Abstract

Fresh-water lenses in carbonate sand and grainstone islands can be modeled using Dupuit-Ghyben-Herzberg methods. The results indicate that the thickness of the lens (H) in a homogeneous, infinite-strip island will be a function of the island's width (a), hydraulic conductivity (K), and the amount of recharge (R). The ratio of R/K in most modern carbonate islands of Holocene sands and Pleistocene rocks is in the range of 10 (super -4) to 10 (super -6) . This means H should be 1% to 3% the magnitude of a. However, vertical and lateral variations in K, variations in island shape, the presence of intra-island evaporitic ponds and marshes, and the presence of a mixing zone result in actual H/a ratios that range from 0.2% to about 2%, with 1% being the most representative value. The thickness of a paleo-lens in an ancient carbonate shoal or reef complex can, therefore, be estimated if the width of the interpreted island can be approximated from facies or isopach maps. An example from the Late Jurassic Smackover Formation in Oaks Field, Louisiana, indicates that the estimated thickness of paleo-lenses is identical to the thickness of the porosity zones in a series of off-lapping oolite shoal complexes. A second example from the Late Permian San Andres Formation in Yates Field, west Texas, reveals that the estimated thickness of paleo-lenses is essentially equivalent to the thickness of a phreatic cave system formed on paleo-islands developed along the San Andres shelf margin. The H/a method for estimating the thickness of paleo-lenses and the possible extent of island-stage fresh-water diagenesis in ancient carbonates is more useful than the Ghyben-Herzberg rule (H = 40 times the elevation of the water table), because the GH rule requires estimation of paleo water-table and paleo-sea level positions to within a couple of centimeters. Such estimates are typically impossible in ancient rocks.

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