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LaTeX Math Block |
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\delta N = A(f) \cdot {\bf u} \cdot \nabla p \cdot \delta V |
where
LaTeX Math Inline |
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body | --uriencoded--%7B\bf u%7D |
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| flow velocity |
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| fluid pressure |
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| normalised noise spectrum, LaTeX Math Inline |
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body | --uriencoded--\displaystyle \int_0%5e\infty A(f) \, df = 1 |
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|
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| noise frequency |
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While propagating through the rocks the different frequencies will decay at different rate
and if noise sensor is located at LaTeX Math Inline |
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body | --uriencoded--%7B\bf r%7D_0 = \%7B0, \, 0, \, 0\%7D |
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then the it will capture: LaTeX Math Block |
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\delta N_S = \int_V A(f) \cdot {\bf u} \cdot \nabla p \cdot \exp[-\alpha(f)r] \cdot \delta V |
The decay decrement
is growing with frequency: LaTeX Math Inline |
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body | --uriencoded--\displaystyle \frac%7Bd \alpha%7D%7Bdf%7D > 0 |
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.
There is no universal model but it can be approximated by a linear dependance:
LaTeX Math Block |
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\alpha = \alpha_1 \cdot f |
with
having much slower dependance on frequency than .
See also
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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid Flow / Percolation / Reservoir Noise
Reference
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McKinley R.M., Bower F.M., Rumble R.C. 1973. The Structure and Interpretation of Noise From Flow Behind Cemented Casing, Journal of Petroleum Technology, 3999-PA
McKinley, R.M. 1994. Temperature, Radioactive Tracer, and Noise Logging for Well Integrity: 112-156