Fahim M.A., Sahhaf T.A., Elkilani A.S. Fundamentals of Petroleum Refining

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Example E3.6

Calculate the molecular weight for the cut with NBP of 216.4



C and K ¼11.94.

Solution:

This cut has a NBP of 216.4



C or 489.55 K and a speciﬁc gravity of 0.8029

from equation (3.5) knowing that K ¼ 11.94. Using equation (3.11), the

molecular weight is calculated to be 170.8.

3.4.2. Viscosity

The following equations can be used to calculate the liquid viscosities of

petroleum fractions at atmospheric pressure and at temperatures of 37.8



(100



F) and 98.9



C (210



F) (Pedersen et al., 1989):

log n

210

¼0:463634  0:166532ðAPIÞþ5:13447  10

4

ðAPIÞ

 8:48995  10

3

KðAPIÞ

8:0325  10

2

K þ1:24899ðAPIÞþ0:197680ðAPIÞ

API þ 26:786  2:6296K

ð3:12Þ

log n

100

¼ 4:39371  1:94733K þ 0:127690K

þ 3:2629  10

4

ðAPIÞ

 1:18246  10

2

KðAPIÞ

0:17161K

þ 10:9943ðAPIÞþ9:50663  10

2

ðAPIÞ

 0:860218KðAPIÞ

API þ 50:3642  4:78231K

ð3:13Þ

where n

100

and n

210

are the kinematic viscosities at 100 and 210



F, in

centistokes.

3.4.3. Refractive Index

The refractive index is a readily measured property that can be used as an

input parameter for other correlations. It is defined as the speed of light in

vacuum with respect to the speed of light in the medium. Since refractive

indices of petroleum fractions are not always known, it is important to

predict the refractive index. The following equation may be used:

n ¼

1 þ 2I

1  I



1=2

ð3:14Þ

Values of I may be calculated from:

I ¼ a expðbT

þ cSG þ dT

SGÞT

ð3:15Þ

Thermophysical Properties of Petroleum Fractions and Crude Oils 49

where a, b, c, d, e,andf are the constants varying with molecular weight range

(Table 3.4), n is the refractive index at 20



C(68



F), I is the Huang

characterization parameter at 20



C(68



F), T

is the mean average boiling

point, in degrees Rankin, M is the molecular weight of petroleum fractions,

and SG is the specific gravity of petroleum fraction, 60



F/60



Example E3.7

Calculate th e kinematic viscosities and the refractive index for oil which has a

MeABP of 320



C and API gravity of 34.

Solution:

The boilin g point is 593.15 K or 1067.7 R. Using equations (3.2) and (3.5), the

speciﬁc gravity is 0.855 and the Watson K factor is 11.95. From equations (3.12)

and (3.13)

100

¼ 5:777 cSt and n

210

¼ 1:906 cSt:

From equations (3.14) and (3.15), the refractive index n is calculated to be

1.481 (M is 257.1 as calculated from equation (3.11)).

3.4.4. Molecular Type Composition of Petroleum Fractions

The following equations are used to predict the fractional composition of

paraffins, naphthenes and aromatics (PNA) contained in both light and heavy

petroleum fractions. The viscosity, specific gravity and refractive index of the

desired fraction are used as input parameters. For heavy fractions (M > 200):

¼ a þ bðR

ÞþcðVGCÞ

¼ d þeðR

Þþf ðVGCÞ

¼ g þ hðR

ÞþiðVGCÞ

ð3:16Þ

Table 3.4 Constants for equation (3.15)

Constants Light fractions Heavy fractions

Molecular weight range 70–300 300–600

Boiling point range (



F) 90–650 650–1000

a 2.266  10

2

2.341  10

2

b 3.905  10

4

6.464  10

4

c 2.468 5.144

d 5.704  10

4

3.289  10

4

e 0.0572 0.407

f 0.720 3.333

50 Chapter 3

where a, b, c, d, e, f, g, h, and i are the constants varying with molecular

weight range as given in Table 3.5; x

, x

, and x

are the mole fraction of

paraffins, naphthenes, and aromatics, respectively; R

is the refractivity

intercept as given by the equation below

¼ n 

ð3:17Þ

where n=refractive index at 20



C (68



F) and 1 atmosphere, d is the liquid

density at 20



C (68



F) and 1 atmosphere in grams per cubic centimetre,

VGC is the viscosity gravity constant as given by equations below.

