viscosity and densety correlations

PLEASE SCROLL DOWN FOR ARTICLE

This article was downloaded by: [Canadian Research Knowledge Network]On: 19 April 2011Access details: Access Details: [subscription number 932223628]Publisher Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Petroleum Science and TechnologyPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713597288

Viscosity and Density Correlations for Hydrocarbon Gases and Pure andImpure Gas MixturesA. A. AlQuraishia; E. M. Shokirb

a Oil and Gas Centre, King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia b

Petroleum and Natural Gas Engineering Department, King Saud University, Riyadh, Saudi Arabia

To cite this Article AlQuraishi, A. A. and Shokir, E. M.(2009) 'Viscosity and Density Correlations for Hydrocarbon Gasesand Pure and Impure Gas Mixtures', Petroleum Science and Technology, 27: 15, 1674 — 1689To link to this Article: DOI: 10.1080/10916460802456002URL: http://dx.doi.org/10.1080/10916460802456002

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article may be used for research, teaching and private study purposes. Any substantial orsystematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply ordistribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae and drug dosesshould be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directlyor indirectly in connection with or arising out of the use of this material.

http://www.informaworld.com/smpp/title~content=t713597288

http://dx.doi.org/10.1080/10916460802456002

http://www.informaworld.com/terms-and-conditions-of-access.pdf

Petroleum Science and Technology, 27:1674–1689, 2009

Copyright © Taylor & Francis Group, LLC

ISSN: 1091-6466 print/1532-2459 online

DOI: 10.1080/10916460802456002

Viscosity and Density Correlations for

Hydrocarbon Gases and Pure and

Impure Gas Mixtures

A. A. AlQuraishi1 and E. M. Shokir2

1Oil and Gas Centre, King Abdulaziz City for Science and Technology,

Riyadh, Saudi Arabia2Petroleum and Natural Gas Engineering Department, King Saud University,

Riyadh, Saudi Arabia

Abstract: In this work, newly developed correlations for hydrocarbon gas viscosity

and density are presented. The models were built and tested using a large database of

experimental measurements collected through extensive literature search. The database

covers gas composition, viscosity, density, temperature, pressure, pseudoreduced pres-

sure and temperature and compressibility factor for different gases, and pure and

impure gas mixtures containing high amount of pentane plus and small concentra-

tion of nonhydrocarbon components. Gas viscosity and gas density models were

built with 800 randomly selected data points extracted from the large database.

The models were developed using the Alternating Conditional Expectations (ACE)

algorithm. The models’ accuracy was validated using the rest of the database, and

their efficiency was tested against some commonly used correlations. The devel-

oped models seemed very efficient and they accurately predicted the experimen-

tal viscosity and density measurements, overcoming several constraints limiting the

other correlations’ accuracy with average absolute errors of 3.95% and 4.93% for

the gas viscosity and gas density models, respectively. Sensitivity analysis of the

proposed gas viscosity model indicated the positive impact of density and pseu-

doreduced temperature and the trivial impact of pseudoreduced pressure. The gas

density model was found to be sensitive to all input parameters of pseudoreduced

temperature, apparent molecular weight, and pseudoreduced pressure listed on the

order of their impact. Negative impact was predicted for reduced temperature, whereas

positive ones werenoticed for the pseudoreduced pressure and gas apparent molecular

weight.

Keywords: alternating conditional expectations algorithms, density, natural gas, vis-

cosity

Address correspondence to Abdulrahman A. AlQuraishi, Oil and Gas Centre,

King Abdulaziz City for Science and Tech., P. O. Box 6086. Riyadh 11442, Saudi

Arabia. E-mail: [email protected]

1674

Downloaded By: [Canadian Research Knowledge Network] At: 20:38 19 April 2011

Viscosity and Density for Hydrocarbon Gases 1675

INTRODUCTION

Gas in general is a fluid characterized by low viscosity and density that has

no specific shape or volume but expands to fill the vessel in which it is

contained. Due to the loose molecular bond, gas properties are considerably

different than those of liquids, and any changes in the state of temperature

and/or pressure will result in a major effect on gas properties. Natural gas

is a subcategory of petroleum that occurs naturally, and it is composed of

a complex mixture of hydrocarbons and a minor amount of inorganic com-

pounds. Natural gasses’ physical properties and, in particular, their variations

with pressure, temperature, and molecular weight are of great importance in

gas engineering calculations, including the estimation of gas reserves and

the pressure gradient of gas wells, changes in reservoir pressure, and gas

compression and gas metering in transporting pipelines. Gas properties are

usually measured experimentally, but when unavailable, they are estimated

using equation of states (EOS) or empirical correlations.

