Cumulative production of all reservoir fluids to the surface from the beginning of production t_0 until current moment of time t adjusted to reservoir conditions:
| (1) | Q^{\uparrow}_t(t)=\int_{t_0}^t q^{\uparrow}_t(\tau) d\tau |
where
q^{\uparrow}_t(\tau) | instantaneous offtakes at time moment \tau |
For the volatile oil fluid model the cumulative offtakes is related to surface flowrates history of fluid components as:
| (2) | Q^{\uparrow}_t(t) = \int_{t_0}^t \left[ B_w \, q^{\uparrow}_W + \frac{B_o - R_v B_g}{1 - R_v R_s} \, q^{\uparrow}_O + \frac{B_g - R_s B_o}{1 - R_v R_s} \, q^{\uparrow}_G \right] d\tau |
where
q^{\uparrow}_W(\tau), \, q^{\uparrow}_O(\tau), \, q^{\uparrow}_G(\tau) | water, oil, gas surface flowrates at time moment \tau |
p_e(\tau), T_e(\tau) | formation pressure and formation temperature at time moment \tau |
B_w(p_e, T_e), \, B_o(p_e, T_e), \, B_g(p_e, T_e) | formation volume factors between separator and sandface pressure/temperature conditions |
R_s(p_e, T_e), \, R_v(p_e,T_e) | Solution GOR and Vaporized oil ratio at sandface pressure/temperature conditions |
The difference between cumulative offtakes and cumulative production is that cumulative offtakes recalculates produced surface volumes to sandface conditions and accounts for the shrinkage factors and cross-phase exchange coefficients dependence on formation pressure p_e(t) and formation temperature T_e(\tau) which may vary over time:
(no reference to the fluid) | (no reference to the fluid) |
|---|---|
Q^{\uparrow}_{\rm off} = \int_0^t B(p_e(\tau), T_e(\tau)) q^{\uparrow}(\tau) d\tau | Q^{\uparrow}_p = \int_0^t q^{\uparrow}(\tau) d\tau |
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis
[ Offtakes ] [ Cumulative Intakes ] [ Cumulative VRR ] [ Cumulative Production ]