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

where where

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

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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)

...

DTR pressure response in 

LaTeX Math Inline
bodym
-well to unit-rate drawdown in the same well 

...

LaTeX Math Inline
bodyp_{ukm}(\tau)

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CTR pressure response

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in 

LaTeX Math Inline
bodym
-well to unit-rate drawdown

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in 

LaTeX Math Inline
bodyk
-well 


The ultimate problem is to find transient responses 

LaTeX Math Inline
bodyp_{ukm}(\tau)
 for cross-well intervals.