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LaTeX Math Block
anchorCase2_PSS
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\delta q_1 / \delta q_2 = - f_{21} = - \frac{V_{\phi, 2}}{ V_{\phi, 1}} = \rm const

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In case when injector W2 supports only one producer W1 then  both wells drain the same volume and 

LaTeX Math Inline
bodyV_{\phi, 2} = V_{\phi, 1}
 and  LaTeX Math Inlinebody
 so that 
LaTeX Math Block Reference
anchorCase2_PSS
 leads to:

LaTeX Math Block
anchor1
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\delta q_1 = -\delta q_2

, which means that producer W1 with constant BHP and finite-reservoir volume will eventually vary its rate at the same volume as injector W2.



If pressure in producer W1 is supported by several injectors 

LaTeX Math Inline
bodyN_{\rm inj} > 1
then over a long period of time one can assume:

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