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Modelling facility for field-average formation pressure
at any time moment as response to production flowrates history:
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| anchor | MatBalSw |
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| alignment | left |
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| \frac{ds_w}{dt} =\frac{1}{A_e \, h_e \, \phi_e(p)} \left[ \int_{p_i}^p \phi_e(p) \, c_t(p) \, dp = \Delta Q (t) = Q^{\downarrow}_tq^{\downarrow}_w(t) - q^{\uparrow}_w(t) + q^{\downarrow}_{WAQ}(t) \right] - \left[ c_r(p) s_w +c_w(p) s_w \right] \frac{dp}{dt}
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| \frac{ds_w}{dt} =\frac{1}{A_e \, h_e \, \phi_e(p)} \left[ q^{\downarrow}_o(t) - Q^q^{\uparrow}_o(t) \right] - \left[ c_r(p) s_o +c_o(p) s_o \right] \frac{dp}{dt}
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| \frac{ds_w}{dt} =\frac{1}{A_e \, h_e \, \phi_e(p)} \left[ q^(t) + Q^{\downarrow}_{GC}g(t) - q^{\uparrow}_g(t) + Q^q^{\downarrow}_{WAQGC}(t) \right] - \left[ c_r(p) s_w +c_g(p) s_g \right] \frac{dp}{dt}
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| s_w + s_o + s_g = 1 |
where
The direct consequence of the above equations:
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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}_{WAQ}(t) |
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):...