This article covers gas physical properties of viscosity and density and

presents some of the commonly used models. In addition, the mathematical

background of the Alternating Conditional Expectation algorithm used to

build the models proposed is discussed and the newly developed models for

gas viscosity and density are introduced.

GAS VISCOSITY

Viscosity is an essential property for the study of the dynamics of fluids

flow in pipelines, porous media, or wherever transport of momentum occurs

in fluids motion. Viscosity is the measure of the internal resistance of a

fluid to flow. Gas viscosity is difficult to measure accurately, especially at

high temperature and pressure. Therefore, it is estimated through correlations

developed with limited careful experimental work rather than through ex-

perimental measurements alone. Typically, the correlations are a function

of temperature, pressure, gas composition, and gas gravity, and they are

corrected for nonhydrocarbon components. Bicher and Katz (1943) developed

the first gas viscosity correlation indicating that viscosity is a function of

pressure, temperature, and molecular weight, reporting an average deviation

of 5.8%. Since then, different mathematical correlations for gas viscosity have

been proposed throughout the years.

The Carr, Kobayashi, and Burrows (1954) correlation, referred to as

CKB, is a three-step process developed to predict the hydrocarbon gas vis-

cosity over temperature ranges of 32 to 400ıF, pressures up to 12000 psi, and

gas gravities in the range of 0.55 to 1.55. The correlation can handle non-

hydrocarbon impurities with concentrations up to 15% each. The correlation

was developed based on 30 data points, and a 0.38% average absolute error

was reported for viscosity at atmospheric pressure. The disadvantage of this


1676 A. A. AlQuraishi and E. M. Shokir

method is the usage of multiple charts that are hard to program. Several curve

fits of these graphs were proposed, but many of them are only good over a

limited range. Dempsey (1965) developed a functional form to approximate

the ratio of gas viscosity at a particular pressure of interest to gas viscosity at

atmospheric conditions (�g=�1atm) but could not predict Carr et al.’s (1954)

data over the entire range successfully.

A commonly used empirical correlation for the estimation of gas mix-

tures’ viscosity is that of Lohrenz-Bray-Clark (LBC; 1964). This model is

based on the original work of Jossi, Stiel, and Thodos (1962) using the same

equation and coefficients derived by Jossi et al. for pure fluids. The model is a

16th-degree polynomial in reduced density; therefore, viscosity estimation is

highly dependent on the accuracy of the experimental density measurements.

Lee, Gonzalez, and Eakin’s (1966) correlation, referred to as (LGE), was

developed to predict hydrocarbon gas viscosity as a function of temperature,

gas density, and gas molecular weight. A large database was used to develop

this semiempirical correlation, and its accuracy is acceptable for pressure

ranges of 100 to 8000 psi and temperature ranges of 100 to 340ıF. They

reported a 2% average absolute error at low pressures and a 4% average

absolute error for high pressures for hydrocarbon gases with specific gravities

below 1.0. For gases with a specific gravity above 1.0, this relation is less

accurate. No corrections were implemented to tune the viscosity equation for

nonhydrocarbon components, and the only one it was able to handle was CO2

with concentrations up to 3.2 mole%.

Londono, Aicher, and Blasingame (2002) suggested a modification to the

previously mentioned Lee et al. (1966) and Jossi et al. (1962) correlations.

In addition, they developed a new implicit correlation for gas viscosity as a

function of gas density and temperature. The correlation is developed based

on 4909 data points of pure components as well as gas mixtures reporting an

average absolute error of 3.05%.

GAS DENSITY

Density is defined as the mass contained in a specific unit volume. Due to

compressibility, most gas viscosity models are density dependent or, more

specifically, gas compressibility factor (z-factor) dependent. Gas density is

pressure and temperature dependent, and it is usually estimated using equa-

tions of state (EOS) modeling the behavior of the z-factor of hydrocarbon

gases (Benedict, Webb, and Rubin, 1940; Dranchuk and Abou-Kassem, 1975;

Nishiumi and Saito, 1975). Equations of state models are implicit in terms

of the z-factor, which implies that the z-factor is determined as a root of the

EOS.

