P/Z plot

Brief

The P/Z plot is a plot of P/Z versus cumulative gas production, G_p.

The interpretation technique is fitting the data points with the straight line to estimate GIIP.

Math & Physics

The P/Z plot is based on the Gas Material Balance equation.

Applying Real gas EOS at reservoir conditions: (1):$PV_r=z\frac{m}{M} RT_r$

Applying Real gas EOS at standard conditions: (2):$P_{SC}V_g=1\frac{m}{M} RT_{SC}$

Dividing eq (2) by eq (1) and rearranging: (3):$V_g=\frac{P}{z} \frac{V_rT_{SC}}{P_{SC}T_{r}}$

$V_g=\frac{P}{z}\frac{V_rT_{SC}}{P_{SC}T_r}$ (3)

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:

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

Discussion

Griffith correlation adds a hook to the originally straight Hagedorn and Brown VLP curve.

Nomenclature

$D$ = pipe diameter, ft

$H_g$ = gas holdup factor, dimensionless

$L_B$ = bubble-slug boundary, dimensionless

$v_g$ = gas velocity, ft/sec

$v_L$ = liquid velocity, ft/sec

$v_s$ = 0.8, slip velocity (difference between average gas and liquid velocities), ft/sec