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q_t = \Big[ B_w Y_wW + \Big( \, (B_o - R_s B_g) + GORY_G \cdot (B_g - R_v B_o) \, \Big) \cdot (1-Y_wW) \Big] \cdot q_L |
where
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| body | --uriencoded--\displaystyle Y_ |
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w frac{q_W}{q_L} 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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. |
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| LaTeX Math Block |
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q_t = \Big[ B_w Y_wW + \Big( \, (B_o - R_s B_g) + GORY_G \cdot B_g \, \Big) \cdot (1-Y_wW) \Big] \cdot q_L |
It simplifies further down to production from undersaturated reservoir as:
| LaTeX Math Block |
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q_t = B_w \, q_W + B_o \, q_O = \Big[ B_w Y_wW + B_o \cdot (1- Y_wW) \Big] \cdot q_L
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and even simpler for single-phase fluid (water, dead oil or dry gas) with surface flow rate
and
formation volume factor B as below:
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