Time Average DTS-Porosity Relationship
Publication Date: 2006-Jan-27
The IP.com Prior Art Database
Porosity from Compressional wave slowness can be estimated using the known Wyllie Time average equation: DTC = Ø DTCfluid + (1 - Ø ) DTCmatrix. Similar equations have been proposed for Shear wave slowness but they are not widely accepted. Theoretically, elastic moduli of rocks lie in between the Hashin-Strikman (HS) upper and lower bounds. For a two-phase material, like a clean rock, HS bounds are functions of the porosity as well as matrix and fluid moduli. In this paper, quartz is used as matrix and water as fluid. For the quartz-water pair, the Wyllie Porosity - DTC relationship falls inside its corresponding HS bounds. However, no simple arithmetic average of the bounds reconstructs Wyllie-type behavior. In order to perform said reconstruction, a weighted average of the bounds is necessary and the same set of weights can be used to build a DTS - Ø relationship. The resulting equation is non-linear, as expected, but for practical purposes and for porosities less than 30%, said equation is approximately linear. This technique is extendable to equations other than Wyllie and other minerals as well. Complex configurations like laminar-dispersed shale and influence of hydrocarbons are under study.