PNA Determination

SOLUTION USING MAGOULAS-TASSIOS’S CORRELATIONS

p_c= exp(5.6656) = 289 psi

FIGURE 2–3 TBP, specific gravity, and molecular weight of a C₇₊fraction.

molecular weight, and specific gravity of each pseudo component usually are taken at the mid-volume percent of the cut, that is, between V_iand V_i–1. The TBP associated with that specific pseudo component i, that is, T_bi, is given by

where V_i–V_i–1 = volumetric cut of the TBP curve associated with pseudo component i T_bt(V)

= true boiling-point temperature versus liquid volume percent distilled.

The mass (m_i) of each distillation cut is measured directly during the TBP analysis.

The cut is quantified in moles n_iwith molecular weight (M_i) and the measured mass (m_i), by definition, as

n_i= m_i/M_i

Volume of the fraction is calculated from the mass and the density (ρ_i) or specific gravity (γ_i) as V_i= m_i /ρ_i

The term M_iis measured by a cryoscopic method, based on freezing-point depression, and γ_iis measured by a pycnometer or electronic densitometer. Note that, when the specific gravity and molecular weight of the plus fraction are the onlydata available, the physical properties of each cut with a specified T_bi can be approximated by assuming a constant K_w (Watson factor) for each fraction. The specific steps of the procedure follow.

Step 1 Calculate the characterization parameter K_wfor the plus fraction from equation (2–1); that is,

or approximated by Whitson’s equation; that is, equation (2–2), as

where T_bis the normal boiling point of the C₇₊in °R.

Step 2 Assuming a constant K_wfor each selected pseudo fraction, calculate the specific gravity of each cut by rearranging equation (2–2):

where T_bi= pseudo compound boiling point as determined from the distillation curve, ^oR, and K_w= Watson characterization parameter for the plus fraction.

Step 3 Estimate the molecular weight of each pseudo component. M_i, from equation (2–2):

Miquel, Hernandez, and Castells (1992) proposed the following guidelines when selecting the proper number of pseudo components from the TBP distillation curve:

M_i =45 69 10. × ⁻⁶γ_i^{5 57196.} K_w^{6 58834.} γ_i ^bi

w

T

= K^{1 3/}

K M

w ≈ ⁺

+

4 5579 ⁷

7 0 15178 0 84573

.

. . C

γC

K T

w

=⎡ b

⎣⎢ ⎤

⎦⎥

+ 1 3

7 /

γ _C

T_bi V V T V dV

i i

bt V

V

i i

= −¹ ₋

∫

₋

1 ₁

( )

1. The pseudo-component breakdown can be made from either equal volumetric frac- tions or regular temperature intervals in the TBP curve. To reproduce the shape of the TBP curve better and reflect the relative distribution of light, middle, and heavy components in the fraction, a breakdown with equal TBP temperature intervals is recommended. When equal volumetric fractions are taken, information about light initial and heavy end components can be lost.

2. Use between 5 and 15 fractions to describe the plus fraction.

3. If the TBP curve is relatively “steep,” use between 10 and 15 fractions.

4. If the curve is relatively “flat,” use 5 to 8 fractions.

5. If the TBP curve contains sections that are relatively “steep” and other sections that are relatively “flat,” use several fractions to describe the “steep” portion of the curve and 1 to 3 to describe the “flat” portion of the curve.

6. Use the specific gravity, molecular weight, and PNA curves to locate the “best break point” for the various fractions. Best break points are qualitatively defined as those that yield component properties that require minimum averaging across a wildly oscillating curve.

7. The number of pseudo components selected has to be enough to reproduce the volatility properties of the fraction properly, especially in fractions with wide boiling- temperature ranges. On the other hand, too many pseudo components require exces- sively long computer time for further calculations (i.e., vapor/liquid equilibria and process simulation calculations).

8. The mean average boiling point (T_b) is recommended as the most representative mix- ture boiling point because it allows better reproduction of the properties of the entire mixture.

