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LaTeX Math Block
anchor1
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p_n(t) 
= p_{i0,n} +  \sum_{k = 1}^N  \int_0^t  p^u_{nk}(t - \tau) \, \dot q_k \, d\tau
\approx p_{i,n} + \sum_{k = 1}^N  \sum_{\alpha= 1}^{N_k} \big( q^{(\alpha)}_k - q^{(\alpha-1)}_k \big) \ p^u_{nk}(t - t_{\alpha k})

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1

LaTeX Math Inline
bodyp_n(t)

pressure at

LaTeX Math Inline
bodyn
-th well at arbitrary moment of time
LaTeX Math Inline
bodyt

2

LaTeX Math Inline
body--uriencoded--p_%7B0n%7D = p_{i,n}n(0)

initial pressure at

LaTeX Math Inline
bodyn
-the well

3

LaTeX Math Inline
bodyq^{(\alpha)}_n

rate value of

LaTeX Math Inline
body\alpha
-th transient at
LaTeX Math Inline
bodyn
-th well

4

LaTeX Math Inline
bodyp^u_{nk} (t)

pressure transient response in

LaTeX Math Inline
bodyn
-th wel to unit-rate production from
LaTeX Math Inline
bodyk
-th well

5

LaTeX Math Inline
bodyt_{\alpha k}

starting point of the

LaTeX Math Inline
body\alpha
-th transient in
LaTeX Math Inline
bodyk
-th well

6

LaTeX Math Inline
bodyN

number of wells in the test
7

LaTeX Math Inline
bodyN_k

number of transients in

LaTeX Math Inline
bodyk
-th well

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