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The MatBal equation
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is often complemented by constant
PI model of Bottom-Hole Pressure ( for
producers and
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| body | p^{\downarrow}_{wf}(t) |
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for
injectors):
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| anchor | BHP_PROD |
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| alignment | left |
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| p^{\uparrow}_{wf, k}(t) = p(t) - {J^{\uparrow}_k}^{-1} \cdot \frac{dQ^{\uparrow}_k}{dt} |
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| anchor | BHP_INJ |
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| alignment | left |
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| p^{\downarrow}_{wf, \, j}(t) = p(t) - {J^{\downarrow}_j}^{-1} \cdot \frac{dQ^{\downarrow}_j}{dt} |
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| where | where |
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| body | p^{\uparrow}_{wf, \, k}(t) |
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| | | LaTeX Math Inline |
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| body | p^{\downarrow}_{wf, \, j}(t) |
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| cumulative offtakes from -th producer by the time moment | | cumulative intakes to -th injector by the time moment |
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In practice there is no way to measure the external influx
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| body | Q^{\downarrow}_{GC}(t) |
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and
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| body | Q^{\downarrow}_{AQ}(t) |
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so that one need to model them and calibrate model parameters to fit available data on
production flowrates history and
formation pressure data records.
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