Generally, five methods are used to define the normal boiling point for petroleum fractions:

1. Volume-average boiling point, defined mathematically by the following expression:

(2–36) where T_bi= boiling point of the distillation cut i, °R, and V_i= volume fraction of the distillation cut i.

2. Weight-average boiling point, defined by the following expression:

(2–37) where w_i= weight fraction of the distillation cut i.

3. Molar-average boiling point (MABP), given by the following relationship:

(2–38) where x_i= mole fraction of the distillation cut i.

MABP=

∑

^{x Ti bi}

i

WABP=

∑

^{w Ti bi}

i

VABP=

∑

^{V Ti bi}

i

4. Cubic-average boiling point (CABP), which is defined as:

(2–39) 5. Mean-average boiling point (MeABP):

(2–40) As indicated by Edmister and Lee (1984), these five expressions for calculating normal boiling points result in values that do not differ significantly from one another for narrow boiling petroleum fractions.

All three parameters (i.e., molecular weight, specific gravity, and VABP/WABP) are employed, as discussed later, to estimate the PNA content of the heavy hydrocarbon frac- tion, which in turn is used to predict the critical properties and acentric factor of the frac- tion. Hopke and Lin (1974), Erbar (1977), Bergman et al. (1977), and Robinson and Peng (1978) used the PNA concept to characterize the undefined hydrocarbon fractions. As a representative of this characterization approach, the Robinson-Peng method and the Bergman method are discussed next.

Peng-Robinson’s Method

Robinson and Peng (1978) proposed a detailed procedure for characterizing heavy hydro- carbon fractions. The procedure is summarized in the following steps.

Step 1 Calculate the PNA content (X_P,X_N,X_A) of the undefined fraction by solving the following three rigorously defined equations:

(2–41) (2–42) (2–43) where

X_P= mole fraction of the paraffinic group in the undefined fraction X_N= mole fraction of the naphthenic group in the undefined fraction X_A= mole fraction of the aromatic group in the undefined fraction WABP = weight average boiling point of the undefined fraction, °R M= molecular weight of the undefined fraction

(M_i) = average molecular weight of each cut (i.e., PNA) (T_b)_i= boiling point of each cut, °R

Equations 2–41 through 2–43 can be written in a matrix form as follows:

(2–44)

1 1 1

[ ] [ ] [ ]

[ ] [ ] [ ]

M T M T M T

M M M

b P b N b A

P N A

i i i

⎡

⎣

⎢⎢

⎢

⎤

⎦

⎥⎥⎥

⎥

⎡

⎣

⎢⎢

⎢

⎤

⎦

⎥⎥

⎥

=

⎡

⎣

⎢⎢

⎢

⎤

⎦

⎥⎥

⎥ X

X X

M M

p N A

1

iWABP

M X_{i i} M

i P N A ⎡⎣ ⎤⎦ =

=

∑

M T X_{i bi i} M

i P N A ⎡⎣ ⎤⎦ =

=

∑

^{( )(WABP)}

X_i

i P N A

=

=

∑

¹

MeABP MABP CABP

= +

2 CABP= ⎡

⎣⎢ ⎤

⎦⎥

∑

^{x Ti bi}

i

1 3 3 /

Robinson and Peng pointed out that it is possible to obtain negative values for thePNA contents. To prevent these negative values, the authors imposed the following constraints:

0 ≤X_P≤0.90 X_N≥0.00 X_A≥0.00

Solving equation (2–44) for the PNA content requires the weight-average boiling point and molecular weight of the cut of the undefined hydrocarbon fraction. If the exper- imental values of these cuts are not available, the following correlations proposed by Robinson and Peng can be used.

For determination of (T_b)_P, (T_b)_N, and (T_b)_A,

Paraffinic group (2–45)

Naphthenic group (2–46)

Aromatic group (2–47)

where n= number of carbon atoms in the undefined hydrocarbon fraction, and a_i= coeffi- cients of the equations, which are given below.

