Difference between revisions of "Oil Flowing Material Balance"

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==Workflow==
 
==Workflow==
 
# Upload the data required  
 
# Upload the data required  
−
# Open the [[Gas Flowing Material Balance]]  tool [https://ep.pengtools.com/matbal/flowing-material-balance/gas here]
+
# Open the [[Oil Flowing Material Balance]]  tool [https://ep.pengtools.com/matbal/flowing-material-balance/oil here]
−
# Calculate the red  <math> \frac{P}{z}</math> line:
+
# Estimate the '''N'''
−
## Given the GIIP
+
# Calculate the average reservoir pressure <math> \bar{P}</math> based on '''N''', known production data and using [[Oil Material Balance]] equation
−
## Calculate the <math> \frac{P}{z}=\frac{P_i}{z_i} \left (1- \frac{G_p}{GIIP}\right )</math>
+
# Calculate the <math> {J_D}_{norm}</math>
−
# Calculate the orange <math> \frac{\bar{P}}{z}</math> curve:
+
# Calculate the <math> {N_p}_{norm}</math>
 +
# Plot the <math> {J_D}_{norm}</math> vs <math> {N_p}_{norm}</math> plot (orange line):
 +
#
 
## Given the flowing wellhead pressures, calculate the flowing bottomhole pressures, <math>P_{wf}</math>
 
## Given the flowing wellhead pressures, calculate the flowing bottomhole pressures, <math>P_{wf}</math>
 
## Convert the flowing pressures to pseudopressures, <math>P_{P_{wf}}</math>
 
## Convert the flowing pressures to pseudopressures, <math>P_{P_{wf}}</math>
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# Save the [[Gas Flowing Material Balance| FMB]] model
 
# Save the [[Gas Flowing Material Balance| FMB]] model
 
# Move to the next well
 
# Move to the next well
−
===Extra Plot to find b<sub>pss</sub>===
 
−
#Calculate the initial pseudopressure, <math>P_{Pi}</math>
 
−
#Calculate the material balance pseudo-time, <math>t_{ca}</math>
 
−
#Plot <math>\frac{P_{P_i}-P_{P_{wf}}}{q_g}</math> versus <math>t_{ca}</math>
 
−
#The intercept with the Y axis gives  <math>b_{pss}</math> and <math>J_D</math>
 
−
 
 
=== Data required ===
 
=== Data required ===
  

Revision as of 07:23, 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 \mu}{kh\ J_D}

Finally, the Oil Flowing Material Balance equation:

\frac{141.2 B \mu}{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 \mu}{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
  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 {J_D}_{norm} vs {N_p}_{norm} plot (orange line):
    1. Given the flowing wellhead pressures, calculate the flowing bottomhole pressures, P_{wf}
    2. Convert the flowing pressures to pseudopressures, P_{P_{wf}}
    3. Given the JD, calculate the b_{pss}
    4. Calculate the pseudopressure, P_{\bar{P}}
    5. Convert the pseudopressure to pressure, \bar{P}
    6. Calculate the \frac{\bar{P}}{z}
  9. Calculate the gray JD curve:
    1. Calculate the gas productivity index, J=\frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}
    2. Calculate the JD, J_D=\frac{1422 \times 10^3\ T_R}{kh} J
  10. Change the red \frac{P}{z} line to match the orange \frac{\bar{P}}{z} curve
    1. Change the GIIP
    2. Change the intitial \frac{P}{z}
  11. Change the flat JD gray line to match the changing JD gray line
  12. Save the FMB model
  13. 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
c = compressibility, psia-1
GIIP = gas initially in place, MMscf
G_p = cumulative gas produced, MMscf
J = gas productivity index, MMscfd/(psia2/cP)
J_D = dimensionless productivity index, dimensionless
kh = permeability times thickness, md*m
P = pressure, psia
\bar{P} = average reservoir pressure, psia
P_P = pseudopressure, psia2/cP
q_g = gas rate, MMscfd
t = time, day
t_{ca} = material balance pseudotime for gas, day
T = temperature, °R
z = gas compressibility factor, dimensionless

Greek symbols

\mu = viscosity, 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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