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.

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. https://ep.pengtools.com/reciprocal/reciprocal-method-eur/index

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

Workflow

1. Upload the data required
2. Open the Reciprocal Rate Method tool
   • Wells tool here
   • Reservoirs 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 / Reservoir

Data required

Wells interpretation:

• Create Field here
• Upload Wells
• Upload Daily Measures

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