Page 409 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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9. APPLICATIONS: PHASE EQUILIBRIUM CALCULATIONS 389
TABLE 9.12—Coefficients (C i ) for Eq. (9.46) for estimation of HFT at very high pressures. Taken
with permission from Ref. [1].
Pressure, bar (psia) Methane Ethane Propane i-Butane n-Butane
414 (6000) 18933 20806 28382 30696 17340
483 (7000) 19096 20848 28709 30913 17358
552 (8000) 19246 20932 28764 30935 17491
620 (9000) 19367 21094 29182 31109 17868
690 (10000) 19489 21105 29200 30935 17868
at given pressure. Calculation of hydrate-formation tempera- ln K VS 406.78 + 1.9711 × 10 T 2
−3
ture (HFT) is very similar to dewpoint temperature calcula- n-C 4 =−37.211 + 1.5582T + T
tion in VLE. The equilibrium ratio for component i between P T T
S
vapor and solid phase is defined as K i VS = y i /x , where x is − 8.6748 T − 8.2183 P + 540.976 P 3
S
i
i
the mole fraction of i in the solid hydrate phase. Hydrate is
3
formed if at given T and P we have + 4.6897 × 10 −3 P − 1.3227 × 10 T 4
−5
T 2
N 45.9039

y i ln K VS − 1.9293 × 10 −4 PT
(9.44) ≥ 1 H 2 S =−6.051 + 0.11146T +
K VS T
i=1 i P P P
+ 1.94087 − 0.64405 ln − 56.87 2
where equality holds at temperature where hydrate forma- T T T
−6
tion begins. In the vapor phase the amount of water is very − 7.5816 × 10 T 3
small (<0.001 mol%) thus its presence in the vapor phase can where T = given temperature in kelvin − 255.4 and
be neglected in the calculations (y i = 0). To find the temper-
W ∼
ature at which a hydrate dissociates and hydrocarbons are P = given pressure in bar
released, a calculation similar to bubble point calculations (9.45)
S
can be performed so that x K i VS ≥ 1. Katz provided charts
i
for calculation of K VS , which later Sloan converted into em- For pressures between 400 and 700 bars (∼6000–10000 psia),
i
pirical correlations in terms of T and P and they are used in a simple empirical method is proposed by McLeod and
Campbell in the following form as given in Ref. [1]:
the petroleum industry [1]. It should be noted that these K i
values are not true VSE ratios as the above calculations are 1/2
N

based on water-free phases. This method can be applied to (9.46) T = 2.16
y i C i
pressures below 70 bar (∼1000 psia). For methane, ethane, i=1
propane, n-butane, and H 2 S the correlations for calculation
of K VS are given as follows [1]: where values of C i for C 1 –C 4 are given in Table 9.12 at several
i
pressures encountered in deep-gaswell drilling.
17.59 3.403 −4 This method can be used for quick estimation of HFT or
VS
ln K = 0.00173 + − + 1.3863 × 10 PT to check the validity of estimated temperatures from other
C 1 T P methods. More sophisticated methods using chemical poten-
1.0356P P P
+ − 0.78338 ln − 23.9804 tial and equations of state are discussed in other references
T T T 2 [1].
P 3 Because of the problems associated with hydrate for-
−6
3
− 1.34136 × 10 T − 1.8834 × 10 −5 mation, hydrate inhibitors are used to reduce HFT. Com-
T 2
monly used hydrate inhibitors are methanol, ethanol, glycols,
161.268 181.267
ln K VS = 3.92157 − + + 1.8933 × 10 −5 P 2 sodium chloride, and calcium chloride. These are nearly the
T P same materials that are used as water antifreeze inhibitors.
C 2
1.04557P P 402.16 Effect of methanol (CH 3 OH) on the depression of HFT of
+ − 1.19703 ln −
T T P 2 methane reservoir fluid is shown in Fig. 9.24 [55]. The com-
position of this condensate sample in terms of mol% is as
T T P
2
− 8.8157 + 0.133231 − 21.2354 follows: 0.64 N 2 , 3.11 CO 2 , 73.03 C 1 , 8.04 C 2 , 4.28 C 3 , 0.73
P P T 2
i-C 4 , 1.5 n-C 4 , 0.54 i-C 5 , 0.6 n-C 5 , and 7.53 C 6+ with mixture
T molecular weight of 32.4. The most commonly used equation

+ 46.13339
P 3 to calculate the degree of decrease in HFT ( T) is given by
26.1422 −5 Hammerschmidt, which is in the following form [1, 14]:
VS
ln K =−7.59224 + − 3.0545 × 10 PT + 2.315
C 3 T Awt%
(9.47)
P 79.3379 M(100 − wt%)
T =
2
−3
× 10 T + 0.12348 ln +
T P 2
where T is the decrease in HFT in C (or in kelvin), wt% is
◦
T T
2
−5
+ 0.05209 −26.4294 + 3.2076 ×10 T 3 the weight percent of inhibitor in the aqueous phase, and M
P P 3 is the molecular weight of the inhibitor. Values of M and A
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