Page 201 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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4.5.4.6 Prediction of Property Distributions
This equation can be used for narrow boiling range fractions
Using Bulk Properties T1: IML 4. CHARACTERIZATION OF RESERVOIR FLUIDS AND CRUDE OILS 181
with M between 70 and 350. In this molecular weight range
As discussed above, Eq. (4.56) can be used as a two-parameter this equation is slightly more accurate than Eq. (2.117). Once
relation with fixed values of B for each property (B M = 1, distribution of I is determined from these equations, if the
∗
B T = 1.5, and B SG = B I = 3). In this case Eq. (4.56) is referred initial values of M o and SG o are correct then I av calculated
as a two-parameter distribution model. In such cases only from the distribution coefficients and Eq. (4.72) should be
parameters P o and A must be known for each property to ex- close to the experimental value obtained from n 7+ . For cases
press its distribution in a hydrocarbon plus fraction. The two- that experimental data on n 7+ is not available it can be esti-
parameter model is sufficient to express property distribu- mated from M 7+ and SG 7+ using Eq. (4.95) or (2.117). Equa-
tion of light oils and gas condensate systems. For very heavy tion (2.117) estimates values of n 7+ for 48 systems [23] with
oils two-parameter model can be used as the initial guess to an average error of 0.4%. Steps to predict M, T b , SG, and I
begin calculations for determination of the three parameters (or n) distributions can be summarized as follows [24]:
in Eq. (4.56). In some cases detailed composition of a C 7+
fraction in a reservoir fluid is not available and the only infor-
mation known are M 7+ and SG 7+ , while in some other cases
in addition to these properties, a third parameter such as re- 1. Read values of M 7+ ,SG 7+ , and I 7+ for a given C 7+ sample.
fractive index of the mixture or the true boiling point (TBP) If I 7+ is not available Eq. (2.117) may be used to estimate
curve are also known. For these two scenarios we show how this parameter.
parameters P o and A can be determined for M, T b , SG, and 2. Guess an initial value for M o (assume M o = 72) and cal-
∗
I 20 . culate M from Eq. (4.93).
av
Method A: M 7+ , SG 7+ , and n 7+ are known—Three bulk 3. Calculate A M from Eq. (4.72) or Eq. (4.74) when B = 1.
properties are the minimum data that are required to predict 4. Choose 20 (or more) arbitrary cuts for the mixture with
complete distribution of various properties [24, 43]. In ad- equal mole fractions (x mi ) of 0.05 (or less). Then calculate
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
dition to M 7+ and SG 7+ , refractive index, n 7+ , can be easily M i for each cut from Eq. (4.56).
measured and they are known for some 48 C 7+ fractions [24]. 5. Convert mole fractions (x mi ) to weight fractions (x wi )
As shown by Eqs. (4.74)–(4.76), if P is known, parameter A through Eq. (1.15) using M i from step 4.
∗
av
can be determined for each property. For example, if M o is 6. Guess an initial value for S o (assume S o = 0.59 as a starting
known, M can be determined from definition of M as: value).
∗
∗
av
7. Calculate 1/J from Eq. (4.80) using SG o and SG 7+ . Then
calculate A SG from Eq. (4.79) using Newton’s method.
(4.93) M =
M av − M ◦
∗
av 8. Using Eq. (4.56) with A SG and S o from steps 6 and 7 and
M ◦
B = 3, SG distribution in terms of x cw is determined and
where M av is the mixture molecular weight of the C 7+ fraction, for each cut SG i is calculated.
which is known from experimental measurement. Similarly, 9. Convert x wi to x vi using Eq. (1.16) and SG i values from
SG ∗ av and I av can be determined from S 7+ and n 7+ (or I 7+ ). step 8.
∗
Parameters A M , A SG , and A I are then calculated from Eqs. 10. For each cut calculate T bi from M i and SG i through
(4.72) and (4.81). For fixed values of B, Eqs. (4.74)–(4.76) Eq. (2.56) or (2.57).
and (4.79) and (4.80) may be used. One should realize that 11. For each cut calculate I i from M i and SG i through
Eq. (4.74) was developed based on cumulative mole fraction, Eq. (2.95).
while Eqs. (4.79) and (4.80) are based on cumulative weight 12. From distribution of I versus x cv find parameters I o , A I
fraction. Once distribution of M and SG are known, distribu- and B I through Eqs. (4.56)–(4.57). Then calculate I av from
tion of T b can be determined using equations given in Chapter Eq. (4.72) and (4.81).
2, such as Eqs. (2.56) or (2.57), for estimation of T b from M 13. Calculate ε 1 =|(I av,calc. − I 7+ )/I 7+ |.
and SG. Based on data for 48 C 7+ samples, the following re- 14. If ε 1 < 0.005, continue from step 15, otherwise go back
lation has been developed to estimate I o from M o and SG o to step 6 with SG o,new = SG o,old + 0.005 and repeat steps
[24]: 7–13.
15. Calculate I o from Eq. (4.94).
16. Calculate ε 2 =|(I ◦,step15 − I ◦,step12 )/I ◦,step15 |.
I ◦ = 0.7454 exp (−0.01151M ◦ − 2.37842SG ◦
(4.94) + 0.01225M ◦ SG ◦ )M 0.2949 SG 1.53147 17. Go back to step 2 with a new guess for M o (higher than the
◦ ◦
previous guess). Repeat steps 2–16 until either ε 2 < 0.005
This equation can reproduce values of I o with an average or ε 2 becomes minimum.
deviation of 0.3%. Furthermore, methods of estimation of 18. For heavy oils large value of ε 2 may be obtained, because
parameter I from either T b and SG or M and SG are given in value of B M is greater than 1. For such cases values of
Section 2.6.2 by Eqs. (2.115)–(2.117). Equation (2.117) may B M = 1.5, 2.0, and 2.5 should be tried successively and
be applied to the molecular weight range of 70–700. However, calculations from step 2 to 17 should be repeated to min-
a more accurate relation for prediction of parameter I from imize ε 2 .
M and SG is Eq. (2.40) with coefficients from Table 2.5 as 19. Using data for T b versus x cw , determine parameters T o , A T ,
follows: and B T from Eqs. (4.56) and (4.57).
20. Print M o , A M , B M ,SG o , A SG , T o , A T , B T , I o , A I , and B I .
I = 0.12399 exp(3.4622 × 10 −4 M + 0.90389SG 21. Generate distributions for M, T b , SG, and n 20 from
(4.95) −6.0955 × 10 −4 MSG)M 0.02264 SG 0.22423 Eq. (4.56).

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