Consider a system of
- producing well W1 draining the reservoir volume V_{\phi, 1}
- water injecting well W2 supporting pressure in reservoir volume V_{\phi, 2} which includes the drainage volume of producer W1 ( V_{\phi, 1}) and potentially other producers.
Problem Defintion #1
Assuming producer is working with constant flowrate q_1 = \rm const, quantify the pressure response in producer W1 draining per unit measure of injection volume in injector W2.
Problem Defintion #2
Assuming producer is working with constant BHP p_1 = \rm const, quantify the pressure response in producer W1 draining per unit measure of injection volume in injector W2.
General case
| (1) | \delta q = - \frac{p_{\rm DTR}(t)}{p_{\rm CTR}(t)} \cdot \delta q_I |
where t is time since the water injection rate has changed by the \delta q_I value.
Pseudo-steady state flow
| (2) | \delta q = -\frac{c_{t,I} V_{\phi, I}}{c_t V_{\phi}} \cdot \delta q_I |
Steady state flow
| (3) | \delta q = -\frac{c_{t,I} V_{\phi, I}}{c_t V_{\phi}} \cdot \delta q_I |