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The drainage volume 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. 

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Case #1


Assuming producer is working with constant flowrate

LaTeX Math Inline
bodyq_1 = \rm const >0
, quantify the  the pressure response 
LaTeX Math Inline
body\delta p_1
in producer W1 to the variation 
LaTeX Math Inline
body\delta q_I
of injection volume in injector W2.:

LaTeX Math Block
anchorDD4HW
alignmentleft
\delta p_1 = - p_{\rm 21}(t) \cdot \delta q_2

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Case #2


Assuming producer is working with constant BHP 

LaTeX Math Inline
bodyp_1 = \rm const
, quantify the flowrate response 
LaTeX Math Inline
body\delta q_1
in producer W1 to the variation 
LaTeX Math Inline
body\delta q_I
of injection volume in injector W2.:

LaTeX Math Block
anchor1
alignmentleft
\delta q = - \frac{p_{\rm 11}(t)}{p_{\rm 21}(t)} \cdot \delta q_2

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