Difference between revisions of "Oil Flowing Material Balance"

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[[Oil Flowing Material Balance]] is applied to determine:  
 
[[Oil Flowing Material Balance]] is applied to determine:  
−
* [[Reservoirs]] STOIIP & [[EUR]]  
+
* [[Reservoirs]] [[STOIIP]]
−
* [[Well]]'s [[EUR]] and [[JD]]
+
* [[Well|Well's]] [[STOIIP]] and [[JD]]
  
−
[[Oil Flowing Material Balance]] uses readily available [[Well]] flowing data: production rate and bottomhole pressure.
+
[[Oil Flowing Material Balance]] uses readily available [[Well]] flowing data: production rate, wellhead pressures and the fluid levels.
  
 
The interpretation technique is fitting the data points with the straight lines to estimate STOIIP and [[JD]].
 
The interpretation technique is fitting the data points with the straight lines to estimate STOIIP and [[JD]].
  
−
[[File:FMB.png|link=https://ep.pengtools.com/matbal/flowing-material-balance/gas]]
+
[[File:oilFMB.png|link=https://ep.pengtools.com/matbal/flowing-material-balance/oil?WellReservoirFilter%5Bcountry_id%5D=&WellReservoirFilter%5Bfield_id%5D=&WellReservoirFilter%5Bfield_id%5D%5B%5D=11&WellReservoirFilter%5Bobject_id%5D=&WellReservoirFilter%5Breservoir_id%5D=23&WellReservoirFilter%5Bwell_id%5D=&WellReservoirFilter%5Bwell_id%5D%5B%5D=25211&WellReservoirFilter%5Bdate_to%5D=&WellReservoirFilter%5Bcumulative_sum_type%5D=cumulative_over_well&WellReservoirFilter%5BshowResultsTable%5D=0&WellReservoirFilter%5Breservoir_pressure%5D=2689&WellReservoirFilter%5Breservoir_temperature%5D=212&WellReservoirFilter%5Bstoiip%5D=2000000.0&WellReservoirFilter%5Bjd%5D=0.5&WellReservoirFilter%5Bdetalization%5D=40&WellReservoirFilter%5BneedToLoad%5D=&WellReservoirFilter%5BlogScaleToJD%5D=1]]
  
−
<center>[[Oil Flowing Material Balance]] in the [https://ep.pengtools.com/matbal/flowing-material-balance/gas E&P Portal]</center>
+
<center>[[Oil Flowing Material Balance]] in the [https://ep.pengtools.com/matbal/flowing-material-balance/oil?WellReservoirFilter%5Bcountry_id%5D=&WellReservoirFilter%5Bfield_id%5D=&WellReservoirFilter%5Bfield_id%5D%5B%5D=11&WellReservoirFilter%5Bobject_id%5D=&WellReservoirFilter%5Breservoir_id%5D=23&WellReservoirFilter%5Bwell_id%5D=&WellReservoirFilter%5Bwell_id%5D%5B%5D=25211&WellReservoirFilter%5Bdate_to%5D=&WellReservoirFilter%5Bcumulative_sum_type%5D=cumulative_over_well&WellReservoirFilter%5BshowResultsTable%5D=0&WellReservoirFilter%5Breservoir_pressure%5D=2689&WellReservoirFilter%5Breservoir_temperature%5D=212&WellReservoirFilter%5Bstoiip%5D=2000000.0&WellReservoirFilter%5Bjd%5D=0.5&WellReservoirFilter%5Bdetalization%5D=40&WellReservoirFilter%5BneedToLoad%5D=&WellReservoirFilter%5BlogScaleToJD%5D=1 E&P Portal]</center>
  
 
== Math & Physics ==
 
== Math & Physics ==
−
 
−
Combining the Darcy's law with the [[Oil Material Balance]] equations:
 
  
 
The total pressure drop at the wellbore is:
 
The total pressure drop at the wellbore is:
Line 26: Line 24:
 
Where  
 
Where  
  
−
:<math> P_i - \bar{P} </math> is pressure drop due to depletion defined by the [[Oil Material Balance]]
+
:<math> P_i - \bar{P} </math>, is pressure drop due to depletion defined by the [[Oil Material Balance]]
  
−
:<math> \bar{P}-P_{wf} </math> is pressure drop due to Darcy's law
+
:<math> \bar{P}-P_{wf} </math>, is pressure drop due to [[Darcy's law]]
  
−
In terms of oil pseudo pressure:
+
In terms of oil pseudo pressure the total pressure drop is:
  
−
:<math> \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})) </math><ref name=Stalgorova2016/>
+
:<math> \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})) </math> <ref name=Stalgorova2016/>
  
