Difference between revisions of "Oil Material Balance"

Revision as of 13:11, 28 March 2018

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 - Swc}- (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)

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_f

= formation compressibility at initial pressure and temperature, 1/psia

c_w

= water compressibility at Pres, 1/psia

G_{gi}

= gas injection volume, scf

HCPV_{gascap}

= gas cap hydrocarbon pore volume, bbl

HCPV_{oil}

= oil hydrocarbon pore volume, bbl

m = \frac{HCPV_{gascap}}{HCPV_{oil}}

, 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

R_{si}

= initial solution oil-gas ratio, scf/bbl

S_{wc}

Swc W_e W_i W_p

B_g

= gas formation volume factor, ft³/scf

B_{gi}

= initial gas formation volume factor, ft³/scf

GIIP

= gas initially in place, scf

G_p

= cumulative gas produced, scf

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 27: / Line 27: @@
 :<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_o</math> = oil formation volume factor at Pres, 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>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> m = \frac{HCPVgascap}{HCPVoil}</math> , initial gas cap oil leg ratio, dimensionless
+:<math> HCPV_{gascap}</math> = gas cap hydrocarbon pore volume, bbl
+:<math> HCPV_{oil}</math> = oil hydrocarbon pore volume, bbl
+:<math> m = \frac{HCPV_{gascap}}{HCPV_{oil}}</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> 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_s</math>
+:<math> R_{si} </math> = initial solution oil-gas ratio, scf/bbl
+:<math> S_{wc}</math>
 :<math> </math>
 :<math> </math>
-R_s
-R_s
-S_{wc}
 Swc
 W_e

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