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  • producing well W1 with total sandface flowrate 
    LaTeX Math Inline
    bodyq_1(t)>0
     and BHP 
    LaTeX Math Inline
    bodyp_1(t)>0
    , draining the reservoir volume
    LaTeX Math Inline
    bodyV_{\phi, 1}
     

  • water injecting well W0 with total sandface flowrate 

    LaTeX Math Inline
    bodyq_0(t) <0
    , supporting pressure in reservoir volume
    LaTeX Math Inline
    bodyV_{\phi, 0}
     which includes the drainage volume 
    LaTeX Math Inline
    bodyV_{\phi, 1}
     of producer W1 and potentially other producers {W1 .. WN}. 


The drainage volume difference

LaTeX Math Inline
body\delta V_{\phi} = V_{\phi, 0} - 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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In case injector W0 supports many producers {W1 .. WN } then all injection shares towards producers are going to sum up to a unit value:

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