Petroleum Refining – Chapter 4: Characterization

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Chapter 4

Numerical Methods for Characterization and Properties Estimation of Petroleum Fuels

Introduction

Methods

Liquid Viscosity

1. The absolute (or dynamic) viscosity.

Defined as the ratio of shear resistance to the shear velocity gradient.

This ratio is constant for Newtonian fluids.

Expressed in Pa.s (poise)

Commonly used unit is mPa.s (centipoise, cP)

2. The kinematic viscosity.

Defined as the ratio between the absolute viscosity and the density.

Expressed in mm2/s (centistokes, cSt)

The liquid dynamic viscosities at 100 ºF and 210 ºF are used to characterize (heavy)

petroleum fractions.

When the viscosities are not known one of the following relations can be used to estimate

them. Abbott et al (1971) for example uses the Watson characterization factor (Kw) and API

gravity (A) to predict viscosity at 100 and 210 °F as follows

𝑙𝑜𝑔𝑣100 = 4.39371 − 1.94733 𝐾𝑤 + 0.12769 𝐾𝑤2

+ 3.2629. 10−4𝐴2 − 1.18246. 10−2𝐾𝑤𝐴

+ (0.171617𝐾𝑤

2 + 10.9943𝐴 + 9.50663. 10−2 𝐴2 − 0.860218 𝐾𝑤𝐴)

(𝐴 + 50.3642 − 4.78231𝐾𝑤)

𝑙𝑜𝑔𝑣210 = 0.463634 − 0.166532 𝐴 + 5.13447. 10−4𝐴2 − 8.48995. 10−3𝐾𝑤𝐴

+ (8.0325. 10−2 𝐾𝑤 + 1.24899𝐴 + 0.19768 𝐴2)

(𝐴 + 26.786 − 2.6296𝐾𝑤)

where

Kw = Watson characterization factor

A = gravity in degrees API

v100 = viscosity at 100 ℉ [mm2/s]

v210 = viscosity at 210 ℉ [mm2/s]

log = common logarithm (base 10)

notes:

Should not be used if Kw < 10 and A < 0.

Recommended for the following range;

0.5 < v100 < 20 mm2/s

Copyright © 2001-2015 Dr. Tareq Albahri, Chemical Engineering, Kuwait University

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0.3 < v210 < 40 mm2/s

Average error about 20%.

Source: M. M. Abbott, T. G. Kaufmann and L. Domash. A correlation for predicting liquid

viscosities of petroleum fractions. The Canadian Journal of Chemical Engineering, Volume 49,

Issue 3, pages 379–384, 1971 (DOI: 10.1002/cjce.5450490314)

Riazi method

Molecular Weight

Can be estimated with two different means (5% ave error)

1. From the normal BP and standard specific gravity.

Riazi method: for light fractions

(sp.gr. < 0.97 & Tb < 840 K).

M = 42.965 (Tb1.26007 S4.98308) [exp(2.097.10-4 Tb – 7.78712 S + 2.08476.10-3 Tb S)]

Lee-Kesler: for heavy petroleum fractions (Tb > 600 K & 60 < MW < 650).

7

2

12

2

3

12272.6 9486.4 (8.3741 5.9917 )

10 222.466 (1 0.77084 0.02058 ) 0.7465

10 17.3354 (1 0.80882 0.02226 ) 0.32284

b

b b

b b

M S T S

S ST T

S ST T

where

M = Molecular weight [kg/kmol].

Tb = Normal boiling point [K].

S = Standard specific gravity.

2. From the viscosities at 210 ºF and 100 ºF and the standard specific gravity (ave. error is 10%).

(1.1228 1.2435) (3.4758 3.038 ) 0.6665

100 210223.56 S SM S

where

M = Molecular weight [kg/kmol].

v100 = viscosity at 100 ºF [mm2/s].

v210 = viscosity at 210 ºF [mm2/s].

S = Standard specific gravity.

Aniline Point (AP)

The equation of Albahri et al. gives the aniline point in ºC, Ri is the refractivity intercept, n is the

refractive index, d is liquid density at reference state of 20⁰C and 1 atm. in g/cm3, Tb is the boiling

point in K, and I is an index in refractive index.

Petroleum Refining – Chapter 4: Characterization

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Ri = n – d/2

n = [(1+2I)/(1–I)]0.5

I = 0.3824 (1.8Tb)-0.02269 SG0.9182

d = 0.98255 (1.8Tb)0.002016 SG1.0055

AP (ºC) = – 9805.269 (Ri) + 711.85761(SG) + 9778.7069

(18)

Pseudo-Critical Constants for Petroleum Fractions.

To make use of the principle of corresponding states.

Use the method of Lee-Kesler (ave. error 10%)

1. Pseudo-Critical Temperature.

189.8 450.6 (0.4244 0.1174 )

(14,410 100,688 )

C b

b

T S T S

S

T

where,

Tc = Pseudo-critical temperature [K].

Tb = Normal boiling point [K].

S = Standard specific gravity.

