View source for P/Z plot

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== Brief ==
The [[P/Z plot]] is a plot of P/z versus cumulative gas production, G<sub>p</sub>.

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:
:<math> PV_r=z\frac{m}{M} RT_r</math> (1)

Applying [[Real Gas]] [[EOS]] at standard conditions:
:<math> P_{SC}V_g=1\frac{m}{M} RT_{SC}</math> (2)

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>

Applying eq. 3 for any point in time:
:<math> GIIP-G_p=\frac{P}{z} \frac{V_rT_{SC}}{P_{SC}T_{r}}</math>

Therefore at any time:
:<math> \frac{G_p}{GIIP}=1-\frac{P}{z} \frac{z_i}{P_i}</math>, or <math> \frac{P}{z}=\frac{P_i}{z_i} \left (1- \frac{G_p}{GIIP}\right )</math>

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  ==

:<math> D </math> = pipe diameter, ft
:<math> H_g </math> = gas holdup factor, dimensionless
:<math> L_B </math> = bubble-slug boundary, dimensionless
:<math> v_g </math> = gas velocity, ft/sec
:<math> v_L </math> = liquid velocity, ft/sec
:<math> v_s </math> = 0.8, slip velocity (difference between average gas and liquid velocities), ft/sec

== References ==
<references>

<ref name= Griffith>{{cite journal
 |last1= Griffith |first1=P.
 |last2= Wallis |first2=G. B.
 |title=Two-Phase Slug Flow
 |journal=Journal of Heat Transfer
 |publisher = ASME
 |date=August 1961
 |volume=83
 |pages=307-320
 |url=http://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleid=1432339&resultClick=3
 |url-access= subscription 
}}</ref>

<ref name= Orkiszewski>{{cite journal
 |last1= Orkiszewski |first1=J.
 |title=Predicting Two-Phase Pressure Drops in Vertical Pipe
 |journal=Journal of Petroleum Technology
 |publisher = SPE
 |number = SPE-1546-PA
 |date=June 1967
 |volume=19
 |url=https://www.onepetro.org/journal-paper/SPE-1546-PA
 |url-access= subscription 
}}</ref>

<ref name=Economides>{{cite book
 |last1= Economides |first1=M.J.
 |last2= Hill |first2=A.D.
 |last3= Economides |first3=C.E. 
 |last4= Zhu |first4=D.
 |title=Petroleum Production Systems
 |edition=2
 |date=2013
 |publisher=Prentice Hall
 |place=Westford, Massachusetts
 |isbn=978-0-13-703158-0
}}</ref>
</references>

[[Category:pengtools]]
[[Category:PQplot]]