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Borehole (Downhole or THP) pressure survey based on the varying pressure response to the varying flow rate variations (also called "cycles" or "pulses" ).


The usual practise is to create 3 - 5 pulses.

The pressure response is recorded in

  • the same well where the flowrate is varying ( and in this case is called Self-Pulse Test

or


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_0 \cdot \cos \left(\frac{2 \pi \, t}{T} \right)
(2) p=p_0 \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

(3) \delta = \frac{\pi}{8} + \frac{L}{\sqrt{\chi \, T}}


phase shift related to the pressure response delay to the flowrate variation

(4) p_0 = \frac{q_0}{\sigma} ...


pressure response to the flowrate variation

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


transmissbility

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


pressure diffusivity


In case of non-harmonic the pressure pulse response is being matched by numerical model.


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