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Abstract

Gas viscosity is an important fluid property in petroleum engineering due to its impact in oil and gas production and transportation where it contributes to the resistance to the flow of a fluid both in porous media and pipes. Although the property has been studied thoroughly at low to intermediate pressures and temperatures, there is lack of detailed knowledge of gas viscosity behavior at high pressures and high temperatures (HPHT) in the oil and gas industry.

The need to understand and be able to predict gas viscosity at HPHT has become increasingly important as exploration and production has moved to ever deeper formations where HPHT conditions are more likely to be encountered. Knowledge of gas viscosity is required for fundamental petroleum engineering calculations that allow one to optimize the overall management of a HPHT gas field and to better estimate reserves. Existing gas viscosity correlations are derived using measured data at low to moderate pressures and temperatures, i.e. less than 10,000 psia and 300

oF, and then extrapolated to HPHT conditions. No measured gas viscosities at HPHT

are currently available, and so the validity of this extrapolation approach is doubtful due to the lack of experimental calibration.

The falling body viscometer is selected to measure gas viscosity for a pressure range of 3,000 to 24,500 psia and temperature range of 100 to 415

oF. Nitrogen was used to calibrate the instrument and to account for the fact

that the concentrations of non-hydrocarbons are observed to increase dramatically in HPHT reservoirs. Then methane viscosity is measured to reflect the fact that, at HPHT conditions, the reservoir fluids will be very lean gases, typically methane with some degree of impurity. The experiments showed that while the correlation of Lee et al. accurately estimates gas viscosity at low to moderate pressure and temperature, it does not provide a good match to gas viscosity at HPHT conditions. Introduction

HPHT gas reservoirs are defined as having pressures greater than 10,000 psia and temperatures over 300ºF. Modeling the performance of these unconventional reservoirs requires the understanding of gas behavior at elevated pressure and temperature. An important fluid property is gas viscosity, as it is used to model the gas mobility in the reservoir that can have a significant impact on reserves estimation during field development planning.

Accurate measurements of gas viscosity at HPHT conditions are both extremely difficult and expensive. Thus, this fluid property is typically estimated from published correlations that are based on laboratory data.

Unfortunately, the correlations available today do not have a sufficiently broad range of applicability in terms of pressure and temperature, and so their accuracy may be doubtful for the prediction of gas viscosity at HPHT conditions.

Gas viscosity can be measured using the following three types of experimental apparatus:

Capillary viscometers Falling body viscometers Vibrating viscometers

IPTC 13528

Measurement of Gas Viscosity at High Pressures and High Temperatures Kegang Ling, Catalin Teodoriu, Ehsan Davani, Gioia Falcone, Texas A&M University

2 IPTC 13528

Other viscometers may be used that combine features from two or three of the above apparatus types. In

general, during the measurements, either the fluid remains stationary and a solid object moves through it, or the object is stationary and the fluid moves past it. The drag caused by the relative motion between the fluid and the solid is a measure of the fluid viscosity. Below is a brief description of the different types of viscometers. Capillary Viscometers

In a capillary viscometer, the fluid viscosity is determined by measuring the flow rate of the fluid flowing

through the capillary tube and the pressure differential between both its ends. The inside of the tube must be thoroughly clean and dry prior to each measurement in order obtain accurate fluid viscosities. Temperature control is also essential as the tube is susceptible to thermal expansion or contraction, especially in lower fluid viscosity ranges, which might introduce measurement errors. This system requires in-line density measurements.

Falling Body Viscometers

With this type of apparatus, fluid viscosity is measured by dropping a cylindrical or spherical rigid body of

known dimensions and density into a fluid sample and recording the falling time over a known distance. The Stokes' Law is then used to calculate the fluid viscosity. A variation of this method consists of measuring the travel time of a piston that moves at constant speed through a fluid sample under the influence of an imposed electromagnetic field. When the body movement occurs horizontally, density measurements are not required. The most common type of falling body viscometer is the rolling ball viscometer, which shows good accuracy when measuring liquid viscosity, but must be used with caution for gas viscosity measurements. In the latter case, replacing the ball with a cylinder (piston) leads to better accuracy. Vibrating Viscometers

These viscometers rely on the damping of an oscillating electromechanical resonator immersed in the fluid

whose viscosity is to be determined. There are three technologies based on this principle: the tuning fork, the oscillating sphere, and the vibrating rod or wire. The first method measures the fluid viscosity by determining the bandwidth and frequency of the vibrating fork resonance. The second technique requires that a sphere oscillate about its polar axis with precisely controlled amplitude and the fluid viscosity is calculated from the power required to maintain this predetermined amplitude of oscillation. This second measurement is density dependent, so the density of the test fluid should be determined independently. The third and final technique estimates fluid viscosity from the rod vibration amplitude while it is immersed in the sample.

