Page 404 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

370 Production

Zs = ZP + (A - B - B*)Z - AB = 0 (6-12)
where b = &,bi for a mixture
bi = 0.08664RTci/P. for a single component
a = Xi Xjx&a,ajj0.5fi - k,) for a mixture
a, = api for a smgle component
a = 0.42748(RTJP/Pci
a$ = 1 + mi(l - T;A)
mi = 0.48 + 1.5740~ - 0.1760f
A = aP/(RT)*, B = bP/RT

The Peng-Robinson equation (PR) is

p=-- RT a
V - b V(V + b) + b(V - b)

Z3 - (1 - B)Z4 + (A - 2B - 3B4)Z - (AB - BP - Bs) 0

where b = Gib.
bi = 0.07t796RT ./Pc
a = XiE,%T(aia$02(l - k,)
ai = aCpi
a. = 0.457237(RT .)4/P,
apz = 1 + mi(l - T?)
m, = 0.37646 + 1.542260, - 0.269920:
A, B as in SRK equation

where P = pressure (absolute units)
T = temperature (OR or K)
R = universal gas constant
Z = compressibility factor
o = acentric Pitzer factor (see Table 6-1)
T,, Pci = critical parameters (see Table 6-1)
k, = interaction coefficient (= 0 for gas phase mixture)

Both SRK and PR equations are used to predict equilibrium constant K value.
See derivation of vapor-liquid equilibrium by equation of state at end of
this subsection.
Full description of gas, oil and water properties are given in Chapter 5,
“Reservoir Engineering.” Reservoir hydrocarbon fluids are a mixture of hydro-
carbons with compositions related to source, history and present reservoir
conditions. Consider the pressurespecific volume relationship for a single-
component fluid at constant temperature, below its critical temperature initially
hold in the liquid phase at an elevated pressure. This situation is illustrated in
Figure 6-2. Bubble point and dew point curves in Figure 6-2a correspond to the
vapor pressure line in Figure 6-2b. A locus of bubble points and a locus of dew
points that meet at a point C (the critical point) indicate that the properties of
liquid and vapor become indistinguishable.
Multicomponent systems have different phase behavior than pure component.
In the P-T diagram instead of the vapor-pressure line we have an area limited
by saturation line (bubble point + dew point), see Figure 6-3. The diagram’s shape
is more or less the same for two or three-component systems as for multicomponent