Advanced Natural Gas Engineering

Advanced Natural Gas Engineering

Xiuli Wang XGAS

Michael Economides University of Houston

Gulf Publishing Company Houston, Texas

Advanced Natural Gas Engineering Copyright © 2009 by Gulf Publishing Company, Houston, Texas. All rights reserved. No part of this publication may be reproduced or transmitted in any form without the prior written permission of the publisher. Gulf Publishing Company 2 Greenway Plaza, Suite 1020 Houston, TX 77046 10 9 8 7 6 5 4 3 2 1 Library of Congress Cataloging-in-Publication Data forthcoming Printed in the United States of America Printed on acid-free paper. ∞ Editing, design and composition by TIPS Technical Publishing, Inc

28 Chapter 1 Natural Gas Basics

Solution For the natural gas in Example 1–3, the gas gravity is 0.65, and therefore, from Figure 1–11 and at T = 180°F, m1atm = 0.0122 cp. Since the pseudoreduced properties are ppr = 5.96 and Tpr = 1.69, then from Figure 1–12, m/m1atm = 1.85, therefore m = 1.85 × 0.0122 = 0.0226 cp. For the sour gas in Example 1–4, the gas gravity is 0.70, which results (from Figure 1–11) in m1atm = 0.0121 cp. However, the presence of nonhydrocarbon gases requires the adjustments given in the insets in Figure 1–11. These adjustments are to be added to the viscosity value and are 0.00005, 0.0001, and 0.0004 cp for the compositions of N2, CO2, and H2S (in Example 1–3), respectively. Therefore, m1atm = 0.0127 cp. Since ppc and Tpc are 777 psi and 407 R, respectively, then ppr = 4,000/777 = 5.15 and Tpr = (190 + 460)/397.4 = 1.60. From Figure 1–12, m/m1atm = 1.84, resulting in m = 0.0127 × 1.84 = 0.0234 cp.

1.6.7 Useful Correlations So far we have introduced the natural gas properties, such as gas specific gravity, gas deviation factor, gas viscosity, compressibility, and density. While these properties can be measured in the laboratory, it is usually expensive and time consuming. Data and graphical representations have been developed and are referred to in this chapter. Early calculations of properties, using graphs, were generally done by hand as shown in this chapter. Some of these graphs date back to early 1940s. With the advent of computers, many correlations have been developed based on the published data. Thus, properties can be computerized and numerically solved. Below is a summary of some useful correlations. Correlations to Calculate Pseudocritical Properties Some useful correlations to calculate pseudocritical properties from gas specific gravity are summarized in Table 1–5.

Example 1–8 Determination of pseudocritical properties Calculate pseudocritical properties by using the Standing (1981) correlations listed in Table 1–5 and by using the properties given in Example 1–3.

1.6 Natural Gas Properties

Table 1–5

29

Correlations to Calculate Pseudocritical Properties from gg

Sutton (1985)

p pc = 756.8 - 131.07g g - 3.6g g 2 Tpc = 169.2 + 349.5g g - 74.0g g 2 The gases used in developing Sutton correlation are high molecular weight gases, which are rich in heptanes plus with minor amount of carbon dioxide and nitrogen, and no hydrogen sulfide. It is valid when 0.57 < gg < 1.68. Guo and Ghalambor (2005)

p pc = 709.604 - 58.718g g Tpc = 170.491 + 307.344g g These are valid for H2S < 3%, N2 < 5%, and total content of inorganic compounds less than 7%. Standing (1981)

p pc = 706 - 51.7g g - 11.1g g 2 Tpc = 187 + 330g g - 71.5g g 2 These correlations are developed based on low molecular weight California natural gases. They work only for natural gases without nonhydrocarbon gases. Elsharkawy et al. (2000)

p pc = 787.06 - 147.34g g - 7.916g g 2 Tpc = 149.18 + 358.14g g - 66.976g g 2 These are developed based on retrograde gases and suitable for gas condensate. Ahmed (1989)

p pc = 678 - 50(g g - 0.5) - 206.7y N2 + 440 yCO2 + 606.7y H2 S Tpc = 326 + 315.7(g g - 0.5) - 240 y N2 - 83.3yCO2 + 133.3y H2 S These correlations are applicable for mixture with impurities such as N2, CO2, H2S.

