Gawish SPE Paper

8/11/2019 Gawish SPE Paper

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This paper was prepared for presentation at the 2005 SPE Technical Symposium of Saudi Arabia

Section held in Dhahran, Saudi Arabia, 14-16 May 2005.

Copyright 2005 Society of Petroleum Engineers

This paper was selected for presentation by the Technical Symposium Program Committee following

review of information contained in full manuscript submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum E ngineers and are subject to correction

by the author(s). The material, as presented, does not necessarily reflect any position of the Society of

Petroleum Engineers, its officers, or members.

ABSTRACT

The influence of fluid viscosity on flow is especially importantin petroleum reservoirs. Gas is now a highly desirable

hydrocarbon resource. An accurate prediction of transport

properties of natural gases is very important in the design and

operation of fluid transportation, production, and processing.

Viscosity is one of these properties. Many viscositycorrelations are available but each has limitations in the range

of applicability1-7

. Only the Carr et al8-12

. charts include the

correction for gas impurities and reservoir pressure andtemperature. Using Carr et al. charts you have to follow five

steps to find the natural gas viscosity at any condition. As a

results, some errors and inaccurated will occur and more time

will be consumed. Standing13,14

proposed a convenientmathematical expressing for calculation the viscosity of the

natural gas at atmospheric pressure and reservoir temperature,

1. Standing also presented equations for describing the effectsof impurities on 1. Dempsey

15expressed the viscosity ratio

(the viscosity at high pressure to the viscosity at 1 atm), by

using reduced pressure and temperature.

Using the Standing equation and the slightly revised Dempseyequation, the natural gas viscosity at high pressure can be

found by one step only. It includes all corrections for gas

impurities. Its also includes any condition at the reservoirpressure and temperature.

BackgroundNatural gas is a homogeneous fluid of low density andviscosity. The high pressure and temperature cause a decrease

in viscosity even at temperatures above the critical. Thevariation in viscosity with molecular weight of gases at

atmospheric pressure is opposite to the variation for liquids,

the viscosity decreases with increase in molecular weight of

gases. The natural gas properties may be obtained from

The Rolling-ball viscosimeter may give viscocities as much as

30% higher when measurment of gas viscosity is taken underpressure. The preferred instrument for gases is the Rankine

viscosimeter in which the pressure gradient for the fluidflowing through the capillary can be very small. The naturalgas viscosity is described by the following function,

( )ig YTPf ,,= 1This relationship simply states that the viscosity of a pure gas

is function of pressure and temperature, but for gas mixture, it

is also a function of the gas composition. Gas viscosity can be

predicated from generalized mathematical expressions.

Herning and Zipperer

Herning and Zipperer

16

method proposed the followingequation to calculate the viscosity of a mixture of gaseous

components.

( )

=

i ii

iigi

gMy

My

)(

2

Where the analysis of the gas mixture is known and the

viscosities of the components are known at the pressure and

temperature of interest.

Dean and Stiel MethodDean and Stiel

17 proposed the following mathematical

expressions for calculating the viscosity of natural gases atatmospheric pressure and reservoir temperature.

m

rT

9

8

5

1

)(*)10(34

= , for Tr=< 1.5 3

m

rT

95

5

1

]0932.01338.0)[10(8.166 =

, for Tr >1.5 4

Where the mis the viscosity parameter of the gas mixture anddefined by the following equation.

32

5.0

61

)()(

)(4402.5

ca

c

m

PMW

T= 5

Dean and Stiel recommended the following equation for

SPE 106326

State of the Art - Natural Gases Viscosity under Reservoir ConditionsAhmed Gawish and Emad Al-HomadhiKing Saud University


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Where:

r

rr

ZT

P27.0= 7

The Lee-Gonzalez Eakin MethodLee et al

8,19 presented a semi-empirical relationship for

calculating the natural gases viscosity. The authors expressedthe gas viscosity in terms of reservoir temperature, gas gravity,

and molecular weight of the gases. Their proposed equation isgiven by:

=

Y

g

g XK4.62

*exp**10 4

8

where: ( ) TMTMK

a

a

+++=

*1920902.04.9

5.1

9

aMT

X 01.0986

5.3 ++= 10

XY 02.4.2 = 11

The proposed above correlation can predict viscosity valueswith a standard deviation of 2.7% and a maximum deviation

of 8.99%. This correlation is valid for 10 < P < 8000 psia , 100

< T < 340oF, and 0.9 < CO 2 < 3.2 mol.%.

