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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 q_t or qB (with the latter does not imply a product) or specifically q^{\uparrow}_t for production and q^{\downarrow}_t 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 q_t 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) 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
(2) q^{\downarrow}_t = q^{\downarrow}_w + q^{\downarrow}_g = B_w \, q^{\downarrow}_W + B_g \, q^{\downarrow}_G



water sandface flowrate, oil sandface flowrategas sandface flowrate


produced water surface flowrate, oil surface flowrategas surface flowrate


injected water surface flowrate,  gas surface flowrate

B_w, \, B_o, \, B_g

formation volume factors for wateroilgas

R_s, \, R_v

Solution GOR and Vaporized oil ratio at sandface pressure/temperature conditions

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

(3) 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


\displaystyle Y_W = \frac{q^{\uparrow}_W}{q^{\uparrow}_L}

Production Water Cut

\displaystyle Y_G = \frac{q^{\uparrow}_G}{q^{\uparrow}_O}

Production Gas-Oil-Ratio = GOR

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

It simplifies for the 
Black Oil model (R_v = 0) to:

(4) q^{\uparrow}_t = B_w \, q^{\uparrow}_W + (B_o - R_s \, B_g) \, q^{\uparrow}_O + B_g \, q^{\uparrow}_G


(5) 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

It simplifies further down to production from
undersaturated reservoir as:

(6) 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

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

(7) 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

See Also

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate

Well & Reservoir Surveillance ]

Sandface flowrates ] [ Oil sandface flowrate ] [ Gas sandface flowrate ] [ Water sandface flowrate ] 

Surface flowrates ] [ Oil surface flowrate ] [ Gas surface flowrate ] [ Water surface flowrate ] [ Liquid production rate ]

Non-linear multi-phase diffusion derivation @model ]

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