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LaTeX Math Block
anchorPCD
alignmentleft
p_m(t) = p_{mi} + \sum_k \delta p_{mk}(t) = p_{mi} +  \sum_k \int_0^t p_{umk}(t-\tau) \, dq_k(\tau) = p_{mi} + \int_0^t p_{umm}(t-\tau) \, dq_m(\tau) + \sum_{k \neq m}  \int_0^t p_{umk}(t-\tau) \, dq_k(\tau)

where

LaTeX Math Inline
bodyp_{mi}

initial formation pressure in

LaTeX Math Inline
bodym
-well

LaTeX Math Inline
body\delta p_{mk}(t)

specific component of 

LaTeX Math Inline
bodym
-well pressure variation caused by 
LaTeX Math Inline
bodyk
-well flowrate history 
LaTeX Math Inline
bodyq_k(t)

LaTeX Math Inline
bodyp_{umm}(\tau)

bottomhole pressure response in 

LaTeX Math Inline
bodym
-well to unit-rate production in the same well (DTR)

LaTeX Math Inline
bodyp_{ukm}(\tau)

bottomhole pressure in 

LaTeX Math Inline
bodym
-well to unit-rate production in 
LaTeX Math Inline
bodyk
-well (CTR),
LaTeX Math Inline
bodyk \neq m

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