Coefficient Paraffin, P Napthene, N Aromatic, A

a₁ 5.83451830 5.85793320 5.86717600

a₂ 0.84909035 ×10^–1 0.79805995 ×10^–1 0.80436947 ×10^–1 a₃ –0.52635428 ×10^–2 –0.43098101 ×10^–2 –0.47136506 ×10^–2 a₄ 0.21252908 ×10^–3 0.14783123 ×10^–3 0.18233365 ×10^–3 a₅ –0.44933363 ×10^–5 –0.27095216 ×10^–5 –0.38327239 ×10^–5 a₆ 0.37285365 ×10^–7 0.19907794 ×10^–7 0.32550576 ×10^–7

For the determination of (M)_P, (M)_N, and (M)_A,

Paraffinic group (M)_P= 14.026n+ 2.016 (2–48)

Naphthenic group (M)_N = 14.026n– 14.026 (2–49)

Aromatic group (M)_A= 14.026n– 20.074 (2–50)

Step 2 Having obtained the PNA content of the undefined hydrocarbon fraction, as out- lined in step 1, calculate the critical pressure of the fraction by applying the following expression:

p_c= X_P(p_c)_P+ X_N(p_c)_N+ X_A(p_c)_A (2–51) where p_c= critical pressure of the heavy hydrocarbon fraction, psia.

The critical pressure for each cut of the heavy fraction is calculated according to the following equations:

Paraffinic group ( ) . . (2–52)

( . . )

p n

c P = n +

+

206 126096 29 67136 0 227 0 340² ln(T_{b A}) ln( . ) [ (a n_i ) ]ⁱ

i

= + − ⁻

∑

=

1 8 6 ¹

1 6

ln(T_{b N}) ln( . ) [ (a n_i ) ]ⁱ

i

= + − ⁻

∑

=

1 8 6 ¹

1 6

ln(T_{b P}) ln( . ) [ (a n_i ) ]ⁱ

i

= + − ⁻

∑

=

1 8 6 ¹

1 6

Naphthenic group (2–53)

Aromatic group (2–54)

Step 3 Calculate the acentric factor of each cut of the undefined fraction by using the fol- lowing expressions:

Paraffinic group (ω)_P= 0.432n+ 0.0457 (2–55)

Naphthenic group (ω)_N= 0.0432n– 0.0880 (2–56)

Aromatic group (ω)_A= 0.0445n– 0.0995 (2–57)

Step 4 Calculate the critical temperature of the fraction under consideration by using the following relationship:

T_c= X_P(T_c)_P+ X_N(T_c)_N+ X_A(T_c)_A (2–58) where T_c= critical temperature of the fraction, °R.

The critical temperatures of the various cuts of the undefined fractions are calculated from the following expressions:

Paraffinic group (2–59)

Naphthenic group (2–60)

Aromatic group (2–61)

where the correction factors Sand S₁are defined by the following expressions:

S= 0.99670400 + 0.00043155n S₁= 0.99627245 + 0.00043155n

Step 5 Calculate the acentric factor of the heavy hydrocarbon fraction by using the Edmister correlation (equation 2–21) to give

(2–62) where

ω= acentric factor of the heavy fraction P_c= critical pressure of the heavy fraction, psia T_c= critical temperature of the heavy fraction, °R T_b= average-weight boiling point, °R

EXAMPLE 2–5

Calculate the critical pressure, critical temperature, and acentric factor of an undefined hydrocarbon fraction with a measured molecular weight of 94 and a weight-average boil- ing point of 655°R. The number of carbon atoms of the component is 7; that is, n= 7.

ω =3 14 7− − 7[log( / . )]1 1

[ ( / ) ] P T T

c

c b

( ) log[( ) ] .

