PROPERTIES OF RESERVOIR GASES - Petroleum Reservoir Fluid Property Correlations - page 17

where

i A j

1 0.3265

2 -1.0700

3 -0.5339

4 0.01569

5 -0.05165

6 0.5475

7 -0.7361

8 0.1844

9 0.1056

10 0.6134

11 0.7210

This combination of correlation equations should predict values of
z-factors from measured values of gas specific gravities to a precision
equal to normal experimental accuracy.

Convergence of the trial-and-error correlation procedures
The best of the z-factor correlation procedures, Hall-Yarborough
and Dranchuk-Abou-Kassem, require very difficult trial-and-error
calculations. The Hall-Yarbrough procedure failed to converge in about
0.5% of the lines of data listed in table 2-1 even though the relatively
robust calculation procedure recommended by Dake was used. 18
A “brute-force” procedure for solving the DAK trial-and-error
calculations converged for every one of the 6,000 lines of data in the
z-factor data set. This procedure is as follows. Start with a first trial
value of z-factor = 1.0. Calculate the pseudoreduced density of the gas
with equation (2.8) and then calculate z-factor with equation (2.7).
Calculate an error function, delta , as the calculated z-factor minus the
trial value of z-factor. If p pr is less than or equal to 2.0, the next trial value
of z-factor will be the previous trial value plus delta . If p pr is greater than
2.0 and less than or equal to 3.0, the next trial value will be the previous
trial value plus delta /2.0. If p pr is greater than 3.0 and less than or equal
to 6.0, the next trial value will be the previous trial value plus delta /3.0.
If p pr is greater than 6.0, the next trial value will be the previous trial
value plus delta /5.0. Occasionally this procedure requires as many as 20
iterations to converge, especially at high pressures, but often less than
five iterations are required.