Thermodynamic Micellization Model of

Asphaltene Precipitation from Petroleum Fluids

Alexey I. Victorov and Abbas Firoozabadi
Reservoir Engineering Research Institute, Palo Alto, CA 94304

A thermodynamic micellization model is proposed for the description of asphaltene

precipitation from petroleum fluids. It describes the solubilization of asphaltene polar
species by resin bipolar molecules in the micelles. A simple form of the standard Gibbs
free energy of micellization is used. The petroleum fluid is assumed to be a dilute solu-
tion with respect to the monomeric asphaltenes, resins, and micelles. The Peng - Robin-
son equation of state (PR-EOS) is applied to describe the fugacity of monomeric as-
phaltene in the bulk of the petroleum fluid. Intermicellar interactions as well as osmotic
pressure effects are neglected. The proposed model shows promising results to describe
asphaltene deposition from crude mixtures. It predicts the change in precipitation power
of different alkane precipitants and the effect of pressure on asphaltene precipitation.
The amount and the onset of predicted asphaltene precipitation are sensitive to the
amount of resins in the crude. All these results are in line with laboratory observations
and oil-field data.

Introduction
A variety of substances of diverse chemical nature consti- experiments are performed to determine the amount of solid
tute petroleum fluids. These include paraffinic, naphthenic, precipitates. It is believed that titration with low molecular
and aromatic hydrocarbons, and polar polyaromatic materials weight alkanes (C, to C,) leads to coprecipitation of both
that contain metals and nitrogen. The polar materials are part resins and asphaltenes (Leontaritis, 1988). Liquid titration
of the heavy nonvolatile end of the crude; they are often with pentane results in nearly pure asphaltene precipitate.
referred to as “resins,” and “asphaltenes” in petroleum chem- The amount of asphaltene precipitate decreases as the
istry and petroleum engineering literature (Altgelt and Bo- molecular weight of the n-alkane titrant increases.
duszynski, 1994). Under certain conditions, asphaltenes and The asphaltenes and resins may associate to form large ag-
resins precipitate from a petroleum fluid (Katz and Beu, 1945; gregates of high molecular weights (Lian et al., 1994; Ander-
Hirshberg et al., 1984). The precipitation in both under- sen and Speight, 1993; Storm et al., 1991). As early as 1938, it
ground petroleum reservoirs and production facilities is un- was recognized that asphaltenes and resins form colloid par-
desirable. It reduces flow rate and may plug the production ticles (Nellensteyn, 1938). Later, Yen (1974) reconfirmed the
facilities. formation of micelles in asphaltene and resin-containing
It is unclear how to exactly define asphaltenes and resins crudes. Currently the micellar nature of these systems is a
as components with a specific molecular structure. The oper- well-established fact (Wiehe and Liang, 1995). On the other
ational definitions of asphaltenes and resins are based on hand, asphaltene precipitation modeling has traditionally
their solubility in different solvents (Speight, 1980; Hirshberg been approached by using a bulk phase equation of state to
et al., 1984). Asphaltenes are often defined as the fraction of describe asphaltene solubility (Hirshberg et al., 1984; James
crude insoluble in normal alkanes such as n-pentane and hot and Mehrotra, 1988; Burke et al., 1990; Kawanaka et al., 1991)
n-heptane. Resins are assumed to be insoluble in liquid neglecting its colloid nature.
propane but soluble in n-pentane. Liquid and gas titration A thermodynamic colloid model of asphaltene precipita-
tion was proposed by Leontaritis and Mansoori (1987). This
model can be used to assess the possibility of precipitation;
Correspondence concerning this article should he addressed to A. Firoozabadi. however, it does not explicitly deal with the dependence of
Permanent address of A. I. Victorov: St. Petershurg State University, St. Peters-
burg, Russia. the micellization process on the characteristics of the mi-

AIChE Journal June 1996 Vol. 42, No. 6 1753

celles. A number of advanced thermodynamic models of mi- Speight, 1980). The role of resins is analogous to that which
cellization (Nagarajan and Ruckenstein, 1991; Blankstein et is played by surfactant amphiphilic molecules in theories of
al., 1985; Puwada and Blankstein, 1992) and colloid stability solubilization. If not for the resins, we believe, most of the
(Kahlweit and Reiss, 1991; Madahevan and Hall, 1990) have asphaltene material would immediately precipitate from the
been elaborated in the physicochemical literature, basically crude due to a low solubility of asphaltene monomeric
for aqueous systems. These models have been applied to pro- molecules in the bulk of the petroleum fluid. The balance
tein flocculation (Madahevan and Hall, 1990; Vlachy et al., between the amount of the asphaltene material solubilized
1993; Chiew et al., 19951, solubilization (Nagarajan and within the micelles and what remains in the form of monomers
Ruckenstein, 1991), and related phenomena. The term solu- is governed by the aggregation equilibrium, which can be
bilization was first introduced by McBain and Hutchinson written (Tanford, 1973; Rusanov, 1992) as
(1955) to denote a pronounced enhancement of the solubility
of a material by its sorption in micelles. In this work, we de-
velop a simple thermodynamic model of solubilization of as-
phaltene material by resins, adopting and modifying the mi- In the preceding equation, p l is the chemical potential of a
cellization models by Nagarajan and Ruckenstein (19911, micelle consisting of n, asphaltene molecules and n2 resin
Blankstein et al. (19851, Puwada and Blankstein (1992). molecules, and and p,$ are the chemical potentials of
This article begins with a discussion of the thermodynam- monomeric asphaltene and resin molecules, respectively. The
ics of aggregation of asphaltene and resin monomeric species medium (petroleum fluid) is noted by index /3 (Figure 1).
to form colloid particles. Then we present the model for as- Equation 1 determines the distribution of micelles over their
phaltene precipitation from crudes. Next, the proposed mi- sizes (n,and n2),and is valid both for the monodisperse (all
cellization model is applied to describe liquid and gas titra- the micelles are of the same size) and polydisperse (the diver-
tion, and to predict the effect of pressure on the stability of a sity of micellar sizes) colloid mixtures. This equation is also
crude with respect to asphaltene precipitation. We conclude valid both for concentrated and for dilute solutions. In our
the article with some propositions for future work. work, it is assumed that the concentrations of resin and as-
phaltene monomeric species and micelles are small enough
to apply thermodynamics of dilute solutions (thus we exclude
Thermodynamics of Micellization heavy oils that might be rich in asphaltene and resin content),
Aggregation equilibrium and therefore we can write:
We assume that an asphaltene colloid particle has a core,
which is formed by n1 aggregated asphaltene molecules; n2
bipolar resin molecules are adhered on the surface of the (3)
core (Figure 1). The aggregate is called a micelle. Several fur-
ther assumptions are made about the structure of a micelle for the monomeric asphaltenes and resins, respectively, and
based on spectroscopic evidence (Espinat and Ravey, 1993;
p M= G g + kT In X , (4)

for the micelles (note that superscript /3 in these and subse-

quent equations is dropped). In Eqs. 2-4, Xi is the mole
fraction of species i and &, pTl, and G F are the standard
chemical potentials. The standard state is chosen to be that
of the petroleum fluid, which is infinitely diluted with respect
to “solutes” (monomeric asphaltenes, resins, and micelles).
Thus, the standard chemical potential of a solute k , &*, is
defined by the properties of the isolated particle k (a
monomer molecule or a micelle) in the solvent (the petroleum
fluid free of asphaltene and resin monomers and micelles),

