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q^{\uparrow} (t) =\exp(-t/\tau) \cdot \left[ \ q^{\uparrow} (0) + \tau^{-1} \cdot \int_0^t \exp(s/\tau) \left[ f \cdot q^{\downarrow}(s) - \gamma \frac{dp}{ds} \right] ds \ \right] |
The objective function is:
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E[\tau, \gamma, f] = \sum_k \big[ q^{\uparrow}(t_k) - \tilde q^{\uparrow}(t_k) \big]^2 \rightarrow \min |
The basic constraints are:
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\tau \geq 0 , \quad \gamma \geq 0, \quad f \geq 0 |
Additional constaints maybe The additional constraints may be imposed as:
which means that a part of injection (
) is going away from the reservoir drained by producer.CRMP – Multi-Injector Capacitance Resistance Model
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