Oil Material Balance

Brief

The general form of the Oil Material Balance equation was first published by Schilthuis in 1941.

Math & Physics

Equating all underground withdrawals to the sum of the volume changes:

$N_p B_o + N_p (R_p - R_s) B_g = N (B_o - B_{oi}) + N (R_{si} - R_s) B_g + m N B_{oi} (\frac{B_g}{B_{gi}} - 1) + (P_i - P_{res}) N (1 + m) B_{oi} \frac{c_w S_{wc} + c_f}{1 - Swc}- (W_p B_w - W_i B_w - G_{gi} B_{gi} - W_e B_w)$

Np * Bo + Np * (Rp - Rs) * Bg = N * (Bo - Boi) + N * (Rsi - Rs) * Bg + m * N * Boi * (Bg / Bgi - 1) + (Pi - Pres)* N * (1 + m) * Boi * (cw * Swc + cf) / (1 - Swc) - (Wp * Bw - Wi * Bw - Ggi * Bgi - We * Bw)

Or

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))

$GIIP \times B_{gi}= (GIIP - G_p) B_g$

See also

P/Z plot

Nomenclature

$B_g$ = 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