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Time interval of pressure transition when pressure drop 

LaTeX Math Inline
body\Delta delta p
 is evolving logarithmically in time:

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LaTeX Math Block
anchorYUKTO
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\Deltadelta p = p_{wf}(0) - p_{wf}(t) \sim p_{wf}(0) - p_i - \frac{q_t}{4 \pi \sigma} \, \bigg[ - 2S +  \gamma 

- \ln \bigg(  \frac{4 \chi t}{r_w^2} \bigg) \bigg]

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LaTeX Math Block
anchor9VWMA
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\Deltadelta p ' = \frac{d \, \Delta p}{d \, \ln t}  =  \frac{q_t}{4 \pi \sigma} = \rm const

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