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A specific implementation of  Well Testing based on the Borehole (Downhole or THP) pressure response to the dedicated flow rate variations (also called "cycles" or "pulses" ).

The usual practise is to create 3 - 5 pulses.

The pressure response can be recorded in

  • the same well where the flowrate is varying ( and in this case it 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_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
(3) p_1 = \frac{q_0}{\sigma} ...


1st harmonic amplitude of pressure response to the flowrate variation

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


phase shift caused by pressure response delay 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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