* - lim ( & - kTln Xk>,

ELL- PX,+O

where the summation extends over different solutes (Prigo-

gine and Defay, 1952): In a dilute solution, the difference
between these standard free energies determines the distri-
bution of micelles over their size and composition. As it can
readily be seen by rewriting the condition of aggregation
equilibrium, Eq. 1, and Eqs. 2-4 to give:

1, = exp((n, pol+ n2 p r l - C$,’)/kTI, (6)

Figure 1. Micelles, monomeric asphaltenes, and resins
in a petroleum fluid medium. or

1754 June 1996 Vol. 42, No. 6 AIChE Journal

 X, = X,.,1X:2 exp{AGE/kT}, (7) expect polydispersity. In this article, we assume that all the
micelles are monodispersed. This assumption is made for the
with the standard Gibbs energy of the formation of a micelle sake of computational simplicity and in principle can be re-
(rnicellization), AGE, defined by moved.

AGE = n, p:, + n 2 p:, - G E . (8)

Gibbs free energy of micellization
A model for the Gibbs energy of micellization should take All the specific features of the micellization model (micel-
into account the micellar size, shape, composition, and should lar structure and molecular characteristics) are contained in
include various contributions to the micellization process. We the standard Gibbs energy term. According to Nagarajan and
will formulate such a model later in this article. Ruckenstein (1991) and Puwada and Blankstein (1992), there
are several major contributions in the process of micelle for-
mation in a dilute solution.
Material balance
(a) Lyophobic Contributions. The lyophobic contribution
In addition to the aggregation equilibrium, one also has to to AGE represents the free-energy gain upon transferring
consider the material balance. Prior to the precipitation of asphaltene and resin molecules from an infinitely diluted
the asphaltene material, crude to a micelle. We shall relate this term with the solubil-
ity of asphaltene in the bulk of the crude at the onset of
asphaltene precipitation. Suppose that the pure solid asphal-
tene phase ( y ) is in equilibrium with the micellar crude solu-
tion (phase p ) , then the chemical potential of the solid
asphaltene, and asphaltene monomers in liquid phase are
equal:

where N, and N, are the gross numbers of asphaltene and

resin molecules in the crude, N,,and N,,are the numbers of
asphaltene and resin monomeric species, and N,(n,, n,) is Here X z = Xi:’ is the equilibrium concentration of
the number of micelles containing n1 asphaltene molecules monomeric asphaltenes in the crude coexisting with the solid
and n2 resin molecules each. The summation is performed asphaltene phase. Under the assumption that the average
over all possible aggregation numbers n, and n 2 . With the state of an asphaltene molecule in the micellar core (more
precipitation of the asphaltene phase, the material balance precisely, in a hypothetical uniform state, corresponding to a
equations should include the amount of the precipitate. If micellar core at the pressure P p , Rusanov (1992)) is similar
the precipitate (phase y ) contains only pure asphaltene ma- to its state in the solid asphaltene phase, one can write:
terial, the first of the preceding equations takes the form:

which is the contribution to the micellization “lyophobic term”

and the second one remains intact.
due to the transfer of an asphaltene molecule. Since the solu-
At a given temperature, pressure, and given gross composi-
bility of asphaltene monomers in the crude is low, the right-
tion, Eq. 9 together with Eq. 7 determine the micellar-mono- hand side of Eq. 13 is substantially negative, and thus the
mer equilibrium and the distribution of the aggregates over
lyophobic effect essentially enhances the solubilization of as-
their size and composition. These equations may be difficult
phaltenes in the micelles (Nagarajan and Ruckenstein, 1991).
to solve, since they contain a very large number of unknowns,
It is this term that makes the aggregated state preferable over
NM(nl,n 2 ) . If the distribution of the micelles were sharp both the monomeric state. Equation 13 is the essence of our phe-
with respect to their composition and with respect to their nomenologic micellization model and is similar to that of
size, we could approximate their distribution by the most Tanford (1973), which we apply here to the solid-liquid equi-
probable terms, and write instead of Eq. 9 librium. The quantity Xi? will be our main parameter. It
reflects how much monomeric asphaltene a crude can hold.
Another contribution to the “lyophobic term”& due to the
transfer of a resin molecule from a dilute crude onto an
asphaltene micellar core. The transfer is associated with
breaking the resin-crude interactions and creating resin-
with the corresponding values of n, = ny and n2 = ni, which asphaltene and resin-resin interactions. This process can be
represent the micelles that are most probable to form. The considered as adsorption of resins from the petroleum fluid
assumption that all the micelles are of the same size can be on asphaltene aggregates. A simple way of expressing the
justified in the case of small colloid particles of spherical free-energy change upon the transfer of a single resin
shape (Nagarajan and Ruckenstein, 1991; Puwada and molecule is to write purely energetic (AU,) and purely en-
Blankstein, 1992). For large platelike aggregates, one would tropic (AS,) terms as

AIChE Journal June 1996 Vol. 42, No. 6 1755

 h = van,/.rrr2, (18)

AS, = - k l n [ l - A , ( n, ) / A , I . ( 14) where v, is the asphaltene molecular volume. Equation 16

then becomes
In Eq. 14, a is the surface area of a resin molecule polar
head, q-, and q-, are the average interaction energies of
the resin molecule head with the crude and with asphaltene
molecules (micellar core), respectively, A , is the total sur-
face area of a micelle, and A,(n2) is the surface area occu-
pied by n2 resin molecules. Since polar resin heads associate (c) Electrostatic Contribution. Electrostatic effects may ac-
with asphaltenes, the AU, term is positive. As a first approxi- company the micellization in highly aromatic crudes where
mation, AU, is considered to have some properly averaged the charged particles can be stabilized. It is unlikely, how-
value, which remains the same for a given petroleum fluid at ever, that these effects can govern the process of micelle for-
a given temperature, and does not change appreciably upon mation in a typically dielectric medium such as a petroleum
the addition of a precipitant, as long as the system remains fluid. In this work, we are concerned with only those AG,?
diluted with respect to resins. This rough approximation may contributions that seem crucial for colloid stability, and elec-
be refined by a more detailed molecular consideration of AU, trostatic effects are neglected.
in future studies. To summarize, we write the final expression for the Gibbs
The AS, term is determined by the probability for a resin energy of micellization as
molecule to find an unoccupied space to be accommodated
on the micellar surface (excluded surface area, repulsion
component of the two-dimensional pressure; Puwada and
Blankstein (1992)). This term always opposes micellization,
giving a negative contribution to A G f , where
Apart from the lyophobic contribution, other terms deter-
mining the free energy of micellization include the following.
(b) Interfacial Contribution. A definite positive interfacial
tension might be attributed to the micellar core in the crude.
The adsorption of bipolar resins on the micellar core surface
is likely to lower the interfacial tension ("interfacial screen- and pf, py are the chemical potentials of asphaltene and
ing effect," Nagarajan and Ruckenstein, 1991; Puwada and resin molecules in a hypothetical uniform micellar phase at
Blankstein, 1992), and to contribute to the colloid stability. pressure P p of the surrounding petroleum fluid and uA, is
Kahlweit and Reiss (1991) have shown that this effect alone defined by Eq. 19. Introducing 0 = A,(n2)/A,, the fraction
can explain the stability of a microemulsion. The interfacial of micellar core surface covered by resins, we can rewrite Ey.
term can be written as. 20 as