Bicker and Katz20

presented a plot of the viscosity of paraffingases at 1 atm as a function of molecular weight. This plot was

slightly revised by Carr, Kobayashi, and Burrows1. It provides

a rapid and reliable method for obtaining the viscosity of

natural gases at 1 atm pressure from knowledge of the gas

gravity and temperature alone. This viscosity must be

corrected for the presence of non-hydrocarbon fractions tends

to increase the viscosity of the gas. Insert plots on Carr et alviscosity charts show corrections for the non-hydrocarbon, the

presence of low concentration of non-hydrocarbon gases, such

as hydrogen sulfide, nitrogen, and carbon dioxide. The effect

of the presence of each of the non-hydrocarbons is to increasethe viscosity of the hydrocarbon gas mixture.

Carr, Kobayashi, and Burrows1 extended the correlation of

Comings et al21

to higher pressures and to complex mixturesof gases. For natural gases, the widely used Carr et al

correlations take the forms:

)....,(1

GasGravityorTMfg =

and, ),(1

rr

g

gTPf=

In 1954 Carr et8 developed graphical correlations for

estimating the viscosity of natural gas as a function oftemperature, pressure and gas gravity or molecular weight.

When mixtures are involved, the pseudocritical pressures and

temperatures of typical natural gases may be estimated from

gas gravity alone. For gases with appreciable concentrations ofgas impurities, the pseudo critical conditions may be

computed from compositions. The gas viscosities can be

obtained from the charts of Carr et al. when gas gravity and

concentration of the non-hydrocarbon constituent are known.Both pseudo-critical pressure and temperature are required

parameters for gas calculations. Available publications have

reported multi-equations to calculate these values for natural

gases. A new correlation was developed with wideapplications and efficient for gas specific gravities varyied

from 0.55 to 1.2.22,23

The critical pressure and temperature equations are:

SGT

SGP

c

c

*0864.3087.173

*541243.50194514.703

+=

=

12

The corrected pseudo-critical temperature and pressure are

presented below:

)1( 22

'

'

'

SHSHC

CC

C

CC

yyT

TP

P

TT

+=

= 13

)(15))()((1204

2

5.0

2

6.1

22

9.0

22 SHSHSHCOSHCO yyyyyy +++= 14

Standing (1977)6,7 proposed a convenient mathematical

expression for calculation the viscosity of the natural gas at

atmospheric pressure and reservoir temperature, 1. Standingalso presented equations for describing effect of impurities on

1. The proposed relationships are:

( ) ( ) ( ) ( ) SHNcoduncorrecte 22211 +++= 15

)log(*10*15.610*188.8)460(

*)*10*062.210*709.1()(

33

65

1

g

g

T

duncorrecte

+

= 16

]59.9)log(*48.8[10*),( 322 +=

gNyN

17

]24.6)log(*08.9[10*),( 322 +=

gCOyCO 18

]73.3)log(*49.8[10*),(3

22 +=

gSHySH 19

Dempsey8 1965 expressed the viscosity ratio by the followingrelationship.

)()(

)(

3

15

2

141312

33

11

2

1098

2

3

7

2

654

3

3

2

210

1

rrrrrrrr

rrrrrrr

g

r

PaPaPaaTPaPaPaaT

PaPaPaaTPaPaPaaTLn

++++++++

+++++++=

20


3/11

XLng =

1

Where:(X)=

++++++++

+++++++

)()()(

)(

3

15

2

141312

33

11

2

1098

2

3

7

2

654

3

3

2

210

rrrrrrrrr

rrrrrrr

TLnPaPaPaaTPaPaPaaT

PaPaPaaTPaPaPaa

21

)(

1

Xe

g =

22

)(

*11

X

g e = 23Results and discussion

The natural gas viscosity is computed from this program easily

by using the Standing and the revised Dempsey equations. Thenatural gas viscosity is calculated at one atmospheric pressure

using the Standing equation, and all the corrections for gas

impurities are done by using equation (16). The natural gasviscosity is corrected for any pressure value by using the

revised Dempsey equation (equation 23).

