Difference between revisions of "Oil Material Balance"
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:<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 - Swc}- (W_p B_w - W_i B_w - G_{gi} B_{gi} - 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 * 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)) | ||
| − | + | 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 - Ggi * Bgi - We * Bw)) / (Bo + (Rp - Rs) * Bg) | ||
Revision as of 12:35, 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:
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))
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)
See also
Nomenclature
= gas formation volume factor, ft3/scf
= initial gas formation volume factor, ft3/scf
= gas initially in place, scf
= cumulative gas produced, scf
References
- ↑ Dake, L.P. (1978). Fundamentals of reservoir engineering. Amsterdam, Hetherlands: Elsevier Science. ISBN 0-444-41830-X.
