Difference between revisions of "Oil Material Balance"

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Equating all underground withdrawals to the sum of the volume changes<ref name=DakeF />:
 
Equating all underground withdrawals to the sum of the volume changes<ref name=DakeF />:
  
−
:<math>N_p B_o + N_p (R_p - R_s) B_g = N (B_o - B_{oi}) + N (R_{si} - R_s) B_g + m N B_{oi} (\frac{B_g}{B_{gi}} - 1) + (P_i - P_{res}) N (1 + m) B_{oi} \frac{c_w S_{wc} + c_f}{1 - Swc}- (W_p B_w - W_i B_w - G_{gi} B_{ginj} - W_e B_w) </math>
+
:<math>N_p B_o + N_p (R_p - R_s) B_g = N (B_o - B_{oi}) + N (R_{si} - R_s) B_g + m N B_{oi} (\frac{B_g}{B_{gi}} - 1) + (P_i - P_{res}) N (1 + m) B_{oi} \frac{c_w S_{wc} + c_f}{1 - S_{wc}}- (W_p B_w - W_i B_w - G_{gi} B_{ginj} - W_e B_w) </math>
  
 
For use in the code to find Pres:
 
For use in the code to find Pres:
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  Np = (N * (Bo - Boi) + N * (Rsi - Rs) * Bg + m * N * Boi * (Bg / Bgi - 1) + N * (1 + m) * Boi * (Pi - Pres) * (cw * Swc + cf) / (1 - Swc) - (Wp * Bw - Wi * Bw - Gging * Bgi - We * Bw)) / (Bo + (Rp - Rs) * Bg)
 
  Np = (N * (Bo - Boi) + N * (Rsi - Rs) * Bg + m * N * Boi * (Bg / Bgi - 1) + N * (1 + m) * Boi * (Pi - Pres) * (cw * Swc + cf) / (1 - Swc) - (Wp * Bw - Wi * Bw - Gging * Bgi - We * Bw)) / (Bo + (Rp - Rs) * Bg)
 +
 +
=== Above the bubble point ===
 +
 +
 +
:<math>N_p B_o = N B_{oi} (P_i - P_{res}) c_e - (W_p B_w - W_i B_w - W_e B_w) </math>
 +
where
 +
:<math>c_e = \frac{c_o S_o + c_w S_{wc} + c_f}{1 - S_{wc}}</math>
 +
 +
 +
:<math>S_o = 1 - S_{wc}</math>
 +
 +
 +
:<math>c_o = \frac{1}{B_{oi}} \frac{B_o-B_{oi}}{Pi - Pres}</math>
  
 
== Discussion  ==
 
== Discussion  ==
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== See also ==
 
== See also ==
 
[[Gas Material Balance]] <BR/>
 
[[Gas Material Balance]] <BR/>
 +
[[Gas Flowing Material Balance]] <BR/>
 +
[[Oil Flowing Material Balance]] <BR/>
  
 
== Nomenclature  ==
 
== Nomenclature  ==
  
 
:<math> B_{g}</math> = gas formation volume factor at Pres, bbl/scf
 
:<math> B_{g}</math> = gas formation volume factor at Pres, bbl/scf
−
:<math> B_{ginj}</math> = initial gas formation volume factor, bbl/scf
+
:<math> B_{gi}</math> = initial gas formation volume factor, bbl/scf
 
:<math> B_{ginj}</math> = injection gas formation volume factor at Pres, bbl/scf
 
:<math> B_{ginj}</math> = injection gas formation volume factor at Pres, bbl/scf
 +
:<math>B_o</math> = oil formation volume factor at Pres, bbl/stb
 
:<math> B_{oi}</math> = initial oil formation volume factor, bbl/stb
 
:<math> B_{oi}</math> = initial oil formation volume factor, bbl/stb
−
:<math>B_o</math> = oil formation volume factor at Pres, bbl/stb
 
