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
or (with the latter does not imply a product) or specifically | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_t |
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for production and | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\downarrow%7D_t |
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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
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:
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q^{\uparrow}_w + q^{\uparrow}_o + q^{\uparrow}_g = B_w \, |
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) \, q^{\uparrow}_O + (B_g - R_v \, |
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| q^{\downarrow}_t = q^{\downarrow}_w + q^{\downarrow}_g = B_w \, q^{\downarrow}_W + B_g \, q^{\downarrow}_G
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where
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| body | --uriencoded--q%5e%7B\uparrow%7D_w |
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, | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_o |
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, | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_g |
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| water sandface flowrate, oil sandface flowrate, gas sandface flowrate |
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| body | --uriencoded--q%5e%7B\uparrow%7D_W |
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, | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_O |
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, | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_G |
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| produced water surface flowrate, oil surface flowrate, gas surface flowrate |
| LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\downarrow%7D_W |
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, | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\downarrow%7D_G |
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| injected water surface flowrate, gas surface flowrate |
| formation volume factors for water, oil, gas |
| Solution GOR and Vaporized oil ratio at sandface pressure/temperature conditions |
The total sandface flowrate | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_t |
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of production is related to Liquid production rate
| LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_L |
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as:| LaTeX Math Block |
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q^{\uparrow}_t = \Big[ B_w Y_W + \Big( \, (B_o - R_s B_g) + Y_G \cdot (B_gq_O
+ \frac{B_g - R_v B_o}{1 - R_v RB_s}o) \, q_G =
\Big) \cdot (1-Y_W) \Big] \cdot q^{\uparrow}_L |
where
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| body | --uriencoded--\displaystyle Y_W = \frac%7Bq%5e%7B\uparrow%7D_W%7D%7Bq%5e%7B\uparrow%7D_L%7D |
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| Production Water Cut |
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| body | --uriencoded--\displaystyle Y_G = \frac%7Bq%5e%7B\uparrow%7D_G%7D%7Bq%5e%7B\uparrow%7D_O%7D |
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| Production Gas-Oil-Ratio = GOR |
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| Expand |
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Starting with definition of Total sandface flowrate | LaTeX Math Block Reference |
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| anchor | qt_VO |
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| page | Total sandface flowrate = qt |
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and substituting the expression of Oil surface flowrate, Gas surface flowrate, Water surface flowrate through Liquid production rate one arrives to | LaTeX Math Block Reference |
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It simplifies for the Black Oil model () to:
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q^{\uparrow}_t = B_w \, qq^{\uparrow}_W
+ (B_o - R_s \, qB_Og) \, \frac{1 - R_{sn}}{1 - R_{vn} R_{sn}}
+ B_g \, q_G \, \frac{1 - R_{vn}}{1 - R_{vn} R_{sn}}
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where
q^{\uparrow}_O + B_g \, q^{\uparrow}_G
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or
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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:
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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
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and even simpler for single-phase fluid (water, dead oil or dry gas) with surface flow rate
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| body | --uriencoded--q%5e%7B\uparrow%7D |
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and formation volume factor B as below:| LaTeX Math Block |
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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
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See Also
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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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| LaTeX Math Inline |
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| body | \{ q_W, \, q_O, \, q_G \} |
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| LaTeX Math Inline |
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| body | \{ B_W, \, B_O, \, B_G \} |
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