Difference between revisions of "Oil Flowing Material Balance"

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(→‎Nomenclature)
(→‎Nomenclature)
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:<math> b_{pss} </math> = reservoir constant, inverse to productivity index, psia<sup>2</sup>/cP/MMscfd
 
:<math> b_{pss} </math> = reservoir constant, inverse to productivity index, psia<sup>2</sup>/cP/MMscfd
 
:<math> B_{o}(P) </math> = oil formation volume factor as a function of pressure, bbl/stb
 
:<math> B_{o}(P) </math> = oil formation volume factor as a function of pressure, bbl/stb
−
:<math> J </math> = gas productivity index, MMscfd/(psia<sup>2</sup>/cP)
 
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
−
:<math> kh</math> = permeability times thickness, md*m
+
:<math> {J_D}_{norm} </math> = dimensionless productivity index in terms of oil pseudo pressure, dimensionless
 +
:<math> kh</math> = permeability times thickness, md*ft
 
:<math> P </math> = pressure, psia
 
:<math> P </math> = pressure, psia
 
:<math> \bar{P} </math> = average reservoir pressure, psia
 
:<math> \bar{P} </math> = average reservoir pressure, psia
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:<math> P_{ref} </math> = reference pressure, 14.7 psia
 
:<math> P_{ref} </math> = reference pressure, 14.7 psia
 
:<math> P_{wf} </math> = well flowing pressure, psia
 
:<math> P_{wf} </math> = well flowing pressure, psia
−
:<math> q_g </math> = gas rate, MMscfd
+
:<math> q_o </math> = oil rate, stb
−
:<math> t </math> = time, day
 
−
:<math> t_{ca} </math> = material balance pseudotime for gas, day
 
−
:<math> T </math> = temperature, °R
 
−
:<math> z </math> = gas compressibility factor, dimensionless
 
−
 
 
 
:<math> N </math> = stock tank oil initially in place, stb
 
:<math> N </math> = stock tank oil initially in place, stb
 +
:<math> {N_p}_{norm} </math> = normalized cumulative oil production, stb
  
 
===Greek symbols===
 
===Greek symbols===

Revision as of 07:45, 10 April 2018

Brief

Oil Flowing Material Balance (Oil FMB) is the advanced engineering technique published in 2005 by Louis Mattar and David Anderson [1].

Oil Flowing Material Balance is applied to determine:

Oil Flowing Material Balance uses readily available Well flowing data: production rate and bottomhole pressure.

The interpretation technique is fitting the data points with the straight lines to estimate STOIIP and JD.

FMB.png

Oil Flowing Material Balance 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}) [1]

Where

P_i - \bar{P} , is pressure drop due to depletion defined by the Oil Material Balance
\bar{P}-P_{wf} , is pressure drop due to Darcy's law

In terms of oil pseudo pressure the total pressure drop is:

\Delta P_{po}=P_{po}(P_i)-P_{po}(P_{wf}) = (P_{po}(P_i) - P_{po}(\bar{P})) + (P_{po}(\bar{P})-P_{po}(P_{wf})) [2]

Where

P_{po}(P) = B_o(P_i) \mu_o(P_i) \int\limits_{P_{ref}}^{P} \frac{1}{B_o(P) \mu_o(P)}dp [2]
P_{po}(\bar{P})-P_{po}(P_{wf}) = q_o \frac{141.2 B_o(P) \mu_o(P)}{kh\ J_D}

Finally, the Oil Flowing Material Balance equation:

\frac{141.2 B_o(P) \mu_o(P)}{kh} \frac{q_o}{\Delta P_{po}}= J_D -\frac{P_{po}(P_i) - P_{po}(\bar{P})}{\Delta P_{po}}N\ \frac{J_D}{N}

Or

{J_D}_{norm} = J_D -{N_p}_{norm} \frac{J_D}{N}

Where

{J_D}_{norm} = \frac{141.2 B_o(P) \mu_o(P)}{kh} \frac{q_o}{\Delta P_{po}}
{N_p}_{norm} = \frac{P_{po}(P_i) - P_{po}(\bar{P})}{\Delta P_{po}}N

Discussion

Oil Flowing Material Balance can be applied to:

  • single well
  • multiple wells producing from the same Reservoir.

The X axis on the Oil Flowing Material Balance Plot can be selected as:

Note what Oil Flowing Material Balance accounts for the changing PVT properties of the oil.

Example 1. Multiple wells producing from the same Reservoir. X axis - Wells cumulative FMBex1.png Example 2. Multiple wells producing from the same Reservoir. X axis - Reservoir cumulative FMBex2.png Example 3. Shifted Model Start (to account for gas injection) FMBex3.png

Workflow

  1. Upload the data required
  2. Open the Oil Flowing Material Balance tool here
  3. Estimate the N (red line X-axis intercept)
  4. Calculate the average reservoir pressure \bar{P} based on N, known production data and using Oil Material Balance equation
  5. Calculate the {J_D}_{norm}
  6. Calculate the {N_p}_{norm}
  7. Plot the orange {J_D}_{norm} vs {N_p}_{norm} line:
  8. Change the N to match the orange line with the red one
  9. Change the gray JD line Y-axis intercept to match the changing JD
  10. Save the Oil Flowing Material Balance model
  11. Move to the next well

Data required

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

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

Nomenclature

b_{pss} = reservoir constant, inverse to productivity index, psia2/cP/MMscfd
B_{o}(P) = oil formation volume factor as a function of pressure, bbl/stb
J_D = dimensionless productivity index, dimensionless
{J_D}_{norm} = dimensionless productivity index in terms of oil pseudo pressure, dimensionless
kh = permeability times thickness, md*ft
P = pressure, psia
\bar{P} = average reservoir pressure, psia
P_i = initial reservoir pressure, psia
P_{po} = oil pseudo pressure, psia
P_{ref} = reference pressure, 14.7 psia
P_{wf} = well flowing pressure, psia
q_o = oil rate, stb
N = stock tank oil initially in place, stb
{N_p}_{norm} = normalized cumulative oil production, stb

Greek symbols

\mu_o(P) = oil viscosity as a function of pressure, cp

Subscripts

g = gas
i = initial
R = °R
wf = well flowing

References

  1. ↑ 1.0 1.1 Mattar, L.; Anderson, D (2005). "Dynamic Material Balance (Oil or Gas-In-Place Without Shut-Ins)" (PDF). CIPC. 
  2. ↑ 2.0 2.1 Stalgorova, Louis; Mattar, Ekaterina (2016). "Analytical Methods for Single-Phase Oil Flow: Accounting for Changing Liquid and Rock Properties". Society of Petroleum Engineers. 
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