Reciprocal Rate Method

Brief

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

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

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: $\Delta P =P_i - P_{wf} = P_{con} = constant$ :

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

As the flowrate decreases to zero (i.e., q_o → 0):

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

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.

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

1. Upload the data required
2. Open the Reciprocal Rate Method tool here
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

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

$\bar{P}$ = 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