Difference between revisions of "Oil Material Balance"

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]

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

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

[DakeF-1] 1.0 ^1.1 Dake, L.P. (1978). Fundamentals of Reservoir Engineering. Amsterdam, Hetherlands: Elsevier Science. ISBN 0-444-41830-X.

[DakeP-2] 2.0 ^2.1 Dake, L.P. (1994). The Practice of Reservoir Engineering. Amsterdam, Hetherlands: Elsevier Science. ISBN 0-444-88538-2.

[1]

[2]

@@ Line 6: / Line 6: @@
 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_{gi} - 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:
-  Pres = Pi - (Np * Bo + Np * (Rp - Rs) * Bg + (Wp * Bw - Wi * Bw - Ggi * Bgi - We * Bw) - (N * (Bo - Boi) + N * (Rsi - Rs) * Bg + m * N * Boi * (Bg / Bgi - 1))) * (1 - Swc) / (N * (1 + m) * Boi * (cw * Swc + cf))
+  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 - Ggi * 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  ==
@@ Line 22: / Line 35: @@
 == See also ==
-[[P/Z plot]]
+[[Gas Material Balance]] <BR/>
+[[Gas Flowing Material Balance]] <BR/>
+[[Oil Flowing Material Balance]] <BR/>
 == Nomenclature  ==
-:<math> B_g </math> = gas formation volume factor, ft<sup>3</sup>/scf
+:<math> B_{g}</math> = gas formation volume factor at Pres, bbl/scf
-:<math> B_{gi} </math> = initial gas formation volume factor, ft<sup>3</sup>/scf
+:<math> B_{gi}</math> = initial gas formation volume factor, bbl/scf
-:<math> GIIP </math> = gas initially in place, scf
+:<math> B_{ginj}</math> = injection gas formation volume factor at Pres, bbl/scf
-:<math> G_p </math> = cumulative gas produced, 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_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_w</math> = water compressibility at Pres, 1/psia
+:<math>G_{gi}</math> = gas injection volume, scf
+:<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_p</math> = oil cumulative production volume, stb
+:<math> P_i</math> = initial reservoir pressure, psia
+:<math> P_{res}</math> = average reservoir pressure, psia
+:<math> R_p = \frac{Gp}{Np}</math> , cumulative GOR, scf/stb
+:<math> R_s</math> = solution oil-gas ratio, scf/bbl
+:<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
+:<math>W_p </math> = water production volume, stb
 == References ==
@@ Line 57: / Line 95: @@
 [[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.
+}}

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