For the pressure diffusion with constant diffusion coefficients and homogeneous boundary conditions the pressure response p(t) in one well to a complex flowrate history q(t) in the same well honours the convolution equation:
| (1) | p(t) = p_0 + \int_0^t p_u(t-\tau) \, dq(\tau) |
In case a well is interfering with the offset wells the pressure in a given well n may respond to the offset wells m \neq n and the multi-well form of convolution is going to be:
| (2) | p_n(t) = p_{n, 0} + \sum_{m=1}^N \int_0^t p_{u,nm}(t-\tau) \, dq_m(\tau) |