30 Chapter 1 Natural Gas Basics

Solution From Example 1–3, the gas specific gravity is calculated as 0.65, therefore pseudocritical properties are

p pc = 706 - 51.7 ¥ 0.65 - 11.1 ¥ 0.652 = 668 psi Tpc = 187 + 330 ¥ 0.65 - 71.5 ¥ 0.652 = 371 R

Correlations to Calculate Gas Viscosity One of the commonly used correlations to calculate gas viscosity is the correlation developed by Lee et al. (1966):

m g = K exp( X rYg ),

(1.19)

where

K=

(9.4 + 0.02 MWg )T 1.5 209 + 19 MWg + T

,

Y = 2.4 - 0.2 X , X = 3.5 +

986 + 0.01MWg . T

(1.20)

(1.21)

(1.22)

This correlation is quite accurate for typical natural gas mixtures with low nonhydrocarbon content. Here temperature (T) is in R, the density (rg) is in gm/cm3 (calculated at the pressure and temperature of the system), which can be predicted by using Kay’s method (1936), and the resulting viscosity is expressed in centipoises (cp). Experimental viscosity data used to develop this correlation were presented for temperatures from 100 to 340°F and pressures from 100 to 8,000 psia. Other correlations to calculate gas viscosity include Dempsey (1965) and Dean and Stiel (1958). Correlations to Calculate Gas Deviation Factor and Compressibility Gas Deviation Factor Correlation by Dranchuk et al. (1974) is introduced below:

1.6 Natural Gas Properties

Z = 1 + ( A1 + A2 / Tr + A3 / Tr3 )rr + ( A4 + A5 / Tr )rr2 + A5 A6 rr5 / Tr + A7 rr2 / Tr3 (1 + A8 rr2 )exp( - A8 rr2 ),

31

(1.23)

where

rr = 0.27(

pr ), ZTr

(1.24)

A1 = 0.31506237 A2 = -1.04670990 A3 = -0.57832729 A4 = 0.53530771 A5 = -0.61232032

(1.25)

A6 = -0.10488813 A7 = 0.68157001 A8 = 0.68446549 The Newton-Raphson iteration method can be used as Z-factor appears on both side of the equation:

Zn +1 = Zn - ( f Z / f Z’ ),

(1.26)

where Zn+1 and Zn are the new and old values of Z-factor, fZ is the function Z described in Dranchuk et al. (1974) correlation, and f Z’ is its derivative. This correlation is valid when the pseudoreduced temperature is between 1.05 and 3.0 and pseudoreduced pressure is between 0 and 30. Other correlations for gas deviation factor include Brill and Beggs (1974), Hall and Yarborough (1973), and Takacs (1976). For sour gas, gas deviation factor can be calculated by using correlations developed by Piper (1993), Wichert and Aziz (1972), and Elsharkawy and Elkamel (2001). With gas deviation correlations, the gas isothermal compressibility, cg, can be calculated by using Eq. (1.17). Detailed calculation procedure can be found in Mattar et al. (1975), Trube (1957), Meehan and Lyons (1979), and Abou-Kassem et al. (1990). The range of validity will be the same as Z-factor.

32 Chapter 1 Natural Gas Basics

1.7

Units and Conversions

We have used “oilfield” units throughout the text, even though this system of units is inherently inconsistent. We chose this system because more petroleum engineers “think” in Mscf/d (thousand standard cubic feet per day) for gas rate and psi for pressure than in terms of m3/s (cubic meter per second) and Pa. All equations presented include the constant or constants needed with oilfield units. To employ these equations with SI units, it will be easier to first convert the SI units to oilfield units, calculate the desired results in oilfield units, and then convert the results to SI units. However, if an equation is to be used repeatedly with the input known in SI units, it will be more convenient to convert the constant or constants in the equation of interest. Conversion factors between oilfield and SI units are given in Table 1–6.

