Sonic Logs

By Luke Stoeckel with edits by Tom Sturman

Sonic logs are produced by a sonde containing an array of acoustic transmitters and receivers which measure the time taken for an acoustic wave to propagate through the formation and return. It has been widely accepted that there exists a close relationship between transit time (DT), from the sonic log, and the degree of porosity of a formation, and if the pore fluid velocity and rock matrix velocity are known then the log can be used to calculate the formation porosity using the Wyllie time equation.
The sonic log measures the velocity of propagation of a P-wave through a rock formation and this velocity is expressed as interval transit time (DT), the reciprocal of velocity. Differences in the interval transit time correspond to the lithology and therefore the density of the formation, e.g. a denser formation will have a higher transit time as the P-wave will take less time to travel through it. The sonic log can be used for determining porosity, calibrating seismic data, interpreting general lithology as well as texture correlation and also estimating compaction, uplift and overpressure values.
The main problem with sonic logs is that they are not able to measure thin facies changes within the stratigraphic column due do the wavelength being used is often much longer than the thickness of the formation resulting in the resolution of the logging tool being low. Generally beds with a thickness of 60cm are not detected the tool, meaning that the sonic log can miss a thin impermeable layer which may impede the flow of a reservoir and hence reducing the productivity of a well.
The sonic log is measured in μs/ft (the reciprocal of velocity) and using by the Wyllie time average equation (Equation below) the porosity of a reservoir unit can be calculated. The Wyllie time average equation is an empirical relation assuming that the total time taken (Δt) is the sum of the Δt in the fluid and the Δt in the matrix. If the Δt of the fluid present in the formation and the Δt of the matrix are both known then the porosity can be estimated, however this relation tends to overestimate the porosity.

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There are some general matrix values which can be used for lithologies and the drilling fluids used in the wells (Figure1). However if an incorrect matrix or fluid value is used it can lead to an incorrect porosity calculation.

matrix2.JPG
Figure 1. General matrix and fluid transit times (Holford, 2010)