Oil Material Balance

From wiki.pengtools.com
Jump to: navigation, search

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)

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_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.