VGC ¼

10 SG  1:0752 logðV

100

 38Þ

10  logðV

100

 38Þ

ð3:18Þ

VGC ¼

SG  0:24  0:022 logðV

210

 35:5Þ

0:755

ð3:19Þ

where SG is the specific gravity at 15.6



C (60



F) and V is the Saybolt

universal viscosity at 37.8 or 98.9



C (100 or 210



F), in Saybolt universal

seconds.

The Saybolt (SUS) universal viscosity (V ) is related to the kinematics

viscosity (n) in cSt by the relation:

100

ðSUSÞ¼4:6324u

100

1þ0:03264u

100

ð3930:2þ262:7u

100

þ1:646u

100

Þ10

5

ð3:20Þ

210

ðSUSÞ¼1:0066856V

100

ðSUSÞð3:21Þ

Table 3.5 Constants for equation (3.16) and (3.24)

Constants Light fraction Heavy fractions

Molecular weight range 70–200 200–600

a 13.359 2.5737

b þ14.4591 þ1.0133

c 1.41344 3.573

d þ23.9825 þ2.464

e 23.333 3.6701

f þ0.81517 þ1.96312

g 9.6235 4.0377

h þ8.8739 þ2.6568

i þ0.59827 þ1.60988

Thermophysical Properties of Petroleum Fractions and Crude Oils 51

For light fractions, M  200, The viscosity gravity function (VGF) can be

calculated as:

VGF ¼1:816 þ 3:484 SG  0:1156 ln n

100

ð3:22Þ

VGF ¼1:948 þ 3:535 SG  0:1613 ln n

210

ð3:23Þ

In this case:

¼ a þ bðR

ÞþcðVGFÞ

¼ d þeðR

Þþf ðVGFÞ

¼ g þ hðR

ÞþiðVGFÞ

ð3:24Þ

In both cases note that: x

þ x

¼ 1

Example E3.8

Calculate the parafﬁns, naphthenes and aromatic mole fraction for the crude

having the properties listed in example E3.7.

Solution:

From example E3.7,SG¼ 0.855 then d ¼ 0.855 g/cm

n ¼ 1.481 then R

¼ 1.0535 from equation (3.17)

M ¼ 257.1 which can be considered heavy fraction

100

¼ 5.777 cSt then VGC ¼ 0.8348 from equation (3.18)

By substituting the constants for the heavy fraction, R

and VGC in

equation (3.16)

¼ 0:789; x

¼ 0:164 and x

¼ 0:046

3.4.5. Pseudo-critical Constants and Acentric Factors

Almost all the methods which are used to calculate the thermodynamic

properties and transport properties rely on the principle of corresponding

states and an equation of state. To use these methods the critical temperature

and pressure and the acentric factor are required as input constants. While

these constants are tabulated for defined components, these have to be

estimated for narrow boiling petroleum cuts or pseudo-components. The

general adopted method in this regard is to calculate these constants from two

characteristic properties; the average boiling point and the specific gravity or

API gravity. While there are several equations available such as those of Riazi

and Daubert (1980), Lee and Kessler (1976), we will use those of Lee and

Kessler because they are used as default methods in process simulators.

52 Chapter 3

3.4.5.1. Pseudo-critical Temperature

¼ 189:8 þ 450:6SGþð0:422 þ 0:1174 SGÞT

ð14; 410  100; 688 SGÞ

ð3:25Þ

where pseudo-critical temperature T

and the average boiling point T

are in K.

3.4.5.2. Pseudo-critical Pressure

ln P

¼ 5:689 SG 

0:0566

 10

3

0:436392 þ

4:12164

0:213426

þ 10

7

4:75794 þ

11:819

1:53015

 10

10

2:45055 þ

9:901

ð3:26Þ

where P

is in bars.

3.4.5.3. Acentric Factor

The equation for calculating the acentric factor depends on the value of the

reduced average NBP T

as follows:

For T

< 0.8

o ¼

ln P

 5:92714 þ 6:09648=T

þ 1:28862 ln T

 0:169347T

15:2518  15:6875=T

 13:4721 ln T

þ 0:43577T

ð3:27Þ

where P

and P

is the pressure at which T

is measured which is

atmospheric pressure.

