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.

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

(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

$\begin{array}{l}q_w\end{array}$ , $\begin{array}{l}q_o\end{array}$ , $\begin{array}{l}q_g\end{array}$	water sandface flowrate, oil sandface flowrate, gas sandface flowrate
$\begin{array}{l}q_W\end{array}$ , $\begin{array}{l}q_O\end{array}$ , $\begin{array}{l}q_G\end{array}$	Water surface flowrate, Oil surface flowrate, Gas surface flowrate
$\begin{array}{l}B_w, \, B_o, \, B_g\end{array}$	formation volume factors between sandface pressure/temperature conditions and surface measurement unit (usually separator or processing plant)
$\begin{array}{l}R_s, \, R_v\end{array}$	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)	$\begin{array}{l}\displaystyle q_t = \Big[ B_w Y_w + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \cdot GOR \right] \cdot (1-Y_w) \Big] \cdot q_L\end{array}$

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

Error rendering macro 'mathblock-ref' : Page Total sandface flowrate (qt) could not be found.

and substituting the expression of Oil surface flowrate, Gas surface flowrate, Water surface flowrate through Liquid production rate one arrives to (2).

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

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

or

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

(5)	$\begin{array}{l}\displaystyle q_t = B_w \, q_W + (B_o - R_s \, B_g) \, q_O + B_g \, q_G = B_w \, q_W + B_o \, q_O + B_g ( q_G - R_s \, q_O ) = B_w \, q_W + \left( 1 + \left( \frac{GOR}{R_s} -1 \right) \cdot \frac{R_s \, B_g}{B_o} \right) \cdot B_o\, q_O\end{array}$

or

(6)

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

It simplifies further down to production from undersaturated reservoir as:

(7)	$\begin{array}{l}\displaystyle q_t = B_w \, q_W + B_o \, q_O = \left[ B_w Y_w + B_o (1- Y_w) \right] q_L\end{array}$

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:

(8)	$\begin{array}{l}\displaystyle q_t = q \cdot B, \quad {\rm meaning:} \quad q_t = q_W \cdot B_w \quad {\rm or} \quad q_t = q_O \cdot B_o \quad {\rm or} \quad q_t = q_G \cdot B_G\end{array}$

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See Also