Reverse the Inverse problem to spatial superposition where pressure response
in -well is decomposed into a sum of individual pressure responses from :| LaTeX Math Block |
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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
with:
| Input | Output |
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| LaTeX Math Inline |
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| body | \{ q_k(t_j) \}_{k=1..N, \, j= 1..T} |
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| flowrate variation history | | Drawdown Transient Response (DTR) |
| LaTeX Math Inline |
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| body | \{ p_k(t_j) \}_{k=1..N, \, j= 1..T} |
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|
| pressure variation history |
| specific component of -well pressure variation caused by -well flowrate history |
| DTR pressure response in -well to unit-rate drawdown in the same well ukmCTR pressure response in -well to unit-rate drawdown in -well | ...
...
