where LaTeX Math Inline |
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body | B_{w,k} = B_w(p_{wf,k}(t)) |
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LaTeX Math Inline |
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body | B_{o,k} = B_o(p_{wf,k}(t)) |
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| | LaTeX Math Inline |
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body | R_{s,k} = R_s(p_{wf,k}(t)) |
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LaTeX Math Inline |
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body | 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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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_rm produparrow}_P} \left[
(R_O - |
| C_O C^{\uparrow}_{O,p}) \cdot q^{\uparrow}_{O, p} + (R_G |
| -C_G - C^{\uparrow}_{G,p}) \cdot q^{\uparrow}_{G, p}
- |
| C_L \cdot q^ C ,p} \cdot q^{\uparrow}_{W, p} |
| N{,rm inj}} C \rm inj \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{ |
| N{,rm inj}} C \rm inj i} \rightarrow \rm max | CAKJPN_rm produparrow}_P} \left[
\left[ (R_O - |
| C_O C^{\uparrow}_{O,p}) + (R_G |
| -C_G - C^{\uparrow}_{G,p}) \cdot |
| GOR (C_L + C_WC^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot Y_ |
| w) {W,p} \cdot q^{\uparrow}_{L, p} |
| {N{N^{\downarrow}_W} C^{\downarrow}_{W,j} \ |
| rm inj}} C\rm inj} i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{ |
| Wi-
LaTeX Math Block |
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| G(t) = \sum_{ |
| jNN^{\uparrow}_P} \left[
\left[ (R_O - C^{\uparrow}_{O,p}) + (R_G - C^{\uparrow}_{G,p}) \cdot Y_{G, |
| \rm inj}} C_{G, \rm inj} p} \right] \cdot (1- Y_{W,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}_{ |
| G\rightarrow \rm max
| LaTeX Math Block |
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- \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: |
| anchor | 343G1N_rm prod\left[C_O C^{\uparrow}_{O,p}) + (R_G |
| -C_G - C^{\uparrow}_{G,p}) \cdot |
| GOR (C_L + C_WC^{\uparrow}_{L,p} - 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} \right] \cdot (1-Y_{W,p})}
\cdot q^{\uparrow}_{ |
| LN{,rm inj}} Crm inj} cdot B_w \cdot q^{\downarrow}_{ |
| WNN^{\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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| rm inj}} C_{G, \rm inj} \cdot q^{\downarrow}_{Gg,i} = J_{g,i} \rightarrow \rm max
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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