[ ( ) ]

T S P

c A

c A A

= + −

+

⎧⎨

⎩

⎫

1 1 3 3 501952

7 1 ω ⎬⎬

⎭(T_{b A})

( ) log[( ) ] .

[ ( ) ]

T S P

c N

c N P

= + −

+

⎧⎨

⎩

⎫

1 1 3 3 501952

7 1 ω ⎬⎬

⎭(T_{b N})

( ) log[( ) ] .

[ ( ) ]

T S P

c P

c P P

= + −

+

⎧⎨

⎩

⎫⎬

1 3 3 501952

7 1 ω ⎭⎭(T_{b P})

( ) . .

( . . )

p n

c A= n −

−

206 126096 295 007504 0 227 0 325²

( ) . .

( . . )

p n

c N = n −

−

206 126096 206 126096 0 227 0 137²

SOLUTION

Step 1 Calculate the boiling point of each cut by applying equations (2–45) through (2–47) to give

Step 2 Compute the molecular weight of various cuts by using equations (2–48) through (2–50) to yield

(M)_P= 14.026 ×7 + 2.016 = 100.198 (M)_N= 14.0129 ×7 – 14.026 = 84.156 (M)_A= 14.026 ×7 – 20.074 = 78.180

Step 3 Solve equation (2–44) for X_P, X_N, and X_A:

to give:

X_P= 0.6313 X_N= 0.3262 X_A= 0.04250

Step 4 Calculate the critical pressure of each cut in the undefined fraction by applying equations (2–52) and (2–54).

Step 5 Calculate the critical pressure of the heavy fraction from equation (2–51) to give p_c= X_P(p_c)_P+ X_N(p_c)_N + X_A(p_c)_A

p_c= 0.6313(395.70) + 0.3262(586.61) + 0.0425(718.46) = 471 psia

Step 6 Compute the acentric factor for each cut in the fraction by using equations (2–55) through (2–57) to yield

(ω)_P= 0.432 ×7 + 0.0457 = 0.3481 (ω)_N= 0.0432 ×7 – 0.0880 = 0.2144 (ω)_A= 0.0445 ×7 – 0.0995 = 0.2120

( ) . .

( . .

p_{c A}= × −

× −

206 126096 7 295 007504

0 227 7 0 325))₂ =718 46.

( ) . .

( . .

p_{c N} = × −

× −

206 126096 7 206 126096

0 227 7 0 137))₂ =586 61.

( ) . .

( . . )

p_{c P} = × +

× +

206 126096 7 29 67136

0 227 7 0 340 ² ==395 70. psia

1 1 1

66689 78 53018 28 49710 753 199 198 84 156 78

. . .

. . ..180

1 61570

94

⎡

⎣

⎢⎢

⎢

⎤

⎦

⎥⎥

⎥

⎡

⎣

⎢⎢

⎢

⎤

⎦

⎥⎥

⎥

=

⎡

⎣ X ⎢

X X

P N A

⎢⎢⎢

⎤

⎦

⎥⎥

⎥ (T_{b A}) exp ln( . ) [ (a n_i ) ]ⁱ

i

= ⎧ + −

⎨⎪

⎩⎪

⎫⎬

⎪

⎭

−

∑

=

1 8 6 ¹

1 6

⎪⎪=635 85. °R (T_{b N}) exp ln( . ) [ (a n_i ) ]ⁱ

i

= ⎧ + −

⎨⎪

⎩⎪

⎫⎬

⎪

⎭

−

∑

=

1 8 6 ¹

1 6

⎪⎪=630°R (T_{b P}) exp ln( . ) [ (a n_i ) ]ⁱ

i

= ⎧ + −

⎨⎪

⎩⎪

⎫⎬

⎪

⎭

−

∑

=

1 8 6 ¹

1 6

⎪⎪=666 58. °R

Step 7 Solve for (T_c)_P, (T_c)_N, and (T_c)_Aby using equations (2–59) through (2–61) to give S= 0.99670400 + 0.00043155 ×7 = 0.99972

