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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:
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q=q_0 \cdot \cos \left(\frac{2 \pi \, t}{T} \right) |
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p=p_0 \cdot \cos \left(\frac{2 \pi \, t}{T} + \delta \right) |
where
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| \delta = \frac{\pi}{8} + \frac{L}{\sqrt{\chi \, T}} |
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phase shift related to the pressure response delay to the flowrate variation |
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| p_0 = \frac{q_0}{\sigma} ... |
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pressure response to the flowrate variation |
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| \sigma = \left< \frac{k}{\mu} \right> h |
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transmissbility |
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| \chi = \left< \frac{k}{\mu} \right> \frac{1}{c_t \, \phi} |
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pressure diffusivity |
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