In case of periodic pulsations and sufficiently long pressure-rate delay and a simple diffusion model (single-bed homogeneous reservoir without boundary) the pressure pulse response can be approximated by analytical model:
q= \sum_k q_k \cdot \cos \left(\frac{2 \pi \, k \, t}{T} \right) |
p = \sum_k p_k \cdot \cos \left(\frac{2 \pi \, k \, t}{T} + \delta_k \right) |
where
distance between the pint of flow variation and point of pressure response, being:
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k-th harmonic amplitude of flowrate variation | ||
| k-th harmonic amplitude of pressure response to the flowrate variation | |
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| formation transmissbility | |
| formation pressure diffusivity |