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.

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

Math & Physics

Applying Real Gas EOS at reservoir conditions:

$PV_r=z\frac{m}{M} RT_r$ (1)

Applying Real Gas EOS at standard conditions:

$P_{SC}V_g=1\frac{m}{M} RT_{SC}$ (2)

Dividing eq. 2 by eq. 1 and rearranging:

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

Applying eq. 3 for initial conditions and for any point in time:

$GIIP=\frac{P_i}{z_i} \frac{V_rT_{SC}}{P_{SC}T_{r}}$

Applying eq. 3 for any point in time:

$GIIP-G_p=\frac{P}{z} \frac{V_rT_{SC}}{P_{SC}T_{r}}$

Therefore at any time:

$\frac{G_p}{GIIP}=1-\frac{P}{z} \frac{z_i}{P_i}$, or $\frac{P}{z}=\frac{P_i}{z_i} \left (1- \frac{G_p}{GIIP}\right )$

Thus a plot of P/z vs cumulative produced gas is a straight line intersecting X axis at GIIP.

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