Page 34 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap02 Final Proof page 23 22.12.2006 7:08pm

PROPERTIES OF OIL AND NATURAL GAS 2/23

1:6
« 3 ¼ 120(A 0:9 A ) þ 15(B 0:5 B 4:0 ) (2:26) m g
m r ¼ ln T pr
m 1
T 0 ¼ T pc « 3 (corrected T pc ) (2:27)
pc 2 3
¼ a 0 þ a 1 p pr þ a 2 p þ a 3 p þ T pr (a 4 þ a 5 p pr
pr
pr
P pc T 0 2 3 2 2
P 0 ¼ pc (corrected p pc ) (2:28) þ a 6 p þ a 7 p ) þ T (a 8 þ a 9 p pr þ a 10 p pr
pr
pr
pr
pc
T pc þ B(1 B)« 3
3
3
þ a 11 p ) þ T (a 12 þ a 13 p pr þ a 14 p 2 pr
pr
pr
Correlations with impurity corrections for mixture 3
pseudo-criticals are also available (Ahmed, 1989): þ a 15 p ), (2:40)
pr
where
p pc ¼ 678 50(g g 0:5) 206:7y N 2 þ 440y CO 2
þ 606:7y H s S (2:29) a 0 ¼ 2:46211820
a 1 ¼ 2:97054714
a 2 ¼ 0:28626405
a 3 ¼ 0:00805420
T pc ¼ 326 þ 315:7(g g 0:5) 240y N 2 83:3y CO 2
þ 133:3y H 2 S : (2:30) a 4 ¼ 2:80860949
a 5 ¼ 3:49803305
Applications of the pseudo-critical pressure and a 6 ¼ 0:36037302
temperature are normally found in petroleum engineer- a 7 ¼ 0:01044324
ing through pseudo-reduced pressure and temperature a 8 ¼ 0:79338568
defined as
a 9 ¼ 1:39643306
p a 10 ¼ 0:14914493
p pr ¼ (2:31) a 11 ¼ 0:00441016
p pc
a 12 ¼ 0:08393872
T a 13 ¼ 0:18640885
T pr ¼ : (2:32) a 14 ¼ 0:02033679
T pc
a 15 ¼ 0:00060958
Thus, once the value of m r is determined from the right-
2.3.3 Viscosity of Gas hand side of this equation, gas viscosity at elevated pres-
Dynamic viscosity (m g ) in centipoises (cp) is usually used in sure can be readily calculated using the following relation:
petroleum engineering. Kinematic viscosity (n g ) is related
to the dynamic viscosity through density (r g ), m g ¼ m 1 e m r (2:41)
T pr
m g
n g ¼ : (2:33) Other correlations for gas viscosity include that of Dean
and Stiel (1958) and Lee et al. (1966).
r g
Kinematic viscosity is not typically used in natural gas
engineering.
Direct measurements of gas viscosity are preferred for a Example Problem 2.3 A 0.65 specific–gravity natural gas
new gas. If gas composition and viscosities of gas com- contains 10% nitrogen, 8% carbon dioxide, and 2%
ponents are known, the mixing rule can be used to deter- hydrogen sulfide. Estimate viscosity of the gas at
mine the viscosity of the gas mixture: 10,000 psia and 1808F.
P p ffiffiffiffiffiffiffiffiffiffiffi
(m gi y i MW i ) Solution Example Problem 2.3 is solved with the spread-
m g ¼ P p ffiffiffiffiffiffiffiffiffiffiffi (2:34) sheet Carr-Kobayashi-Burrows-GasViscosity.xls, which is
(y i MW i )
attached to this book. The result is shown in Table 2.3.
Viscosity of gas is very often estimated with charts or 2.3.4 Gas Compressibility Factor
correlations developed based on the charts. Gas viscosity Gas compressibility factor is also called ‘‘deviation factor’’
correlation of Carr et al. 1954 involves a two-step pro- or ‘‘z-factor.’’ Its value reflects how much the real gas
cedure: The gas viscosity at temperature and atmospheric deviates from the ideal gas at a given pressure and tem-
pressure is estimated first from gas-specific gravity and perature. Definition of the compressibility factor is
inorganic compound content. The atmospheric value is expressed as
then adjusted to pressure conditions by means of a correc-
tion factor on the basis of reduced temperature and pres- z ¼ V actual : (2:42)
sure state of the gas. The atmospheric pressure viscosity V ideal gas
(m 1 ) can be expressed as
Introducing the z-factor to the gas law for ideal gas results
þ m 1H 2 S , (2:35) in the gas law for real gas as
m 1 ¼ m 1HC þ m 1N 2 þ m 1CO 2
pV ¼ nzRT, (2:43)
where
where n is the number of moles of gas. When pressure p is
3
m 1HC ¼ 8:188 10 3 6:15 10 3 log (g g ) entered in psia, volume V in ft , and temperature in 8R, the
psia ft 3
6
þ (1:709 10 5 2:062 10 g g )T, (2:36) gas constant R is equal to10.73 mole R .

Gas compressibility factor can be determined on the basis
¼ [9:59 10 3 þ 8:48 10 3 , (2:37) of measurements in PVT laboratories. For a given amount
m 1N 2 log (g g )]y N 2
of gas, if temperature is kept constant and volume is mea-
¼ [6:24 10 3 þ 9:08 10 3 , (2:38) sured at 14.7 psia and an elevated pressure p 1 , z-factor can
m 1CO 2 log (g g )]y CO 2
then be determined with the following formula:
m 1H 2 S ¼ [3:73 10 3 þ 8:49 10 3 log (g g )]y H 2 S , (2:39)
p 1 V 1
z ¼ , (2:44)
Dempsey (1965) developed the following relation: 14:7 V 0