In an attempt to provide an explicit relation to predict the z-factor, Beggs

and Brill (1973) presented a closed-form expression for the z-factor prediction

using 94 data points reporting an average absolute error of 0.19%. The model



can only be used in the range of 1.2 � Tr � 2.4 and 0.0 � pr � 10. The

accuracy of the relation is relatively low, except at moderate pressures and

temperatures.

Dranchuk and Abou-Kassem (1975) developed a gas density correlation

using 1500 data points, including pure gases and gas mixtures from differ-

ent sources. They developed their EOS based on a Han-Starling form of

the Benedict-Webb-Rubin (1940) EOS, reporting an average absolute error

of 0.486% when specifically used within the pseudoreduced pressure and

temperature ranges of 0.2 to 30 and 1.0 to 3.0, respectively. Nishiumi and

Saito (1975) developed their EOS to estimate thermodynamic properties. The

model provides better performance than Dranchuk and Abou-Kassem (1975)

in the vicinity of the critical isotherm.

The Dranchuk and Abou-Kassem (1975) and Nishiumi and Saito (1975)

models have been optimized by Londono et al. (2002) using two sets of data.

The first consisted of 5960 data points taken from the Poettmann-Carpenter

(1952) database reporting 0.412% and 0.426% for the two models, respec-

tively. The second set of data consisted of pure hydrocarbon components from

methane to pentane in addition to the Poettmann-Carpenter (1952) database

totaling 8256 data points. They reported an average absolute error of 0.821%

and 0.733% for the two models, respectively.

ALTERNATING CONDITIONAL

EXPECTATION ALGORITHM

The general form of a linear regression model is given by

Y D ˇ0 C

pX

iD1

ˇi Xi C "; (1)

where ˇ0, ˇ1, : : : , ˇp are the regression coefficients to be estimated and " is

the error term (Breiman and Freidman, 1985; Wang and Murphy, 2004).

Conventional multiple regressions require a linear functional form to be

presumed a priori for the regression surface, thus reducing the problem to that

of estimating a set of parameters. When the relationship between the response

and predictor variables is unknown or inexact, linear parametric regression

can yield erroneous results. This is the primary reason for the use of nonpara-

metric regression techniques. These nonparametric regression methods can be

broadly classified into those that do not transform the response variable, such

as generalized additive models, and those that do, such as the ACE.

The ACE nonparametric regression model has the following general form

(Breiman and Freidman, 1985; Wang and Murphy, 2004):

�.Y / D ˛ C

nX

iD1

�i .Xi / C "; (2)



where � is a function of the response variable, Y, and �i are functions of

the predictors X1, X2, : : : , Xn. Thus, the ACE model replaces the problem

of estimating a linear function of a n-dimensional variable by estimating n

separate one-dimensional functions �i and � using an iterative method. These

transformations are achieved by minimizing the unexplained variance of a

linear relationship between the transformed response variable and the sum of

transformed predictor variables. For a given data set consisting of a response

variable Y and predictor variables X1, X2, : : : , Xn, the ACE algorithm

starts out by defining arbitrary measurable mean-zero transformations �.Y /;

�1.X1/; : : : , �n.Xn/. The error variance ."2/ that is not explained by a

regression of the transformed dependent variable on the sum of transformed

independent variables, under the constraint EŒ�2.Y /� D 1, is determined as

follows:

"2.�; �1; : : : ; �n/ D E

( "

�.Y / �

nX

iD1

�i .Xi /

#) 2

: (3)

The minimization of ."2/ with respect to �1.X1/; : : : , �n.Xn/ and �.Y / is

carried out through a series of single-function minimizations, resulting in the

following equations:

�i .Xi / D E

2

4�.Y / �

nX

j ¤i

�j .Xj /jXi

3

5 (4)

�.Y / D E

"

nX

iD1

�i .Xi /jY

# ,ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

E

"

nX

iD1

�i .Xi /jY

#ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

ˇ

(5)

The final �i .Xi /; and �.Y / after the minimization are estimates of the optimal

transformation ��i .Xi / and ��.Y /. In the transformed space, the response and

predictor variables are related to each other as follows:

��.Y / D

nX

iD1

��i .Xi / C e�; (6)

where e� is the error not captured by the use of the ACE transformations and

is assumed to have a normal distribution with a zero mean. The minimum

regression error (e�) and maximum multiple correlation coefficients (��) are

related by the following relationship:

e�2 D 1 � ��: (7)



RESULTS AND DISCUSSION

The large database of measured gas properties collected by Londono et al.

