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publications > paper > carbonate porosity versus depth: a predictable relation for south florida > porosity versus depth
Porosity Versus DepthExponential RepresentationThe least-squares exponential fit to the data set described in the previous section is shown in Figure 5. The locations of porosity-depth values also are plotted in Figure 5 to show the envelope of data represented by the exponential curve. In the regression-curve calculations, intervals are considered to be of equal importance in describing carbonate porosity and are not weighted according to thickness. An exponential fit is a reasonably good visual representation of the data and serves to quantify comparisons and discussions. The correlation coefficient is -0.81 and the standard error of estimate - the root-mean-square of the porosity deviations about the exponential curve - is 5.1 porosity units. Based on statistical parameters (correlation coefficient, variance, and standard error of estimate), there is little difference in the fit between linear and exponential regression lines. However, high porosities of the near surface and residual porosities below about 16,000 ft (4,900 m) are not well represented by a linear regression line. For these reasons, the exponential function is used here to quantify the decrease of carbonate porosity with depth. Similar exponential functions have been used since the 1930s to quantify shale compaction (e.g., Athy, 1930; Hedberg, 1936; Maxant, 1980). The equation for the exponential regression curve shown in Figure 5 is:
where
Equation 1 is analogous to the equation describing radioactive decay. It is useful to describe radioactive decay in terms of a half life, and porosity "decay" can similarly be described in terms of a "half depth." In the South Florida basin, the half depth of carbonate porosity - the depth interval over which porosity is reduced by a factor of two - is 5,682 ft (1,732 m). The broad significance of these results is that there is a close relation between porosity and depth in carbonate rocks representing a wide range of ages, lithologies, depositional environments, and diagenetic processes. The scatter in the porosity trend is not negligible, and is due to the secondary dependence of porosity on non-depth-related factors as well as to experimental errors. Nevertheless, a predictable decrease of porosity with depth exists in the data. Sunniland TrendThe average porosity of producing intervals in the Sunniland Limestone is about 18% and the average producing depth is 11,500 ft (3,500 m) (Feitz, 1976; Tyler and Erwin, 1976). The expected porosity of south Florida carbonate rocks at this depth is about 10% (equation 1). Thus, the porosity of productive Sunniland Limestone is higher than the expected regional value. This anomalously high porosity could have been a primary reason for the initial localization of hydrocarbons. High porosity may have been preserved by oil, emplaced when the rocks were shallower and more porous. Processes associated with the generation and migration of hydrocarbons may have created late secondary porosity. Unfortunately, such interesting and important questions can not be resolved using the data of this report. Comparison to Published Porosity DataQuantitative comparison of the south Florida porosity-depth curve (equation 1), representing lithified rocks, to laboratory sediment-compaction data (e.g., Terzaghi, 1940; Fruth et al, 1966; Robertson, 1967; Morelock and Bryant, 1971) is of limited significance. Laboratory experiments do not duplicate very well the stress fields, changes in pore-fluid composition, and time spans involved in the lithification of carbonate rocks. The only published porosity-depth data analogous to this study that we are aware of relate to chalks and pelagic calcareous sediments. Neugebauer (1973, 1974) examined (theoretically) the loss of porosity in chalks, but did not quantify his results to the point of calculating porosity-depth relations. Representative empirical curves of porosity versus depth for chalks (Scholle, 1977; Lockridge and Scholle, 1978) and for deep-sea calcareous sediments (Schlanger and Douglas, 1974; Hamilton, 1976) are shown in Figure 6. Porosity-depth curves for the composite south Florida data set (equation 1) and for south Florida Gulf-age rocks only, are also shown for comparison in Figure 6. In the wells studied here, the Gulfian section consists primarily of chalks, but its porosity-depth curve does not differ substantially from that of the composite data set.
The chalk and pelagic-ooze data shown in Figure 6 form a porosity envelope which is greater in the near surface than the south Florida curve, but which decreases more rapidly with depth. The results of the present study do not agree with published porosity-depth data representing chalks and oozes. Because of a more porous initial depositional texture and the greater chemical stability of low-magnesium calcite, chalks may be less subject to early diagenetic alteration than most shallow-water carbonates, and may be buried with a generally higher initial porosity (Scholle, 1977), as indicated by Figure 6. Precise reasons for the more rapid porosity decrease with depth of the deep-water carbonates (Fig. 6) are not obvious to us. In a general sense, differences in trace and minor elements, grain size and shape, and rock texture, as well as external factors such as pore-fluid composition, geothermal gradient, and rate of subsidence, could cause variations in the response of shallow-water and deep-water carbonates to increasing burial depth. However, the relative importance of these and other factors on the depth dependence of carbonate porosity is poorly understood. |
U.S. Department of the Interior, U.S. Geological Survey
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Last updated: 10 December, 2004 @ 11:52 AM(TJE)
= 41.73 e -z/8197 (ft)
