Specific implementation of pressure spatial decomposition based on recognising the time pattern of flowrate variation pulse sequence in pressure response.
It constitutes the key interpretation procedure for PCT.
The decomposition algorithm is based on the minimisation of correlation functional between generating well pressure variation p_G(t) and delta pressure \delta p_R(t) at receiving well after deducting the simulated pressure pulse-code response:
| (1) | X[p_{uGG}, p_{uGR}] = \left < | \delta p_R(t) | , \, |p_G(t)| \right > \rightarrow \min |
where
| (2) | p_G(t) = p_{G,0}(t) - \int_0^t p_{uGG}(t-\tau) \, dq_G(\tau) |
| (3) | p^*_R(t) = p_{R,0}(t) - \int_0^t p_{uGR}(t-\tau) \, dq_G(\tau) |
| (4) | \delta p_R(t) = p_R(t) - p^*_R(t) |
The result of decomposition is the set of the unit-rate transient responses, DTRs p_{uGG}(\tau) and CTRs p_{uGR}(\tau)), which characterise reservoir properties.