Dictionary:Time-average equation

{{#category_index:T|time-average equation}} 1. An empirical equation stating that the transit time ${\textstyle \Delta t={\frac {1}{V}}}$ through a rock with matrix velocity V_m and porosity ${\textstyle \phi }$ that is filled with fluid of velocity V_f is approximately

$\Delta t={\frac {1}{V}}={\frac {(1-\phi )}{V_{ma}}}+{\frac {\phi }{V_{f}}}$.

This relation works well in clean consolidated formations with uniformly distributed pores. In formations containing vugs, the sonic log may not reflect the secondary porosity, and in unconsolidated formations, this relationship may overestimate porosity. The formula may be empirically modified to give better values. Also called Wyllie relationship.

2. A generalization of the foregoing equation for other constituents, weighting the velocity of each according to its volume fraction.

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