Consider a well-reservoir system consisting of:
- producing well W1 draining the reservoir volume
- water injecting well W2 supporting pressure in reservoir volume which includes the drainage volume of producer W1 and potentially other producers.
The drainage volume difference
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| body | \delta V_{\phi} = V_{\phi, 2} - V_{\phi, 1} >0 |
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may be related to the fact that water injection
W2 is shared between
and another reservoir or with another producer.
Case #1 – Constant flowrate production
The pressure response
in producer
W1 to the flowrate variation
in injector
W2:
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\delta p_1 = - p_{u,\rm 21}(t) \cdot \delta q_2 |
where
Case #2 – Constant BHP
The flowrate response
in producer
W1 to the flowrate variation
in injector
W2:
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\delta q_1 = - \frac{p_{u,\rm 21}(t)}{p_{u,\rm 11}(t)} \cdot \delta q_2 |
where
Pseudo-steady state flow
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\delta q_1 = -\frac{c_{t,2} V_{\phi, 2}}{c_{t,1} V_{\phi, 1}} \cdot \delta q_2 |
Steady state flow
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\delta q_1 = -\frac{c_{t,2} V_{\phi, 2}}{c_{t,1} V_{\phi, 1}} \cdot \delta q_2 |
