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Comparison with theoretical and empirical formulae

A number of theoretical methods have been proposed for describing the properties of sedimentary rock. Bounding methods are rigorously based on microstructural information. The best bounds on the properties of a two-phase composite without specifying any geometric information beyond porosity are the Hashin-Shtrikman bounds [Hashin and Shtrikman 1963]. Higher order bounds can be derived [Milton 1982], but the microstructural information needed to evaluate the results is not easy to obtain. A second approach is to assume a specific inclusion or pore shape, for which the dilute effect on the elastic properties can be analytically calculated. Various effective medium approaches [Hashin 1983] can then be used to systematically approximate the results to higher porosity systems. Certain microstructures have been shown to correspond to these theories but the physical structures are not realistic. Experimental measurements have often shown that relatively simple empirical relationships can be used to describe the properties of sedimentary rock. In this section we compare a number of well-known bound predictions, effective medium and empirical results with the numerically "exact" data computed from the microtomographic images discussed in the previous section.

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