Approximation of Material Balance Pressure @model for slightly compressibility flow:
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| p(t) = p_i + \frac{\Delta Q(t)}{V_\phi \cdot c_t} |
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| \Delta Q = - \frac{B_o - R_s \, B_g}{1- R_s \, R_v} \cdot \, Q^{\uparrow}_O + \frac{ B_g - R_v \, B_o}{1- R_s \, R_v} \cdot \, \left( Q^{\downarrow}_G - Q^{\uparrow}_G + Q^{\downarrow}_{GCAP} \ \ \right) + B_w \, \left( Q^{\downarrow}_W - Q^{\uparrow}_W + Q^{\downarrow}_{WAQ} \ \ \right) |
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where
The equations
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and | LaTeX Math Block Reference |
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are often used in express assessment of thief water production share | LaTeX Math Inline |
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| body | --uriencoded--\Omega%5e%7B\uparrow%7D_W = Q%5e%7B\uparrow%7D_%7BW,%7B\rm true%7D%7D \, / \,Q%5e%7B\uparrow%7D_W |
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and thief water injection share | LaTeX Math Inline |
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| body | --uriencoded--\Omega%5e%7B\downarrow%7D_W = Q%5e%7B\downarrow%7D_%7BW,%7B\rm true%7D%7D \, / \,Q%5e%7B\downarrow%7D_W |
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| p_i - p(t) = \alpha \cdot Q^{\uparrow}_O(t) + \beta \cdot Q^{\uparrow}_W(t) - \gamma \cdot Q^{\downarrow}_W(t) |
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| anchor | conditions |
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| alignment | left |
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| \alpha > 0, \quad \beta > 0, \quad \gamma > 0 |
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| V_\phi = \frac{ 1 }{ \alpha \cdot c_t} \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
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| anchor | omega_up |
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| alignment | left |
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| \Omega^{\uparrow}_W = \frac{Q^{\uparrow}_{W,{\rm true}}}{Q^{\uparrow}_W} = \frac{\beta}{\alpha} \cdot \frac{1}{B_w} \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
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| anchor | omega_down |
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| alignment | left |
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| \Omega^{\downarrow}_W = \frac{Q^{\downarrow}_{W, {\rm true}}}{Q^{\downarrow}_W} =\frac{\gamma}{\alpha} \cdot \frac{1}{B_w} \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
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| bgColor | papayawhip |
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| title | ARAX |
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| The MatBal equation | LaTeX Math Block Reference |
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| anchor | MatBal |
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| page | Material Balance Pressure @model |
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can be re-written as following:| LaTeX Math Block |
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| anchor | MatBal_formula |
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| alignment | left |
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| p = p_i + \frac{\delta Q}{c_\phi \, V_\phi} + \delta p_i |
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| anchor | MatBal_formula |
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| alignment | left |
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| \delta p_i = \frac{ B_{og} \, F_{Oi} + B_{go} \, F_{Gi} + B_w \, F_W -1}{c_\phi} |
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| B_{og} = \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
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| B_{go} = \frac{ B_g - R_v \, B_o}{1- R_s \, R_v} |
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where |
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[ Derivation of Slightly compressible Material Balance Pressure @model ]
[ Capacitance-Resistivity Model (CRM) @model ]
