Page 289 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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6. THERMODYNAMIC RELATIONS FOR PROPERTY ESTIMATIONS 269
of gases in water versus temperature as given by Sandler [22]:
methane (275–328) ln x =−416.159289 + 15557.5631/T + 65.2552591 ln T − 0.0616975729T
ethane (275–323) ln x =−11268.4007 + 221617.099/T + 2158.421791 ln T − 7.18779402T + 4.0501192 × 10 T 2
−3
propane (273–347) ln x =−316.46 + 15921.2/T + 44.32431 ln T
n-butane (276–349) ln x =−290.238 + 15055.5/T + 40.1949 ln T
(6.192) i-butane (278–343) ln x = 96.1066 − 2472.33/T − 17.3663 ln T
H 2 S (273–333) ln x =−149.537 + 8226.54/T + 20.2308 ln T + 0.00129405T
−3
CO 2 (273–373) ln x =−4957.824 + 105, 288.4/T + 933.17 ln T − 2.854886T + 1.480857 × 10 T 2
N 2 (273–348) ln x =−181.587 + 8632.129/T + 24.79808 ln T
H 2 (274–339) ln x =−180.054 + 6993.54/T + 26.3121 ln T − 0.0150432T
For each gas the range of temperature (in kelvin) at which
the correlation is applicable is given in parenthesis. T is the tion of solubility of water in some undefined petroleum frac-
absolute temperature in kelvin and x is the mole fraction of tions:
dissolved gas in water at 1.013 bar. Henry’s constant of light 1841.3
hydrocarbon gases (C 1 ,C 2 ,C 3 ,C 4 , and i−C 4 ) in water may be naphtha log x H 2 O = 2.94 − T
10
estimated from the following correlation as suggested by the 2387.3
API-TDB [5]: kerosene log x H 2 O = 2.74 −
10
(6.195) T
A 3
(6.193) ln k gas–water = A 1 + A 2 T + + A 4 ln T 1708.3
T paraffinic oil log x H 2 O = 2.69 −
10
T
where k gas–water is the Henry’s constant of a light hydrocarbon 1766.8
gas in water in the unit of bar per mole fraction and T is the gasoline log x H 2 O = 2.63 − T
10
absolute temperature in kelvin. The coefficients A 1 –A 4 and
the range of T and P are given in Table 6.12. In the above equations T is in kelvin and x H 2 O is the mole
To calculate solubility of a hydrocarbon liquid mixture in fraction of water in the petroleum fraction. Obviously these
the aqueous phase, the following relation may be used: correlations give approximate values of water solubility as
composition of each fraction vary from one source to another.
ˆL
f i
ˆ x i = x i L 6.8.2.3 Equilibrium Ratios (K i Values)
f
i
The general formula for VLE calculation is obtained through
where ˆx i is the solubility of component i in the water when it definition of a new parameter called equilibrium ratio shown
is in a liquid mixture. x i is the solubility of pure i in the water. by K i :
f ˆL is the fugacity of i in the mixture of liquid hydrocarbon
i
L
phase and f is the fugacity of pure i in the liquid phase. More (6.196) K i ≡ y i
i
accurate calculations can be performed through liquid–liquid x i
phase equilibrium calculations. K i is a dimensionless parameter and in general varies with
For calculation of solubility of water in hydrocarbons the T, P, and composition of both liquid and vapor phases.
following correlation is proposed by the API-TDB [5]: In many references, equilibrium ratios are referred as K i
value and can be calculated from combining Eq. (6.176) with
4200 1

log x H 2 O =− + 1050 × − 0.0016 Eq. (6.196) as in the following form:
10
CH weight ratio T
L
(6.194) ˆ φ (T, P, x i )
i
(6.197) K i =
V
ˆ φ (T, P, y i )
where T is in kelvin and x H 2 O is the mole fraction of water i
in liquid hydrocarbon at 1.013 bar. CH weight ratio is the In high-pressure VLE calculations, K i values are calculated
carbon-to-hydrogen weight ratio. This equation is known as from Eq. (6.197) through Eq. (6.126) for calculation of
Hibbard correlation and should be used for pentanes and fugacity coefficients with use of cubic equations (SRK or
heavier hydrocarbons (C 5+ ). The reliability of this method is PR). In calculation of K i values from a cubic EOS use of
±20% [5]. If this equation is applied to undefined hydrocar- binary interaction parameters (BIPs) introduced in Chapter 5
bon fractions, the CH weight ratio may be estimated from the is required specially when components such as N 2 ,H 2 S, and
methods discussed in Section 2.6.3 of Chapter 2. However, CO 2 exist in the hydrocarbon mixture. Also in mixtures when
API-TDB [5] recommends the following equation for calcula- the difference in molecular size of components is appreciable
TABLE 6.12—Constants for Eq. (6.193) for estimation of Henry’s constant for light gases in water [5].
Gas T range, K Pressure range, bar A 1 A 2 A 3 A 4 %AAD
Methane 274–444 1–31 569.29 0.107305 −19537 −92.17 3.6
Ethane 279–444 1–28 109.42 −0.023090 −8006.3 −11.467 7.5
Propane 278–428 1–28 1114.68 0.205942 −39162.2 −181.505 5.3
n-Butane 277–444 1–28 182.41 −0.018160 −11418.06 −22.455 6.2
i-Butane 278–378 1–10 1731.13 0.429534 −52318.06 −293.567 5.3

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