Reverse the problem to spatial superposition where pressure response  in -well is decomposed into a sum of individual pressure responses from :

p_m(t) = p_i + \sum_k \delta p_{mk}(t) = p_i + \sum_k  \int_0^t p_{umk}(t-\tau) \, dq_k(\tau)

where  is a specific component of -well pressure variation caused by -well flowrate history ,

and  is a pressure response in -well to unit-rate drawdown in -well 

The ultimate problem is to find transient responses .