Griffith correlation

Brief

The Griffith correlation is an empirical correlation which defines:

• The boundary between the bubble and slug flow
• The void fraction of gas in bubble flow - gas hold up H_g

Math & Physics

The bubble flow exist when:

$\frac{v_g}{v_g + v_L} < L_B$

$L_B = 1.071 - 0.2218 \frac{(v_g+v_L)^2}{D}$, with the limit $L_B \geqslant 0.13$

The gas holdup:

$H_g = \frac{1}{2}\ \left ( 1 + \frac{v_g+v_L}{v_s} - \sqrt{ \left ( 1 + \frac{v_g+v_L}{v_s} \right )^2 - 4 \frac{v_g}{v_s}} \right )$

Nomenclature

$H_g$ = gas holdup factor, dimensionless

$f$ = friction factor, dimensionless

$GLR$ = gas-liquid ratio, scf/bbl

$M$ = total mass of oil, water and gas associated with 1 bbl of liquid flowing into and out of the flow string, lb_m/bbl

$N_D$ = pipe diameter number number, dimensionless

$N_GV$ = gas velocity number, dimensionless

$N_L$ = liquid viscosity number, dimensionless

$N_LV$ = liquid velocity number, dimensionless

$p$ = pressure, psia

$q_c$ = conversion constant equal to 32.174, lb_mft / lb_fsec²

$q_L$ = total liquid production rate, bbl/d

$Re$ = Reynolds number, dimensionless

$R_s$ = solution gas-oil ratio, scf/stb

$SG$ = specific gravity, dimensionless

$T$ = temperature, °R or °K, follow the subscript

$v$ = velocity, ft/sec

$WOR$ = water-oil ratio, bbl/bbl

$z$ = gas compressibility factor, dimensionless