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q^{\uparrow}(t) =  f \, q^{\downarrow}(t)  - \tau \cdot \frac{ d q^{\uparrow}}{ dt }  - J \cdot \tau \cdot \frac{d p_{wf }}{dt}


The target function is:

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q^{\uparrow}_j (t) = \sum_i^{n_i} f_{ij} q^{\downarrow}_i(t)  - \tau_j \cdot  \frac{ d q^{\uparrow}_j}{ dt }  - J_j \cdot  \tau_j \cdot  \frac{d p_{wf, \, j }}{dt}j}{dt}


The target function is:

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\sum_k \sum_j \big[ q^{\uparrow}_j(t_k) - \tilde q^{\uparrow}_j(t_k) \big]^2   \rightarrow \min 

ICRM  – Multi-Tank Integrated Capacitance Resistance Model

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Q^{\uparrow}_j (t) = \sum_i^{n_i} f_{ij} Q^{\downarrow}_i(t)  - \tau_j \cdot \big[ q^{\uparrow}_j(t) - q^{\uparrow}_j(0) \big]  - J_j \cdot  \tau_j \cdot  \big[ p_j - p_{wf, \, j }(t) - p_{wf, \, j }(00) \big]


The target function is:

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\sum_k \sum_j \big[ Q^{\uparrow}_j(t_k) - \tilde Q^{\uparrow}_j(t_k) \big]^2   \rightarrow \min 



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Expand
titleDerivation
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p_{wf}(t) = p_r(t) - \frac{q(t)}{J}
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p_r(t) = p_i + \frac{1}{c_t \, V_{\phi}} \, \Bigg[ \int_0^t q_i(\tau) d\tau - \int_0^t q(\tau) d\tau  \Bigg]

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