Page 406 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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AT029-Manual
386 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
of vapor produced in equilibrium with liquid is quite small so
L
i
that the problem of asphaltene precipitation reduces to LSE. activity coefficient form (γ )as L L
L

The effect of temperature on asphaltene precipitation is the (9.34) γ = exp ln V i L + 1 − V i L + V i (δ i − δ m) 2
L
i
same as for wax precipitation, that is, as the temperature de- V m V m RT
creases the amount of precipitation increases. The effect of Once γ is known f ˆL can be calculated from Eq. (6.114) and
L
i
i
pressure on asphaltene precipitation depends on the type of after substituting into Eq. (9.32) we get the following relation
oil. For crude oils (free of light gases) and live oils above their for the volume fraction of asphaltene in the liquid solution
bubble point pressure, as pressure increases the amount of as- [38]:
phaltene precipitation decreases, but for live oils at pressures L L
below the bubble point pressure, as the pressure increases (9.35) = exp V A − 1 − V A (δ A − δ m) 2
L
A
asphaltene precipitation also increases so that at the bubble V m L RT
point the amount of precipitation is maximum [48]. where is the volume fraction of asphaltenes in the oil
L
A
There are specific thermodynamic models developed for (liquid) phase at the time solid has been precipitated. Once
prediction of asphaltene precipitation; these are based on is known, amount of asphaltene precipitated can be cal-
L
A
the principles of SLE and the model adopted for the mecha- culated from the difference between the initial amount of as-
nism of precipitation. These mechanisms were discussed in phaltene in liquid and its amount after precipitation as
Section 9.3.1. Most thermodynamic models are based on two L L
models assumed for asphaltene precipitation: colloidal and m AD = m AT − ρ A V T
A
micellization models. A molecular thermodynamic frame- m AT = 0.01 × (initial asphaltenes in liquid, wt%) × ρ L V T L
work based on colloid theory and the SAFT model has been mix

established to describe precipitation of asphaltene from crude m AD
asphaltene precipitated wt% = 100 × L L
oil by Wu–Prausnitz–Firoozabadi [39, 49]. Mansoori [29] also ρ mix V T
discusses various colloidal models and proposed some ther- (9.36)
modynamic models. Pan and Firoozabadi have also devel-
oped a successful thermodynamic micellization models for where m AD is the mass of asphaltenes deposited (precipitated)
asphaltene precipitation [20, 36]. and m AT is the mass of total asphaltene initially dissolved in
L
Most thermodynamic models consider asphaltene as poly- the liquid (before precipitation) both in g. ρ A and ρ mix are
mer molecules. Furthermore, it is assumed that the solid mass densities of asphaltenes and initial liquid oil (before
L
3
phase is pure asphaltene. The solution is a mixture of oil precipitation) in g/cm . V is the total volume of liquid oil
T
3
L
(asphaltene-free) specified by component B and asphaltene before precipitation in cm . ρ mix can be calculated from an
component specified by A. Applying the principle of SLE EOS or from Eq. (7.4). In determination of m AT , the initial wt%
to asphaltene component of crude oil in terms of equality of of asphaltenes in oil (before precipitation) is needed. This
fugacity parameter may be known from experimental data or it can be
considered as one of the adjustable parameters to match other
(9.32) f ˆL A = f A S experimental data. m AT can also be determined from Eq. (9.35)
from the knowledge of asphaltene composition in liquid at
L onset
L
T
where f ˆL A is fugacity of asphaltene (A) in the liquid solution the onset when m AD is zero and m AT = ρ A ( V ) . A more
A
(A and B) and f A S is fugacity of pure solid asphaltene. One accurate model for calculation of asphaltene precipitation is
good theory describing polymer–solution equilibrium is the based on Chung’s model for SLE [44]. This model gives the
Flory–Huggins (FH) theory, which can be used to calculate following relation for asphaltene content of oil at temperature
solubility of a polymer in a solvent. Many investigators who T and pressure P [51]: --`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
studied thermodynamic models for asphaltene precipitation H A f T MA V A S 2
have used the FH theory of polymer solutions for calculation x A = exp − 1 − T − RT (δ A − δ m)
RT MA
of chemical potential of asphaltenes dissolved in oil [38, 50].
L
L L V − V S × (P − P MA)
Nor-Azian and Adewumi [48] also used FH theory for the as- (9.37) − ln V A − 1 + V A + A A
phaltic oils. Moreover, they also considered the vapor phase V m L V m L RT
in their model with VLE calculations between liquid oil and where subscript A refers to asphaltene component and P MA is
its vapor. According to the FH theory the chemical potential the pressure at melting point T MA . All other terms are defined
of component i (polymer) in the solution is given as
previously. The last term can be neglected when assumed
S
L ∼
L ◦L L L V = V . This model has been implemented into some reser-
ˆ μ − μ i V i V i 2 A A
i
(9.33) = ln ( i) + 1 − + (δ i − δ m) voir simulators for use in practical engineering calculations
RT V L RT
m related to petroleum production [51].
x i V L N L As mentioned earlier (Table 9.6), in absence of actual data,
i
where i = L , δ m = i=1 i δ i ,ˆμ is the chemical potential 3
i
V m ◦L ρ A and M A may be assumed as 1.1 cm /g and 1000 g/mol, re-
of component i in the liquid phase, and μ i is the chemical
potential at reference state, which is normally taken as pure spectively. Other values for asphaltene density are also used
L
liquid i. i is the volume fraction of i, V is the liquid molar by some researchers. Speight [15] has given a simplified
i
volume of pure i at T and P of the solution, R is the gas version of Eq. (9.37) in terms of asphaltene mole fraction
L
constant, V is the liquid molar volume of mixture, and δ i is (x A )as
m
the solubility parameter for component i at T of the solution. M A (δ L − δ A) 2
The above equation can be conveniently converted into an (9.38) ln x A =−
RTρ A
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