In case of harmonic pulsations and sufficiently long pressure-rate delay and a simple diffusion model (single-bed homogeneous reservoir without boundary) the test data can be approximated by analytical model:
(1) | q=q_1 \cdot \cos \left(\frac{2 \pi \, t}{T} \right) |
(2) | p=p_1 \cdot \cos \left(\frac{2 \pi \, t}{T} + \delta \right) |
where
L | distance between the pint of flow variation and point of pressure response, this is going to be well radius L=r_w for Self-Pulse Test and distance between generating and receiving well L= \sqrt{ \left({\bf r}_{\rm Generator} - {\bf r}_{\rm Receiver} \right ) ^2} for Pressure Pulse Interference Test | ||
---|---|---|---|
q_1 | 1st harmonic amplitude of flowrate variation | ||
| 1st harmonic amplitude of pressure response to the flowrate variation | ||
| phase shift caused by pressure response delay to the flowrate variation | ||
| formation transmissbility | ||
| formation pressure diffusivity |