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The equations
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and
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are often used in express assessment of thief water production and water injection:
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| p_i - p(t) = \alpha \cdot Q^{\uparrow}_O + \beta \cdot Q^{\uparrow}_W - \gamma \cdot Q^{\downarrow}_W |
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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{\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{\gamma}{\alpha} \cdot \frac{1}{B_w} \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
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