Example 1–9 Equations for the gas formation volume factor Develop expressions for the gas formation volume factor and density in SI units, in terms of p, T and Z. Note: the standard conditions are: psc= 14.7 psia and Tsc = 520 R. Solution The standard conditions for SI units are as follows: SI: p = 101,325 Pa, T = 288.7 K, R = 8.314 J/mol-K. Thus, the formation volume factor in SI units is:

Bg =

Ê ZT ˆ ÁË p ˜¯ res

Ê ZnRT ˆ ÁË p ˜¯ res

Vres ZT m3 = 350.7 ( = = ), Vsc Ê ZnRT ˆ p sm3 Ê (1)(288..7) ˆ ÁË (101, 325) ˜¯ ÁË p ˜¯ sc sc

while in oilfield units it is 0.0282

(1.27)

ZT res ft 3 ( ). p scf

For gas density:

rg =

(

p MWg RTZ

) = p ( MW ) g

(8.314)TZ

whereas, in oilfield units it is

=

(

0.1203 p MWg TZ

(

0.0932 p MWg TZ

) (kg/m ), 3

) (lbm/ft ) . 3

(1.28)

1.8 References

33

Table 1–6 Typical Units for Reservoir and Production Engineering Calculations (Earlougher, 1977) Variable

Oilfield Units

SI

Conversion (Multiply Oilfield Unit)

Area

acre

m2

4.04 × 103

Compressibility

psi-1

Pa–1

1.45 × 10–4

Length

ft

m

3.05 × 10–1

Permeability

md

m2

9.9 × 10–16

Pressure

psi

Pa

6.9 × 103

Rate (oil)

stb/d

m3/s

1.84 × 10–6

Rate (gas)

Mscf/d

m3/s

3.28 × 10–4

Viscosity

cp

Pa-s

1 × 10–3

1.8

References

Abou-Kassem, J.H., L. Mattar, and P.M. Dranchuk. 1990. Computer calculations of compressibility of natural gas. JCPT 29 (Sept.–Oct.): 105. Ahmed, T. 1989. Hydrocarbon Phase Behavior. Houston, TX: Gulf Publishing Co. Brill, J.P. and H.D. Beggs. 1974. Two-phase flow in pipes. Intercomp Course, The Hague. Brown, G.G., D. L Katz, C.G. Oberfell, and R.C. Alden. 1948. Natural gasoline and the volatile hydrocarbons. NGAA, Tulsa, OK. Carr, N.L., R. Kobayashi, and D.B. Burrows. 1954. Viscosity of hydrocarbon gases under pressure. Trans. AIME 201: 264–272. Dean, D.E. and L.I. Stiel. 1958. The viscosity of non-polar gas mixtures at moderate and high pressures. AICHE J. 4: 430–6. Dempsey, J.R. 1965. Computer routine treats gas viscosity as a variable. Oil & Gas J. (August): 141. Dranchuk, P.M., R.A. Purvis, and D.B. Robinson. 1974. Computer calculations of natural gas compressibility factors using the Standing and Katz correlation. Institute of Petroleum Technical Series IP 74-008. Earlougher, R.C., Jr. 1977. Advances in Well Test Analysis. SPE monograph, SPE 5, Richardson, TX. Economides, M.J., A.D. Hill, and C.A. Ehlig-Economides. 1994. Petroleum Production Systems. New York: Prentice Hall. Elsharkawy, A.M., Y. Kh. Hashem, and A.A. Alikhan. 2000. Compressibility factor for gas condensate reservoirs. Paper SPE 59702.