Total produced or injected flowrate of all fluids across the well-reservoir contact with the volumes measured at the sandface temperature and pressure conditions.

Usually abbreviated as $\begin{array}{l}q_t\end{array}$ or $\begin{array}{l}qB\end{array}$ .

The concept applies both to producing and injecting wells.

The main purpose of describing the intakes and offtakes in terms of the Total sandface flowrate $\begin{array}{l}q_t\end{array}$ is that it measures the actual flowing volumes in porous formations and as such directly relate to reservoir pressure.

(1)	$\begin{array}{l}\displaystyle q_t = q_w + q_o + q_g = B_w \, q_W + (B_o - R_s \, B_g) \, q_O + (B_g - R_v \, B_o) \, q_G\end{array}$

where

$\begin{array}{l}q_w, \, q_o, \, q_g\end{array}$	water, oil and gas sandface flowrates
$\begin{array}{l}q_W, \, q_O, \, q_G\end{array}$	water, crude oil and natural gas surface flowrates
$\begin{array}{l}B_w, \, B_o, \, B_g\end{array}$	formation volume factors between separator and sandface pressure/temperature conditions
$\begin{array}{l}R_s, \, R_v\end{array}$	Solution GOR and Vaporized oil ratio at sandface pressure/temperature conditions

It is related to Liquid production rate $\begin{array}{l}q_L\end{array}$ as:

(2)	$\begin{array}{l}\displaystyle q_t = \left[ B_w Y_w + \left[ (B_o - R_s B_g] + (B_g - R_v B_o) \, GOR \right] \cdot (1-Y_w) \right] \cdot q_L\end{array}$

where

$\begin{array}{l}\displaystyle Y_w = \frac{q_W}{q_L}\end{array}$	Production Water Cut
$\begin{array}{l}\displaystyle GOR= \frac{q_G}{q_O}\end{array}$	Production Gas-Oil-Ratio

Derivation

Starting with definition of Total sandface flowrate

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It simplifies for the Black Oil model to:

(3)	$\begin{array}{l}\displaystyle q_t = B_w \, q_W + (B_o - R_s \, B_g) \, q_O + B_g \, q_G = B_w \, q_W + B_o \, q_O + B_g ( q_G - R_s \, q_O )\end{array}$

and simplifies further down to production from undersaturated reservoir as:

(4)	$\begin{array}{l}\displaystyle q_t = B_w \, q_W + B_o \, q_O\end{array}$

and even simpler for single-phase fluid (water, dead oil or dry gas) with surface flow rate $\begin{array}{l}q\end{array}$ and formation volume factor B as below:

(5)	$\begin{array}{l}\displaystyle q_t = q \cdot B\end{array}$

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See Also