Available Experimental Databases

The first step in ensuring the validity of any gas viscosity correlation at HPHT conditions is to evaluate the

measured data upon which the correlation is based. A large database was reviewed for this research, which revealed that most of the published data on gas

viscosity are extremely limited in terms of both conditions and quantity, and in some cases their accuracy is unknown. All of the currently available viscosity correlations were developed from measured data at low to moderate pressures and temperatures, and their applicability at HPHT conditions is doubtful.

HPHT reservoir fluids tend to be very lean gases, typically methane with some degree of impurity (mainly nitrogen and carbon dioxide). Table 1 presents a summary of the databases that are commonly used in the petroleum industry to develop gas viscosity correlations.

The review shows that very little data are available for methane and nitrogen viscosities at HPHT conditions, which impairs the development of gas viscosity correlations for these extreme conditions.

IPTC 13528 3

Table 1. Available gas viscosity databases

Authors Year Temperature Pressure Method Composition

oF psia

Boyd1 1930 86-158 1,073-2,631

Transpiration method (same principle as capillary viscometer) N2

Michels & Gibson2 1931 77-167 226-14,196 Capillary tube N2

Sage & Lacey3 1937 100-220 up to 2,600 Rolling ball CH4

Bicher & Katz4 1943 77-437 14.7-500 Rolling ball CH4, CH4-C3H8

Comings5 1944 86-203 14.7-2,514 Capillary tube CH4

Iwasaki6 1954 77-302 up to 2,940 Oscillating disc N2

James & George7 1957 -58-77 514.7-10,014.7 Capillary tube N2, CH4

Baron8 1959 125-275 114.7-8,014.7 Capillary tube N2, CH4

Kestin & Leidenfrost9 1959 66-77 2-922 Oscillating disc N2

Swift10

1959 -238-(-117) 350-710 Falling body CH4

Golubev11

1959 -58-1292 14.7-14,700 Capillary tube N2, CH4

Swift12

1960 -220-(-115.6) 85-675 Falling cylinder CH4

Flynn13

1963 -108-212 100-2,587 Capillary tube N2

Barua14

1964 -58-302 up to 2,940 Capillary tube CH4

Carmichael15

1965 40-400 14.7-5,000 Rotating cylinder CH4

Lee16

1965 100-460 200-8,000 Capillary tube CH4

Giddings17

1965 40-280 100-8,000 Capillary tube CH4

Lee, Gonzales and Eakin18

1966 100-340 14.8-8,000 Capillary tube Natural gas

Gonzalez19

1966 100-340 200-8,000 Capillary tube CH4

Huang20

1966 -274-32 up to 5,000 Falling cylinder CH4

Van Itterbeek21

1966 -334-(-298) 7.35-1,441 Oscillating disk CH4

Boon22

1967 -296-(-255) Vapor pressures Capillary tube N2, CH4

Kestin23

1968 68-86 14.7-368 Oscillating disk N2, CH4

Grevendonk24

1970 -341-(-236) up to 2,842 Torsionally vibrating crystal N2

Helleman25

1970 -287-(-123) up to 1,470 Oscillating disk CH4

Diehl26

1970 32-302 14.7-735 Geopal viscometer N2 and pure hydrocarbons

Latto27

1972 -298-260 14.7-2,205 Capillary tube N2

Stephan28

1979 -342-1880 14.7-20,290 Various N2, CH4, n-decane, CO2

Diller29

1980 -280-80 up to 4,350 Torsionally oscillating crystal CH4

Diller30

1983 -298-80 up to 4,350 Torsionally oscillating crystal N2

Hongo31

1988 77-212 up to 729 Oscillating disk CH4

Van Der Guilk32

1988 77 14.5-14,500 Vibrating-wire CH4

Vogel33

1999 8-188 up to 2,916 Vibrating-wire CH4

Canet34

2002 68-212 up to 20,412 Falling body CH4-C10H22

Baylaucq & Canet35

2003 68-212 up to 20,412 Falling body CH4-Toluene

Audonnet & Pádua36

2003 77-248 up to 10,935 Vibrating-wire CH4-C10H22

Schley37

2004 8-188 up to 4,228 Vibrating-wire CH4

Seibt38

2006 77-302 up to 5,103 Vibrating-wire N2

Available Correlations

Several well-known correlations are used in the petroleum industry to determine values of gas viscosity. What

follows is a discussion of the most commonly adopted correlations, namely the Carr, Kobayashi and Burrow correlation

39, and the Lee, Gonzalez and Eakin correlation

18. The National Institute of Standards and Technology

(NIST)42

has developed a computer program that predicts thermodynamic and transport properties of hydrocarbon fluids, which allows comparison of its values with those from correlations and gives an insight into the current understanding of gas viscosity correlations. Note that Viswanathan

