Page 139 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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3. CHARACTERIZATION OF PETROLEUM FRACTIONS 119
since ν 38(100) > 1.5 and ν 99(210) < 1.5 cSt we have c 38(100) = 0
not seriously affect the predicted mixture properties. Use of
and c 99(210) = 0.0392. From Eq. (2.132), A 1 = 10.4611, B 1 = PNA composition in terms of weight, volume, or mole does
−4.3573, D 1 =−0.4002, D 2 =−0.7397, and from Eq. (2.130) bulk properties such as T b and SG to calculate mixture prop-
at T = 140 F (60 C) we calculate the kinematic viscosity. It erties as described for petroleum fractions cannot be used for
◦
◦
should be noted that in calculation of ν 60(140) from Eq. (2.130) a synthetic and ternary mixture of C 5 –C 10 –C 25 . Another exam-
trial and error is required for calculation of parameter c.At ple of a mixture that bulk properties directly cannot be used to
first it is assumed that c = 0 and after calculation of ν 60(140) if calculate its properties is a crude oil or a reservoir fluid. For
it is less than 1.5 cSt, parameter c should be calculated from such mixtures exact knowledge of composition is required
Eq. (2.131) and substituted in Eq. (2.130). Results of calcula- and based on an appropriate mixing rule a certain physical
tions are as follows: ν 38(100) = 1.8 and ν 60(140) = 1.27 cSt. Com- property for the mixture may be estimated. The most simple
paring with the experimental values, the percent relative de- and practical mixing rule that is applicable to most physical
viations for kinematic viscosities at 100 and 140 F are 8.4 and properties is as follows:
◦
3.3%, respectively. The result is very good, but usually higher
N
errors are observed for estimation of kinematic viscosity of (3.45) θ m = x i θ i
petroleum fractions from this method. i=1
where x i is the fraction of component i in the mixture, θ i is a
3.4 GENERAL PROCEDURE FOR property for pure component i, and θ m is property of the mix-
PROPERTIES OF MIXTURES ture with N component. This mixing rule is known as Kay
mixing rule after W. B. Kay of Ohio State, who studied mix-
ture properties, especially the pseudocritical properties in the
Petroleum fluids are mixtures of hydrocarbon compounds, 1930s and following several decades. Other forms of mixing
which in the reservoirs or during processing could be in the rules for critical constants will be discussed in Chapter 5 and
form of liquid, gas, or vapor. Some heavy products such as more accurate methods of calculation of mixture properties
asphalts and waxes are in solid forms. But in petroleum proc- are presented in Chapter 6.
essing most products are in the form of liquid under atmo-
spheric conditions. The same liquid products during proc- Equation (3.45) can be applied to any property such as crit-
essing might be in a vapor form before they are stored as a ical properties, molecular weight, density, refractive index,
product. Certain properties such as critical constants, acen- heat capacity, etc. There are various modified version of Eq.
tric factor, and molecular weight are specifications of a com- (3.45) when it is applied to different properties. Type of com-
pound regardless of being vapor of liquid. However, physical position used for x i depends on the type of property. For exam-
properties such as density, transport, or thermal properties ple, to calculate molecular weight of the mixture (θ = M) the
depend on the state of the system and in many cases sepa- most appropriate type of composition is mole fraction. Sim-
rate methods are used to estimate properties of liquid and ilarly mole fraction is used for many other properties such
gases as will be discussed in the following chapters. In this as critical properties, acentric factor, and molar properties
section a general approach toward calculation of such prop- (i.e., molar heat capacity). However, when Eq. (3.45) is ap-
erties for liquids and gases with known compositions is pre- plied to density, specific gravity, or refractive index parameter
[I = (n − 1)/(n + 2)], volume fraction should be used for x i .
2
2
sented. Since density and refractive index are important phys- For these properties the following mixing rule may also be
ical properties in characterization or petroleum fractions they applied instead of Eq. (3.45) if weight fraction is used:
are used in this section to demonstrate our approach for mix-
ture properties. The same approach will be applied to other
N
properties throughout the book. (3.46) 1/θ m = x wi /θ i
i=1
where x wi is the weight fraction and the equation can be ap-
3.4.1 Liquid Mixtures
plied to d, SG, or parameter I. In calculation of these proper-
In liquid systems the distance between molecules is much ties for a mixture, using Eq. (3.45) with volume fraction and
smaller than in the case of gases and for this reason the inter- Eq. (3.46) with weight fraction gives similar results. Applica-
action between molecules is stronger in liquids. Therefore, the tion of these equations in calculation of mixture properties
knowledge of types of molecules in the liquid mixtures is more will be demonstrated in the next chapter to calculate proper-
desirable than in gas mixtures, especially when the mixture ties of crude oils and reservoir fluids.
constituents differ significantly in size and type. For example, For liquid mixtures the mixing rule should be applied to the
consider two liquid mixtures, one a mixture of a paraffinic hy- final desired property rather than to the input parameters. For
drocarbon such as n-eicosane (n-C 20 ) with an aromatic com- example, a property such as viscosity is calculated through
pound such as benzene (C 6 ) and the second one a mixture of a generalized correlation that requires critical properties as
benzene and toluene, which are both aromatic with close the input parameters. Equation (3.45) may be applied first
molecular weight and size. The role of composition in the to calculate mixture pseudocritical properties and then mix-
n-C 20 –benzene mixture is much more important than the ture viscosity is calculated from the generalized correlation.
role of composition in the benzene–toluene mixture. Simi- An alternative approach is to calculate viscosity of individual
larly the role of type of composition (weight, mole, or volume components in the mixture for the generalized correlation
fraction) is more effective in mixtures of dissimilar con- and then the mixing rule is directly applied to viscosity. As
stituents than mixtures of similar compounds. It is for this it is shown in the following chapters the second approach
reason that for narrow-range petroleum fractions, use of the gives more accurate results for properties of liquid mixtures,

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