Difference between revisions of "Reciprocal Rate Method"

Revision as of 20:59, 28 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.

Case Study

This Case Study demonstrates the application of the Oil Flowing Material Balance engineering technique using the E&P Portal.

The Study is based on the oil well from a field in West Siberia, Russia.

It is shown how to:

Input the data to the E&P Portal;
Apply the Oil FMB to estimate the well's STOIIP and JD;
Save and export the analysis results.

All the input data is attached to the Case Study for the reference.

Download Case Study (pdf)

Download the input well production data (csv)

Workflow

Upload the data required
Open the Oil Flowing Material Balance tool here
Estimate the N (red line X-axis intercept)
Calculate the average reservoir pressure $\bar{P}$ based on N, known production data and using Oil Material Balance equation
Calculate the ${J_D}_{norm}$
Calculate the ${N_p}_{norm}$
Plot the orange ${J_D}_{norm}$ vs ${N_p}_{norm}$ line:
Change the N to match the orange line with the red one
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

Create Field here
Create or Upload Reservoirs here
Input the Reservoirs GIIP and STOIIP here
Create or Upload PVT (SG, Pi, Ti) here
Upload Wells
Create or Upload Wells Perforations here
Create or Upload kh and JD here
Upload Daily Measures

In case you need to calculate the flowing bottomhole pressure from the wellhead pressure:

Calculate the flowing bottomhole pressures using BHP Calculator
Export flowing bottomhole pressures to Daily Measures here

In case you want to add the static reservoir pressures on the FMB Plot:

Create or Upload the static reservoir pressures, here
Calculate Monthly Measures from the Daily Measures using Monthly Data Calculator

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

P

= pressure, psia

\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 88: / Line 88: @@
 :<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

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