(2002) was used to build and test the proposed models. The data are for

hydrocarbon gases and gas mixtures containing nonhydrocarbon impurities

such as carbon dioxide, hydrogen sulfide, nitrogen, and helium gathered

from different sources (Poettmann and Carpenter, 1952; Lee, 1965; Diehl

et al., 1970; Gonzalez, Eakin, and Lee, 1970; Stezmann and Wagner, 1991).

The database includes gas composition, temperature, pressure, pseudoreduced

properties of pressure and temperature, compressibility factors, and experi-

mentally measured viscosity and density. The quality of the data were judged

and compared and only those showing a similar trend for a given variable

were considered. In addition, liquids like gas, gas mixtures containing C6C,

and gas properties measured below 32ıF and 14.7 psi were discarded. As a

result, a total of 4445 data points were considered for this work, composed

of 1853 for pure gases and 2592 for gas mixtures.

GAS VISCOSITY MODEL

Eight hundred data points were randomly selected out of the large database

gathered and used to build the ACE viscosity model. The rest of the data

were used to test the efficiency of the developed model in predicting the

experimentally measured viscosity. The model correlates gas viscosity (�) to

the independent variables of gas density (�) and pseudoreduced properties

of pressure (Ppr) and temperature (Tpr). The model is efficient over wide

ranges of pressure, temperature, and density, and Table 1 lists the ranges of

the independent and dependent variables used in model building and testing

stages constituting the limits of the model.

The graphical user interface program GRACE (Xue, Datta-Gupta, Valko,

and Blasingame, 1997) was used to derive the general viscosity model pro-

posed in this work. Figure 1 is a plot of the resulting natural logarithm of the

inverse of the optimal transformation of the dependent variable (�) versus

Table 1. Dependent and independent variables ranges of the data used to build and

test the gas viscosity model

Building Testing

Variables Minimum Maximum Minimum Maximum

� 0.00072 0.74 0.00038 0.738

Ppr 0.021 26.6 0.021 26.56

Tpr 0.582 3.35 0.581 3.35

� 0.011 0.991 0.0103 0.953



Figure 1. Optimal transformation of the dependent variable versus the sum of the

optimal transformation of independent variables.

the sum of the optimal transformations of the independent variables (�, Ppr,

and Tpr). A good fit was found with r2 of 0.999.

Figure 2 presents the natural logarithm of experimental measurements

of the dependent variable (�) versus the resulting natural logarithm of the

inverse of the optimal transformation of the general dependent variable. This

yields the following final viscosity model:

ln.�/ D �0:0067857z4 C 0:023545z3 � 0:0012250z2

C 0:90903z � 2:9392; (8)

Figure 2. Experimentally measured gas viscosity versus the resulted inverse optimal

transformation of viscosity dependent variable.



Table 2. Resulting coefficients for gas viscosity model input parameters

x A4 A3 A2 A1 A0

�r 3.0182 � 101 �3.8300 � 101 2.0939 � 101 �1.9945 � 10�1 �1.4369 � 100

Tpr �3.8910 � 10�7 2.0181 � 10�5 �3.1054 � 10�4 1.6436 � 10�3 �2.3367 � 10�3

Ppr �1.2522 � 10�2 1.3118 � 10�1 �5.0317 � 10�1 1.0563 � 100 �7.7197 � 10�1

where

z D

nD3X

iD1

Zn (9)

and

Zn D A4nXn C A3nXn C A2nXn C A1nXn C A0n: (10)

Table 2 lists the values of the coefficients A0 to A4 used to determine Zn.