S₁= 0.99627245 + 0.00043155 ×7 = 0.99929

Step 8 Solve for (T_c) of the undefined fraction from equation (2–58):

T_c = X_P(T_c)_P+ X_N(T_c)_N+ X_A(T_c)_A= 964.1°R

Step 9 Calculate the acentric factor from equation (2–62) to give

Bergman’s Method

Bergman et al. (1977) proposed a detailed procedure for characterizing the undefined hydrocarbon fractions based on calculating the PNA content of the fraction under consid- eration. The proposed procedure was originated from analyzing extensive experimental data on lean gases and condensate systems. The authors, in developing the correlation, assumed that the paraffinic, naphthenic, and aromatic groups have the same boiling point.

The computational procedure is summarized in the following steps.

Step 1 Estimate the weight fraction of the aromatic content in the undefined fraction by applying the following expression:

w_A= 8.47 – K_w (2–63)

where

w_A= weight fraction of aromatics

K_w= Watson characterization factor, defined mathematically by the following expression

K_w= (T_b)^1/3/γ (2–64)

γ= specific gravity of the undefined fraction T_b= weight average boiling point, °R

Bergman et al. imposed the following constraint on the aromatic content:

0.03 ≤w_A≤0.35

Step 2 With the estimate of the aromatic content, the weight fractions of the paraffinic and naphthenic cuts are calculated by solving the following system of linear equations:

w_P+ w_N= 1 – w_A (2–65)

(2–66)

w_P w w

P N N

A

γ + γ = −1γ γA

ω =3 471 7 14 7− − = 7 964 1 655[log( . / . )]1 1 0 36

[ ( . / ) ] . 880

( ) . log[ . ] .

[ .

T_{c A}= + −

0 99929 1 3 718 46+ 3 501952

7 1 0 2112 635 85 1014 9

] . .

⎧⎨

⎩

⎫⎬

⎭ = °R

( ) . log[ . ] .

[ .

T_{c N} = + −

0 99929 1 3 586 61+ 3 501952

7 1 0 21144 630 947 3

] .

⎧⎨

⎩

⎫⎬

⎭ = °R

( ) . log[ . ] .

[ .

T_{c P} = + −

0 99972 1 3 395 7+ 3 501952

7 1 0 34881 666 58 969 4

] . .

⎧⎨

⎩

⎫⎬

⎭ = °R

where

w_P= weight fraction of the paraffin cut w_N= weight fraction of the naphthene cut γ= specific gravity of the undefined fraction

γ_P, γ_N, γ_A = specific gravity of the three groups at the weight average boiling point of the undefined fraction. These gravities are calculated from the following relationships:

γ_P= 0.582486 + 0.00069481(T_b– 460) – 0.7572818(10^–6)(T_b– 460)² (2–67) + 0.3207736(10^–9)(T_b– 460)³

γ_N= 0.694208 + 0.0004909267(T_b– 460) – 0.659746(10^–6)(T_b– 460)² (2–68) + 0.330966(10^–9)(T_b– 460)³

γ_A= 0.916103 – 0.000250418(T_b– 460) + 0.357967(10^–6)(T_b– 460)² (2–69) – 0.166318(10^–9) (T_b– 460)³

A minimum paraffin content of 0.20 was set by Bergman et al. To ensure that this minimum value is met, the estimated aromatic content that results in negative values of w_P is increased in increments of 0.03 up to a maximum of 15 times until the paraffin content exceeds 0.20. They pointed out that this procedure gives reasonable results for fractions up to C₁₅.

Step 3 Calculate the critical temperature, the critical pressure, and acentric factor of each cut from the following expressions.

