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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.
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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 + (B_o - R_s \, B_g) \, |
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q^{\uparrow}_O + (B_g - R_v \, B_o) \, q^{\uparrow}_G
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| | LaTeX Math Block |
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| q^{\downarrow}_t = q^{\downarrow}_w + q^{\downarrow}_g = B_w \, |
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q^{\downarrow}_W + B_g \, q^{\downarrow}_G
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where
q| --uriencoded--q%5e%7B\uparrow%7D_w |
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\, q | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_o |
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\, q and flowratesq| --uriencoded--q%5e%7B\uparrow%7D_W |
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, | LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\ |
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, q_O, \, q_Gwater, crude oiland natural gas surface flowrates between separator and 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
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| --uriencoded--q%5e%7B\uparrow%7D_L |
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as:| LaTeX Math Block |
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qq^{\uparrow}_t = \leftBig[ B_w Y_wW + \left[Big( \, (B_o - R_s B_g]) + Y_G \cdot (B_g - R_v B_o) \, GOR \right]Big) \cdot (1-Y_wW) \rightBig] \cdot qq^{\uparrow}_L |
where
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle Y_ |
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w frac{q_W}{q_L}| 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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| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle |
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GORfrac{q_G}{q_O}
| 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:
| LaTeX Math Block |
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| anchor | F50QC42VE8 |
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| alignment | left |
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q_t = q_w + q_o + q_gq^{\uparrow}_t = B_w \, qq^{\uparrow}_W + \left( B_o - (\frac{GOR}{R_s} -1 \, B_g) \cdot R_s \,, q^{\uparrow}_O + B_g \right) \, q_O
q^{\uparrow}_G
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or
| LaTeX Math Block |
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| anchor | qt_BOBA9QP |
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| alignment | left |
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qq^{\uparrow}_t = \Big[ B_w \, qY_W + \Big( \, (B_o - R_s \, B_g) \,+ qY_OG +\cdot B_g \, q_G = B_w \, q_W + B_o \, q_O + B_g ( q_G - R_s \, q_O )
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\Big) \cdot (1-Y_W) \Big] \cdot q^{\uparrow}_L |
It simplifies further down to production from undersaturated reservoir as:
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qq^{\uparrow}_t = B_w \, qq^{\uparrow}_W + B_o \, qq^{\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 | q--uriencoded--q%5e%7B\uparrow%7D |
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and
formation volume factor B as below:
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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
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