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Specific implementation of pressure spatial decomposition based on recognizing recognising the time pattern of flowrate variation pulse sequence in pressure response.
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The decomposition algorithm is based on the minimisation of correlation functional between generating well pressure variation
and
delta pressure delta pressure at receiving well after deducting the simulated pressure pulse-code response:
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X[p_{umk}] = \left < p_m \delta p_R(t) , \, p_G(t) \right > \rightarrow \min |
where
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p_G(t) = p_{G0} - \int_0^t p_{mi} uGG}(t-\tau) \, dq_G(\tau) |
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p*_R(t) = p_{R0} +- \sum_k \int_0^t p_{umkuGR}(t-\tau) \, dq_kG(\tau) , \, |
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\delta p_kR(t) \right > \rightarrow \min= p_R(t) - p*_R(t) |
The result of decomposition is the set of the unit-rate transient responses, DTRs
and
CTRs
), which characterise reservoir properties.
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