For paraffins,

(T_c)_P= 275.23 + 1.2061(T_b– 460) – 0.00032984(T_b– 460)² (2–70) (p_c)_P= 573.011 – 1.13707(T_b– 460) + 0.00131625(T_b– 460)² (2–71)

– 0.85103(10^–6)(T_b– 460)³

(ω)_P= 0.14 + 0.0009(T_b– 460) + 0.233(10^–6) (T_b– 460)² (2–72) For naphthenes,

(T_c)_N= 156.8906 + 2.6077(T_b– 460) – 0.003801(T_b– 460)² (2-73) + 0.2544(10^–5)(T_b– 460)³

(p_c)_N= 726.414 – 1.3275(T_b– 460) + 0.9846(10^–3)(T_b– 460)² (2–74) – 0.45169(10^–6)(T_b– 460)³

(ω)_N= (ω)_P– 0.075 (2–75)

Bergman et al. assigned the following special values of the acentric factor to the C₈, C₉, and C₁₀naphthenes:

C₈ (ω)_N= 0.26 C₉ (ω)_N= 0.27 C₁₀ (ω)_N= 0.35 For the aromatics,

(T_c)_A= 289.535 + 1.7017(T_b– 460) – 0.0015843(T_b– 460)² (2–76) + 0.82358(10^–6)(T_b– 460)³

(p_c)_A= 1184.514 – 3.44681(T_b– 460) + 0.0045312(T_b– 460)² (2–77) – 0.23416(10^–5) (T_b– 460)³

(ω)_A= (ω)_P– 0.1 (2–78)

Step 4 Calculate the critical pressure, the critical temperature, and acentric factor of the undefined fraction from the following relationships:

p_c= X_P(p_c)_P+ X_N(p_c)_N+ X_A(p_c)_A (2–79) T_c= X_P(T_c)_P+ X_N(T_c)_N+ X_A(T_c)_A (2–80)

ω= X_P(ω)_P+ X_N(ω)_N+ X_A(ω)_A (2–81)

Whitson (1984) suggested that the Peng-Robinson and Bergman PNA methods are not recommended for characterizing reservoir fluids containing fractions heavier than C₂₀.

Based on Bergman et al.’s work, Silva and Rodriguez (1992) suggested the use of the following two expressions when the boiling point temperature and specific gravity of the cut are not available:

Use the preceding calculated value of T_bto calculate the specific gravity of the fraction from the following expression:

γ= 0.132467 ln(T_b– 460) + 0.0116483

where the boiling point temperature T_bis expressed in °R.

Graphical Correlations

Several mathematical correlations for determining the physical and critical properties of petroleum fractions have been presented. These correlations are readily adapted to com- puter applications. However, it is important to present the properties in graphical forms for a better understanding of the behaviors and interrelationships of the properties.

Boiling Points

Numerous graphical correlations have been proposed over the years for determining the physical and critical properties of petroleum fractions. Most of these correlations use the normal boiling point as one of the correlation parameters. As stated previously, five meth- ods are used to define the normal boiling point:

1. Volume-average boiling point (VABP).

2. Weight-average boiling point (WABP).

3. Molal-average boiling point (MABP).

4. Cubic-average boiling point (CABP).

5. Mean-average boiling point (MeABP).

Figure 2–4 shows the conversions between the VABP and the other four averaging types of boiling-point temperatures.

T M

b = ⎛

⎝⎜ ⎞

⎠⎟ + 447 08723

64 2576 460

. ln

.

FIGURE 2–4Correction to volumetric average boiling points. Source: GPSA Engineering Data Book, 10th ed. Tulsa, OK: Gas Processors Suppliers Association, 1987. Courtesy of the Gas Processors Suppliers Association.

The following steps summarize the procedure of using Figure 2–4 in determining the desired average boiling point temperature.

Step 1 On the basis of ASTM D-86 distillation data, calculate the volumetric average boiling point from the following expressions:

VABP = (t₁₀+ t₃₀+ t₅₀+ t₇₀+ t₉₀)/5 (2–82)

where tis the temperature in °F and the subscripts 10, 30, 50, 70, and 90 refer to the vol- ume percent recovered during the distillation.

