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