While fluid percolates through porous media in infinitesimal volume generates the noise of the power
in a wide frequency range:
\delta N = A(f) \cdot {\bf u} \cdot \nabla p \cdot \delta V |
where
| flow velocity | |
| fluid pressure | |
normalised noise spectrum, | |
| noise frequency |
While propagating through the rocks the different frequencies will decay at different rate and if noise sensor is located at
then the it will capture:
\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:
.
There is no universal model but it can be approximated by a linear dependance:
\alpha = \alpha_1 \cdot f |
with having much slower dependance on frequency than
.
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid Flow / Percolation / Reservoir Noise
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