For T

> 0.8 the equation to use is:

o ¼7:904 þ 0:1352K  0:007465K

þ 8:359T

þð1:408  0:01063KÞ=T

ð3:28Þ

where K is the Watson characterization factor.

Example E3.9

Calculate the critical temperature and pressure and the acentric factor for an oil

which has a MeABP of 320



C and 34 API gravity.

Solution:

The boiling point is 593.15 K and the speciﬁc gravity is 0.855. Using equations

(3.25) and (3.26), T

¼ 764.17K and P

¼ 15.26 bar.

The acentric factor is 0.777.

Thermophysical Properties of Petroleum Fractions and Crude Oils 53

3.4.6. Generalized Equation for Thermophysical Properties

Riazi and Al-Sahhaf (1996) presented a method for the calculation of

different properties such as the NBP, density, refractive index, critical

temperature, pressure and density, acentric factor, solubility parameter and

surface tension given only the molecular weight and using the following

general equation

y ¼ y

 expða  bM

Þð3:29Þ

where y can be any one of the properties mentioned above. M is the

molecular weight and y

is the limiting value for any property as M!1.

This generalized equation can be used to calculate the following properties

knowing the molecular weight.



, the mean average boiling point, K



SG, the specific gravity



, the liquid density at 20



Cor68





I, the Huang characterization parameter



¼ T

, the reduced boiling point which is used to calculate the

critical temperature in K



, the critical pressure in bars



, the critical density in g/cm



o, the acentric factor



s, the surface tension in dynes/cm



d, the solubility parameter, in (cal/cm

)

The constants a, b and c for each property are given in Table 3.6 .

The application of this co rrelati on is simple. You only nee d t o know

the average NBP of the petroleum fraction. First, the molecular weight

is calculated from the correlation using the const ants for the boiling

Table 3.6 Constants for the Riazi–Al-Sahhaf equation

abc

1080 6.97996 0.01964 0.67

SG 1.07 3.56073 2.93886 0.1

1.05 3.80258 3.12287 0.1

I 0.34 2.30884 2.96508 0.1

1.20 0.34742 0.02327 0.55

P

0 6.34492 0.72390 0.3

d

0.22 3.2201 0.00090 1

o 0.30 6.2520 3.64457 0.1

S 30.3 17.45018 9.70188 0.1

D 8.60 2.29195 0.54907 0.3

54 Chapter 3

point. Once the mo lecular wei ght is known, othe r proper ties ca n be

calculated using equation (3.29) with the appropriate constants from

Table 3.6.

Example E3.10

Use the Riazi and Al-Sahhaf (1996) equation to calculate the properties for an

oil which has a MeABP of 320



C and 34 API gravity.

Solution:

The molecular weight is calculated as 256 from equation (3.29) using the

boiling point. Using this value, other properties are calculated, and the values are

shown below.

SG 0.859 d

0.252

0.855 o 0.798

I 0.2824 s 28.55

773 d 8.055

12.5

3.5. Calculation of Enthalpy of Petroleum

Fractions

The design of process equipment, such as heat exchangers and com-

pressors requires the calculation of enthalpy and entropy. While there are

different methods for the calculation of thermodynamic properties, we will

concentrate in this section on Lee–Kessler method which is suitable for

hand calculation. Equations of state, such as the Soave–Redlich–Kwong

and the Peng–Robinson, are widely used in process simulation programs.

The Lee–Kessler generalized correlation (Kessler and Lee, 1976) has the

following expression for the compressibility factor:

Z ¼ Z

þ oZ

ð3:30Þ

Equation (3.30) can be used to calculate the molar volume as: V ¼ RT/P or

the mass density as r ¼ M/V.

The departure functions H  H

is given by

H  H



H  H



þ o

H  H



ð3:31Þ

Thermophysical Properties of Petroleum Fractions and Crude Oils 55

The superscripts

and

denote the value for the simple fluid and the

correction terms, respectively. These values are obtained from published

tables which can be found in standard chemical engineering thermodynam-

ics textbooks as functions of the reduced temperature and pressure (Smith

et al., 1999). The critical temperature, critical pressure and the acentric

factor for the petroleum fraction can be obtained from the equations

in Section 3.4.5. If the fraction is treated as being made up of pseudo-

components, the critical temperature, critical pressure and acentric factor

can be calculated using the following simple mixing rule equations:

o ¼

ð3:32Þ

Where y

is the mole fraction of each pseudo-component.