43 modified the Lee, Gonzalez and Eakin

correlation18

by combining NIST values and laboratory data.

4 IPTC 13528

Carr, Kobayashi and Burrows correlation39

This correlation is a two-step process to estimate natural gas viscosity. Firstly, a value of gas viscosity at

atmospheric pressure is determined and corrections are applied to account for the effect of impurities such as nitrogen, carbon dixode and hydrogen sulphide on natural gas viscosity (Figure 1). Dempsey

40 later provided

Eqs.1 through 5 that allow computation of the corrected atmospheric viscosity without having to use a chart. The value of gas viscosity at atmospheric conditions is adjusted to reservoir conditions by obtaining a value of gas viscosity ratio (μg/μ1atm) from either of the charts presented in Figures 2 and 3.

Figure 1. Viscosity of hydrocarbon gas mixture at atmospheric pressure and correction for N2, CO2 and H2S, from Carr et al.

39.

)correction()correction()correction(d)uncorrecte( 22211 SHCONatmatm ........................................................ (1)

gTgatm log3

1015.63

10188.86

10062.25

10709.1duncorrecte1

. .......................................... (2)

31059.9log

31048.8

2correction2

gNyN . ............................................................................................. (3)

31024.6log

31008.9

2correction2

gCOyCO . ......................................................................................... (4)

31073.3log

31049.8

2correction2

gSHySH . ......................................................................................... (5)

where

atm1 - Gas viscosity at 1 atm, cp

g - Gas specific gravity (air = 1)

SHCONy222 ,, - Mole fraction of the non-hydrocarbon components

T - Temperature, oF

IPTC 13528 5

Figure 2. Viscosity ratio vs. pseudo-reduced pressure for hydrocarbon gases, from Carr et al.

39.

Figure 3. Viscosity ratio vs. pseudo-reduced temperature for hydrocarbon gases, from Carr et al.

39.

The advantage of the Carr, Kobayashi and Burrow correlation is that it can correct for the effect of non-

hydrocarbons that significantly affect the gas viscosity.

Lee, Gonzalez and Eakin correlation

18

The input data required in this correlation are gas density, gas molecular weight and temperature. Values of these input data can be readily obtained if reservoir temperature and pressure and gas specific gravity are known. Eqs. 6 through 9 are used to obtain gas viscosity, provided that the molecular weight and density at the relevant conditions are known.

4

10 exp( )Y

g gK X

................................................................................................................................................ (6)

TM

TMK

w

w

26.192.209

)01607.0379.9(5.1

.......................................................................................................................................... (7)

where

wMT

X 01009.04.986

448.3

....................................................................................................................................... (8) XY 2224.0447.2 .................................................................................................................................................... (9)

g - gas viscosity, cp

g - gas density, g/cc

MW- Molecular weight T - Temperature, R

6 IPTC 13528

The correlation by Lee et al., which fits their 234 data points with an average absolute error of 2.0% and 4% at

low and high pressures, respectively, provides better results if the gas specific gravity is less than unity. The correlation can be used to forecast gas viscosities at temperatures from 100 to 340

oF and pressures from 100 to

8,000 psi. However, this correlation does not consider natural gases that contain high quantities of non-hydrocarbon

components. Jeje and Mattar

41 compared the Lee et al. correlation to the Carr et al. correlation for both sweet and sour

gases. They found that both give almost identical results for the former, but there were significant differences for the latter. This suggested that the Lee et al. correlation, which was derived for sweet gases only, should not be applied to sour gases.