Figure 3 is a plot of the predicted model versus the experimentally

measured gas viscosity. A good match is observed with an average absolute

error of 4.05%. The model’s ability to predict the experimentally measured

viscosity of 3645 data points not used in building the ACE model was then

tested. Using the same 3645 data points, the proposed model’s efficiency

was compared to existing correlations such as Lohrenz et al. (1964), Lee

et al. (1966), and Londono et al. (2002). Figure 4 is a plot of the predicted

versus experimentally measured viscosities using the proposed new ACE

viscosity model and the three previously mentioned correlations. It indicates

that the new proposed viscosity model (Figure 4a) outperforms the other

Figure 3. Predicted versus experimentally measured gas viscosity based on ACE

algorithm for randomly selected 800 points used for viscosity model building.



Figure 4. Predicted versus experimentally measured gas viscosity based on (a)

developed model, (b) Lohrenz et al.’s correlation, (c) Lee et al.’s correlation, and

(d) Londono et al.’s correlation.

tested correlations in predicting the experimentally measured viscosity with

an average absolute error of 3.95%.

Poor correlation is observed when using the Lohrenz et al. (1964) model

as indicated by the significant departure from the 45ı line (Figure 4b). This

deviation might be due to the nature of the correlation, which is restricted

to pure gases with a density below 2.0 gm/cc, whereas the database used

covers gas mixtures with a reduced density up to 3.4 gm/cc. The correlation

is greatly dependent on gas viscosity at low pressure, which is not available in

our database and is calculated using the Londono et al. (2002) correlation for

viscosity at atmospheric pressure. Similarly, Lee et al.’s (1966) correlation

was assessed (Figure 4c) and shows a significant departure from the 45ı

line, underestimating gas viscosity at a higher end of the viscosity scale and

reporting an average absolute error of 12.75% when applied with the currently

collected database. The higher deviation noticed compared to what the authors

reported originally is believed to be due to the limited data used in building

the original correlation in addition to the limited ranges of pressure and

temperature in which the model is applicable compared to the database used

in this work. Londono et al.’s (2002) correlation (Figure 4d) also indicates



poor correlation, but it is better than that seen with the other two tested

correlations with some overestimated and underestimated points. It is worth

noting that Londono et al. (2002) underscaled their figures to 0.35 cp, which

might have outscaled some of the points calculated using their model.

GAS DENSITY MODEL

Again, 800 data points were selected randomly to build the ACE density

model. The model correlates gas density to the independent variables of gas

apparent molecular weight (AMW) and pseudoreduced properties of pressure

(Ppr) and temperature (Tpr). Table 3 lists the ranges of the independent and

dependent variables used in the building and testing stages constituting the

limits of the model.

Figure 5 is a plot of the resulted inverse of the optimal transformation

of the dependent variable (density) versus the sum of the natural logarithm

of optimal transformations of the independent variables (AMW, Pr and Tr ).

The data were fitted and a good match was found with r2 of 0.993. Figure 6

presents the experimental measurements of the dependent variable (density)

versus the resulted inverse of the optimal transformation of the general de-

pendent variable yielding the following density model:

� D 0:88485E � 3z6 � 0:47324E � 2z5 C 0:29710E � 2z4

C 0:20923E � 1z3 � 0:50211E � 1z2 C 0:15268z C 0:4506; (11)

where

z D

nD3X

iD1

Zn (12)

and

Zn D A6nXn C A5nXn C A4nXn C A3nXn C A2nXn C A1nXn C A0n: (13)

Table 3. Dependent and independent variables ranges of the data used to build and

test the gas density model

Building Testing

Variables Minimum Maximum Minimum Maximum

MW 16.0 117 16.0 117

Ppr 0.302 24.2 0.142 26.6

Tpr 0.582 3.27 0.582 3.35

� 0.0084 0.73 0.0049 0.74



Figure 5. Optimal transformation of the general dependent variable versus the sum

of the optimal transformation of the independent variables.

Table 4 lists the values of the coefficients A0 to A6 used to determine Zn.

Figure 7 is a plot of the model’s predicted density versus the experimen-

tally measured density. A good match is observed with an average absolute

error of 4.93%. The model’s ability to predict the experimentally measured

density of the 3645 measurement not used in building the ACE model was

then validated. The proposed model’s capability was compared to some of

the currently existing correlations such as Dranchuk and Abou-Kassem [8],

Beggs and Brill [10], and Londono et al. modified Nishiumi and Saito’s [6]

Figure 6. Experimentally measured gas density versus the resulted inverse optimal

transformation of the density dependent variable.