where u is the true interfacial tension between a micelle and

the petroleum fluid, go is the interfacial tension at zero ad- where
sorption of resins onto a micelle, and a, is the interfacial
tension at an interface fully saturated by resins. We assume
that resins are surface active with respect to micelles, and
that us= 0 (Puwada and Blankstein, 1992; Kahlweit and
Reiss, 1991). Thus Eq. 15 becomes (see Appendix A),
Equations 23 and 24 are essentially our micellization model.
These two equations combined with the aggregation equilib-
uA, = a , [ A , - A r ( n 2 ) l . (16) rium equation (Eq. 7) and material balance relations deter-
mine the micellar-monomer equilibrium.
Until now we have not considered the micellar shape.
However, A , and A,(n,) can be expressed in terms of micel-
lar size and geometric characteristics of asphaltene and resin Micellar size and composition distribution
molecules for a given micellar shape. We use the platelike Equation 7 determines the concentration of micelles as a
model of a micelle (Figure l), a popular point of view function of aggregation numbers nl and n2 for given concen-
(Speight, 1980), which is in agreement with the spectroscopic trations of monomeric asphaltenes and resins. It should suf-
measurements by Espinat and Ravey (1993). Denoting by n i fice then to determine what kind of micelles (of what size
the maximum number of the resin molecules (heads), which and what composition) are most probable to form at a given
can be accommodated on the flat surfaces of a micellar core, state of the crude. We expect that the distribution over the
we express the micellar core radius, r , and the micellar core various micellar compositions (or, equivalently, coverages 0)
thickness, h, as is narrow enough (Puwada and Blankstein, 1992) to repre-
sent the whole population of micelles by those having the
optimum composition. We consider monodisperse micelles,

1756 June 1996 Vol. 42, No. 6 AIChE Journal

not only because the problem is simplified, as was stated ear- X,o;S is the concentration of asphaltene monomers in the
lier, but also because it is unlikely that the account of the crude in equilibrium with the pure solid asphaltene phase. It
polydispersity could significantly change the model’s ability to is the maximum concentration of monomeric asphaltenes in a
explain the phenomenon of asphaltene precipitation. The op- crude at given conditions. This quantity is a characteristic of
timum composition of a micelle of a given size, n = n , + n 2 , a given crude, and is adjusted from experimental data on as-
is determined by phaltene deposition for each individual crude mixture.
n is the micellar size for the “monodispersed”model. Its
(T)
=o, n (25)
value was chosen to a large extent arbitrarily, just to ensure
that stable micelles are present in the crude, and that their
size is in line with the spectroscopic data. The sensitivity of
which, by virtue of Eqs. 7, 23, and 24, becomes (see Appendix the model to n was also examined. In principle, this parame-
A) ter can be removed, as discussed earlier.

Incorporation of the Equation of State

An equation of state can be used to express the chemical
potential of all the monomers in the crude. In this manner,
the effect of pressure, temperature, and composition of the
petroleum fluid can be taken into account. Since the main
contribution to the micellization Gibbs free energy is the
where “lyophobic term,” Eq. 13, let us start with the consideration
of its EOS-dependence, leaving all the other contributions
(27) intact. This is equivalent to saying that the bulk asphaltene
solubility determines the asphaltene precipitation process,
through the formation and destruction of the micelles. The
is determined by the geometrical characteristics of the as- quantity X:? changes by adding a solvent or changing the
phaltene and resin molecules and by micellar radius. Equa- pressure along the equilibrium solid-fluid line:
tion 26 determines the most probable composition of a
micelle, 0,provided the total aggregation number, n is given.

Micellization model parameters where &(T, P, x*) is the standard chemical potential of
The parameters that determine the micellization process monomeric asphaltene, and x* denotes the composition of
have “molecu1ar”meaning and, in principle, can be estimated the “solvent” (petroleum fluid diluted with respect to as-
phaltenes, resins, and micelles). Any conventional bulk EOS
or regressed from experimental data. The parameters are:
AU,/RT characterizes the difference between the inter- can be used to estimate dpa1(T,P , x ) . Even the extreme po-
action energy of a resin molecule head with the petroleum larity of asphaltene molecules does not matter anymore, since
medium and the interaction energy of the resin molecule head the solution is dilute. In the present work, the Peng-Robin-
son equation of state (PR-EOS, Peng and Robinson, 1976) is
with asphaltenes in a micellar core. This parameter corre-
lates with the heat of adsorption of resins on solid as- used.
phaltenes, but unfortunately there are no relevant data in the
literature. The value of this parameter was guessed by some Solvent inmenee
preliminary calculations of asphaltene micellization for a In the liquid titration experiments an asphaltene precipi-
model crude and was kept constant for all the crudes consid- tant (an alkane) is added to a crude oil at a constant temper-
ered in this work. ature and pressure. For such a process,
u,,a/RT characterizes the interfacial tension between the
asphaltene micellar core and the crude. To our knowledge,
there is no direct experimental measurement of this parame-
ter either. We also guessed this parameter and kept it con-
stant for all the crudes (to be presented later in the results which upon expressing the standard chemical potential by an
section). EOS and integration, gives
b is the “molecular”geometrica1 parameter (Eq. 27) that
is related to n$ (or, equivalently, the micellar radius, r , see
Eq. 17). For a given micellar radius, parameters b and n; can
be estimated from the knowledge of the resin molecule head’s
specific surface area, a, and the solid asphaltene specific vol- (30)
ume, ua (Eqs. 17 and 27). There are no direct experimental
measurements of a and u,. However, a reasonable estimate where q$ is the fugacity coefficient of monomeric asphal-
of their magnitude can be made. The spectroscopic data on tene species in the petroleum fluid medium, given by a bulk
micellar radius, thickness, and the estimates of the aggrega- phase equation of state, and “ratio” is the dilution ratio, a
tion numbers are available (Espinat and Ravey, 1993; Storm compositional variable used normally in liquid titration ex-
and Sheu, 1993, 1994). periments, which is defined as the added volume of solvent

