Verification of Gardner's equation and derivation of an empirical equation for anhydrite rocks in Sirte basin, Libya: case study

Bulk density is a physical property of rocks measured in the laboratory on rock samples or obtained from oil field logging tools. When bulk density is not measured, a synthetic bulk density log can be calculated, for which Gardner's equation is the most widely used. However, Gardner's equation might not be appropriate for regions in which the density–velocity relationship does not conform to Gardner's curves. Here, we verified the applicability of Gardner's equation to calculation of synthetic bulk density of anhydrite rocks in the Sirte Basin (Libya) and compared the results to those obtained from an equation derived from the available measured bulk density and sonic logs. We used fifteen wells to calibrate Gardner's equation and three wells to derive an equation for the anhydrite rocks. The anhydrite rocks were 10–510 feet thick. The bulk density calculated by Gardner's equation differed only slightly from the measured log values, with the exception of the eastern part of the Sirte Basin. The average of the differences in bulk density between the measured values and Gardner's equation results were 0.022–0.040 g/cm(3), and between the measured values and the derived equation results 0.002–0.045 g/cm(3), both with a standard error of about 0.01 of the bulk density estimated results. We conclude that while Gardner's equation is more appropriate for estimating the bulk density of anhydrite rocks in the eastern part of the basin, the derived equation could be more appropriate for the western region.