Difference between revisions of "Reciprocal Rate Method"

Revision as of 15:02, 29 May 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 60: / Line 60: @@
 '''Example 3. EUR results table for 22 wells. Automatically interpreted wells have "No" flag,  manually interpreted "Yes" flag in the last column.'''
-[[File:EUR results table for 22 wells.png|https://ep.pengtools.com/reciprocal/reciprocal-method-eur/index]]
+[[File:Reciprocal Rate Method Example 3.png|https://ep.pengtools.com/reciprocal/reciprocal-method-eur/index]]
 '''Example 4. "B2" reservoir [[Reciprocal Rate Method]] plot showing the Reservoir EUR.'''

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