AIChE Journal June 1996 Vol. 42, No. 6 1757

divided by the amount of the original crude; ratio = 0 de- cient of monomeric asphaltene is negative. This means that
notes the original state before dilution. According to Eq. 30, lowering the pressure will lower X,q"", and therefore the abil-
the micellization parameter, X,q"S(T,P, ratio) is related to the ity of the crude to carry asphaltene material reduces at lower
fugacity of the monomeric asphaltene species calculated from pressures. In other words, we would expect the asphaltene
the EOS. Note that this quantity depends both on the amount material to precipitate by depressurizing the crude, which is
of the added solvent (i.e., ratio) and the type of the solvent in agreement with experimental observations (Hirshberg et
(i.e., pentane, heptane, etc.). X:y(T, P,ratio = 0) has, of al., 1984; Burke et al., 1990). However, Eq. 32 also implies
course, the same value for different solvents and is the char- that at certain conditions, we might expect the opposite be-
acteristic of the particular crude mixture. havior. At high temperatures and low pressures, pressurizing
a mixture will cause precipitation if the derivative in the left-
hand side of Eq. 32 becomes negative.
Pressure influence
Similar considerations can be applied to estimate the ef-
fects of pressure on X:?. We integrate Eq. 28 from the ini- Calculation Results
tial pressure P to the final pressure P'. Assuming that solid
asphaltene is incompressible, and that it has the same molec- Prior to the presentation of results, we will briefly outline
ular volume as in the micellar core, we get: the calculation procedure. For a given temperature, pressure,
and gross composition, there are five unknowns X u l ,X , , , X,,
n,, and n,. There are also five equations, Eqs. 7, l l a , l l b ,
and 26, and n = n, + n,; n, X:?, and the micellization model
parameters are provided. With the initial guess for X,, and
(31)
X r l , Eq. 26 is solved for micellar size, 0.From n = n , n2 +
and 0 = n,/[n,b + nil, n , and n2 are obtained and Eq. 23 is
used to calculate AGE. The mole fraction of micelles can be
where X:?( P') is the monomeric asphaltene concentration calculated from Eq. 7, and updated X u l , X,, are obtained
at pressure P', and x' is the composition at P'. Upon differ- from the material balance equations, Eqs. l l a and l l b , until
entiation, convergence. If X 2 < X T , the asphaltene phase would not
precipitate; otherwise, there would be precipitation and the
amount can be calculated from Eq. 10. Note that X f y in Eq.
26 should be either obtained from Eq. 30 or Eq. 31.
T,x'
The preceding model has been applied to describe asphal-
tene precipitation in liquid (Hirshberg et al., 1984) and gas
titration experiments (Burke et al., 19901, and upon depres-
surizing of a live oil (Hirshberg et al., 1984; Burke et al., 1990).
The composition of the crudes studied was obtained by a
The lefthand side of Eq. 32 is positive at moderate and high standard characterization procedure (see Appendix B) and is
pressures provided that the derivative of the fugacity coeffi- given in Table 1. The contribution of the osmotic pressure

Table 1. Petroleum Fluid Mixtures and the Gas Mixture Used in the Titration Experiments
Fluid number"
1 2 3 4 ~
5
Component rnol % rnol wt. rnol % mol wt. rnol % rnol wt. mol % rnol wt. rnol %
- - 0.57 0.51 3.17
N2
co2 - - 2.46 1.42 17.76
c, 0.10 0.07 36.37 6.04 30.33
c2 0.48 0.07 3.47 7.00 26.92
c3 2.05 0.87 4.05 6.86 13.09
i-C, 0.88 0.53 0.59 0.83 1.26
n-C, 3.16 2.44 1.34 3.35 4.66
i-C, 1.93 1.71 0.74 0.70 0.77
n-C, 2.58 2.36 0.83 3.46 1.26
c6 4.32 4.32 1.62 3.16 0.78
c:
ps-1 47.45 151.7 24.00 133.5 18.20 142.0 16.67 130.5 -
ps-2 24.84 239.3 23.00 171.0 13.98 274.0 17.77 222.0 -
-
ps-3 5.46 669.4 23.83 230.3 3.69 350.9 20.58 276.9
ps-4 - - 12.75 340.0 - - 3.79 430.0 -
ps-5 - - 2.069 693.7 - - - - -
resin 5.73 603.0 1.836 603.0 8.93 603.0 5.80 603.0 -
-
asphalt 1.02 850.0 0.145 850.0 3.17 850.0 2.06 850.0
*These numbers correspond to the following mixtures from the original works: 1= Hirshberg et al., 1984, tank oil No. 1; 2 = Hirshberg et al., 1984, tank
oil No. 2; 3 = Burke et al., 1990, live oil No. 1; 4 = Burke e t al., 1990, live oil No. 2; 5 = Burke et al., 1990, gas solvent used in the gas titration
experiment.