2. Pseudo-Critical Pressure

3

2

7 2

2

10 3

2

0.0566ln 5.68925

4.12164 0.213426 10 0.436392

11.819 1.53015 10 4.75794

9.901 10 2.45055

C

b

b

b

PS

TS S

TS S

TS

where,

Pc = Pseudo-critical pressure [bar].

ln = Napierian logarithm

Tb = Normal boiling point [K].

S = Standard specific gravity.

Acentric Factor for Petroleum Fractions.

For Tr < 0.8

27.904 0.1352 0.007465

1.408 0.1063 8.359

W W

W

br

br

K K

KT

T

b

br

c

TT

T

where

Copyright © 2001-2015 Dr. Tareq Albahri, Chemical Engineering, Kuwait University

4-4

ω = acentric factor.

Tbr = reduced boiling point temperature.

Kw = Watson characterization factor.

For Tr > 0.8 (use Edmister's equation)

3(log 1.0057)

7 1c

xP

x

where b

c

Tx

T and

Pc = Pseudo-critical pressure [bar].

Tc = Pseudo-critical temperature [K].

log = common logarithm (base 10)

Tb = Normal boiling point [K].

Specific Heat of Petroleum Fraction in the Ideal Gas State

5432325.2 FTETDTCTBTAH gp

432 5432185.4 FTETDTCTBC pgp

'8.1 TT

SKB W

2846.029502.002972.035644.0

'24

05543.05524.19247.22

10CKKC WW

SC

0694.50283.6'

0844.06946.13

10 7

D

2

410.7.0885.010

118.12

SS

KK WW

Kw = Watson characterization factor

S = standard specific gravity

Flash Point, The API method (error 5°C)

TT

T f

ln 10

10

0034254.084947.2

02421.0

1

T10 = temperature at the 10% volume distilled point from ASTM D86 [k].

Liquid Enthalpy

Petroleum Refining – Chapter 4: Characterization

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HL = A1 7.259T A2 22 7.259T A3 33 7.259T

A1= 10 -3

WW

KK 4653582.1149)907.24722.23(26.1171

A2= 10 -6

817.13086.56)82463.00.1( WK

A3= -10 -9

3653.26757.9)82463.00.1( WK

Temperature (T)

Specific Gravity (SG)

Characterization Factor (Kw)

Vapor enthalpy

266.5507.4 512.0

64.0 8.0

33

3

22

21

C

O

C

C

CCLV

RT

HH

MW

RTTTB

TTBTTBHH

SBKB W

46.24802.29572.2944.356310

41

SBKKB WW

46.25342.301)772.262.77(24.146610

42

4

95.2487.569103 BB

2

107.0885.00.10

0.10.18.12 4

4

SS

KKB

WW

HL = Liquid Enthalpy of Petroleum Fractions

T = Temperature

Tc = Critical Temperature

R = Gas Constant

MW = Molecular Weight

ω = Acentric Factor

S = Specific Gravity

KW = Watson Characterization Factor

(Ho- H)/RTC = Pressure Effect on Enthalpy

Hv = Vapor Enthalpy of Petroleum Fractions

Calculation of Density by the Lee and Kesler Method

Copyright © 2001-2015 Dr. Tareq Albahri, Chemical Engineering, Kuwait University

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RTz

PM

VT

VVc

Vri

Di

Vri

Ci

Vri

Bi

Tr

Vrizi

T

ddD

T

c

T

ccC

T

b

T

b

T

bbB

ww

wwZZZZ

ZZwZZ

l

l

rir

ri

ii

ri

ii

r

iii

r

i

r

iii

r

i

r

i

r

iii

23

224

52

21

3

321

3

4

2

321

12

1121

121

)exp()(

1Pr

)(

)('''5138.2

Pressure for Saturation

exp[ ( , )]m ms c r mP P f T

0 0( , ) ln ln

mr m r m rf T P P

6

0

6.09648ln 5.92714 1.28862ln 0.169347

m m

m

r r r

r

P T TT

1

615.6875ln 15.2518 13.4721ln 0.43577

r m m

m

r r

r

P T TT

Pressure Correction for Density

1 ln1 s

s

B PC

B P

0.0861488 0.0344483 mC

4

1

a 1k

cm k

k

B P

1/3

1mr

T

Estimation of the pour point (page 172): )333.031.0(

100

)474.0612.0(971.247.130SS

EC vMST

Estimation of the Interfacial Tension of Petroleum fractions: (page 167)

Kw

Tcff

232.1]15.293

1[7.673

Petroleum Refining – Chapter 4: Characterization

4-7

Thermal Conductivities of Liquids: (page 132)

TEl 4418.117.0

Influence of Pressure on the Viscosity of Liquids (Kouzel's method):

)4479.14829.5)((log 181.0 EMsEPsPMs

M

Specific Heats for liquid Petroleum Fractions (Lee Kessler 1975) Page 121:

))410*508.5310*467.1(16734.03065.0)(055.035.0(185.4 STSKwl

Cp