| Expand |
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| LaTeX Math Inline |
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| body | q^{\downarrow| 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 |
} \cdot q^{\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^{\ |
sum=1}^{N^}) + (R_G - C^{\uparrow}_ |
Pleft[
\left[ (R_O - cdot Y_{G,p} \right] \cdot q^{\uparrow}_{O, p}
- C^{\uparrow}_{ |
O) +(R_GG) gW,p} \cdot q^{\uparrow}_{L, p}
\right]
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\ |
uparrowOpi}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\ |
uparrowLpuparrowLp} - C^
| LaTeX Math Block |
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| G(t) = \sum_{p=1}^{N^{\uparrow}_ |
{W,p} \cdot Y_{w,p} \cdot q^P} \left[
\left[ (R_O - C^{\uparrow}_{ |
L
\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}) + (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_{w,p}
\right] \cdot q^{\ |
downarrowGj | | LaTeX Math Block |
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| G(t) =p{N^{\uparrow}_P} \left[
\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G -uparrowGp) Ygp\right] \cdot (1- Y_{w,p})
-
- \sum_{j=1}^{N^{\downarrow}_G} C^{\ |
uparrowLpuparrowLp} - C^{\uparrowTranslating p} \cdot Y_{w,p}
\right] \cdot and uparrowL p}
- \sum_{i=1}^{N^ to Sandface flowrates W} C^ and W \cdot with formation volume factor and substituting liquid production rate downarrowW i}
- 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_{ |
j{N^{\downarrow}_G} C^downarrow{G,jcdot 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 left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G, |
|
j} to Sandface flowrates | LaTeX Math Inline |
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body | q^{\downarrow}p}) \cdot Y_{g,p} \right] \cdot (1- Y_{w, |
|
i} and | LaTeX Math Inline |
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body | q^{\downarrowg j} with formation volume factor and substituting liquid production rate | LaTeX Math Inline |
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body | q^L, p} from | LaTeX Math Block Reference |
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| anchor | qL |
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| page | Liquid production rate |
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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}W,p} \cdot Y_{W,p} }
{B_w Y_{W,p} + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \, Y_{G,p} |
) g\right] \cdot (1- Y_{w,p})
-q^{\uparrow}_{t, p}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\ |
uparrowLp}uparrowLpC^{uparrow}W,p} \cdot Y_{w,p} }
{B_w Y_{w,p} + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \, Y_{g,p} \right] \cdot (1-Y_{w,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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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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Depending on Lift mechanism the rates in equation | LaTeX Math Block Reference |
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may be set directly or calculated from THP and formation pressure (which is a usual case in injection wells):| LaTeX Math Block |
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| q^{\uparrow}_{t, k} = J_{t,k} \cdot ( p_{e,k} - p_{wf,k} ) |
| LaTeX Math Block |
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| q^{\downarrow}_{w,i} = J_{w,i} \cdot ( p_{wf,i} - p_{e,i} ) |
| LaTeX Math Block |
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| q^{\downarrow}_{g,i} = J_{g,i} \cdot ( p_{wf,i} - p_{e,i} ) |
Producing wells may spontaneously vary between Constant rate production: qL = const and Constant pressure production: pwf = const (see Constant rate production: qL = const for alternation details).
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