1758 June 1996 Vol. 42, No. 6 AIChE Journal

(Mahadevan and Hall, 1990) due to the presence of micelles 0.0025 7

was neglected. Somewhat arbitrarily, we assigned the molecu-

lar weights of the monomeric asphaltenes and resins, and kept
them the same for all the mixtures (Table 1).The asphaltene 0.0020
molar volume was estimated as u, = 0.5 m3/kmol. The resin C
molecule polar head surface area was taken to be a = 40 A', .-0
-Id
close to the surface area reported by Nagarajan and Rucken- 0 0.001 5
stein (1991) for alkyl glucoside polar head group. The interfa- F
'c
cial tension between a polar asphaltene micellar core and
apolar crude is supposed to be large, and we set it to be ; 0.0010 4 1
u,,= 0.040 N/m. After some preliminary calculations, the E
resins adsorption energy was chosen to be (q-,q-,)-
0.073 J/(mol* m2). This value ensures the possibility of the
=
00.0005
- Xa(rario), see Eq. (30)
monomeric asphaltene mole fraction
X
existence of stable micelles and corresponds to a molar ad-
sorption energy of approximately 18 kJ/mol, a value that
seems reasonable for the adsorption of a polar aromatic resin 0 0000
group onto asphaltene solid core.
dilution ratio, cm3/g
There is an element of arbitrariness in assigning the model
parameter values, due to a lack of the experimental informa-
- Figure 3. Dilution diagram for tank oil 1 (Table 1) with
tion. As an example, there are no data on a,, a, or (Ur-c - n-octadecane as a precipitant at 295 K.
a,-,). There is also uncertainty in the characterization of real
petroleum fluids, leaving doubts about the mole fractions of
Figures 2 and 3 illustrate the process of precipitation in
the components, which are the input in our model. This makes
terms of monomer-micellar equilibrium. If there were no mi-
questionable an explicit proof of the model validity. Our ma-
celles, the chemical potential of the asphaltene monomers,
jor goal is, therefore, to show that with some reasonable val-
Eq. 2, would only decrease upon the addition of solvent (due
ues assigned to the parameters, the model would describe the
to the decrease of the asphaltene mole fraction). In this case,
main features of asphaltene precipitation from crudes. In our
the crude either expels the asphaltene material originally, or
calculations, X,snS is adjusted individually for every petroleum
becomes even less likely to form precipitate when diluted. In
fluid mixture while other parameters are kept constant.
the case of monomer-micellar equilibrium, however, the ad-
dition of a solvent destroys the micelles, and the concentra-
Liquid titration tion of monomeric asphaltenes grows (Figures 2 and 3), and
For the liquid titration experiments the amount of resin is so does the chemical potential of monomeric asphaltene
estimated to be the difference between the reported amount species in the petroleum medium. At the same time, the
of asphalt and asphaltene material in the crude (Hirshberg et quantity X,q"S(T,P , ratio), which is given by Eq. 30, decreases
al., 1984). The quantity X,q.S is obtained by adjusting the cal- (Figures 2 and 3). When the concentration of monomers in
culated amount of asphaltene precipitated by n-decane. We the petroleum fluid equals X,q"s(T,P, ratio) (the intersection
found Xzy = 2.4 X mole fraction for tank oil 1 (Table of the solid and dashed curves in Figure 21, the asphaltene
1) assuming monodispersed micelles with n = 250 and ni = begins to precipitate. Starting from this dilution ratio, Eq. 28
200. determines the amount of precipitated asphaltene phase. As
the concentration of monomeric asphaltenes in the petroleum
medium becomes very small (at high dilution ratios), part of
the solid asphaltene material may dissolve back into the crude.
0.0°z5 1 However, since this phenomenon has not been observed ex-
perimentally (Hirshberg et al., 19841, we did not consider this
0.0020
process. Note that in Figure 3, the addition of n-octadecane
to the crude decreases the monomeric asphaltene fugacity too
little to result in asphaltene precipitation.
0.001 5
The calculated characteristics of the micelles formed in the
crude are in agreement with the spectroscopic studies. The
7

0 core radius is determined by the values assigned to a and to

X
0.0010
n i ; r = 35.7 A (Storm and Sheu (1994), give 50-100 A as an
estimate of the micellar diameter); the optimum composition
corresponds to 42 asphaltene molecules and 208 resin
0.0005 - molecules per micelle (solubilization ratio n 1/n2 = 0.201,
which gives the apparent molecular weight of a micelle of
about 160,000 149,700- 136,800 according to Espinat and
0.0000
Ravey (19931, and 100,000 given by Storm and Sheu (199411.
The micellar core thickness is h = 8.7 A [its spectroscopic es-
timate is 6-10 A, Espinat and Ravey (1993)l.
Figure 2. Dilution diagram for tank oil 1 (Table 1) with At higher dilution ratios the micelles become bigger (which
n-decane as a precipitant at 295 K. has been observed experimentally upon adding heptane to

AIChE Journal June 1996 Vol. 42, No. 6 1759

 with n-pentane is in accord with the operational definition of

- $ 1 A *A Experimental data
asphaltene (Figure 4a). This fact was by no means built into
our model in advance and thus might be considered as a
strong argument for the model validation.

4
Effect of micellization parameters
L= 2.0
.-0 We have already stated that several assumptions have been
made in model derivation and for model parameters that
P should be verified, or at least the sensitivity of the calculated
-c10
4a, 1.0 results to these assumptions should be examined.
0 One of the assumptions of our model is monodispersity.
.-Q
4

.-0 We have studied the sensitivity of the calculated results to

the aggregation number, n, in the range between 100 and
2
QO.0 2,000. The calculations performed for n-decane titration show
' 2l5 3b 315 4b 45 50
dilution ratio, cm3/g a strong dependence of the onset on the micellar size. Small
micelles are originally unstable in the crude, and would pre-
cipitate without addition of a diluent, while big micelles re-
main more stable than the solid phase until higher dilution
ratios. However, CMC is nearly the same, and so is the total
amount of the precipitated solid. As a result, the slope of the
precipitation curves is steeper for bigger micelles. Probably
A *A Experimental data
the polydispersity of micelles is important for quantitative
-
- - Calculated, 15.6 weight % of resins
Calculated, 19.5 weight of resins
% predictions, and it may be a useful next step for the future
development of the model.
The results are also strongly dependent upon the amount
of resins present in the crude. Depending on the resin con-
tent, a crude may be originally unstable or reveal no precipi-
tation until very high dilution ratios. Figure 4b demonstrates
the sensitivity of precipitation to the resin content of the oil.
Calculation results based on resin contents of 15.6 and 19.5
wt. % for three precipitants-n-C,, n-C,, and n-C,,,- show
that as the resin content of tank oil 1 increases, a higher dilu-
tion ratio is required for the onset of precipitation. However,
dilution ratio, cm3/g for precipitants that can expel1 all the asphaltene material
from the crude, there are always some high dilution ratios to
(b) ensure that all of the asphaltene drops out, no matter what
Figure 4. (a) Liquid titration precipitation curves for tank the initial concentration of resins is. In fact, all the character-
oil 1 (Table 1) at 295 K; (b) effect of resin con- istics of a crude that affect the mole fractions of resins and
tent on the predicted precipitation curves for asphaltenes have a strong effect on the calculated results,
tank oil 1 (Table 1) at 295 K. since the mole fractions determine the aggregation equilib-
rium, Eq. 7. Good estimates of the monomers' molecular
weight are important to reliably predict the asphaltene pre-
asphaltene suspended in toluene; Espinat and Ravey (1993)), cipitation. Therefore a detailed characterization of the crude
and then the critical micelle concentration (CMC; Tanford, heavy end, which is usually not important for vapor-liquid
1973; Rusanov, 1992) is reached (for decane at a dilution ra- equilibrium calculations, is indispensable for asphaltene pre-
tio of about 4.6 cmyg). At CMC, the solubilization ratio is cipitation modeling.
0.21 and h = 9.0 A. Beyond this dilution ratio, the asphaltene The molecular geometry characteristics of resins and as-
precipitation is determined by the bulk phase thermodynam- phaltenes and micellization free energy parameters also
ics, which is the dilute solution-pure solid equilibrium. strongly affect the behavior of a crude. The increase of the
The resulting precipitation curves for tank oil 1 with vari- resin molecule head surface area, a, increases crude stability.
ous precipitants are shown in Figure 4a. The model gives the For the decane titration of tank oil 1, a = 35 A' leads to the
onsets of precipitation and amounts of asphaltene precipitate initial instability and precipitation of 2.4 wt. % of asphaltene
for different n-alkanes added to this crude. It predicts that material, whereas a = 45 A2 results in no precipitation at all.
the precipitation ability of a-alkanes decreases with their The asphaltene molecular volume affects the onset, but not
chain length, so that n-heptane, for example, precipitates the amount of the precipitated material; the crude is more
more asphaltene material than n-decane, whereas long-chain stable for smaller ua (it is originally unstable for a volume of
alkanes (octadecane, and higher) do not result in precipita- about 0.65 mykmol and higher).
tion. The amount of the asphaltene precipitated by different Parameters a,, and (u,-, u,-J
- also play an important
alkanes agrees well with the experimental data. Very iinpor- role in the micellization process. Lowering a,,, as it might be
tant is that the predicted amount of asphaltene precipitated expected, increases stability of the aggregate. For the decane

