Difference between revisions of "Reciprocal Rate Method"

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==Brief==
 
==Brief==
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[[Reciprocal Rate Method]] - is
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[[Reciprocal Rate Method]] is the method to estimate oil [[Well]]s and [[Reservoirs]] [[EUR]] using only rate-time production data<ref name=1_q/> published in '''2007''' by Thomas Blasingame et al.
  
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The methodology does presume that flowing well bottomhole pressures are approximately constant<ref name=1_q/>.
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The interpretation technique is fitting the data points with the straight line to estimate the slope which gives [[EUR]].
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[[File:ReciprocalRateMethod.png|link=https://ep.pengtools.com/reciprocal/reciprocal-method/well-reciprocal-rate?WellFilter%5Bfield_id%5D=&WellFilter%5Bfield_id%5D%5B%5D=11&WellFilter%5Bshop_id%5D=&WellFilter%5Bpad_id%5D=&WellFilter%5Bwell_id%5D=25214]]
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<center>[[Reciprocal Rate Method]] in the [https://ep.pengtools.com/reciprocal/reciprocal-method/well-reciprocal-rate?WellFilter%5Bfield_id%5D=&WellFilter%5Bfield_id%5D%5B%5D=11&WellFilter%5Bshop_id%5D=&WellFilter%5Bpad_id%5D=&WellFilter%5Bwell_id%5D=25214 E&P Portal]</center>
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== Math & Physics ==
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The total pressure drop at the wellbore is:
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:<math> \Delta P =P_i - P_{wf} = (P_i - \bar{P}) + (\bar{P}-P_{wf}) </math>
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Where:
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:<math> P_i - \bar{P} = m_{mb} N_p</math>, is pressure drop due to depletion defined by the [[Oil Material Balance]] for black oil at P>P<sub>b</sub>,
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:<math> \bar{P}-P_{wf} = b_{pss} q_o</math>, is pressure drop due to [[Darcy's law]]
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Where:
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:<math> m_{mb} = \frac{B_o}{N c_t B_{oi}}</math>
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:<math> b_{pss} = \frac{141.2 \mu_o B_o}{k_o h J_D}</math>
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The total pressure drop at the wellbore now can be rewritten as:
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:<math> \Delta P =P_i - P_{wf} = m_{mb} N_p +  b_{pss} q_o </math>
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Dividing both sides by the assumed constant: <math> \Delta P =P_i - P_{wf} = P_{con} = constant </math> <ref name=1_q/>:
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:<math> 1 = m_{mb}^' N_p +  b_{pss}^' q_o </math>
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As the flowrate decreases to zero (i.e., q<sub>o</sub> → 0)<ref name=1_q/>:
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<math>\lim_{q_{o}\rightarrow 0} N_p=\frac{1}{m_{mb}^'}= EUR</math>
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Therefore a plot of '''1/q<sub>o</sub>''' versus '''Np/q<sub>o</sub>''' yields a straight-line trend where the slope of the line is inversely proportional to the [[EUR]]<ref name=1_q/>.
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==Discussion==
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[[Reciprocal Rate Method]] can be applied to estimate:
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*single [[Well]] [[EUR]]
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*single [[Reservoirs| Reservoir]] [[EUR]].
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[[Reciprocal Rate Method]] can be used for fracture and refracture analysis, sidetrack analysis etc.
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[[:Category:E&P Portal |E&P Portal]] has the capability to automatically calculate [[EUR]] for a number of [[Well]]s or [[Reservoirs]] through the [https://ep.pengtools.com/reciprocal/reciprocal-method/recalculate-well EUR calculator].
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==Examples==
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'''Example 1. Well "21" refrac doubles the EUR as indicated by the slope change.'''
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[[File:Reciprocal Rate Method Example 2.png|link=https://ep.pengtools.com/reciprocal/reciprocal-method/well-reciprocal-rate?WellFilter%5Bfield_id%5D=&WellFilter%5Bfield_id%5D%5B%5D=11&WellFilter%5Bshop_id%5D=&WellFilter%5Bpad_id%5D=&WellFilter%5Bwell_id%5D=25197]]
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'''Example 2. 22 wells on the [[Reciprocal Rate Method]] plot showing the well's EUR spread. Well "19" trend is highlighted.'''
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[[File:Reciprocal Rate Method Example 1.png|link=https://ep.pengtools.com/daily/measures/oil-producers?WellFilter%5Bfield_id%5D=&WellFilter%5Bfield_id%5D%5B%5D=11&WellFilter%5Bshop_id%5D=&WellFilter%5Bpad_id%5D=&WellFilter%5Bwell_id%5D=&WellFilter%5Bwell_id%5D%5B%5D=25205&dataRangeHelper=&WellFilter%5Bdate_from%5D=&WellFilter%5Bdate_to%5D=]]
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'''Example 3. EUR results table for 22 wells. Automatically interpreted wells have "No" flag,  manually interpreted "Yes" flag in the last column.'''
