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 $\begin{array}{l}qB\end{array}$ (with the latter does not imply a product) or specifically $\begin{array}{l}q^{\uparrow}_t\end{array}$ for production and $\begin{array}{l}q^{\downarrow}_t\end{array}$ for injection.

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.

For volatile oil fluid model the total sandface flowrate is related to surface flowrates of fluid components as:

(1)	$\begin{array}{l}\displaystyle q^{\uparrow}_t = q^{\uparrow}_w + q^{\uparrow}_o + q^{\uparrow}_g = B_w \, q^{\uparrow}_W + (B_o - R_s \, B_g) \, q^{\uparrow}_O + (B_g - R_v \, B_o) \, q^{\uparrow}_G\end{array}$

(2)	$\begin{array}{l}\displaystyle q^{\downarrow}_t = q^{\downarrow}_w + q^{\downarrow}_g = B_w \, q^{\downarrow}_W + B_g \, q^{\downarrow}_G\end{array}$

where

$\begin{array}{l}q^{\uparrow}_w\end{array}$ , $\begin{array}{l}q^{\uparrow}_o\end{array}$ , $\begin{array}{l}q^{\uparrow}_g\end{array}$	water sandface flowrate, oil sandface flowrate, gas sandface flowrate
$\begin{array}{l}q^{\uparrow}_W\end{array}$ , $\begin{array}{l}q^{\uparrow}_O\end{array}$ , $\begin{array}{l}q^{\uparrow}_G\end{array}$	produced water surface flowrate, oil surface flowrate, gas surface flowrate
$\begin{array}{l}q^{\downarrow}_W\end{array}$ , $\begin{array}{l}q^{\downarrow}_G\end{array}$	injected water surface flowrate, gas surface flowrate
$\begin{array}{l}B_w, \, B_o, \, B_g\end{array}$	formation volume factors for water, oil, gas
$\begin{array}{l}R_s, \, R_v\end{array}$	Solution GOR and Vaporized oil ratio at sandface pressure/temperature conditions

The total sandface flowrate $\begin{array}{l}q^{\uparrow}_t\end{array}$ of production is related to Liquid production rate $\begin{array}{l}q^{\uparrow}_L\end{array}$ as:

(3)	$\begin{array}{l}\displaystyle q^{\uparrow}_t = \Big[ B_w Y_W + \Big( \, (B_o - R_s B_g) + Y_G \cdot (B_g - R_v B_o) \, \Big) \cdot (1-Y_W) \Big] \cdot q^{\uparrow}_L\end{array}$

where

$\begin{array}{l}\displaystyle Y_W = \frac{q^{\uparrow}_W}{q^{\uparrow}_L}\end{array}$	Production Water Cut
$\begin{array}{l}\displaystyle Y_G = \frac{q^{\uparrow}_G}{q^{\uparrow}_O}\end{array}$	Production Gas-Oil-Ratio = GOR

Derivation

Starting with definition of Total sandface flowrate (1) and substituting the expression of Oil surface flowrate, Gas surface flowrate, Water surface flowrate through Liquid production rate one arrives to (3).

It simplifies for the Black Oil model ( $\begin{array}{l}R_v = 0\end{array}$ ) to:

(4)	$\begin{array}{l}\displaystyle q^{\uparrow}_t = B_w \, q^{\uparrow}_W + (B_o - R_s \, B_g) \, q^{\uparrow}_O + B_g \, q^{\uparrow}_G\end{array}$

or

(5)	$\begin{array}{l}\displaystyle q^{\uparrow}_t = \Big[ B_w Y_W + \Big( \, (B_o - R_s B_g) + Y_G \cdot B_g \, \Big) \cdot (1-Y_W) \Big] \cdot q^{\uparrow}_L\end{array}$

It simplifies further down to production from undersaturated reservoir as:

(6)	$\begin{array}{l}\displaystyle q^{\uparrow}_t = B_w \, q^{\uparrow}_W + B_o \, q^{\uparrow}_O = \Big[ B_w Y_W + B_o \cdot (1- Y_W) \Big] \cdot q^{\uparrow}_L\end{array}$

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

(7)	$\begin{array}{l}\displaystyle q^{\uparrow}_t = q^{\uparrow} B, \quad {\rm meaning:} \quad q_t = q^{\uparrow}_W \cdot B_w \quad {\rm or} \quad q_t = q^{\uparrow}_O \cdot B_o \quad {\rm or} \quad q_t = q^{\uparrow}_G \cdot B_G\end{array}$

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Total sandface flowrate = qt

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