 
:<math>B_w</math> = water formation volume factor at Pres, bbl/stb
 
:<math>B_w</math> = water formation volume factor at Pres, bbl/stb
 +
:<math>c_e</math> = effective system compressibility at Pres, 1/psia
 
:<math>c_f</math> = formation compressibility at initial pressure and temperature, 1/psia
 
:<math>c_f</math> = formation compressibility at initial pressure and temperature, 1/psia
 
:<math>c_w</math> = water compressibility at Pres, 1/psia
 
:<math>c_w</math> = water compressibility at Pres, 1/psia
 
:<math>G_{gi}</math> = gas injection volume, scf
 
:<math>G_{gi}</math> = gas injection volume, scf
−
:<math> m = \frac{HCPVgascap}{HCPVoil}</math> , initial gas cap oil leg ratio, dimensionless
+
:<math>G_p</math> = gas cumulative production volume, scf
 +
:<math> HCPV_{gascap}</math> = initial gas cap hydrocarbon pore volume, bbl
 +
:<math> HCPV_{oil}</math> = initial oil hydrocarbon pore volume, bbl
 +
:<math> m = \frac{HCPV_{gascap}}{HCPV_{oil}}=\frac{S_g}{S_o}</math> , initial gas cap oil leg ratio, dimensionless
 
:<math> N </math> = stock tank oil initially in place, stb
 
:<math> N </math> = stock tank oil initially in place, stb
 
:<math> N_p</math> = oil cumulative production volume, stb
 
:<math> N_p</math> = oil cumulative production volume, stb
 +
:<math> P_i</math> = initial reservoir pressure, psia
 
:<math> P_{res}</math> = average reservoir pressure, psia
 
:<math> P_{res}</math> = average reservoir pressure, psia
−
:<math> P_i</math> = initial reservoir pressure, psia
 
−
:<math> R_{si} </math> = solution oil-gas ratio, scf/bbl
 
 
:<math> R_p = \frac{Gp}{Np}</math> , cumulative GOR, scf/stb
 
:<math> R_p = \frac{Gp}{Np}</math> , cumulative GOR, scf/stb
−
:<math> </math>
+
:<math> R_s</math> = solution oil-gas ratio, scf/bbl
−
:<math> </math>
+
:<math> R_{si} </math> = initial solution oil-gas ratio, scf/bbl
−
 
+
:<math> S_{g}</math> = initial gas saturation, fraction
−
 
+
:<math> S_{o}</math> = initial oil saturation, fraction
−
 
+
:<math> S_{wc}</math> = connate water saturation, fraction
−
 
+
:<math> W_e </math> = water influx volume, stb
−
 
+
:<math> W_i</math> = water injection volume, stb
−
R_s
+
:<math>W_p </math> = water production volume, stb
−
R_s
 
−
S_{wc}
 
−
Swc
 
−
W_e
 
−
W_i
 
−
W_p
 
−
 
 
−
 
 
−
:<math> B_g </math> = gas formation volume factor, ft<sup>3</sup>/scf
 
−
:<math> B_{gi} </math> = initial gas formation volume factor, ft<sup>3</sup>/scf
 
−
:<math> GIIP </math> = gas initially in place, scf
 
−
:<math> G_p </math> = cumulative gas produced, scf
 
  
 
== References ==
 
== References ==
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[[Category:E&P Portal]]
 
[[Category:E&P Portal]]
 +
 +
{{#seo:
 +
|title=Oil Material Balance
 +
|titlemode= replace
 +
|keywords=reservoir engineering, material balance, petroleum engineering, equation
 +
|description=Oil Material Balance is the most powerful tool for investigating reservoirs and understanding their performance.
 +
}}

Latest revision as of 11:36, 20 April 2024

Brief

The general form of the Oil Material Balance equation was first published by Schilthuis in 1941[1].