Table 4. Resulting coefficients for the gas density model input parameters

x A6 A5 A4 A3

MW �3.1795 � 10�2

6.5424 � 10�1 �5.5948 � 10

02.5529 � 10

1

Tpr �4.5271 � 10�3

3.1741 � 10�2 �7.6181 � 10

�24.1825 � 10

�2

Ppr 3.6619 � 10�1 �1.4792 � 10

03.5476 � 10

�11.5948 � 10

0

x A2 A1 A0

MW �6.5553 � 101

8.9938 � 101 �5.2099 � 10

1

Tpr 1.5700 � 10�1

1.4421 � 10�1 �6.8357 � 10

�1

Ppr 6.7552 � 10�1 �2.6058 � 10

01.9148 � 10

�1

correlations using the same data. Figure 8 is a plot of the predicted versus

the experimentally measured densities using the proposed new model and the

three previously mentioned correlations. Figure 8a is the proposed ACE model

indicating a good agreement between the predicted and measured densities

with an average absolute error of 4.75%, indicating good performance of the

model.

Dranchuk and Abou-Kassem’s correlation (Figure 8b) outperforms all the

other correlations investigated, including the developed one with an average

absolute error of 3.53%. Deviation is clear when estimating high-density val-

ues. Beggs and Brill and Londono modified Mishiumi and Saito’s correlations

(Figures 8c and 8d), which does not seem to work fine with our database,

especially at higher density values where data are either overestimated or

underestimated.

Figure 7. Predicted versus experimentally measured gas density based on ACE

algorithm for randomly selected 800 points used for density model building.



Figure 8. Predicted versus experimentally measured gas density based on (a) de-

veloped model, (b) Dranchuk and Abou-Kassem correlation, (c) Beggs and Brill

correlation, and (d) Londono et al.’s modified Nishiumi and Saito correlation.

SENSITIVITY ANALYSIS

Sensitivity analysis is the study of how the model output varies with changes

in model inputs. @risk software was used to assess the sensitivity analysis of

the two developed viscosity and density models. This is conducted by trying

all valid combinations of values for input variables to simulate all possible

outcomes. The higher the correlation between any independent variable and

dependent output, the higher the influence of that dependent variable on

determining the output value.

The analysis conducted was based on the rank correlation coefficient

calculated between the output variable (density or viscosity) and the samples

for each of the input distributions. Figure 9 is a tornado plot indicating

the dependence of gas viscosity on independent variables of pseudoreduced

temperature, pseudoreduced pressure, and gas density. The figure indicates

the significant impact of gas density and the trivial impact of pseudoreduced

pressure. Gas density and pseudoreduced temperature have a positive impact,

indicating that viscosity increases with the increase of any of the independent

variables.



Figure 9. Sensitivity analysis of the proposed gas viscosity model.

Similarly, Figure 10 is a tornado plot determining the impact of pseudore-

duced pressure, pseudoreduced temperature, and apparent molecular weight

on gas density. The figure indicates the positive impact of reduced pressure

and apparent molecular weight and the significant negative impact of reduced

temperature. This agrees with the known behavior of these independent

variables on gas density, where density increases with increasing molecular

weight and reduced pressure and decreases with increasing temperature.

Figure 10. Sensitivity analysis of the proposed gas density model.



CONCLUSIONS

Hydrocarbon gas viscosity and density models have been developed using a

large database of experimental measurements covering wide ranges of pres-

sure and temperature. An alternating conditional expectation algorithm was

used to derive the models, and their efficiency was tested and a comparison

was carried out with existing correlations. Based on the results obtained, the

following points are concluded:

� The new viscosity model provides an accurate prediction of the experimen-

tal measurements and outperforms the other tested models with the lowest

average absolute error of 3.95%.� The proposed gas viscosity model is independent of gas viscosity at atmo-

spheric pressure as required by most of the existing correlations.� The proposed density model comes in second place after Dranchuk and

Abou-Kassem’s (1975) correlation with an average absolute error of 4.93%.

