An Equation of State for Condensate Fluids
- Harvey T. Kennedy (Texas A and M U.) | NANIK S. Bhagia (Ministry Of Mines And Hydrocarbons)
- Document ID
- Society of Petroleum Engineers
- Society of Petroleum Engineers Journal
- Publication Date
- September 1969
- Document Type
- Journal Paper
- 279 - 286
- 1969. Society of Petroleum Engineers
- 4.6 Natural Gas, 5.2.1 Phase Behavior and PVT Measurements, 5.2.2 Fluid Modeling, Equations of State, 5.2 Reservoir Fluid Dynamics, 5.8.8 Gas-condensate reservoirs
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An equation of state has been developed for determining the molal volumes of both liquids and vapors of pure hydrocarbons from methane through hexanes. It is also applicable to nitrogen, hydrogen sulfide and carbon dioxide. A modification of the equation has been formulated specifically for application to condensate reservoir fluids.
The equation is of the same form as that proposed by Redlich and Kwong. However, a and b proposed by Redlich and Kwong. However, a and b are functions of temperature instead of being constants of each material. The equation as applied to pure gases and liquids, has an average absolute deviation from experimental values of 0.16 percent and 0.18 percent, respectively. As applied to 4,465 data points on condensate reservoir fluids, with temperatures to 322 degrees F and pressures to 15,500 psi, the average deviation was pressures to 15,500 psi, the average deviation was 1.48 percent. The equation compares favorably with other published works.
Many equations of state for hydrocarbons have become available in recent years. One might question the need for further research effort in this direction. We feel this work is justified because it: (1) has provided greater accuracy over extended ranges of provided greater accuracy over extended ranges of both temperature and pressure; (2) has been applied to about six times as many data points as the previously most useful equation; and (3) is simpler previously most useful equation; and (3) is simpler than any other equation that approaches its accuracy.
The equation was developed primarily to predict the volumes of mixtures of gases under high pressure in condensate reservoirs. We found it gave the simplest and most accurate means of estimating the volumes of pure hydrocarbon gases, using the same constants for the individual components. When a set of constants and the appropriate root were selected for least error as applied to pure hydrocarbon liquids, the most favorable equation for this purpose resulted.
Other similar methods have been proposed.
DEVELOPMENT OF EQUATIONS
PURE COMPONENTS PURE COMPONENTS Experimental data on PVT relations for pure materials were obtained from Refs. 4 through 8. The Redlich-Kwong equations may be written as
a RT = (p + ------------)(V -b) . 5 M T V (V +b) M M . . . . . . . . . . . . . . . . . . . .(1)
Pairs of data points from numerous isotherms were substituted in Eq. 1, and the two resulting equations were solved simultaneously for a and b. Subscripts 1 and 2 represent these distinct points. The solution yields an expression that is cubic in b (Eq. 2).
3 E 2 G H b + (----) b + (----)b+ ------ = 0 E E E . . . . . . . . . . . . . . (2)
C = RT - p V 1 1M
D = RT - p V 2 2M
E = C - D
F = V V (p -p ) + RT (V -V ) 1m 2m 1 2 2M 1M
2 2 G = DV - CV 2M 1M
H = V V (CV -DV ) 1M 2M 2M 2M
Eq. 2 is of third degree in b. It must have three roots, equal or unequal, real or imaginary. in most cases only one real rooc exists. When three roots exist, two of them are negative, and the positive root is always selected. Solution of the cubic equation is found in Ref. 10.
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