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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
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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 injectionshare 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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:
(t)_i(t) = \alpha \cdot Q^{\uparrow}_O(t) + \beta \cdot Q^{\uparrow}_W(t) |
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++ \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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p- \frac{ 1 }{ \alpha \cdot c_t} \cdot \frac{B_o - R_s \, B_g}{1- R_s \, R_v} |
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pomega^- B_w^{-1} \cdot \beta \cdot V_\phi \cdot c_t LaTeX Math Block |
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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\frac{Q^{\uparrow}_{W,{\rm true}}}{Q^{\uparrow}_W} = \frac{\beta}{\alpha} \cdot \frac{1}{B_w} \cdot \frac{B_o - R_s \, B_ |
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o \cdot \, \left( | LaTeX Math Block |
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anchor | omega_down |
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alignment | left |
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| \Omega^{\downarrow}_W = \frac{Q^{\downarrow}_ |
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G - uparrowG + Q^downarrow_GCAPright) + ,left( Q^{\downarrow}_WQ^{\uparrow}_W + Q^{\downarrow}_{WAQ} \right)R_s \, B_g}{1- R_s \, R_v} |
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Panel |
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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 ]