The power of the model is its capability to predict gas density without a

gas compressibility factor.� The gas viscosity model is positively sensitive to changes of density and

pseudoreduced temperature with negligent sensitivity to changes in pseu-

doreduced pressure. On the other hand, the gas density model is sensitive

to all input parameters of pseudoreduced temperature, apparent molecular

weight, and pseudoreduced pressure mentioned on the order of their im-

pact. A negative impact was predicted for reduced temperature, whereas

positive ones were noticed for the pseudoreduced pressure and gas apparent

molecular weight.

REFERENCES

Beggs, H. D., and Brill, J. P. (1973). Study of two-phase flow in inclined

pipes. J. of Pet. Tech. May:607–617.

Bendict, M., Webb, G. B., and Rubin L. C. (1940). An empirical equation for

hydrocarbon thermodynamic properties of light hydrocarbons and their

mixtures: Methane, ethane, propane, and n-butane. J. of Chem. Phys.

8:334–345.

Bicher, L., and Katz, D. (1943). Viscosity of the methane-propane system.

Indust. Eng. Chem. 35:754.

Breiman, L., and Freidman, J. (1985). Estimating optimal transformations for

multiple regression and correlation. J. of Am. Stat. Assoc. 80:580–587.

Carr, N. L., Kobayashi, R., and Burrows, D. B. (1954). Viscosity of hydro-

carbon gases under pressure. Trans., AIME, 201:264–272.

Dempsey, J. R. (1965). Computer routine treats gas viscosity as a variable.

Oil and Gas J. Aug.:141–143.



Diehl, J., Gondouin, M., Houpeurt, A., Neoschil, J., Thelliez, M., Verrien,

J. P., and Zurawsky, R. (1970). Viscosity and Density of Light Paraffins,

Nitrogen and Carbon Dioxide. Paris: Editions Technip, CREPSI Geopet-

role.

Dranchuk, P. M., and Abou-Kassem, J. H. (1975). Calculation of z-factors for

natural gases using equations of state. J. of Canad. Pet. Tech. 14:34–36.

Gonzalez, M. H., Eakin, B. E., and Lee, A. L. (1970). Viscosity of natu-

ral gases. American Petroleum Institute, Monograph on API Research

Project, 65, NY.

Jossi, J. A., Stiel, L. I., and Thodos, G. (1962). The viscosity of pure

substances in the dense gaseous and liquid phases. AIChE Journal. 8:59–

62.

Lee, A. L. (1965). Viscosity of light hydrocarbons. American Petroleum

Institute, Monograph on API Research Project, 65.

Lee, A. L., Gonzalez, M. H., and Eakin, B. E. (1966). The viscosity of natural

gases. J. of Pet. Tech. Aug.:997–1000.

Lohrenz, J., Bray, B. and Clark, C. (1964). Calculating viscosities of reservoir

fluids from their composition. SPE Paper 915, 2002 Annual Fall Meeting,

Houston, TX, October 11–14.

Londono, F. E., Aicher, R. A., and Blasingame, T. A. (2002). Simplified

correlations for hydrocarbon gas viscosity and gas density validation and

correlation behavior using a large scale database. SPE Paper 75721, 2002

SPE Gas Technology Symposium, Calgary, Canada, April 30–May 2.

Nishiumi, H., and Saito, S. (1975). An improved generalized BWR equation

of state applicable to low reduced temperatures. J. of Chem. Eng. of

Japan. 8:356–360.

Poettmann, H. F., and Carpenter, P. G. (1952). The Multiphase Flow of Gas,

Oil, and Water through Vertical Flow String with Application to the

Design of Gas-lift Installations. Drilling and Production Practice. 257–

317.

Setzmann, U., and Wagner, W. (1991). A new equation of state and tables

of thermodynamic properties for methane covering the range from the

melting line to 625 K at pressures up to 1000 MPa. J. of Phys. Chem.,

20:1061–1155.

Wang, D., and Murphy, M. (2004). Estimating optimal transformations for

multiple regressions using ACE algorithm. J. of Data Sci. 2:329–346.

Xue, G., Datta-Gupta, A., Valko, P., and Blasingame, T. A. (1997). Opti-

mal transformations for multiple regression: Application to permeability

estimation from well logs. SPE Formation Evaluation Journal. 12:85–93.


viscosity and densety correlations

Documents