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Consider a well-reservoir system consisting of:

  • producing well W1 draining the reservoir volume
    LaTeX Math Inline
    bodyV_{\phi, 1}
  • water injecting well W2 supporting pressure in reservoir volume
    LaTeX Math Inline
    bodyV_{\phi, 2}
     which includes the drainage volume of volume 
    LaTeX Math Inline
    bodyV_{\phi, 1}
     of producer W1 (and potentially other producers. 

The difference

LaTeX Math Inline
body\delta V_{\phi} = V_{\phi, 2} - V_{\phi, 1} >0
 may be related to the fact that water injection W2 is shared between
LaTeX Math Inline
bodyV_{\phi, 1}

...

 and another reservoir   or with another producer

Problem

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#1


Assuming producer is working with constant flowrate

LaTeX Math Inline
bodyq_1 = \rm const
, quantify the pressure response in producer W1 draining per  to the unit measure variation of injection volume in injector W2.


Problem

...

#2


Assuming producer is working with constant  BHP BHP 

LaTeX Math Inline
bodyp_1 = \rm const
, quantify the pressure flowrate response in producer W1 draining per  to the unit measure variation of injection volume in injector W2.General case


LaTeX Math Block
anchor1
alignmentleft
\delta q = - \frac{p_{\rm DTR}(t)}{p_{\rm CTR}(t)} \cdot \delta q_I

...