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anchor | MatBal |
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alignment | left |
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| (B_o - R_s \, B_g) \, G_O +(B_g - R_V \, B_o) \, G_G + (B_w \, G_W - \phi_n )\, (1- R_s \, R_v) = 0 |
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| G_O = V_e^{-1} \, \delta \, Q_O + \left[ \frac{s_{oi}}{B_{oi}} + \frac{R_{vi}\, s_{gi}}{B_{gi}}\right] |
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| \delta \, Q_O = - Q^{\uparrow}_O |
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| G_G = V_e^{-1} \, \delta \, Q_G + \left[ \frac{R_{si}\, s_{oi}}{B_{oi}} + \frac{ s_{gi}}{B_{gi}}\right] |
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| \delta \, Q_G = Q^{\downarrow}_G - Q^{\uparrow}_G + Q^{\downarrow}_{GCAP} |
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| G_W = V_e^{-1} \, \delta \, Q_W + \frac{ s_{wi}}{B_{wi}} |
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| \delta \, Q_W = Q^{\downarrow}_W - Q^{\uparrow}_W + Q^{\downarrow}_{WAQ} |
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| \phi_n = 1 + c_\phi \, (p-p_i) + 0.5 \, c^2_\phi \, (p-p_i)^2 |
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where
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body | --uriencoded--Q%5e%7B\uparrow%7D_O(t) |
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| initial oil+gas pay drainage volume (excluding the aquifer and gas cap) | LaTeX Math Inline |
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body | --uriencoded--Q%5e%7B\uparrow%7D_G(t) |
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| pore compressibility | LaTeX Math Inline |
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body | --uriencoded--Q%5e%7B\uparrow%7D_W(t) |
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body | --uriencoded--s_%7Bwi%7D |
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| initial water saturation | LaTeX Math Inline |
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body | --uriencoded--Q%5e%7B\downarrow%7D_W(t) |
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body | --uriencoded--s_%7Bgi%7D |
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| initial gas saturation | LaTeX Math Inline |
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body | --uriencoded--Q%5e%7B\downarrow%7D_G(t) |
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body | --uriencoded--s_%7Boi%7D |
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| initial oil saturation: LaTeX Math Inline |
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body | --uriencoded--s_%7Boi%7D = 1 - s_%7Bwi%7D - s_%7Bgi%7D |
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body | --uriencoded--Q%5e%7B\downarrow%7D_%7BWAQ%7D(t) |
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| Cumulative water influx from Aquifer Expansion by the time moment |
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body | --uriencoded--Q%5e%7B\downarrow%7D_%7BGCAP%7Dt) |
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| Cumulative gas influx from Gas Cap expansion by the time moment |
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The MatBal equation
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is often complemented by constant
PI model of Bottom-Hole Pressure ( for
producers and
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body | p^{\downarrow}_{wf}(t) |
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for
injectors):...