Difference between revisions of "JD"

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==Brief==
 
==Brief==
  
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[[JD]] - dimensionless productivity index, inverse of dimensionless pressure (based on average pressure) <ref name = pushing/>.
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[[JD]] - dimensionless productivity index<ref name = pushing/>, inverse of dimensionless pressure (based on average pressure) which contains the type of flow regime, boundary condition, drainage shape and stimulation <ref name = DW/>.
  
 
==Math & Physics==
 
==Math & Physics==
  
−
From the [[Darcy's law]] for an unfractured well located in the center of a circular
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:<math> {J_D} = \frac{1}{\bar{P}_D} </math>
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drainage area, the [[JD]] in pseudo-steady state is as follows:
 
−
:<math> {J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}} </math>
 
  
−
Oil
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From the [[Darcy's law]] for the unfractured well the [[JD]] is:  
−
:<math> {J_D} = \frac{141.2 B \mu}{kh} \frac{q}{\bar{P} - P_{wf}} </math>
 
  
−
Gas
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<table width="100%" border="1" cellpadding="3" cellspacing="1">
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<tr>
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<th></th>
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<th>Well in circular drainage area</th>
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<th>Well in a drainage area with the shape factor <math> {C_A}</math><ref name = DW/></th>
 +
 
 +
</tr>
 +
 
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<tr>
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<td>Steady state</td>
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<td><math> {J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{1}{2}+S}} </math></td>
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<td><math>{J_D} = \frac{1}{\frac{1}{2}ln{\frac{4.5A}{C_A{r_w}^2}+S}}</math></td>
 +
 
 +
</tr>
 +
 
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<tr>
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<td>Pseudo steady state</td>
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<td><math> {J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}} </math></td>
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<td><math>{J_D} = \frac{1}{\frac{1}{2}ln{\frac{2.25A}{C_A{r_w}^2}+S}}</math></td>
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</tr>
 +
 
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</table>
 +
 
 +
 
 +
Some typical <math> {C_A}</math> values: circle 31.6, square 30.88 <ref name = Dietz/>.
 +
 
 +
===Oil===
 +
:<math> {J_D} = \frac{141.2 B \mu}{kh} \frac{q}{\bar{P} - P_{wf}} = \frac{141.2 B \mu}{kh} J</math>
 +
 
 +
:<math> {q} = \frac{kh}{141.2 B \mu} (\bar{P} - P_{wf}) J_D </math>
 +
 
 +
===Gas===
 
:<math>J_D=\frac{1422 \times 10^3\ T_R}{kh} \frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}</math>
 
:<math>J_D=\frac{1422 \times 10^3\ T_R}{kh} \frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}</math>
 +
 +
==Maximum <math>J_D</math>==
 +
 +
The undamaged unstimulated vertical well potential in a pseudo steady radial flow in a circular drainage area:
 +
 +
:<math> {J_D}_{max} \approx \frac{1}{ln{\frac{500}{0.1}-\frac{3}{4}+0}} \approx 0.1287</math>
 +
 +
The maximum possible stimulated well potential for pseudo steady linear flow is:
 +
 +
<math>{J_D}_{max}= \frac{6}{\pi} \approx 1.91 </math> , see [[6/π stimulated well potential]]
 +
 +
The maximum possible stimulated well potential for steady state linear flow is:
 +
 +
<math>{J_D}_{max}= \frac{4}{\pi} \approx 1.27 </math> , see [[4/π stimulated well potential]]
  
 
== Nomenclature  ==
 
== Nomenclature  ==
 
:<math> B </math> = formation volume factor, bbl/stb
 
:<math> B </math> = formation volume factor, bbl/stb
 +
:<math> C_A </math> = Dietz shape factor, dimensionless
 +
:<math> J </math> = productivity index, stb/psia
 +
:<math> J_D </math> = dimensionless productivity index, dimensionless
 
:<math> kh</math> = permeability times thickness, md*ft
 
:<math> kh</math> = permeability times thickness, md*ft
 
:<math> \bar{P} </math> = average reservoir pressure, psia
 
:<math> \bar{P} </math> = average reservoir pressure, psia
 +
:<math> \bar{P}_D</math> = dimensionless pressure (based on average pressure), dimensionless
 +
:<math> P_{\bar{P}} </math> = average reservoir pseudopressure, psia<sup>2</sup>/cP
 
:<math> P_{wf} </math> = well flowing pressure, psia
 
:<math> P_{wf} </math> = well flowing pressure, psia
 +
:<math> P_{P_{wf}} </math> = average well flowing pseudopressure, psia<sup>2</sup>/cP
 +
:<math> q </math> = flowing rate, stb/d
 +
:<math> q_g </math> = gas rate, MMscfd
 
:<math> r_w </math> = wellbore radius, ft
 
:<math> r_w </math> = wellbore radius, ft
 
:<math> r_e </math> = drainage radius, ft
 
:<math> r_e </math> = drainage radius, ft
 
:<math> S </math> = skin factor, dimensionless
 
:<math> S </math> = skin factor, dimensionless
 +
:<math> T </math> = temperature, °R
 +
 +
===Greek symbols===
 +
 +
:<math> \mu </math> = viscosity, cp
 +
 +
==See Also==
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 +
* [[Darcy's law]]
 +
* [[JD]]
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* [[Productivity index|J]]
 +
* [[Production Potential]]
  
