The Capacitance-Resistance Model (CRM) is a class of mathematical models relating the production rate history to the offset injection rate history with ability to account for the producers bottom-hole pressure variation.
In case he bottom-hole pressure data is not available it is considered constant over time.
CRM does not pretend to predict pressure and reserves distribution as 3D dynamic model does.
It only provides hints for misperforming wells and sectors which need a further focus.
CRM is built around production data against material balance and require current FDP volumetrics, PVT and SCAL models.
The CRM has certain specifics for oil producers, water injectors, gas injectors and field/sector analysis.
The CRM analysis is
The simulation is based on the following equation:
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:
\sum_k \big[ q^{\uparrow}(t_k) - \tilde q^{\uparrow}(t_k) \big]^2 \rightarrow \min |
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} |
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_{wf, \, j }(t) - p_{wf, \, j }(0) \big] |
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