1760 June 1996 Vol. 42, No. 6 AIChE Journal

 weak linear dependence of (ar-, - Ur-,) on the dilution ratio
-the simplest possible form of a concentration dependence
-Cur-, - U,-,) = const. + 0.00001 *ratio. Figure 5 shows the
results for decane titration. As can be seen, even a very weak
-A-A- Experimental data concentration dependency changes the shape of the precipi-
~ Calculated tation curve. The amount of the precipitate is also affected.
The most important contribution to the standard micelliza-
*
62.0
.-
i
3 tion free energy is due to the X:
? term, and the model is far
more sensitive to this parameter than to all the other quanti-
ties discussed earlier. This phenomenologic parameter was
estimated by matching with experimental data on the drop-out
4
n1.0 j 0
0
0
curves. In principle, one data point on a drop-out curve suf-
fices to estimate this parameter value for a particular crude,
and this value can be used for further predictions (other pre-
cipitants, effect of pressure, etc).
L
0-0.0 , I I # j # , ' $ , , ,&, ,
I I I I '+ I / ' * ' , , 'B, I i ' d , , i,,, I I i'2 I 'i'3 As we discussed before, several improvements and refine-
ments can be made, but the model even in its present simple
dilution ratio, cm3/g form captures the basic features of the liquid titration proc-
Figure 5. Sensitivity of the predicted precipitation curve ess and gives reasonable estimates of the amounts of solid
of tank oil 1 (Table 1) with n-decane to con- precipitated by different diluents.
centration dependent AU,.
Pressure eflect
titration of Hirshberg et al. (1984), there is no precipitation The effect of pressure on the asphaltene precipitation was
examined for a mixture of tank oil 2/propane (weight ratio
with a o = O . O 1 N/m; for cro=0.06 N/m, the crude is origi-
1:7) at 295 and 366 K (Hirshberg et al., 19841, and for fluid
nally unstable and precipitates 2.2 wt. % asphaltene phase.
The increase of the (or-,
- q-,) parameter to 0.078 J/(mol.
number 3 (live oil) at 373 K (Burke et al., 1990), Table 1. In
agreement with the experimental observations, the asphal-
m2) shifts the onset to ratio = 7.4 cmyg and gives 0.1 wt. %
tene material precipitates as the pressure decreases.
precipitated amount of asphaltene for the titration with de-
cane. At (q-,
- Ur-,>= 0.079 J/(mol-m2) there is no precip-
For tank oil 2 with propane, all the asphaltene material
precipitates as the pressure drops from 1,000 to 970 bar (we
itation with any amount of decane. We assumed that (&-, -
q-,) remains constant, as the crude is diluted with n-al- set X:
? =9X mole fraction). This is in line with the
kanes. However, the difference between the resin-asphal- data, where the amount of precipitate at high pressures
tene and resin-crude interactions is most likely to grow, as roughly corresponds to the asphaltene content of the crude.
we increase the amount of n-alkanes, and the crude becomes However, a more detailed comparison cannot be made, be-
more and more apolar. A proper model for the concentration cause resins were reported to coprecipitate with asphaltenes,
dependence of (a,-,- Ur-,) should be obtained by statistical- whereas our model in its present form applies only to asphal-
tene precipitation.
mechanical considerations, but in the present study we merely
examine the importance of this dependency. Let's assume a A better comparison with the experimental data can be
made for fluid number 3 (live oil). For this fluid we set n =

1
500, and X,q.S = 5 X mole fraction, keeping all the other
1.6 7
* Experimentaldata parameters the same as before. The crude is stable at high
__ Calculated pressures, and in agreement with the experiment shows the
asphaltene precipitation at about 275 bar (Figure 6). Accord-

a 1.2
->
.- n
I
ing to our model the precipitation upon depressurizing is,
however, different from that in the liquid titration process.
As the pressure decreases, the monomers are expelled from
the petroleum fluid and there is no destruction of the mi-
celles. The contribution of the lyophobic term becomes over-
whelmingly important with the decrease of pressure. As a
* result, most of the asphaltene material remains in the crude
in the form of micelles. At pressures below 208 bar (the cal-
culated bubble point pressure, Table 2) the mixture is in a
$0.4 k
two-phase vapor-liquid region. We performed conventional
vapor-liquid flash calculations at several pressures to obtain
.-0 the composition of the liquid phase. This composition was
al the input for the asphaltene precipitation modeling. At pres-
L
sures below 150 bar the liquid phase does not show any as-
75 1 0 1 5 1 0 phaltene precipitation. In the experiment, the ability of the
pressu re/Ba r crude to precipitate asphaltenes also reduces at lower pres-
Figure 6. Effect of pressure on precipitation curve for sures. Nevertheless, the model somewhat overestimates the
live oil 3 (Table 1) at 373 K. effect of pressure (Figure 6).

AIChE Journal June 1996 Vol. 42, No. 6 1761

 Table 2. Bubble-Point Pressures of Petroleum Fluids

3 4 6
Fluid Number*
7 8 9 10
.-
-
0
-- Experimentaldata
Calculated
*
T ,K
Pcalc. bar
P e r p , bar
373
208
201
38
41
75
71
3 7 6
148
157
218
255
333
135
134
359
257
248