Math & Physics

Equating all underground withdrawals to the sum of the volume changes[1]:

N_p B_o + N_p (R_p - R_s) B_g = N (B_o - B_{oi}) + N (R_{si} - R_s) B_g + m N B_{oi} (\frac{B_g}{B_{gi}} - 1) + (P_i - P_{res}) N (1 + m) B_{oi} \frac{c_w S_{wc} + c_f}{1 - S_{wc}}- (W_p B_w - W_i B_w - G_{gi} B_{ginj} - W_e B_w)

For use in the code to find Pres: 

Pres = Pi - (Np * Bo + Np * (Rp - Rs) * Bg + (Wp * Bw - Wi * Bw - Ggi * Bginj - We * Bw) - (N * (Bo - Boi) + N * (Rsi - Rs) * Bg + m * N * Boi * (Bg / Bgi - 1))) * (1 - Swc) / (N * (1 + m) * Boi * (cw * Swc + cf))

For use in the code to find Np: 

Np = (N * (Bo - Boi) + N * (Rsi - Rs) * Bg + m * N * Boi * (Bg / Bgi - 1) + N * (1 + m) * Boi * (Pi - Pres) * (cw * Swc + cf) / (1 - Swc) - (Wp * Bw - Wi * Bw - Gging * Bgi - We * Bw)) / (Bo + (Rp - Rs) * Bg)

Above the bubble point

N_p B_o = N B_{oi} (P_i - P_{res}) c_e - (W_p B_w - W_i B_w - W_e B_w)

where

c_e = \frac{c_o S_o + c_w S_{wc} + c_f}{1 - S_{wc}}


S_o = 1 - S_{wc}


c_o = \frac{1}{B_{oi}} \frac{B_o-B_{oi}}{Pi - Pres}

Discussion

... most powerful tool for investigating reservoirs and understanding their performance ...
— L.P. Dake [2]
... the safest technique in the business since it's minimum assumption route through the subject of reservoir engineering ...
— L.P. Dake [2]

See also

Gas Material Balance
Gas Flowing Material Balance
Oil Flowing Material Balance

Nomenclature

B_{g} = gas formation volume factor at Pres, bbl/scf
B_{gi} = initial gas formation volume factor, bbl/scf
B_{ginj} = injection gas formation volume factor at Pres, bbl/scf
B_o = oil formation volume factor at Pres, bbl/stb
B_{oi} = initial oil formation volume factor, bbl/stb
B_w = water formation volume factor at Pres, bbl/stb
c_e = effective system compressibility at Pres, 1/psia
c_f = formation compressibility at initial pressure and temperature, 1/psia
c_w = water compressibility at Pres, 1/psia
G_{gi} = gas injection volume, scf
G_p = gas cumulative production volume, scf
HCPV_{gascap} = initial gas cap hydrocarbon pore volume, bbl
HCPV_{oil} = initial oil hydrocarbon pore volume, bbl
m = \frac{HCPV_{gascap}}{HCPV_{oil}}=\frac{S_g}{S_o} , initial gas cap oil leg ratio, dimensionless
N = stock tank oil initially in place, stb
N_p = oil cumulative production volume, stb
P_i = initial reservoir pressure, psia
P_{res} = average reservoir pressure, psia
R_p = \frac{Gp}{Np} , cumulative GOR, scf/stb
R_s = solution oil-gas ratio, scf/bbl
R_{si} = initial solution oil-gas ratio, scf/bbl
S_{g} = initial gas saturation, fraction
S_{o} = initial oil saturation, fraction
S_{wc} = connate water saturation, fraction
W_e = water influx volume, stb
W_i = water injection volume, stb
W_p = water production volume, stb

References

  1. ↑ 1.0 1.1 Dake, L.P. (1978). Fundamentals of Reservoir Engineering. Amsterdam, Hetherlands: Elsevier Science. ISBN 0-444-41830-X. 
  2. ↑ 2.0 2.1 Dake, L.P. (1994). The Practice of Reservoir Engineering. Amsterdam, Hetherlands: Elsevier Science. ISBN 0-444-88538-2. 
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