Cemented porous grains model Franklin Ruiz*, OHM Rock Solid Images, Jack Dvorkin, Stanford University Summary We propose an effective-medium model for estimating the elastic properties of a random aggregate of identical, spherical, cemented poroelastic grains. These estimates are achieved using a two-stage approach where the elastic properties of the porous grains are calculated first, followed by the elastic properties of an aggregate of the homogenized spherical grains. In the first stage, the effective elastic moduli of the poroelastic grains are calculated using an effective medium model or the combination of effective medium model with Gassmann’s equation, depending on the connectivity of the intragranular porosity. The intragranular pore space may be either air- or liquid-filled. In the second stage, we proceed to calculate the elastic properties of a dry aggregate of such grains using the cementation theory. In the third stage we use the self-consistent approximation to estimate the elastic properties of the aggregate at all cement concentrations. This model may be applied to diatomaceous and carbonate rocks. The microstructural parameters of our models can be associated to diagenesis and may be varied to mimic diagenetic processes of carbonates Introduction In this study we develop a methodology to determine the effective elastic moduli of porous grain aggregate with different textures. This work is an extension of the porous- grain model proposed by Ruiz and Dvorkin (2009). This extension combine the self-consistent approximation (Berryman, 1980) with the cementation theory (Dvorkin et al., 1994) to account for intergranular cement volume fractions from 0 to 1; and d) considering the effect of frequency. We treat a saturated porous-grain as an elastic solid with ellipsoidal inclusions filled with compressible fluid. The cemented porous-grains model is used to determine the elastic moduli of a cemented porous grain aggregate at low cement concentration. This is achieved by introducing the porous grain concept into the cementation theory (Dvorkin et al., 1994). Then, by combining the cementation theory (Dvorkin et al., 1994) for porous grain material with a self-consistent approximation, specifically, the coherent potential approximation (CPA) (Berryman, 1980), we are allowed to estimate the elastic properties of cemented porous grain aggregates at all cement concentrations (Dvorkin et al. 1999). Our approach and models for non-cemented aggregates may be applied to sediment, such as calcareous and diatomaceous ooze, opal, and chalks. Our approach for cemented aggregates may be applied to carbonate rocks. The microstructural parameters of these models can be related to diagenesis and may be varied to mimic diagenetic processes of calcareous and diatomaceous ooze, and cemented and non-cemented carbonate rocks. Cemented aggregate of porous grains Cementation theory (Dvorkin et al., 1994) predicts that even a small amount of contact cement reinforces the grains contact, causing a large increase of the elastic moduli of the aggregate. The initial volume of cement added in the opening between grains is the most important. This theoretical prediction has been supported by several experiments (Ying, 1993; Tutuncu et al., 1997). Even by adding cement in the entire intergranular pore space, it is not possible to achieve the high relative stiffness increase produced by small volumes of cement at the grain contacts (Dvorkin et al., 1994; Dvorkin et al., 1999; Ying, 1993; Tutuncu et al., 1997). If we assume that the intergranular porosity reduction ( ic φ ), in a porous-grain aggregate is due to cementation exclusively, the ic φ of an uncemented sample is decreased to i φ by the addition of a cement material gradually. Once a given volume of cement is added, the effective bulk and shear elastic moduli of the aggregate of cemented porous grains are calculated as a function of the added cement. If only small amount of cement are considered, the calculation of the elastic properties of a cemented porous grains aggregate is conducted by introducing the porous grain concept (Ruiz and Dvorkin, 2009) into the cementation model (Dvorkin et al., 1994) following the two stage approach proposed by Ruiz and Dvorkin (2009). In this study we call this model “the slightly cemented porous grains model (CPG)”. Figure 1 shows the Vp velocity predicted by the soft and stiff porous grains models (Ruiz and Dvorkin, 2009), PGSO and PGST, respectively; by Waton-Rough model (Walton, 1987) for porous grains, and by CPG. The assumptions made in cementation theory (Dvorkin et al., 1994) are appropriate for high-porosity cemented aggregates, where only a small amount of cement is placed in the area close to the contact between grains. When the volume of cement in the intergranular pore space is high, the intergranular porosity and the connectivity among pores are reduced. For the determination of the elastic moduli of greatly cemented aggregate, an inclusion model is more appropriate because it is more consistent with the material microstructure than a granular-medium model. Thus, to determine the elastic properties of the aggregate in the 2720 SEG Denver 2010 Annual Meeting © 2010 SEG Downloaded 21 Feb 2012 to 216.198.85.26. 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