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Plotting BHP  p_{wf}(t) and formation pressure  p_e(t) vs cumulatives  Q(t) = \int_0^t q_t(\tau) d\tau


It shows unit slope for PSS flow regime:

(1) p_{wf}(t) = p_i - J^{-1} q_t - \frac{1}{ V_{\phi} \, c_t} Q(t)
(2) p_e(t) = p_i - \frac{1}{ V_{\phi} \, c_t} Q(t)

while  p_{wf}(t) and  p_e(t) are being parallel to each other.


The difference between two straight lines  \Delta p = | p_e(t) - p_{wf}(t) | = \rm const is related to productivity index J and flowrate q_t which stay constant during the PSS flow regime:

(3) J = \frac{q_t}{\Delta p} = \rm const


The increase/decrease in gap between parallel lines is indicating increase/decrease in productivity index  J.

The increase/decrease of the parallel lines slope is indicating decrease/increase (inverse response) of the drainage volume.

Flattening out of parallel lines is indicating transition to Steady-State flow regime.


See Also


Petroleum Industry / Upstream /  Production / Subsurface Production / Field Study & Modelling / Production Analysis

0D Material Balance @model

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