Difference between revisions of "P/Z plot"

Revision as of 08:49, 21 November 2017

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.

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

^[1]

L_B = 1.071 - 0.2218 \frac{(v_g+v_L)^2}{D}

, with the limit

L_B \geqslant 0.13

^[2]

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 )

^[2]

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

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

↑ Economides, M.J.; Hill, A.D.; Economides, C.E.; Zhu, D. (2013). Petroleum Production Systems (2 ed.). Westford, Massachusetts: Prentice Hall. ISBN 978-0-13-703158-0.
↑ ^2.0 ^2.1 Orkiszewski, J. (June 1967). "Predicting Two-Phase Pressure Drops in Vertical Pipe". Journal of Petroleum Technology. SPE. 19 (SPE-1546-PA).

Cite error: <ref> tag with name "Griffith" defined in <references> is not used in prior text.

@@ Line 9: / Line 9: @@
 The [[P/Z plot]] is based on the [[Gas Material Balance]] equation.
-:<math> P_rV_r=z\frac{m}{M} RT_r</math> (1)
+Applying [[Real gas]] [[EOS]] at reservoir conditions:
+(1):<math> PV_r=z\frac{m}{M} RT_r</math>
+Applying [[Real gas]] [[EOS]] at standard conditions:
+(2):<math> P_{SC}V_g=1\frac{m}{M} RT_{SC}</math>
+Dividing eq (2) by eq (1) and rearranging:
+(3):<math> V_g=\frac{P}{z} \frac{V_rT_{SC}}{P_{SC}T_{r}}</math>
-:<math> P_{SC}V_g=1\frac{m}{M} RT_{SC}</math> (2)
-(1) -> (2)
 :<math> V_g=\frac{P}{z}\frac{V_rT_{SC}}{P_{SC}T_r}</math> (3)