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doi:10.2204/iodp.proc.322.201.2013 Archie porosity estimationTo estimate porosity from the LWD resistivity data, Archie’s equation is used. Archie (1942) determined an empirical relationship between the porosity (φ) of a formation and the formation factor (FF):
where a is a constant and m reflects the pore geometry and interpore connections (known as the cementation exponent). Usually m and a are determined from core sample measurements. The formation factor (FF), originally defined by Sundberg (1932), is the ratio of resistivity of a fully water-saturated rock (Ro) to the resistivity of the saturating fluid (Rw):
By combining Equations 1 and 2 to produce Equation 3, it is possible to relate the formation resistivity (Ro) to the porosity (φ):
If the resistivity of the saturating fluid, cementation exponent, and constant a are known, then the porosity can be calculated from the measured LWD resistivity (Equation 4), as the LWD resistivity measures the resistivity of the fully saturated rock (Ro):
The resistivity of the formation water, in this case dominantly seawater, changes with temperature. Shipley, Ogawa, Blum, et al. (1995) defined the relationship between the fluid resistivity (Rw) and borehole temperature as
where T is the temperature in degrees Celsius (Shipley, Ogawa, Blum, et al., 1995). In order to use the above equation, a downhole temperature profile must be estimated. Given the lack of any bottom-hole temperatures from the logging data, core data thermal conductivity measurements were used to estimate temperature gradients. |
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