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q^{\uparrow}(t) = f \, q^{\downarrow}(t) - \tau \cdot \frac{ d q^{\uparrow}}{ dt } - \beta \cdot \frac{d p_{wf}}{dt} |
where
| average surface production per well | ||||
| average surface injection per well | ||||
| average bottomhole pressure in producers | ||||
| unitless constant, showing the share of injection which actually contributes to production | ||||
| time-measure constant, related to well productivity | ||||
| storage-measure constant, related to dynamic drainage volume and total compressibility |
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\tau = \frac{\beta}{J} = \frac{c_t V_\phi}{J} |
where
| total formation-fluid compressibility | ||||
| drainable reservoir volume | ||||
| total rock volume within the drainage area | ||||
| average effective reservoir porosity | ||||
| total fluid productivity index |
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c_t = c_r + s_w c_w + s_o c_w + s_g c_g |
where
| rock compressibility | ||||
| water, oil, gas compressibilities | ||||
| water, oil, gas formation saturations |
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