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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) + Q^{\downarrow}_{GC}(t) + Q^{\downarrow}_{AQ}(t) |
where
Q^{uparrow}ttcumulative offtakes by the time moment downarrow intakes\phieeffective porosity cptotal compressibility as function of formation pressure p() | | | LaTeX Math Inline |
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| body | Q^{\downarrow}_{GC}(t) |
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| cumulative volumetric inflow from gas cap expansion |
| | | LaTeX Math Inline |
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| body | Q^{\downarrow}_{AQ}(t) |
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| cumulative volumetric inflow from aquifer expansion |
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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