Difference between revisions of "P/Z plot"

Revision as of 08:54, 21 November 2017

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:

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:

Failed to parse (syntax error): \frac{G_p}{GIIP}=1-\frac{P}{z} \frac{z_i}{P_i}}

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

References

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@@ Line 15: / Line 15: @@
 :<math> P_{SC}V_g=1\frac{m}{M} RT_{SC}</math> (2)
-Dividing eq (2) by eq (1) and rearranging:
+Dividing eq. 2 by eq. 1 and rearranging:
 :<math> V_g=\frac{P}{z} \frac{V_rT_{SC}}{P_{SC}T_{r}}</math>(3)
+Applying eq. 3 for initial conditions and for any point in time:
+:<math> GIIP=\frac{P_i}{z_i} \frac{V_rT_{SC}}{P_{SC}T_{r}}</math>
-The bubble flow exist when:
+Applying eq. 3 for any point in time:
-:<math> \frac{v_g}{v_g + v_L} < L_B </math><ref name= Economides />
+:<math> GIIP-G_p=\frac{P}{z} \frac{V_rT_{SC}}{P_{SC}T_{r}}</math>
-:<math> L_B = 1.071 - 0.2218 \frac{(v_g+v_L)^2}{D}</math>, with the limit <math> L_B \geqslant 0.13 </math><ref name= Orkiszewski />
+Therefore at any time:
+:<math> \frac{G_p}{GIIP}=1-\frac{P}{z} \frac{z_i}{P_i}}</math>
-The gas holdup:
-:<math> 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 ) </math><ref name= Orkiszewski />
 == Discussion  ==

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