−
where
+
Where
  
−
:<math> b_{pss} = \frac{1422 \times 10^3\ T_R}{kh\ J_D}</math>
+
:<math> 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</math> <ref name=Stalgorova2016/>
  
−
Material balance pseudo-time:
+
:<math> P_{po}(\bar{P})-P_{po}(P_{wf}) = q_o \frac{141.2 B_o(P) \mu_o(P)}{k_oh\ J_D} </math>
  
−
:<math> t_{ca} = \frac{\mu_{gi} c_{gi}}{q_g}\int\limits_{0}^{t}\frac{q_g}{\bar{\mu_g} \bar{c_g}}dt</math>
+
Finally, the [[Oil Flowing Material Balance]] equation:
 +
 
 +
:<math> \frac{141.2 B_o(P) \mu_o(P)}{k_oh} \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}</math>
 +
 
 +
Or
 +
 
 +
:<math> {J_D}_{norm} = J_D -{N_p}_{norm} \frac{J_D}{N}</math>
 +
 
 +
Where
 +
 
 +
:<math> {J_D}_{norm} = \frac{141.2 B_o(P) \mu_o(P)}{k_oh} \frac{q_o}{\Delta P_{po}} </math>
 +
 
 +
:<math> {N_p}_{norm} = \frac{P_{po}(P_i) - P_{po}(\bar{P})}{\Delta P_{po}}N</math>
  
 
==Discussion==
 
==Discussion==
  
−
[[Gas Flowing Material Balance]] can be applied to:
+
[[Oil Flowing Material Balance]] can be applied to:
 
*single well
 
*single well
 
*multiple wells producing from the same [[Reservoirs| Reservoir]].
 
*multiple wells producing from the same [[Reservoirs| Reservoir]].
  
−
The X axis on the [[Gas Flowing Material Balance]] Plot can be selected as:
+
The X axis on the [[Oil Flowing Material Balance]] Plot can be selected as:
 
*[[Well]] cumulative  
 
*[[Well]] cumulative  
 
*[[Reservoirs| Reservoir]] cumulative
 
*[[Reservoirs| Reservoir]] cumulative
  
−
'''Example 1. Multiple wells producing from the same Reservoir. X axis - Wells cumulative'''
+
Note what [[Oil Flowing Material Balance]] accounts for the changing PVT properties of the oil with pressure.
−
[[File:FMBex1.png|link=https://ep.pengtools.com/matbal/flowing-material-balance/gas]]
+
 
−
'''Example 2. Multiple wells producing from the same Reservoir. X axis - Reservoir cumulative'''
+
==Case Study==
−
[[File:FMBex2.png|link=https://ep.pengtools.com/matbal/flowing-material-balance/gas]]
+
This Case Study demonstrates the application of the [[Oil Flowing Material Balance]] engineering technique using the [[:Category:E&P Portal | E&P Portal]].
−
'''Example 3. Shifted Model Start (to account for gas injection)'''
+
 
−
[[File:FMBex3.png|link=https://ep.pengtools.com/matbal/flowing-material-balance/gas]]
+
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 [[:Category:E&P Portal | E&P Portal]];
 +
*Apply the [[Oil Flowing Material Balance|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.
 +
 
 +
[[File:oilFMB_Case_Study.png|200px |link=https://wiki.pengtools.com/images/4/47/OilFMB_CaseStudy.pdf ]]
 +
 
 +
[[Media:oilFMB_CaseStudy.pdf|Download Case Study (pdf)]]
 +
 
 +
[[Media:well 8 daily data.csv|Download the input well production data (csv)]]
  
 
==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''' (red line X-axis intercept)
−
## 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>
−
## Given the flowing wellhead pressures, calculate the flowing bottomhole pressures, <math>P_{wf}</math>
+
# Plot the orange <math> {J_D}_{norm}</math> vs <math> {N_p}_{norm}</math> line:
−
## Convert the flowing pressures to pseudopressures, <math>P_{P_{wf}}</math>
+
# Change the '''N''' to match the orange line with the red one
−
## Given the [[JD]], calculate the <math> b_{pss}</math>
+
# Change the gray [[JD]] line Y-axis intercept  to match the changing [[JD]]
−
## Calculate the pseudopressure, <math> P_{\bar{P}}</math>
+
# Save the [[Oil Flowing Material Balance]] model
−
## Convert the pseudopressure to pressure, <math> \bar{P}</math>  
 
−
## Calculate the <math> \frac{\bar{P}}{z}</math>
 
−
# Calculate the gray [[JD]] curve:
 
−
## Calculate the gas productivity index, <math>J=\frac{q_g}{P_{\bar{P}}-P_{P_{wf}}}</math>
 
