Cumulative injection of all surface fluids into a reservoir from the beginning of production $\begin{array}{l}t_0\end{array}$ until current moment of time $\begin{array}{l}t\end{array}$ adjusted to reservoir conditions:

(1)	$\begin{array}{l}\displaystyle Q^{\downarrow}_t(t)=\int_{t_0}^t q^{\downarrow}_t(\tau) d\tau\end{array}$

where

$\begin{array}{l}q^{\downarrow}_t(\tau)\end{array}$

instantaneous intakes at time moment $\begin{array}{l}\tau\end{array}$

Depending on context may mean:

Water Injection

Gas Injection

Water Injection + Gas Injection

(2)	$\begin{array}{l}\displaystyle Q^{\downarrow}_W(t)=\int_{t_0}^t B_w q^{\downarrow}_W(\tau) d\tau\end{array}$

(3)	$\begin{array}{l}\displaystyle Q^{\downarrow}_G(t)=\int_{t_0}^t B_g q^{\downarrow}_G(\tau) d\tau\end{array}$

(4)	$\begin{array}{l}\displaystyle Q^{\downarrow}_t(t)=Q^{\downarrow}_W(t) + Q^{\downarrow}_G(t)\end{array}$

where

$\begin{array}{l}q^{\downarrow}_W(\tau), \, q^{\downarrow}_G(\tau)\end{array}$	water, gas surface flowrates at time moment $\begin{array}{l}\tau\end{array}$
$\begin{array}{l}p_e(\tau), T_e(\tau)\end{array}$	formation pressure and formation temperature at time moment $\begin{array}{l}\tau\end{array}$
$\begin{array}{l}B_w(p_e(\tau), T_e(\tau)), \, B_g(p_e(\tau), T_e(\tau))\end{array}$	formation volume factors between separator and sandface pressure/temperature conditions

The difference between cumulative intakes and cumulative injection is that cumulative intakes accounts for the shrinkage factors and cross-phase exchange coefficients which depend on formation pressure $\begin{array}{l}p_e(t)\end{array}$ and formation temperature $\begin{array}{l}T_e(\tau)\end{array}$ and may vary over time:

Cumulative Intakes

^{(no reference to the fluid)}

Cumulative Injection

^{(no reference to the fluid)}

$\begin{array}{l}Q^{\downarrow}_{\rm in} = \int_0^t B(p(\tau), T(\tau)) q^{\downarrow}(\tau) d\tau\end{array}$

$\begin{array}{l}Q^{\downarrow}_{\rm inj} = \int_0^t q^{\downarrow}(\tau) d\tau\end{array}$

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See Also

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Cumulative intakes

See Also