 
== References ==
 
== References ==
Line 36: Line 98:
 
  |url=https://www.onepetro.org/conference-paper/SPE-91760-MS
 
  |url=https://www.onepetro.org/conference-paper/SPE-91760-MS
 
  |url-access=registration  
 
  |url-access=registration  
 +
}}</ref>
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<ref name=DW>
 +
{{cite book
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|last1= Wolcott |first1=Don
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|title=Applied Waterflood Field Development
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|date=2009
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|publisher=Energy Tribune Publishing Inc
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|place=Houston
 +
|url=https://www.amazon.com/Applied-Waterflood-Field-Development-Wolcott/dp/0578023946/ref=sr_1_1?ie=UTF8&qid=1481788841&sr=8-1&keywords=Don+wolcott
 +
|url-access=subscription
 
}}</ref>
 
}}</ref>
  
 +
<ref name= Dietz >{{cite journal
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|last1=Dietz|first1=D.N.
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|title=Determination of Average Reservoir Pressure From Build-Up Surveys
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|publisher=J Pet Technol
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|number=SPE-1156-PA
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|date=1965
 +
|url=https://doi.org/10.2118/1156-PA
 +
|url-access=registration
 +
}}</ref>
 
</references>
 
</references>
  
 
[[Category:optiFrac]]
 
[[Category:optiFrac]]
 +
[[Category:optiFracMS]]
 +
[[Category:fracDesign]]
 
[[Category:pengtools]]
 
[[Category:pengtools]]
 
[[Category:E&P Portal]]
 
[[Category:E&P Portal]]
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 +
{{#seo:
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|title=Dimensionless Productivity Index
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|titlemode= replace
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|keywords=hydraulic fracturing, hydraulic fracturing formulas, well potential, productivity index
 +
|description=JD dimensionless productivity index
 +
}}
 +
<div style='text-align: right;'>By Mikhail Tuzovskiy on {{REVISIONTIMESTAMP}}</div>

Latest revision as of 12:32, 12 July 2023

Brief

JD - dimensionless productivity index[1], inverse of dimensionless pressure (based on average pressure) which contains the type of flow regime, boundary condition, drainage shape and stimulation [2].

Math & Physics

{J_D} = \frac{1}{\bar{P}_D}

From the Darcy's law for the unfractured well the JD is:

Well in circular drainage area Well in a drainage area with the shape factor {C_A}[2]
Steady state {J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{1}{2}+S}} {J_D} = \frac{1}{\frac{1}{2}ln{\frac{4.5A}{C_A{r_w}^2}+S}}
Pseudo steady state {J_D} = \frac{1}{ln{\frac{r_e}{r_w}-\frac{3}{4}+S}} {J_D} = \frac{1}{\frac{1}{2}ln{\frac{2.25A}{C_A{r_w}^2}+S}}


Some typical {C_A} values: circle 31.6, square 30.88 [3].

Oil

{J_D} = \frac{141.2 B \mu}{kh} \frac{q}{\bar{P} - P_{wf}} = \frac{141.2 B \mu}{kh} J
{q} = \frac{kh}{141.2 B \mu} (\bar{P} - P_{wf}) J_D

Gas

J_D=\frac{1422 \times 10^3\ T_R}{kh} \frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}

Maximum J_D

The undamaged unstimulated vertical well potential in a pseudo steady radial flow in a circular drainage area:

{J_D}_{max} \approx \frac{1}{ln{\frac{500}{0.1}-\frac{3}{4}+0}} \approx 0.1287

The maximum possible stimulated well potential for pseudo steady linear flow is:

{J_D}_{max}= \frac{6}{\pi} \approx 1.91 , see 6/π stimulated well potential

The maximum possible stimulated well potential for steady state linear flow is:

{J_D}_{max}= \frac{4}{\pi} \approx 1.27 , see 4/π stimulated well potential

Nomenclature

B = formation volume factor, bbl/stb
C_A = Dietz shape factor, dimensionless
J = productivity index, stb/psia
J_D = dimensionless productivity index, dimensionless
kh = permeability times thickness, md*ft
\bar{P} = average reservoir pressure, psia
\bar{P}_D = dimensionless pressure (based on average pressure), dimensionless
P_{\bar{P}} = average reservoir pseudopressure, psia2/cP
P_{wf} = well flowing pressure, psia
P_{P_{wf}} = average well flowing pseudopressure, psia2/cP
q = flowing rate, stb/d
q_g = gas rate, MMscfd
r_w = wellbore radius, ft
r_e = drainage radius, ft
S = skin factor, dimensionless
T = temperature, °R

Greek symbols

\mu = viscosity, cp

See Also

References

  1. ↑ Rueda, J.I.; Mach, J.; Wolcott, D. (2004). "Pushing Fracturing Limits to Maximize Producibility in Turbidite Formations in Russia"Free registration required (SPE-91760-MS). Society of Petroleum Engineers. 
  2. ↑ 2.0 2.1 Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 
  3. ↑ Dietz, D.N. (1965). "Determination of Average Reservoir Pressure From Build-Up Surveys"Free registration required (SPE-1156-PA). J Pet Technol. 
By Mikhail Tuzovskiy on 20230712123204
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