B_{g,k} = B_g(p_{wf,k}(t)) |
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| | LaTeX Math Inline |
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body | R_{v,k} = R_v(p_{wf,k}(t)) |
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Expand |
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Panel |
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borderColor | wheat |
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bgColor | mintcream |
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borderWidth | 7 |
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LaTeX Math Block |
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| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \left[
(R_O - C^{\uparrow}_{O,p}) \cdot q^{\uparrow}_{O, p} + (R_G - C^{\uparrow}_{G,p}) \cdot q^{\uparrow}_{G, p}
- C^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot q^{\uparrow}_{W, p}
\right]
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}
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LaTeX Math Block |
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| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \left[
\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{ | gG,p} \right] \cdot q^{\uparrow}_{O, p}
- C^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot Y_{ | wW,p} \cdot q^{\uparrow}_{L, p}
\right]
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}
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LaTeX Math Block |
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| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \left[
\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{ | gG,p} \right] \cdot (1- Y_{ | wW,p})
- C^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot Y_{w,p}
\right] \cdot q^{\uparrow}_{L, p}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}
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Translating LaTeX Math Inline |
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body | q^{\downarrow}_{W, i} |
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| and LaTeX Math Inline |
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body | q^{\downarrow}_{G, j} |
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| to Sandface flowrates LaTeX Math Inline |
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body | q^{\downarrow}_{w, i} |
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| and LaTeX Math Inline |
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body | q^{\downarrow}_{g, j} |
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| with formation volume factor and substituting liquid production rate from LaTeX Math Block Reference |
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anchor | qL |
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page | Liquid production rate = qL |
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| one arrives to: LaTeX Math Block |
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| G(t) = \sum_{p=1}^{N^{\uparrow}_P} \frac{\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{g,p} \right] \cdot (1- Y_{w,p})
- C^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot Y_{ | wwW,p} + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \, Y_{ | gG,p} \right] \cdot (1-Y_{ | wW,p})}
\cdot q^{\uparrow}_{t, p}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot B_w \cdot q^{\downarrow}_{w, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot B_g \cdot q^{\downarrow}_{g, j}
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which is equivalent to LaTeX Math Block Reference |
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| . |
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