Step 2 Calculate the 10% to 90% “slope” of the ASTM distillation curve from the follow- ing expression:

Slope = (t₉₀– t₁₀)/80 (2–83)

Enter the value of the slope in the graph and travel vertically to the appropriate set for the type of boiling point desired.

Step 4 Read from the ordinate a correction factor for the VABP and apply the relationship:

Desired boiling point = VABP + correction factor (2–84) The use of the graph can best be illustrated by the following examples.

EXAMPLE 2–6

The ASTM distillation data for a 55°API gravity petroleum fraction is given below. Calcu- late WAPB, MABP, CABP, and MeABP.

Cut Distillation % Over Temperature, °F

1 IBP* 159

2 10 178

3 20 193

4 30 209

5 40 227

6 50 253

7 60 282

8 70 318

9 80 364

10 90 410

Residue EP** 475

*Initial boiling point.

** End point.

SOLUTION

Step 1 Calculate VABP from equation (2–82):

VABP = (178 + 209 + 253 + 318 + 410)/5 = 273°F

Step 2 Calculate the distillation curve slope from equation (2–83):

Slope = (410 – 178)/80 = 2.9

Step 3 Enter the slope value of 2.9 in Figure 2–4 and move down to the appropriate set of boiling point curves. Read the corresponding correction factors from the ordinate to give

Correction factors for WABP = 6°F Correction factors for CABP = –7°F Correction factors for MeABP = –18°F Correction factors for MABP = –33°F

Step 4 Calculate the desired boiling point by applying equation (2–84):

WABP = 273 + 6 = 279°F CABP = 273 – 7 = 266°F MeABP = 273 – 18 = 255°F MABP = 273 – 33 = 240°F Molecular Weight

Figure 2–5 shows a convenient graphical correlation for determining the molecular weight of petroleum fractions from their MeABP and API gravities. The following example illus- trates the practical application of the graphical method.

EXAMPLE 2–7

Calculate the molecular weight of the petroleum fraction with an API gravity and MeABP as given in Example 2–6.

SOLUTION

From Example 2–6, API = 55°

MeABP = 255°F

Enter these values in Figure 2–5 to give MW = 118

Critical Temperature

The critical temperature of a petroleum fraction can be determined by using the graphical correlation shown in Figure 2–6. The required correlation parameters are the API gravity and the molal-average boiling point of the undefined fraction.

EXAMPLE 2–8

Calculate the critical temperature of the petroleum fraction with physical properties as given in Example 2–6.

SOLUTION

From Example 2–6, API = 55°

MABP = 240°F

Enter the above values in Figure 2–6 to give T_c= 600°F.

FIGURE 2–5Relationship among molecular weight, API gravity, and mean average boiling points. Source:GPSA Engineering Data Book, 10th ed. Tulsa, OK: Gas Processors Suppliers Association, 1987. Courtesy of the Gas Processors Suppliers Association.

FIGURE 2–6 Critical temperature as a function of API gravity and boiling points.

Source: GPSA Engineering Data Book, 10th ed. Tulsa, OK: Gas Processors Suppliers Association, 1987. Courtesy of the Gas Processors Suppliers Association.

Critical Pressure

Figure 2–7 is a graphical correlation of the critical pressure of the undefined petroleum fractions as a function of the mean-average boiling point and the API gravity. The follow- ing example shows the practical use of the graphical correlation.

FIGURE 2–7 Relationship among critical pressure, API gravity, and mean-average boiling points.

Source: GPSA Engineering Data Book, 10th ed. Tulsa, OK: Gas Processors Suppliers Association, 1987. Courtesy of the Gas Processors Suppliers Association.

EXAMPLE 2–9

Calculate the critical pressure of the petroleum fraction from Example 2–6.

SOLUTION

From Example 2–6, API = 55°

MeABP = 255°F

Determine the critical pressure of the fraction from Figure 2–7, to give p_c= 428 psia.