Page 243 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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This method is also included in the API-TDB [59]. Another
Eq. (5.121) can be rearranged to get Z RA :
approach to estimate density of defined liquid mixtures at its
1/n 17:42 5. PVT RELATIONS AND EQUATIONS OF STATE 223

(5.123) Z RA = MP c bubble point pressure is through the following mixing rule:
RT c d T
N
where n is calculated from Eq. (5.121) at temperature T 1 x wi
at which density is known. For hydrocarbon systems and (5.126) ρ bp = i=1 ρ i sat
petroleum fractions usually specific gravity (SG) at 15.5 Cis
◦
known and value of 288.7 K should be used for T. Then d T (in where x wi is weight fraction of i in the mixture. ρ i sat (= M/V i sat )
3
g/cm ) is equal to 0.999SG according to the definition of SG is density of pure saturated liquid i and should be calculated
by Eq. (2.2). In this way predicted values of density are quite from Eq. (5.121) using T ci and Z RAi .
accurate at temperatures near the reference temperature at For petroleum fractions in which detailed composition is
which density data are used. The following example shows not available Eq. (5.121) developed for pure liquids may be
the procedure. used. However, Z RA should be calculated from specific grav-
ity using Eq. (5.123) while T c and P c can be calculated from
Example 5.7—For n-octane of Example 5.2, calculate satu- methods given in Chapter 2 through T b and SG.
rated liquid molar volume at 279.5 C from Rackett equation
◦
using predicted Z RA . 5.8.3 Effect of Pressure on Liquid Density
Solution—From Example 5.2, M = 114.2, SG = 0.707, T c = As shown in Fig. 5.1, effect of pressure on volume of liquids
3
295.55 C (568.7 K), P c = 24.9 bar, R = 83.14 cm · bar/mol · K, is quite small specially when change in pressure is small.
◦
and T r = 0.972. Equation (5.123) should be used to predict When temperature is less than normal boiling point of a liq-
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
Z RA from SG. The reference temperature is 288.7 K, which uid, its saturation pressure is less than 1.0133 bar and den-
gives T r = 0.5076. This gives n = 1.8168 and from Eq. (5.123) sity of liquid at atmospheric pressure can be assumed to be
we calculate Z RA = 0.2577. (Z RA = 0.2569 from Table 5.12). the same as its density at saturation pressure. For temper-
From Eq. (5.121), V sat is calculated: n = 1 + (1 − 0.972) 2/7 = atures above boiling point where saturation pressure is not
3
1.36, V sat = (83.14 × 568.7/24.9) × 0.2577 1.36 = 300 cm /mol. greatly more than 1 atm, calculated saturated liquid density
3
Comparing with actual value of 304 cm /mol gives the er- may be considered as liquid density at atmospheric pressure.
ror of –1.3%. Calculated density is ρ = 114.2/300 = 0.381 Another simple way of calculating liquid densities at atmo-
3
g/cm . spheric pressures is through Eq. (2.115) for the slope of den-
sity with temperature. If the only information available is spe-
5.8.2 Defined Liquid Mixtures and cific gravity, SG, the reference temperature would be 15.5 C
◦
Petroleum Fractions (288.7 K) and Eq. (2.115) gives the following relation:
o
Saturation pressure for a mixture is also called bubble point ρ = 0.999SG − 10 −3 × (2.34 − 1.898SG) × (T − 288.7)
T
bp
pressure and saturation molar volume is shown by V . Liquid (5.127)
bp
density at the bubble point is shown by ρ , which is related
◦
◦
◦
to V bp by the following relation: where SG is the specific gravity at 15.5 C (60 F/60 F) and T
3
o
is absolute temperature in K. ρ is liquid density in g/cm at
M T
(5.124) ρ bp = temperature T and atmospheric pressure. If instead of SG at
V bp
15.5 C (288.7 K), density at another temperature is available
◦
3
where ρ bp is absolute density in g/cm and M is the molec- a similar equation can be derived from Eq. (2.115). Equation
ular weight. V bp can be calculated from the following set of (5.127) is not accurate if T is very far from the reference tem-
equations recommended by Spencer and Danner [65]: perature of 288.7 K.
N The effect of pressure on liquid density or volume becomes

T ci n
V bp = R x i Z RAm important when the pressure is significantly higher than 1
P ci
◦
i=1 atm. For instance, volume of methanol at 1000 bar and 100 C
n = 1 + (1 − T r) 2/7 is about 12% less than it is at atmospheric pressure. In gen-
eral, when pressure exceeds 50 bar, the effect of pressure on
N
liquid volume cannot be ignored. Knowledge of the effect of
Z RAm = x i Z RAi
i=1 pressure on liquid volume is particularly important in the de-
sign of high-pressure pumps in the process industries. The
T r = T/T cm
following relation is recommended by the API-TDB [59] to
N calculate density of liquid petroleum fractions at high pres-
(5.125)
N
T cm = φ i φ j T cij sures:
i=1 j=1
ρ o P
x i V ci (5.128) = 1.0 −
N ρ B T
φ i = !
i=1 x i V ci
o
where ρ is the liquid density at low pressures (atmospheric

T cij = T ci T c j 1 − k ij
pressure) and ρ is density at high pressure P (in bar). B T
is called isothermal secant bulk modulus and is defined
⎤3
$
⎡ 1/3 1/3 o
V ci V c j as −(1/ρ )( P/ V) T . Parameter B T indicates the slope of
change of pressure with unit volume and has the unit of pres-
⎦
k ij = 1.0 − ⎣ 1/3 1/3 %
V + V 2
ci c j sure. Steps to calculate B T are summarized in the following
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