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LaTeX Math Block |
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anchor | MatBal |
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alignment | left |
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| A_e \, h_e \int_{p_i}^p \phi_e(p) \, c_t(p) \, dp = \Delta Q (t) = Q^{\downarrow}_t(t) - Q^{\uparrow}_t(t) + V^{\downarrow}_{GC}(t) + V^{\downarrow}_{AQ}(t) |
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LaTeX Math Block |
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anchor | BHP_PROD |
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alignment | left |
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| p^{\uparrow}_{wf, k}(t) = p(t) - \frac{1}{J^{\uparrow}_k} \frac{dQ^{\uparrow}_k}{dt} |
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LaTeX Math Block |
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anchor | BHP_INJ |
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alignment | left |
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| p^{\downarrow}_{wf, k}(t) = p(t) - \frac{1}{J^{\downarrow}_i} \frac{dQ^{\downarrow}_k}{dt} |
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where
For low compressibility rocks and fluids
LaTeX Math Inline |
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body | \{ \phi_e = {\rm const}, \ c_t = {\rm const} \} |
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the
MatBal equation
LaTeX Math Block Reference |
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can be explicitly integrated:
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