NIST Program42

The NIST program, which estimates of thermodynamic and transport properties of hydrocarbons, can provide

viscosities of both pure components and mixtures at pressures up to 44,100 psi and temperatures up to 1,340 oF.

However, the program predicts the fluid properties using correlations developed for low to moderate pressure and temperature. Its applicability to HPHT conditions has not been validated against experimental data.

Viswanathan Correlation43

Viswanathan used a Cambridge Viscosity SPL440 system to measure the viscosity of pure methane at

pressures from 5,000 to 30,000 psi and temperatures from 100 to 400oF. Based on the results from the

measurements, Viswanathan modified the correlation by Lee et al. as follows:

Y

gg XK exp ................................................................................................................................................... (10)

TM

TMK

w

w

9.128.443

)2888.00512.5(*0001.0832.1

................................................................................................................... (11)

where

wMT

X 3938.09437.3084

1166.6

.................................................................................................................... (12)

XY 1563.05893.0 .................................................................................................................................................. (13)

Viswanathan then compared the modified Lee et al. correlation to the NIST values for pure methane. The results showed a very good match with the NIST values compared to the performance of the original correlation by Lee et al. However, Viswanathan’s findings cannot be directly extrapolated to situations where impurities are present in the gas.

The above review of existing gas viscosity correlations reveals that there are no measurements available at

HPHT conditions. Correlations derived from data at low to moderate pressures and temperatures should not be simply extrapolated to HPHT conditions without validation against experimental measurements. Although it would be desirable to have a unique correlation capable of covering both low and high pressure and temperature ranges, it cannot be said for sure if this is possible unless more laboratory data are obtained. Experimental Facility

The facility used for this work consists of a gas source, a gas booster system, a measuring system, and a data acquisition system. Figure 4 illustrates the layout of the facility.

IPTC 13528 7

Figure 4. The Experimental Facility at Texas A&M University

Gas Source

Nitrogen and methane have been used in the tests described here. A gas tank, which supplies the gas at low

pressure, is connected to the inlet of the gas booster system where gas is compressed to high pressure.

Gas Booster System

The gas booster system, which consists of a hydraulic pump coupled with a booster cylinder to increase the

pressure of a given gas sample, comresses gas from 1,000 psig to 25,000 psig. The system is rated for use up to 30,000 psig and has a one-to-one ratio. Displacement per stroke is 112 cubic inches.

Measurement System - Cambridge Sensor

In this research, the Cambridge SPL440 High Pressure Research Viscosity Sensor was used to measure gas

viscosities at HPHT conditions. This technology is based on an electromagnetic concept, with two coils moving a piston back and forth magnetically at a constant force. The piston’s two-way travel time is then related to the fluid’s viscosity by a proprietary equation. The viscosity range for the system is 0.02 to 0.2 cp, with a reported accuracy of 1% of full scale. The maximum operating pressure is 20,000 psig.

Data Acquisition System

The SPL440 sensor was integrated with RS-232 serial communication support, allowing synchronization of the measurements with a desktop computer. The Cambridge ViscoLab PVT software was used to record the measurements. Through a data acquisition system, the measured pressure, average temperature, average gas viscosity, current temperature, and current gas viscosity could be output and stored for analysis.

8 IPTC 13528

Data Analysis

Nitrogen Viscosity

For this study, nitrogen viscosity was measured at pressures between 3,000 and 24,500 psig and temperatures between 116 and 350

oF. A total of 88 experiments were run. The laboratory results were then

compared with NIST values and data at low to moderate pressure and temperature from previous investigators. The comparison shows that the laboratory data match the NIST values as well as those reported by other investigators at low to moderate pressures, while they are lower at high pressure. The difference between measured data and NIST values increases as temperature decreases; this difference also increases as pressure increases. Figures 5 and 6 show nitrogen viscosity for the entire pressure range that was investigated, and for temperatures of 200 and 350

oF. The mismatch that is observed at high pressure suggests the need for a new gas

viscosity correlation for gas reservoirs with moderate to high nitrogen concentration at HPHT conditions.