The enthalpy change of a fluid from state 1 at T

and P

to state 2 at T

and P

is given by:

 H

¼ðH

 H

ÞþðH

 H

ÞðH

 H

Þð3:33Þ

To calculate the enthalpy with respect to a reference state set, H

¼H

ref

¼0.

If the reference state is at low pressure (ideal gas), then ðH

 H

Þ¼0.

The enthalpy equation becomes

H ¼ðH  H

ÞþðH

 H

ref

Þð3:34Þ

The ideal gas enthalpy change is calculated from the integration of the ideal

gas heat capacity with temperature:

 H

dT ð3:35Þ

The ideal gas heat capacity for petroleum fractions is given by

¼ A þ BT þ CT

ð3:36Þ

Integration of equation (3.36) yields:

 H

¼ AðT

 T

Þþ

ðT

 T

Þþ

ðT

 T

Þð3:37Þ

56 Chapter 3

The constants A, B, and C can be estimated from the following relations

proposed by Lee and Kessler as:

A ¼ 4:1843Mð0:33886 þ 0:02827K  0:26105 CF þ 0:59332o CFÞ ð3:38Þ

B ¼7:5318M



ð0:9291  1:1543K þ 0:0368K

Þ10

4

þ CFð4:56  9:48oÞ10

4



ð3:39Þ

C ¼ 13:5573M



 1:6658  10

7

þ CFð0:536  0:6828oÞ10

7



ð3:40Þ

where

CF ¼

ð12:8 KÞð10  KÞ

10o



ð3:41Þ

K is the Watson characterization factor and M is the molecular weight. The

calculated heat capacity in equation (3.36) with T in K is in kJ/(kg mol K).

To convert the value to kJ/(kg K), divide by M.

Example E3.11

Calculate the molar volume and enthalpy of an oil at 450



C and 3.45 bar. The

oil has a MeABP of 320



C and 34 API gravity. The reference state is ideal gas at

298 K.

Solution:

The speciﬁc gravity is 0.855 and the K factor is 11.95 . Using equations (3. 25)

and (3.26): T

¼ 765.5 K and P

¼ 15.26 bar. The acentric factor is 0.777. The

molecular weight from equation (3.11) is 257.12.

¼ 0:9447 and P

¼ 0:2261:

From the Lee–Kessler tables:

¼ 0:9029; Z

¼0:0325

Z ¼ 0 :9029 þð0:777Þð0:0325Þ¼0:8776

V ¼

ZRT

ð0:8776Þð8:3143Þð450 þ 273:15Þ

0:345

¼ 15294:5cm

=mol

From the Lee–Kessler tables:

H  H



¼0:1487;

H  H



¼0:2882

Thermophysical Properties of Petroleum Fractions and Crude Oils 57

From equation (3. 31),

H  H



¼0:1487 þð0:777Þð0:2882Þ¼0:3727

ðH  H

Þ¼2371:9kJ=kg mol

For the ideal heat capacity and from equations (3.38) to (3.41)

A ¼ 8:74721; B ¼ 1:44929 and C ¼ 0:000581

From equation (3. 37) and for temperatures between 298 and 723.15 K;

 H

¼ AðT

 T

Þþ

ðT

 T

Þþ

ðT

 T

ðH

 H

ref

Þ¼312; 088:8kJ=kg mol

Therefore,

From equation (3.34)

H ¼ðH  H

ÞþðH

 H

ref

Þ¼2371:9 þ 312; 088:8

H ¼ 309; 717 kJ=kg mol or 1223 kJ=kg

3.6. Estimation of Properties Related to

Phase Changes

In petroleum refining, crude oil and petroleum fractions are separated

into narrower fractions by unit operations that utilize the phase equilibrium

between the hydrocarbons in the liquid and vapour phases such as distilla-

tion, adsorption, condensation and evaporation. When water is present,

such as the case in the atmospheric distillation column, liquid–liquid–vapour

equilibrium is encountered.

Equilibrium K

values, that is (y

) are the fundamental building blocks

of all unit operations involving phase change. Traditional older methods for

calculations of K

values rely on methods or charts which are based on

temperature and pressure only with no composition dependence.

3.6.1. Cubic Equations of State

With the development of more accurate equations of state and with the

widespread use of computer simulation in process design, these methods are

replaced with computer packages which rely on equations of state for phase

58 Chapter 3