Figure (1) shows the natural gas viscosity at 1 atm fordifferent specific gas gravities (0.55-3.75) and temperature

(50-4000F) of the reservoir without impurties while figure (2)

shows the gas viscosity with corrections taking into

consideration the non-hydrocarbon impurities effects on gasviscosity. The figures are the same as Carr et al.chart. Figure

(3) shows the ratio of gas viscosity at reservoir pressure to theviscosity at 1 atm pressure as a function of the reduced

pressure and temperature. This figure is also the same as Carr

et al. chart. Figure (4) shows the gas viscosity for differentpressure values as a function in temperature. This chart is the

result of the spread sheet program in table (1). Figure (5)

shows the natural gas viscosity as a function of reducedpressure and temperature for any gas gravity or molecular

weight. Fig. (5) is plotted at semi-log scale.

Table (1) represents a spread sheet program for all calculationsin order to find the natural gas viscosity with and without any

presence of impurities and at any pressure and temperature

values. By interring the values for impurities, gas gravity,pressure, and temperature in overshadow cells (input data), the

critical pressure and temperature, and corrected criticalpressure and temperature for impurities, reduced pressure andtemperature are calculated. The natural gas viscosity at

reservoir conditions can be calculated directly without usingany charts.

Designing and evaluating existing correlations for gas

viscosity

In table (2) the spreed sheet program for calculating gasviscosity by using different gas viscosity correlations includes

micros for solving z-factor The figures (6 to 13) show the gas

The gas viscosity increase in a linear relation with increasing

reservoir pressure at a low gas gravity, but not a linear for a

higher gas gravity during the test pressure periods.

Conclusions

1. Many errors will be eliminated and time will be saved byusing the new charts and the spread sheet program.

2. The results become very important and will help to

calculate the value of the natural gas viscosity at any

condition.

3. This program can easily respond to the changes in the gasfluid properties and impurities for producing tables and

charts, which can be used for the prediction of the natural

gas viscosity.

4. For any gas at different values of pressure and temperature,

and with any kind of impurities, it is easy to find the

natural gas viscosity from spread sheet program.

5. The design and evaluation of most gas correlations in one

sheet program become easy.

Nomenclatures

g = Gas viscosity at reservoir pressure and temperature, cp1= Gas viscosity at atmospheric pressure and reservoir temperature, cp

r= Reduced gas density as defined by:g= Ib/ft3, =cp, Ma= molecular weight of gas, and T= R

o.

'' , cc PTare corrected critical temperature (oR) and pressure (psia).

T Rreservoir temperature, oR,

g Gas gravity, and, andyN2, yCO2, and yH2Smole fraction of N2, CO2, and H2S.

Table (4 ) for constant used in gas correlations.

a0 -2.46211820 a8 -0.793385648

a1 2.970547414 a9 1.39643306a2 -0.286264054 a10 -0.149144925

a3 0.00805420522 a11 0.00441015512

a4 2.080860949 a12 0.0839387178a5 -3.49803305 a13 -0.18648848

a6 0.3603702 a14 0.0203367881

a7 -0.01044324 a15 -0.000609579263

References:

1. Kumar Sanjay,:"Gas Production Engineering" volume (4) Chapter

(1) Gulf Publication Company, Houston, Texas 1987.

2. Ikoku Chi U.,:"Natural Gas Production Engineering", Jone Wiley

& Sons Inc., Canada, Toronto, 1984.

3. Katz D. et al "Handbook of Natural Gas Engineering", 1959 byMcGraw-Hill Book Company, Inc. Printed in the USA, New

York, Toronto, and London.