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[[File:Reciprocal Rate Method Example 3.png|https://ep.pengtools.com/reciprocal/reciprocal-method-eur/index]]
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'''Example 4. "B2" reservoir [[Reciprocal Rate Method]] plot showing the Reservoir EUR.'''
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[[File:Reciprocal Rate Method Example 4.png|https://ep.pengtools.com/reciprocal/reciprocal-method/reservoir-reciprocal-rate?ReservoirFilter%5Bcountry_id%5D=&ReservoirFilter%5Bfield_id%5D=&ReservoirFilter%5Bfield_id%5D%5B%5D=11&ReservoirFilter%5Bobject_id%5D=&ReservoirFilter%5Breservoir_id%5D=23]]
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==Workflow==
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# Upload the data required
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# Open the [[Reciprocal Rate Method]] tool
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#* [[Well]]s tool [https://ep.pengtools.com/reciprocal/reciprocal-method/well-reciprocal-rate here]
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#* [[Reservoirs]] tool [https://ep.pengtools.com/reciprocal/reciprocal-method/reservoir-reciprocal-rate here]
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# Fit data with the red trend line
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# Calculate the slope of the line and [[EUR]]
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# Save the [[Reciprocal Rate Method]] model
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# Move to the next [[Well]] / [[Reservoirs|Reservoir]]
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== Data required ==
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[[Well]]s interpretation:
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* Create [[Field]] [https://ep.pengtools.com/field/index  here]
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* [[Upload Wells]]
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* [[Upload Daily Measures]]
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[[Reservoirs]] interpretation:
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* Create or Upload [[Reservoirs]] [https://ep.pengtools.com/reservoir/index here]
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* Upload [[Perforations]] to connect [[Well]]s to the [[Reservoirs]]
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== Nomenclature  ==
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:<math> B_{o} </math> = oil formation volume factor, bbl/stb
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:<math> B_{oi} </math> = initial oil formation volume factor, bbl/stb
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:<math> b_{pss} </math> = reservoir constant, inverse to productivity index, psia/stb/d
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:<math> b_{pss}^' = \frac{b_{pss}}{P_{con}}</math> = reservoir constant, inverse to productivity index, 1/stb/d
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:<math> c_t </math> = total compressibility, psia<sup>-1</sup>
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:<math> J_D </math> = dimensionless productivity index, dimensionless
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:<math> k_oh</math> = oil permeability times thickness, md*ft
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:<math> m_{mb} </math> = slope term, psia/stb
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:<math> m_{mb}^' = \frac{m_{mb}}{P_{con}}</math> = slope term, 1/stb
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:<math> N </math> = stock tank oil initially in place, stb
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:<math> N_p </math> = cumulative oil production, stb
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:<math> \bar{P} </math> = average reservoir pressure, psia
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:<math> P_{i} </math> = initial pressure, psia
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:<math> P_{con} </math> = constant, psia
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:<math> P_{wf} </math> = well flowing pressure, psia
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:<math> q_o </math> = oil rate, stb/d
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===Greek symbols===
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:<math> \mu_o </math> = oil viscosity , cp
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== References ==
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<references>
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<ref name=1_q>{{cite journal
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|first1=Thomas Alwin |last1= Blasingame
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|first2= Dilhan |last2=Ilk
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|first3=Parker D. |last3=Reese
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|title=Estimation of Reserves Using the Reciprocal Rate Method
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|number=SPE-107981-MS
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|publisher=Society of Petroleum Engineers
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|date=2007
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|url=https://www.onepetro.org/conference-paper/SPE-107981-MS
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|url-access=registration
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}}</ref>
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</references>
  
