Model 3 - Hydrate cements the grains

In this model we assume that hydrate is formed at grain contacts and thus strongly reinforces the sediment. As model 2, it yields a porosity reduction which is equivalent to the one in equation 7. The effective bulk and shear moduli of the dry rock frame cemented by gas hydrate can then be calculated using the cementation theory by Dvorkin and Nur 1993:

$$\begin{eqnarray} &K_{dry}&\:=\:{1\over6}\:n\:(1-\phi)\:(K_h\:+\:{4\over3}\:G_h)\... ...:=\:{3\over5}\:K_{dry}\:+\:{3\over20}\:n\:(1-\phi)\:G_h\:S_{\tau};\end{eqnarray}$$

where S_n and $S_{\tau}$ are proportional to the normal and shear stresses of a cemented two-grain combination and depend on the amount of hydrate at grain contacts, and on the sediment and grain moduli. The exact formulas for S_n and $S_{\tau}$ are given in appendix A. The saturated rock properties are again calculated using Gassman's equations (5).