Difference between revisions of "Oil Material Balance"

Revision as of 12:58, 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, bbl/scf

B_{ginj}

= initial gas formation volume factor, bbl/scf

B_{ginj}

= injection gas formation volume factor, bbl/scf

B_{oi}

= initial oil formation volume factor, bbl/stb

B_o

= oil formation volume factor, bbl/stb

B_w

water formation volume factor, bbl/stb

c_f c_w G_{gi} M m N N N N N_p N_p P_{res} P_i R_{si} R_p R_s R_s 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 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 - Swc}- (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)
 == Discussion  ==

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