Page 466 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

444 Production

(ht continuad fsom page 419)
while the data from Table 6-20 was used for the Benedict-Webb-Rubin equation
modified by Starling [16].
Applying Peng-Robinson equation

or

A z + (za5 + 1)~
hei = - h(Z - B) + (Z - 1)BI - -(A; - B;) 1 (6-536)
2l.5 B Z - (qas - l)B

where

bi
Bi =- (6-54)
b

(6-55)

Notations are as in Equations 6-13 and 6-14.
The objectives of any equation-of-state solution method are the reliable and
accurate prediction of the volumetric properties of the fluid mixture under
consideration. The overall solution procedure is as follows:
fix the total composition, temperature and pressure
calculate constants for the equation of state
solve equation for the volumetric property (specific volume, density or
compressibility factor)

When pressure and temperature fall to a two-phase region, the equation must
be solved twice, separately for vapor and liquid. The composition of each phase
will be different so the equation of state constants will have to be evaluated for
both the liquid and the vapor phases. Both SRK and PR are cubic equations,
so the solution always gives three roots, as is shown in Figure 631 [17]. However,
the Pr-Vr relationship at a given T, is discontinuous at Vr = b;, Vr = b;, and
Vr = b;. We are interested in only Vr > b;, which in case the SRK equation is
equal 0.08664 and 0.077796 for the PR equation. For Vr > b; and T, > 1.0, there
is only one value of the compressibility factor that will satisfy the equation of
state. For Vr > b; and Tr < 1.0 we will get three values of Z. The largest Z of
the vapor Z’s is chosen for the vapor and the smallest amount the liquid Z’s is
chosen for the liquid. However, in an earlier stage of the iterative VLE calcula-
tions, it is not Uncommon to encounter a single root, mainly because of incorrect
compositions [17].
A logic diagram for a trial-and-error solution procedure for cubic equations
of state is given in Figure 6-32. This diagram shows a traditional Newton-
Raphson approach with an interval halving limiting procedure superimposed on