Figure 5. Nitrogen Viscosity vs. Pressure at 200 oF

Figure 6. Nitrogen Viscosity vs. Pressure at 350 oF

IPTC 13528 9

Methane Viscosity

Methane viscosity was measured at pressures between 4,500 and 25,000 psig and temperatures between 100 and 415

oF. A total of 51 experiments were run. As per the nitrogen results, the methane laboratory data were also

compared with NIST values and data from previous investigators. The comparison shows a good match at low to moderate pressure, but the new experimental viscosities are higher at high pressure. The mismatch decreases as temperature increases, and increases as pressure increases. Figures 7 to 9 show methane viscosity for the entire pressure range and for temperatures of 220, 300, and 415

oF. The difference between measured and reported

data (NIST and previous investigators) at high pressure indicates that a new correlation for nitrogen viscosity is necessary for gas reservoirs with moderate to high nitrogen concentration at HPHT conditions.

Figure 7. Methane Viscosity vs. Pressure at 220

oF

Figure 8. Methane Viscosity vs. Pressure at 300

oF

10 IPTC 13528

Figure 9. Pressure vs. Methane Viscosity at 415

oF

Conclusions

Gas viscosity correlations derived from data obtained at low to moderate pressures and temperatures cannot be confidently extrapolated to HPHT conditions.

The gas viscosity correlations that are currently available to the petroleum industry were derived from data obtained with gases with limited impurities, and so their accuracy for use with gases containing large quantities of impurities is unknown.

The laboratory investigations performed at TAMU show that, at high pressure, the experimental nitrogen viscosities are lower than the values provided by the NIST and by previous investigators. The observed mismatch increases as temperature decreases, and it increases as pressure increases. For methane, the TAMU investigations show that, at high pressure, the experimental viscosities are higher than the values provided by the NIST and by previous investigators. The difference increases as temperature decreases and increases as pressure increases.

These preliminary results stress the importance of obtaining an exhaustive range of measurements of the viscosity of natural gases under HPHT conditions in order to ensure better reserves estimation. To this aim, further tests are ongoing at Texas A&M University.

Acknowledgements The authors would like to thank the sponsors of the Crisman Petroleum Research Institute at Texas A&M

University for supporting this project.

Nomenclature

Symbol Description

atm atmosphere

atms atmospheres, pressure unit

bar pressure unit, 1 bar = 0.987 atms

cm centimeter

cp centipoise oC Celsius temperature

ft foot or feet

IPTC 13528 11

oF degree Fahrenheit

g gram

g gas

in inch

kg kilogram

K constant in Equations (7), (11), and (15) for viscosity correlation

Kpa thousand Pascal oK Kelvin temperature

m meter

Mpa million Pascal

Mw molecular weight

N2 nitrogen

pc critical pressure

ppc pseudocritical pressure

psi gauge pressure

psia absolute pressure

psig gauge pressure

P poise

Pa Pascal

ppr pseudoreduced pressure

pr reduced pressure

s second

sec second

T temperature

Tc critical temperature

Tpc pseudocritical temperature

Tpr pseudoreduced temperature

Tr reduced temperature

X constant in Equations (8), (12), and (16) for viscosity correlation

2COy mole fraction of carbon dioxide in vapor

SHy2

mole fraction of hydrogen sulfide in vapor

2Ny mole fraction of nitrogen in vapor

yN2, CO2, H2S mole fraction of the non-hydrocarbon component

Y constant in Equations (9), (13), and (17) for viscosity correlation

Greek

g gas specific gravity

viscosity

atm1 gas viscosity at 1 atmosphere

g gas viscosity

density

f fluid density

g gas density

Subscripts

1atm 1 atmosphere

CO2 carbon dioxide

G gas

H2S hydrogen sulfide

N2 nitrogen

12 IPTC 13528

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