In case of harmonic pulsations and sufficiently long pressure-rate delay time and a simple diffusion model (single-bed homogeneous reservoir without boundary) the pressure pulse response can be approximated by analytical model:

q=q_1 \cdot \cos \left(\frac{2 \pi \, t}{T} \right)


p=p_1 \cdot \cos \left(\frac{2 \pi \, t}{T}  + \delta_1 \right)

where





distance between the point of flow variation (pressure pulse generating well) and point of pressure response (pressure pulse receiving well), being:

1st harmonic amplitude of flowrate variation


p_1 = \frac{q_1}{\sigma} ...



1st harmonic amplitude of pressure response to the flowrate variation


\delta_1 = \frac{\pi}{8} + \frac{L}{\sqrt{\chi \, T}}



phase shift caused by pressure response delay to the flowrate variation


\sigma = \left< \frac{k}{\mu} \right> h



formation transmissbility


\chi = \left< \frac{k}{\mu} \right> \frac{1}{c_t \, \phi}



formation pressure diffusivity


References



Pressure Pulse Calculator  –  Excel Calculator for Harmonic Pressure Pulsations interpretation