*The numbers correspond to the following fluids: 3 = see Table 1; 4 = see

Table 1; 6-8 = gas titration experiment, Burke et al., 1990; 6 = 80 mol
Y
(3
3’0 1
% of mixture 4 + 20 mol % of gas mixture 5, see Table 1; 7 = 50 mol %
of mixture 4+50 mol % of gas mixture 5; 8 = 30 mol % of mixture 4 + 70 I *
mol % of gas mixture 5; 9 = Hirshberg et al., 1984, live oil No. 1 (corre- * \
sponds to the tank oil No. 1, see Table 1); 10 = Hirshberg et al., 1984,
\ *
live oil No. 2 (corresponds to the tank oil No. 2, see Table 1). \
\
*
\
\
As was discussed earlier, the model predictions are sensi- \
tive to the resin content of the oil. There are no data on the
resin content of fluid 3, and the amount of resin shown in 1 .b
Table 1 for this oil is arbitrary to a large extent. For instance, mole fraction of solvent
if we increase the resin amount of this oil 1.15 times (which Figure 7. Effect of solvent content on precipitationcurve
corresponds to 10.3 mol % of resin), then there will be no for live oil 4 (Table 1) at 376 K.
precipitation at all in the pressure range shown in Figure 6
regardless of what value is assigned to Xzy. Most of the
available data on crude oil compositions do not report the (Blankstein et al., 1985; Chiew et al., 19951, and the osmotic
resin content. We recommend resin content measurement for pressure effect could be included. The effect of electrical
asphaltene precipitation studies. charges could also be incorporated in the model to interpret
recent conductivity measurements of asphaltene precipita-
Gas titration tion.
On the other hand, more experimental information is
The calculated precipitation curve and the experimental needed to further validate the model and remove the uncer-
data by Burke et al. (1990) for gas titration are presented in tainties in some of its parameter values. More detailed com-
Figure 7. Fluid 4 (Table 1) has been diluted with a gas titrant positional measurements o n petroleum fluids are necessary
(mixture 3,as is explained in Table 2. The bubble-point for reliable predictions. First, the amount of resin and as-
pressures of the resulting fluids (mixtures 6, 7, 8) are also phaltene material in the crude should be measured. Their
given in Table 2. The asphaltene precipitation was modeled relative amounts determine the colloid stability. Reliable data
at pressures above the saturation pressure. As before, we set on the molecular weight of asphaltene and resin monomers
n = 500; other parameters have the previous values except are also required. Data on asphaltene and resin molecular
X t F . This latter parameter differs from crude to crude and geometry would be very useful. Experimental information on
has been set equal to 9* mole fraction. Figure 7 shows asphaltene phase/petroleum fluid interfacial tension as well
there is qualitative agreement between the data and the cal- as on the heat of the adsorption of resins on asphaltene solids
culated results. The model predicts that at high solvent ratios would be of value to provide micellization parameters.
the asphaltene material does not precipitate. The model also
predicts, in agreement with the data, that when precipitation
takes place, most of the asphaltene material still remains in Acknowledgments
the crude. We thank Norsk Hydro, Saudi Aramco, and Texaco for their sup-
port of this project. The authors are also thankful to Mr. Carlos
Lira-Galeana for helpful discussions and for providing the software
Concluding Remarks to carry out petroleum fluids characterization and bubble-point cal-
culations.
The simple model proposed in this work can describe as-
phaltene stability and precipitation from crude mixtures. The
model captures the basic features of the behavior of asphal- Notation
tene-containing petroleum fluids. It predicts the change in k = Boltzmann constant
the precipitation power of different alkane precipitants with y.=number of moles of species i
R = gas constant
their molecular weight. It gives the proper amount of precipi- T = temperature
tated asphaltene in liquid titration experiments and allows Xi= mole fraction of species i
one to estimate the effect of pressure on asphaltene precipi-
tation.
The model could be improved by relaxing some of the Literature Cited
assumptions. Micellar size could be allowed to vary with Altgelt, K. H., and M. M. Boduszynski, Composition and Analysis of
pressure, temperature, and composition. More physically Heay Petroleum Fractions, Marcel Dekker, New York (1994).
Andersen, S. I., and J. G. Speight, “Observations on the Critical Mi-
sound EOS could be used for the description of the bulk- celle Concentration of Asphaltenes,” Fuel, 72, 1343 (1993).
crude phase, instead of the PR-EOS. The interaction be- Blankstein, D., G. M. Thurston, and G. Benedek, “Theory of Phase
tween micelles could be taken into account in different ways Separation in Micellar Solutions,” Phys. Reu. Let., 54(9), 955 (1985).

1762 June 1996 Vol. 42, No. 6 AIChE Journal

Burke, N. E., R. E. Hobbs, and S. F. Kashou, “Measurement and Tanford, C., Hydrophobic Effect: Formation of Micelles and Biologcal
Modeling of Asphaltene Precipitation,” J . Pet. Techn., 1440 (1990). Membranes, Wiley, New York (1973).
Cavett, R. H., “Physical Data for Distillation Calculations, Vapor- Vlachy, V., H. W. Blanch, and J. M. Prausnitz, “Liquid-Liquid Phase
Liquid Equilibria,” Proc. Midyear Meeting, API Div. of Refining, Separations in Aqueous Solutions of Globular Proteins,” AIChE
San Francisco (May 15, 1964). J., 39(2), 215 (1993).
Chiew, Y. C., D. Kuehner, H. W. Blanch, and J. M. Prausnitz, Whitson, C. H., “Characterizing Hydrocarbon Plus Fractions,” Soc.
“Molecular Thermodynamics for Salt-Induced Protein Precipita- Petrol. Eng. J., 683 (Aug., 1983).
tion,’’ AIChE J., 41, 2150 (1995). Wiehe, L. A,, and K. S. Liang, “Asphaltenes, Resins, and Other
Cotterman, R. L., and J. M. Prausnitz, “Phase Equilibria for Mix- Petroleum Macromolecules,” Int. Conf. Fluid Properties and Phase
tures Containing Very Heavy Components. Development and Ap- Equilibria for Chemical Process Design, Snowmass, CO (June 18-23,
plication of Continuous Thermodynamics for Chemical Process 1995).
Design,” Ind. Eng. Chem. Proc. Des. Deu., 24, 194 (1985). Yen, T. F., “Structure of Petroleum Asphaltene and Its Significance,”
Edmister, W. C., “Compressibility Factors and Equation of State,” Energv Sources, 1, 447 (1974).
Pet. Refiner, 37(4), 173 (1958).
Espinat, D., and J. C. Ravey, “Colloidal Structure of Asphaltene So-
lutions and Heavy-Oil Fractions Studied by Small-Angle Neutron Appendix A: Derivation of Eq. 26
and X-Ray Scattering,” Int. Symp. Oilfield Chemistiy, SPE 25187,
New Orleans (Mar. 2-5, 1993). From Eq. 7 one can write:
Hirschberg, A., L. N. J. de Jong, B. A. Schipper, and J. G. Meijers,
“Influence of Temperature and Pressure on Asphaitene Floccula-
tion,”Soc. Pet. Eng. J., 283 (June, 1984).
In X,,, = n1In X,, + n2In X,., + AGF/kT, (Al)
James, N., and A. K. Mehrotra, “V-L-S Multiphase Equilibrium in
Bitumen-Diluent Systems,” Can. J . Chem. Eng., 66, 870 (1988). where the last term can be calculated from Eq. 23. The next
Kahlweit, M., and H. Reiss, “On the Stability of Microemulsions,” step is to perform differentiation in Eq. 25; it is more conve-
Langmuir, 7, 2928 (1991).
Katz, D. L., and K. E. Beu, “Nature of Asphaltic Substances,” Ind.
nient to use ( n , O ) variables than ( n l ,nz). The relationships
Eng. Chem., 37, 195 (1945). between these variables are given by
Katz, D. L., and A. Firoozabadi, “Predicting Phase Behavior of Con-
densate/Crude-Oil Systems Using Methane Interaction Coeffi-
cients,”J. Pet. Tech., 1649 (Nov., 1978).
Kawanaka, S., S. J. Park, and G. A. Mansoori, “Organic Deposition
From Reservoir Fluids: A Thermodynamic Predictive Technique,”
SPE Reservoir Eng., 185 (1991).
Leontaritis, K. J., “Asphaltene Deposition: A Thermodynamic-Col- where b is given in Eq. 27. From the preceding equations:
loidal Model,” PhD Thesis, Univ. of Illinois, Chicago (1988).
Leontaritis, K. J., and G. A. Mansoori, “Asphaltene Flocculation n - nS,O
During Oil Production and Processing: A Thermodynamic Col- n, = (A3)
l+bO ’
~

