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
| LaTeX Math Inline |
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| body | \delta V_{\phi} = V_{\phi, 2} - V_{\phi, 1} >0 |
|---|
|
may be related to the fact that water injection
W2 is shared between
and another reservoir or with another producer.
Problem #1
Assuming producer is working with constant flowrate
, quantify the pressure response
in producer
W1 to the variation
of injection volume in injector
W2.
| LaTeX Math Block |
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\delta p_1 = - p_{\rm CTR}(t) \cdot \delta q_I |
Problem #2
Assuming producer is working with constant BHP
, quantify the flowrate response
in producer
W1 to the variation
of injection volume in injector
W2.
| LaTeX Math Block |
|---|
|
\delta q = - \frac{p_{\rm DTR}(t)}{p_{\rm CTR}(t)} \cdot \delta q_I |
where
is time since the water injection rate has changed by the
value.
Pseudo-steady state flow
| LaTeX Math Block |
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\delta q = -\frac{c_{t,I} V_{\phi, I}}{c_t V_{\phi}} \cdot \delta q_I |
Steady state flow
| LaTeX Math Block |
|---|
|
\delta q = -\frac{c_{t,I} V_{\phi, I}}{c_t V_{\phi}} \cdot \delta q_I |