−
## Calculate the [[JD]], <math>J_D=\frac{1422 \times 10^3\ T_R}{kh} J</math>
 
−
# Change the red <math> \frac{P}{z}</math> line to match the orange <math> \frac{\bar{P}}{z}</math> curve
 
−
## Change the GIIP
 
−
## Change the intitial <math> \frac{P}{z}</math>
 
−
# Change the flat [[JD]] gray line to match the changing [[JD]] gray line
 
−
# 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 ==
  
 
{{Data required for Gas Flowing Material Balance}}
 
{{Data required for Gas Flowing Material Balance}}
Line 93: Line 101:
 
== Nomenclature  ==
 
== Nomenclature  ==
  
−
:<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> c </math> = compressibility, psia<sup>-1</sup>
 
−
:<math> GIIP </math> = gas initially in place, MMscf
 
−
:<math> G_p </math> = cumulative gas produced, MMscf
 
−
:<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 the oil pseudo pressure, dimensionless
 +
:<math> k_oh</math> = oil permeability times thickness, md*ft
 +
:<math> N </math> = stock tank oil initially in place, stb
 +
:<math> {N_p}_{norm} </math> = normalized cumulative oil production, stb
 
:<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
−
:<math> P_P </math> = pseudopressure, psia<sup>2</sup>/cP
+
:<math> P_{i} </math> = initial pressure, psia
−
:<math> q_g </math> = gas rate, MMscfd
+
:<math> P_{po} </math> = oil pseudo pressure, psia
−
:<math> t </math> = time, day
+
:<math> P_{ref} </math> = reference pressure, psia
−
:<math> t_{ca} </math> = material balance pseudotime for gas, day
+
:<math> P_{wf} </math> = well flowing pressure, psia
−
:<math> T </math> = temperature, °R
+
:<math> q_o </math> = oil rate, stb/d
−
:<math> z </math> = gas compressibility factor, dimensionless
 
  
 
===Greek symbols===
 
===Greek symbols===
  
−
:<math> \mu </math> = viscosity, cp
+
:<math> \mu_o(P) </math> = oil viscosity as a function of pressure, cp
−
 
 
−
===Subscripts===
 
−
 
 
−
:g = gas<BR/>
 
−
:i = initial<BR/>
 
−
:R = °R<BR/>
 
−
:wf = well flowing <BR/>
 
  
 
== References ==
 
== References ==
Line 134: Line 133:
  
 
<ref name=Stalgorova2016>{{cite journal
 
<ref name=Stalgorova2016>{{cite journal
−
  |last1= Stalgorova |first2=Ekaterina
+
  |last1= Stalgorova |first1=Ekaterina
−
  |last2=Mattar|first1=Louis
+
  |last2=Mattar|first2=Louis
 
  |title=Analytical Methods for Single-Phase Oil Flow: Accounting for Changing Liquid and Rock Properties
 
  |title=Analytical Methods for Single-Phase Oil Flow: Accounting for Changing Liquid and Rock Properties
 
  |publisher=Society of Petroleum Engineers
 
  |publisher=Society of Petroleum Engineers
Line 147: Line 146:
  
 
[[Category:E&P Portal]]
 
[[Category:E&P Portal]]
 +
 +
{{#seo:
 +
|title=Oil Flowing Material Balance
 +
|titlemode= replace
 +
|keywords=reservoir engineering, flowing material balance, petroleum engineering, equation
 +
|description=Oil Flowing Material Balance is the advanced engineering technique applied to determine reservoirs and wells oil reserves and productivity index.
 +
}}

Latest revision as of 16:08, 21 March 2022

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, wellhead pressures and the fluid levels.

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

OilFMB.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)}{k_oh\ J_D}

Finally, the Oil Flowing Material Balance equation:

\frac{141.2 B_o(P) \mu_o(P)}{k_oh} \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)}{k_oh} \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 with pressure.

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.

OilFMB Case Study.png

Download Case Study (pdf)

Download the input well production data (csv)

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_{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 the oil pseudo pressure, dimensionless
k_oh = oil permeability times thickness, md*ft
N = stock tank oil initially in place, stb
{N_p}_{norm} = normalized cumulative oil production, stb
P = pressure, psia
\bar{P} = average reservoir pressure, psia
P_{i} = initial pressure, psia
P_{po} = oil pseudo pressure, psia
P_{ref} = reference pressure, psia
P_{wf} = well flowing pressure, psia
q_o = oil rate, stb/d

Greek symbols

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

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, Ekaterina; Mattar, Louis (2016). "Analytical Methods for Single-Phase Oil Flow: Accounting for Changing Liquid and Rock Properties". Society of Petroleum Engineers. 
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