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0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0 20 40 60 80 100

Molecular Weight

Viscosityat1atm,cp

50 oF 100 oF 150 oF 200 oF

250 oF 300 oF 350 oF 400 oF

Fig. (1) Viscosity of the Sweet Natural Gases at 1.0 atm.

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0 20 40 60 80 100

Molecular Weight

Viscosityat1atm,cp

50 oF 100 oF 150 oF 200 oF

250 oF 300 oF 350 oF 400 oF

Fig. (2) Viscosity of the Natural Gases at 1.0 atm. with Impurities Corrections.

1

10

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Pseudo Reduced Temperature

Viscosity

R

atio

1 2 3 4 5

6 8 10 15 20

Fig. (3) Viscosity Ratio versus Pseudo Reduced Temperature.

0.01

0.10

1.00

0 0.5 1 1.5 2 2.5 3

Pseudo Reduced Temperature

N.

Gas

Viscosity,cp

1 2 3 4 56 8 10 15

Fig. (4) Viscosity versus Pseudo Redued Temperature.

Pr


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6

0.01

0.10

1.00

0 200 400 600 800 1000

Temperature, oF

N.

gas

Viscosity,

cp

612 1225 1837 2450 3062 3675

4900 6125 9187

Pressure, psi

Fig. (5) Viscosity versus Temperature for Different Pressures .

Sp.Gr.=0.7

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Pressure, psi

Viscosity,cp

Dempsey

Lee

Dean & Stiel

Fig. (6) Viscosity versus Temperature for Different Preesures at 0.7 Sp.Gr.

Sp.Gr.= 0.8

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Pressure, psi

N.

G

as

Viscosity

Dempsey

Lee

Dean & Stiel

Fig. (7) Viscosity versus Temperature for Different Pressures at 0.8 Sp.Gr.

Sp.Gr.=0.9

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Pressure, psi

N.

GasViscosity

Dempsey

Lee

Dean & Stiel

Fig. (8) Viscosity versus Temperature for Different Pressures at 0.9 Sp.Gr


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8

Sp.Gr=1.4

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Pressure, psi

GasViscosity,cp

Dempsey

Lee

Dean & Stiel

Fig. (13) Viscosity versus Temperature for Different Preesures at 1.4 Sp.Gr.


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Table (1) Spread Sheet Program for Calculate Natural Gas Viscosity by Dempsey Correlation.

Step 1 Enter the values of impur ties in overshadow cells

YN2 0.05 YCO2 0.05 YH2S 0.2 28.09

Step 2 Enter the value of gas sp. Gr.

SG 0.6 or Mw 17.4

Tc 358.55

Pc 672.87

T'c 330.46

P'c 612.48

Step 3 Enter pseudo reduced pressure and temperature

P 612 1225 1837 2450 3062 3675 4900 6125 9187 12250

Pr 1 2 3 4 5 6 8 10 15 20

T Tr ln(g/g1) ln(g/g1) ln(g/g1) ln(g/g1) ln(g/g1) ln(g/g1) ln(g/g1) ln(g/g1) ln(g/g1) ln(g/g1)

330 1 0.27 0.79 1.23 1.58 1.86 2.07 2.32 2.40 2.33 2.70

397 1.2 0.16 0.52 0.83 1.09 1.30 1.47 1.70 1.82 1.89 2.14

463 1.4 0.09 0.34 0.55 0.74 0.90 1.03 1.24 1.38 1.55 1.72

529 1.6 0.05 0.21 0.36 0.49 0.61 0.72 0.90 1.05 1.28 1.41

595 1.8 0.03 0.14 0.24 0.33 0.42 0.51 0.67 0.81 1.06 1.19

661 2 0.03 0.10 0.17 0.24 0.31 0.38 0.51 0.64 0.90 1.03

727 2.2 0.03 0.08 0.14 0.19 0.25 0.30 0.42 0.53 0.77 0.92

793 2.4 0.04 0.08 0.12 0.17 0.22 0.26 0.35 0.45 0.66 0.84

859 2.6 0.04 0.07 0.11 0.15 0.19 0.23 0.31 0.38 0.57 0.76

925 2.8 0.03 0.06 0.09 0.12 0.15 0.19 0.25 0.31 0.48 0.66

991 3 0.00 0.02 0.04 0.06 0.08 0.11 0.16 0.23 0.39 0.53

Step 4 Natural gas viscosity ratio will be calculated

P 612 1225 1837 2450 3062 3675 4900 6125 9187 12250

Pr 1 2 3 4 5 6 8 10 15 20

T Tr (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1)

