 1990 .Our application of the volume-shifted PREOS is different

Ž .from that of K okal and Sayegh 1990 for supercritical com-ponents. We calculate the volume-offset of a supercritical

component by comparison with molar volumes obtained fromŽ .the Schreiber-Pitzer eq uation 1989 at system pressure and

temperature. Further, because the Rackett constant is oftenunavailable, especially fo r pseudocomponents, we calculate

the Rackett constant from a single measured liquid density.

For a discrete component of a crude o il, the required experi-

mental liquid density is available a t a mbient conditions. For a

pseudocomponent, the required single liquid density is pro-

vided by our C q chara cterization procedure, as d iscussed in7Appendix B .

To illustrate, Figure A1 shows calculated and observed liq-

uid molar volumes for two crude oils at saturation conditions.Ž .Experimental data are from H ong et al. 1994 . Compared

with the original PREOS, the improvement of the volume-

shifted method is significant. As pointed out by P enelouxŽ .1982 , the volume-shifted method does not affect VLE cal-

culations provided that the volume correction is applied toboth liquid and vapor phases.

Appendix B: C Characterization Method7Ž .qHeptane-plus C fraction refers to the components of a7

reservoir fluid with molecular weight or normal bo iling point

higher than those for n -hexane. Typically, C q is a complex7mixture of heavy paraffins, naphthenes, and aroma tics. Cha r-

acterization of the C q fraction is important for calculation7



12/13

of phase equilibria o f reservoir fluids. The C q characteriza-7tion for a heavy crude oil should be based on experimental

measurements from distillation or chromatographic fraction-Ž .ation Alexander et al., 1985 . U nfortunately, such detailed

information is generally not available in the literature for as-

phaltene-containing mixtures. Some methods characterize a

C q fraction ba sed on molecular weight or boiling-point tem-7perature; the C q fraction is represented by a set of pseudo-7

Žcomponents or by a continuous distribution function Whit-

.son et al., 1990, and references therein . The advantage of atraditional method is that it can represent reasonably well

Žqone particular property of the C fraction such as molecu-7.lar-weight distribution , but it usually provides no informa-

Žt ion for other propert ies of practica l interest such as.boiling-point temperature o r density . As a result, when a cu-

bic equation of state is used to describe the phase behavior

of a reservoir fluid, the eq uation-of-state pa rameters are esti-

mated using empirical correlations based only on one prop-

erty. Subsequent calculations could be unreliable because

components having one identical property may differ signifi-

cantly in o ther properties.

The need to include both molecular-weight a nd density in-

formation was shown over 20 years ago by Katz and Firooz-

Ž .abadi 1978 . Here we describe a n alternative method tocharacterize C q fractions.7

First, a C q fraction is divided into a set of pseudocompo-7nents based on known average molecular weight and on a n

assumed variance; here the molecular weight o f the C q frac-7t ion is represented by a -distribution function, and the

G aussian q uadrat ure method is used to convert the continu-Žous distribution to obtain pseudocomponents Cot terman and

.Prausnitz, 1985 . Then the density of each pseudocomponentat ambient conditions is calculated from a correlation be-

tween the density and molecular weight. Our C q characteri-7zation method requires average and variance of molecular-

weight distribution, and average density at ambient condi-

tions. If a n experimental variance is not available, we use 700

for a typical crude oil. Six quadrat ure points are used in most

( ) ( )TableB1. Molecular Weight MW and Density d of C Hydrocarbons7

y3T MW d 103H ydrocarbon K D a kgrm

Toluene 293 92.141 0.867c -H eptane 293 98.189 0.811,2-Dimethylcyclopentane , c is 289 98.189 0.7771,2-Dimethylcyclopenane, t rans 289 98.189 0.756Ethylcyclopentane 289 98.189 0.771Methylcyclohexane 289 98.189 0.7741-H eptene 293 98.189 0.6972,3,3-Tr imet hyl-1-b ut ene 293 98. 189 0.705

n -H eptane 293 100.205 0.6842-Methylhexane 293 100.205 0.6793-Methylhexane 293 100.205 0.6872,2-D imethylhexane 293 100.205 0.6742,3-D imethylhexane 293 100.205 0.6952,4-D imethylhexane 293 100.205 0.6733,3-D imethylhexane 293 100.205 0.6933-Ethylpentane 293 100.205 0.6982,3,3-Trimet hylbuta ne 293 100.205 0.69

Average 292.1 98.90 0.73

The density is measured at temperature T a nd a tmospheric pressure.

Figure B1. Molecular weights and densities of theGaussian-quadrature points for a C frac-7tion in crude oil.

For this fraction, the average molecular weight s 253 D aand the average mass density s 960 kgrm 3; the calculationuses 20 quadrature points.

of our calculations. In general, VLE calculations are not sen-

sitive to the variance and number of quadrature points.ŽHowever, dew point calculations are sensitive to the distri-

.bution of very heavy component s. This new procedure repre-sents each pseudocomponent, with two properties, molecular

weight and liquid density, at ambient conditions.

The correlation between density at a mbient conditions, d ,i Ž . Ž . qgrmL and molecular weight M grm ol o f a C pseudo-i 7component is empirically represented by

1 1 c c 1 2s q q , B 1Ž .

2d 1.2 M M i i i

where c and c are calculated from the mole fraction of1 2each pseudocomponent, x , f rom minimum and averagei

qmolecular weights M an d M of the C fraction, and from0 7qminimum and average densities d and d o f t he C f ra c-0 7

tion,

1 1 1 1 x i 2M y y M y Ý0ž / ž /1.2 d 1.2 M d 0 i i c s B 2Ž .1 x i

1y M Ý0 M i i

1 1 1 1M y y M y0 ž /ž /d 1.2 1.2d 0

c s M . B 3Ž .2 0 x i 1y M Ý0

M i i

In d eriving Eq . A1, we assume that the maximum density of a

hydrocarbon component in the C q fraction at ambient con-7



13/13

ditions is 1.2 grmL. M an d d are assumed to be the same0 0as those averages of typical C components given in Table7B 1, d s0.73 grmL, M s98.9 grmol.0 0

The ambient-condition densities of C q pseudocompo-7nents are not sensitive to d and M . Figure B1 shows the0 0densities of pseudocomponents for two C q fractions with7the same average molecular weight and variance as well as

Žaverage density d s0.96 grmL, M s253 grmol, and vari-.ance s700 , but different minimum densities and molecular

Žweights; the first uses d s0.70 grmL, M s84 grmol they0 0correspond to the average values for typical C hydrocar-6

.bons , a nd the second uses d s0.73 grmL, M s98.9 grmol.0 0For a careful comparison of density distributions for the C q7fraction, 20 quadrature points are used in Figure B1. The

densities of pseudocomponents are essentially identical for

the two sets of d and M .0 0

In general, the density of a C q pseudocomponent is much7larger than that of a normal alkane of the same molecular

weight because a C q psuedocomponent usually has higher7aromaticity. For VLE calculations, we estimate the critical

properties of a pseudocomponent fro m its ambient-conditionŽ .density and molecular weight using Twu’s correlation 1984 ,

and the acentric factor from Lee-Kesler’s correlation of a cen-

tric factor with critical temperature and normal boiling pointŽ .Reid et al., 1986 . We expect that these critical properties

are more reliable than those obtained using only molecularweight.

M anuscript recei ®ed Jan 22, 1999, and re ®ision recei ®ed Aug. 2, 1999.


Molecular Thermodynamics of Asphaltene Precipitation in Reservoir Fluids

Documents

Transcript of Molecular Thermodynamics of Asphaltene Precipitation in Reservoir Fluids