Reverse the problem to spatial superposition where pressure response p_m(t) in m-well is decomposed into a sum of individual pressure responses from :
| (1) | 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
\delta p_{mk}(t) | specific component of m-well pressure variation caused by k-well flowrate history q_k(t) |
p_{umm}(\tau) | DTR pressure response in m-well to unit-rate drawdown in the same well |
p_{ukm}(\tau) | CTR pressure response in m-well to unit-rate drawdown in k-well |
The ultimate problem is to find transient responses p_{ukm}(\tau) for cross-well intervals.