330 1 1.31 2.21 3.42 4.87 6.42 7.91 10.17 11.07 10.30 2.70

397 1.2 1.17 1.69 2.30 2.98 3.68 4.36 5.48 6.17 6.65 2.14

463 1.4 1.09 1.40 1.74 2.09 2.45 2.81 3.45 3.96 4.70 1.72

529 1.6 1.05 1.24 1.43 1.64 1.84 2.05 2.46 2.84 3.58 1.41

595 1.8 1.03 1.15 1.27 1.40 1.53 1.67 1.95 2.24 2.90 1.19

661 2 1.03 1.10 1.19 1.27 1.36 1.46 1.67 1.90 2.45 1.03


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Continues Table (1) Spread Sheet Program for Calculate Natural Gas Viscosi ty by Dempsey Correlation.

T Tr (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1) (g/g1)

727 2.2 1.03 1.09 1.15 1.21 1.28 1.36 1.52 1.69 2.15 0.92

7932.4

1.04 1.08 1.13 1.18 1.24 1.30 1.43 1.56 1.94 0.84859 2.6 1.04 1.08 1.12 1.16 1.21 1.26 1.36 1.47 1.77 0.76

925 2.8 1.03 1.06 1.09 1.13 1.17 1.20 1.28 1.37 1.62 0.66

991 3 1.00 1.02 1.04 1.06 1.09 1.11 1.18 1.25 1.47 0.53

Step 5 Natural gas viscosity at any pressure will be calculated

P 612 1225 1837 2450 3062 3675 4900 6125 9187 12250

Pr 1 2 3 4 5 6 8 10 15 20

T Tr g g g g g g g g g g

330 1 0.0206 0.0349 0.0539 0.0767 0.1011 0.1246 0.1602 0.1744 0.1622 0.0426397 1.2 0.0197 0.0284 0.0387 0.0501 0.0619 0.0732 0.0921 0.1037 0.1118 0.0360

463 1.4 0.0195 0.0250 0.0310 0.0373 0.0438 0.0501 0.0616 0.0706 0.0840 0.0307

529 1.6 0.0199 0.0234 0.0271 0.0309 0.0349 0.0388 0.0466 0.0537 0.0677 0.0266

595 1.8 0.0206 0.0229 0.0253 0.0279 0.0305 0.0333 0.0389 0.0447 0.0578 0.0237

661 2 0.0216 0.0232 0.0249 0.0267 0.0287 0.0307 0.0351 0.0398 0.0515 0.0216

727 2.2 0.0228 0.0240 0.0253 0.0267 0.0283 0.0299 0.0335 0.0373 0.0475 0.0203

793 2.4 0.0239 0.0250 0.0261 0.0274 0.0286 0.0300 0.0329 0.0361 0.0448 0.0193

859 2.6 0.0250 0.0260 0.0270 0.0281 0.0292 0.0304 0.0328 0.0354 0.0427 0.0182

925 2.8 0.0259 0.0267 0.0276 0.0285 0.0294 0.0303 0.0323 0.0345 0.0408 0.0166

991 3 0.0263 0.0268 0.0273 0.0279 0.0285 0.0292 0.0309 0.0329 0.0386 0.0140


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Table (2) Spread Sheet Program for Calculate of the Existing Correlations for Natural Gas Viscosity

YN2 0.05 YCO2 0.05 YH2S 0.2 28.09

Sp. Gr. 0.6 T ABS. 600 T oF = 140

Tc 358.55 1 0.0127 Standing

Pc 672.87 1 0.0121 Dean & Stiel when Tr

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Gawish SPE Paper