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| LaTeX Math Block |
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p(t) = p_0 + \int_0^t p_u(t-\tau) \, dq(\tau) = p_0 + \int_0^t p_u(t-\tau) \, \dot q(\tau) \, d\tau |
where
In case a well is interfering with the offset wells the pressure in a given well
may respond to the offset wells
and the multi-well form of
convolution is going to be:
| LaTeX Math Block |
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p_n(t) = p_{n, 0} + \sum_{m=1}^N \int_0^t p_{u,nm}(t-\tau) \, dq_m(\tau) = p_{n, 0} + \sum_{m=1}^N \int_0^t p_{u,nm}(t-\tau) \, \dot q_m(\tau) \, d\tau = p_{n, 0} + \int_0^t p_{u,nn}(t-\tau) \, \dot q_n(\tau) \, d\tau + p_{n, 0} + \sum_{m \neq n}^N \int_0^t p_{u,nm}(t-\tau) \, \dot q_m(\tau) \, d\tau |
where
See also
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See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing
[ Well & Reservoir Surveillance ] [ Pressure Diffusion ] [ Pressure drawdown ]
[ Convolution @math ]
