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

P/Z plot is a part of the Reservoir Management workflow of the E&P Portal to estimate Reservoirs GIIP.

Gas Flowing Material Balance is the more advanced tool to determine the Reservoirs GIIP as well as Well's EUR and JD.

Nomenclature

$GIIP$ = gas initially in place, scf

$G_p$ = cumulative gas produced, scf

$P$ = reservoir pressure (changing), psia

$P_{i}$ = initial reservoir pressure (constant), psia

$P_{SC}$ = pressure at standard conditions, psia

$T_i$ = initial reservoir pressure (constant), °R

$T_r$ = reservoir pressure (constant), °R

$T_{SC}$ = temperature at standard conditions (constant), °R

$V_g$ = volume of gas in reservoir converted to standard conditions (changing), scf

$V_r$ = reservoir volume, ft³

$z$ = gas compressibility factor (changing), dimensionless

$z_i$ = initial gas compressibility factor (constant), dimensionless