CRM – Capacitance Resistivity Model

The Capacitance-Resitivity Model is a class of mathematical models relating the production rate history to the history of bottom-hole pressure and injection rate history of the offset wells.

It can be considered as the PDG interpretation.

(1)	$\begin{array}{l}\displaystyle q_j (t) = \sum_i^{n_i} f_{ij} I_i(t) - \tau_j \, \frac{ d q_j(t) }{ dt } - J_j \, \tau_j \, \frac{d p_{wf, j }(t)}{dt}\end{array}$

Derivation

(2)	$\begin{array}{l}\displaystyle p_{wf}(t) = p_r(t) - \frac{q(t)}{J}\end{array}$

(3)	$\begin{array}{l}\displaystyle p_r(t) = p_i + \frac{1}{c_t \, V_{\phi}} \, \Bigg[ \int_0^t q_i(\tau) d\tau - \int_0^t q(\tau) d\tau \Bigg]\end{array}$

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CRM – Capacitance Resistivity Model