Difference between revisions of "Reciprocal Rate Method"

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.

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>P_b,

\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., q_o → 0)^[1]:

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

Therefore a plot of 1/q_o versus Np/q_o 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:

single Well EUR
single Reservoir EUR.

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.

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

Example 3. EUR results table for 22 wells. Automatically interpreted wells have "No" flag, manually interpreted "Yes" flag in the last column.

Example 4. "B2" reservoir Reciprocal Rate Method plot showing the Reservoir EUR.

Workflow

Upload the data required
Open the Reciprocal Rate Method tool
- Wells tool here
- Reservoirs tool here
Fit data with the red trend line
Calculate the slope of the line and EUR
Save the Reciprocal Rate Method model
Move to the next Well / Reservoir

Data required

Wells interpretation:

Reservoirs interpretation:

Create or Upload Reservoirs here
Upload Perforations to connect Wells to the Reservoirs

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

↑ ^1.0 ^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" (SPE-107981-MS). Society of Petroleum Engineers.

[1_q-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" (SPE-107981-MS). Society of Petroleum Engineers.

[1]

@@ Line 1: / Line 1: @@
 ==Brief==
-[[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.
+[[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.
 The methodology does presume that flowing well bottomhole pressures are approximately constant<ref name=1_q/>.
@@ Line 32: / Line 32: @@
 :<math> \Delta P =P_i - P_{wf} = m_{mb} N_p +  b_{pss} q_o </math>
-Or:
+Dividing both sides by the assumed constant: <math> \Delta P =P_i - P_{wf} = P_{con} = constant </math> <ref name=1_q/>:
-:<math> \frac{\Delta P}{q_o} =  b_{pss} + m_{mb} \frac{N_p}{q_o}</math>
+:<math> 1 = m_{mb}^' N_p +  b_{pss}^' q_o </math>
+As the flowrate decreases to zero (i.e., q<sub>o</sub> → 0)<ref name=1_q/>:
+<math>\lim_{q_{o}\rightarrow 0} N_p=\frac{1}{m_{mb}^'}= EUR</math>
+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/>.
 ==Discussion==
@@ Line 42: / Line 48: @@
 *single [[Reservoirs| Reservoir]] [[EUR]].
-==Case Study==
+[[Reciprocal Rate Method]] can be used for fracture and refracture analysis, sidetrack analysis etc.
-This Case Study demonstrates the application of the [[Oil Flowing Material Balance]] engineering technique using the [[:Category:E&P Portal | E&P Portal]].
-The Study is based on the oil well from a field in West Siberia, Russia.
+[[: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].
-It is shown how to:
+==Examples==
-*Input the data to the [[:Category:E&P Portal | E&P Portal]];
+'''Example 1. Well "21" refrac doubles the EUR as indicated by the slope change.'''
-*Apply the [[Oil Flowing Material Balance|Oil FMB]] to estimate the well's STOIIP and [[JD]];
+[[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]]
-*Save and export the analysis results.
-All the input data is attached to the Case Study for the reference.
+'''Example 2. 22 wells on the [[Reciprocal Rate Method]] plot showing the well's EUR spread. Well "19" trend is highlighted.'''
+[[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=]]
-[[File:oilFMB_Case_Study.png|200px |link=https://wiki.pengtools.com/images/4/47/OilFMB_CaseStudy.pdf ]]
+'''Example 3. EUR results table for 22 wells. Automatically interpreted wells have "No" flag,  manually interpreted "Yes" flag in the last column.'''
+[[File:Reciprocal Rate Method Example 3.png|https://ep.pengtools.com/reciprocal/reciprocal-method-eur/index]]
-[[Media:oilFMB_CaseStudy.pdf|Download Case Study (pdf)]]
+'''Example 4. "B2" reservoir [[Reciprocal Rate Method]] plot showing the Reservoir EUR.'''
+[[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]]
-[[Media:well 8 daily data.csv|Download the input well production data (csv)]]
 ==Workflow==
 # Upload the data required
-# Open the [[Oil Flowing Material Balance]]  tool [https://ep.pengtools.com/matbal/flowing-material-balance/oil here]
+# Open the [[Reciprocal Rate Method]] tool
-# Estimate the '''N''' (red line X-axis intercept)
+#* [[Well]]s tool [https://ep.pengtools.com/reciprocal/reciprocal-method/well-reciprocal-rate here]
-# Calculate the average reservoir pressure <math> \bar{P}</math> based on '''N''', known production data and using [[Oil Material Balance]] equation
+#* [[Reservoirs]] tool [https://ep.pengtools.com/reciprocal/reciprocal-method/reservoir-reciprocal-rate here]
-# Calculate the <math> {J_D}_{norm}</math>
+# Fit data with the red trend line
-# Calculate the <math> {N_p}_{norm}</math>
+# Calculate the slope of the line and [[EUR]]
-# Plot the orange <math> {J_D}_{norm}</math> vs <math> {N_p}_{norm}</math> line:
+# Save the [[Reciprocal Rate Method]] model
-# Change the '''N''' to match the orange line with the red one
+# Move to the next [[Well]] / [[Reservoirs|Reservoir]]
-# Change the gray [[JD]] line Y-axis intercept  to match the changing [[JD]]
-# Save the [[Oil Flowing Material Balance]] model
-# Move to the next well
 == Data required ==
-{{Data required for Gas Flowing Material Balance}}
+[[Well]]s interpretation:
+* Create [[Field]] [https://ep.pengtools.com/field/index  here]
+* [[Upload Wells]]
+* [[Upload Daily Measures]]
+[[Reservoirs]] interpretation:
+* Create or Upload [[Reservoirs]] [https://ep.pengtools.com/reservoir/index here]
+* Upload [[Perforations]] to connect [[Well]]s to the [[Reservoirs]]
 == Nomenclature  ==
+:<math> B_{o} </math> = oil formation volume factor, bbl/stb
+:<math> B_{oi} </math> = initial oil formation volume factor, bbl/stb
+:<math> b_{pss} </math> = reservoir constant, inverse to productivity index, psia/stb/d
+:<math> b_{pss}^' = \frac{b_{pss}}{P_{con}}</math> = reservoir constant, inverse to productivity index, 1/stb/d
+:<math> c_t </math> = total compressibility, psia<sup>-1</sup>
+:<math> J_D </math> = dimensionless productivity index, dimensionless
+:<math> k_oh</math> = oil permeability times thickness, md*ft
+:<math> m_{mb} </math> = slope term, psia/stb
+:<math> m_{mb}^' = \frac{m_{mb}}{P_{con}}</math> = slope term, 1/stb
+:<math> N </math> = stock tank oil initially in place, stb
+:<math> N_p </math> = cumulative oil production, stb
+:<math> \bar{P} </math> = average reservoir pressure, psia
+:<math> P_{i} </math> = initial pressure, psia
+:<math> P_{con} </math> = constant, psia
+:<math> P_{wf} </math> = well flowing pressure, psia
+:<math> q_o </math> = oil rate, stb/d
+===Greek symbols===
+:<math> \mu_o </math> = oil viscosity , cp
 == References ==
@@ Line 100: / Line 131: @@
 [[Category:E&P Portal]]
 [[Category:Reservoir Management]]
+{{#seo:
+|title=Reciprocal Rate Method
+|titlemode= replace
+|keywords=Reciprocal Rate Method
+|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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