Dranchuk correlation

Brief

Dranchuk correlation is the fitting equation of the classic Standing and Katz gas compressibility factor correlation.

Math & Physics

A1 = 0.3265
A2 = –1.0700
A3 = –0.5339
A4 = 0.01569
A5 = –0.05165
A6 = 0.5475
A7 = –0.7361
A8 = 0.1844
A9 = 0.1056
A10 = 0.6134
A11 = 0.7210

$z = 1-z+ \left(A_1 +\frac{A_2}{T_{pr}} +\frac{A_3}{T^3_{pr}} +\frac{A_4}{T^4_{pr}} +\frac{A_5}{T^5_{pr}} \right)\ \rho_r+ \left(A_6 +\frac{A_7}{T_{pr}} +\frac{A_8}{T^2_{pr}} \right)\ \rho^2_r -A_9\ \left(\frac{A_7}{T_{pr}}+\frac{A_8}{T^2_{pr}}\right) +A_{10}\ \left(1+A_{11}\ \rho^2_r\right)\ \frac{\rho^2_r}{T^3_{pr}} \ e^{(-A_{11}\ \rho^2_r)}$

where

$\rho_r = \frac{0.27\ P_{pr}}{{z\ T_{pr}}}$

$P_{pr} = \frac{P}{P_{pc}}$

$T_{pr} = \frac{T}{T_{pc}}$

Workflow

To solve the Dranchuk equation use the iterative secant method.

To find the pseudo critical properties given the gas specific gravity:

$P_{pc} = 4.6+0.1\ SG_g-0.258\ SG^2_g$

$T_{pc} = 99.3+180\ SG_g-6.94\ SG^2_g$

Discussion

Application range:

$0.2 \ll P_pr < 30 ; 1.0 < T_pr \ll 3.0$ & $P_pr < 1.0 ; 0.7 < T_pr \ll 1.0$

Nomenclature

$A_1..A_{11}$ coefficients

$\rho_r$ = reduced density, dimensionless

$P$ = Pressure, psia

$P_{pc}$ = pseudo critical pressure, psia

$P_{pr}$ = pseudoreduced pressure, dimensionless

$SG_g$ = gas specific gravity, dimensionless

$T$ = temperature, °R

$T_{pc}$ = pseudo critical temperature, °R

$T_{pr}$ = pseudoreduced temperature, dimensionless

$z$ = gas compressibility factor, dimensionless