 
[[Category:E&P Portal]]
 
[[Category:E&P Portal]]
 
[[Category:Reservoir Management]]
 
[[Category:Reservoir Management]]
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{{#seo:
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|title=Reciprocal Rate Method
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|titlemode= replace
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|keywords=Reciprocal Rate Method
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|description=Reciprocal Rate Method is the method to estimate oil well's and reservoirs expected ultimate recovery using only rate-time production data published in 2007 by Thomas Blasingame et al..
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}}

Latest revision as of 09:26, 6 December 2018

Brief

Reciprocal Rate Method is the method to estimate oil Wells and Reservoirs EUR using only rate-time production data[1] published in 2007 by Thomas Blasingame et al.

The methodology does presume that flowing well bottomhole pressures are approximately constant[1].

The interpretation technique is fitting the data points with the straight line to estimate the slope which gives EUR.

ReciprocalRateMethod.png

Reciprocal Rate Method in the E&P Portal

Math & Physics

The total pressure drop at the wellbore is:

\Delta P =P_i - P_{wf} = (P_i - \bar{P}) + (\bar{P}-P_{wf})

Where:

P_i - \bar{P} = m_{mb} N_p, is pressure drop due to depletion defined by the Oil Material Balance for black oil at P>Pb,
\bar{P}-P_{wf} = b_{pss} q_o, is pressure drop due to Darcy's law

Where:

m_{mb} = \frac{B_o}{N c_t B_{oi}}
b_{pss} = \frac{141.2 \mu_o B_o}{k_o h J_D}

The total pressure drop at the wellbore now can be rewritten as:

\Delta P =P_i - P_{wf} = m_{mb} N_p + b_{pss} q_o

Dividing both sides by the assumed constant: \Delta P =P_i - P_{wf} = P_{con} = constant [1]:

1 = m_{mb}^' N_p + b_{pss}^' q_o

As the flowrate decreases to zero (i.e., qo → 0)[1]:

\lim_{q_{o}\rightarrow 0} N_p=\frac{1}{m_{mb}^'}= EUR

Therefore a plot of 1/qo versus Np/qo yields a straight-line trend where the slope of the line is inversely proportional to the EUR[1].

Discussion

Reciprocal Rate Method can be applied to estimate:

Reciprocal Rate Method can be used for fracture and refracture analysis, sidetrack analysis etc.

E&P Portal has the capability to automatically calculate EUR for a number of Wells or Reservoirs through the EUR calculator.

Examples

Example 1. Well "21" refrac doubles the EUR as indicated by the slope change. Reciprocal Rate Method Example 2.png

Example 2. 22 wells on the Reciprocal Rate Method plot showing the well's EUR spread. Well "19" trend is highlighted. Reciprocal Rate Method Example 1.png

Example 3. EUR results table for 22 wells. Automatically interpreted wells have "No" flag, manually interpreted "Yes" flag in the last column. https://ep.pengtools.com/reciprocal/reciprocal-method-eur/index

Example 4. "B2" reservoir Reciprocal Rate Method plot showing the Reservoir EUR. https://ep.pengtools.com/reciprocal/reciprocal-method/reservoir-reciprocal-rate?ReservoirFilter%5Bcountry_id%5D=&ReservoirFilter%5Bfield_id%5D=&ReservoirFilter%5Bfield_id%5D%5B%5D=11&ReservoirFilter%5Bobject_id%5D=&ReservoirFilter%5Breservoir_id%5D=23

Workflow

  1. Upload the data required
  2. Open the Reciprocal Rate Method tool
  3. Fit data with the red trend line
  4. Calculate the slope of the line and EUR
  5. Save the Reciprocal Rate Method model
  6. Move to the next Well / Reservoir

Data required

Wells interpretation:

Reservoirs interpretation:

Nomenclature

B_{o} = oil formation volume factor, bbl/stb
B_{oi} = initial oil formation volume factor, bbl/stb
b_{pss} = reservoir constant, inverse to productivity index, psia/stb/d
b_{pss}^' = \frac{b_{pss}}{P_{con}} = reservoir constant, inverse to productivity index, 1/stb/d
c_t = total compressibility, psia-1
J_D = dimensionless productivity index, dimensionless
k_oh = oil permeability times thickness, md*ft
m_{mb} = slope term, psia/stb
m_{mb}^' = \frac{m_{mb}}{P_{con}} = slope term, 1/stb
N = stock tank oil initially in place, stb
N_p = cumulative oil production, stb
\bar{P} = average reservoir pressure, psia
P_{i} = initial pressure, psia
P_{con} = constant, psia
P_{wf} = well flowing pressure, psia
q_o = oil rate, stb/d

Greek symbols

\mu_o = oil viscosity , cp

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 Blasingame, Thomas Alwin; Ilk, Dilhan; Reese, Parker D. (2007). "Estimation of Reserves Using the Reciprocal Rate Method"Free registration required (SPE-107981-MS). Society of Petroleum Engineers. 
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