loidal Model,” SPE 16258, SPE Int. Symp. Oilfield Chemisty, San
Antonio, TX (Feb. 4-6, 1987).
Lian, H., J.-R. Lin, and T. F. Yen, “Peptization Studies of Asphal- nb + n;
tene and Solubility Parameter Spectra,” Fuel, 73, 423 (1994). n2 = -O0. (A4)
l+bO
Mahadevan, H., and C. K. Hall, “Statistical-Mechanical Model of
Protein Precipitation by Nonionic Polymer,” AIChE J., 36(10), 1517
(1990). To find how nl and b change with 0,one needs a detailed
McBain, M. E., and E. Hutchinson, Solubilization and Related Phe- knowledge of the geometry of an asphaltene molecule and
nomena, Academic Press, New York (1955). how it is accommodated within a micelle. Since such informa-
Nagarajan, R., and E. Ruckenstein, “Theory of Surfactant Self- tion is not currently available, one simple approach is to as-
Assembly: A Predictive Molecular Thermodynamic Approach,”
Langmuir, 7, 2934 (1991). sume that b and nS, do not depend on coverage fraction, @,
Nellensteyn, F. I., “The Colloidal Structure of Bitumens,” The Sci- at constant n (for our model, this assumption implies that the
ence of Petroleum, Vol. 4, Oxford Univ. Press, London, p. 2760 micellar radius, Eq. 17, does not change with coverage frac-
(1938). tion). One can then proceed to calculate
Peng, D.-Y., and D. B. Robinson, “ A New Two-Constant Equation
of State,” Ind. Eng. Chem. Fundam., 15, 59 (1976).
Prigogine, I., and R. Defay, Chemical Thermodynamics, Longmans,
Green, New York (1952).
Puwada, S., and D. Blankstein, “Thermodynamic Description of Mi-
cellization, Phase Behavior, and Phase Separation of Aqueous So-
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Rusanov, A. I., Micelle Formation in Surfactant Solutions, in Russian,
Chimia, St. Petersburg (1992).
Speight, J. G., The Chemistry and Technology of Petroleum, Marcel
Dekker, New York (1980). Combining Eqs. Al, 23-25, A5,and A6 results in Eq. 26 of
Storm, D. A., R. J. Barresi, and S. J. DeCanio, “Colloidal Nature of the text.
Vacuum Residue,” Fuet, 70, 779 (1991).
Storm, D. A., and E. Y. Sheu, “Characterization of the Asphaltenic
Colloidal Particle in Heavy Oil,”Eastern Oil Shale Symp., Institute Appendix B: Characterization of Petroleum Fluids
for Mining and Minerals Research, Univ. of Kentucky, Lexington
(Nov. 16-19, 1993). The three-parameter gamma-distribution (Whitson, 1983)
Storm, D. A,, E. Y. Sheu, and M. M. De Tar, “Macrostructure of was used to describe the C,, residue and a quadrature tech-
Asphaltenes in Vacuum Residue by Small-Angle X-ray Scattering,” nique (Cotterman and Prausnitz, 1985) was used to perform
Fuel, 72, 917 (1993). lumping. The C7+ residue was represented by 3 to 5 pseudo-
Storm, D. A,, and E. Y . Sheu, “Evidence for Micelle-Like As-
phaltenes in Crude Oi1,”Colloid and Surface Science Symp. Amer. components (ps-1, ps-2, etc.). In this procedure, the as-
Chem. SOC.,Stanford, CA (June 19-22, 1994). phaltenes were excluded from the C7+ residue, and the resins

AIChE Journal June 1996 Vol. 42, No. 6 1763

 TabIe Al. Acentric Factors, Critical Temperatures and Critical Pressures of Heavy Ends of Petroleum Fluid Mixtures
Fluid Number*
--__ _________________ _ _ _ ~
Heavy 1 2 3 4
Ends w T,,K P,,bar w T,,K P,,bar w T,,K P,,bar w T,,K P,,bar
ps-1 0.630 629.2 24.0 0.553 601.1 26.1 0.590 614.7 25.1 0.540 596.2 26.5
ps-2 0.948 729.0 16.6 0.706 655.8 22.1 1.064 757.2 14.7 0.889 713.0 17.8
ps-3 1.20 942.4 8.5 0.917 720.9 17.2 1.322 806.5 11.7 1.074 759.4 14.5
ps-4 -
-
-
- -
- 1.286 800.4 12.0 -
-
-
-
-
-
1.580
-
846.1
-
10.0
-
ps-5 1.35 951.1 8.5
Resin 1.4 917.5 8.6 1.4 917.5 8.6 1.4 917.5 8.6 1.4 917.5 8.6
Asphalt 1.8 1,003 8.8 1.8 1,003 8.8 1.8 1,003 8.8 1.8 1,003 8.8
*See Table 1.

were introduced by dividing the heaviest pseudocomponent temperatures for the heavy ends of various fluid mixture of
into two; resins of a predetermined molecular weight, and Table 1 are given in Table Al.
the remainder of the heaviest pseudocomponent. The results Methane interaction coefficients for the PR-EOS were
of the characterization are shown in Table 1. The Cavett from Katz and Firoozabadi (1978) using the molecular weight
(1964) correlation was then used to obtain critical properties rather than density correlation. The interaction coefficients
of the PR-EOS. The acentric factors of the very heavy ends of asphaltenes with the other components of the crude were
of the crudes have been assigned the following values: 1.8 for assigned the following values: 0.15 (Cl), 0.11 (C,), 0.09 (CJ,
the asphaltenes; 1.4 for the resins. These and other values of 0.05 (Cd), 0.04 (C5), 0.02 (C& 0.01 (C, to C,,), and zero
acentric factors (Edmister, 1958) provide reasonable calcu- with the heavier fractions. The resin interaction coefficients
lated bubblepoint pressure (Table 2). The latter were com- were set. to zero.
puted from the PR-EOS for liquid compositions obtained by
taking into account the micellization equilibrium in the crude.
The values of acentric factors, critical pressures, and critical Manuscript receiwd Feb. 14, 1995, and reuision receiwd Sept. 18, 1995.

1764 June 1996 Vol. 42, No. 6 AIChE Journal