CONCLUSIONS

The ``random polycrystals of porous laminates'' model introduced and studied here has been shown to be a useful tool for studying some very difficult technical issues concerning how geomechanical constants of reservoirs behave as a function of changes of pore fluid and varying degrees of heterogeneity. This model has the advantage that rigorous bounds [the Hashin-Shtrikman bounds of Peselnick and Meister (1965) and Watt and Peselnick (1980)] on the geomechanical constants (bulk and shear moduli) are available. Furthermore, due to the refined formulation of these bounds presented here, it is also possible to obtain self-consistent estimates directly from these bounds (Berryman, 2004b; 2005). This situation is particularly beneficial as the rigorous bounds then provide immediate theoretical error bars for the self-consistent estimates - a situation that is sometimes but not always true for other effective medium theories (Berryman, 1995). The model should therefore prove useful for a range of applications in geomechanics.

The results obtained for the specific application considered here, i.e., pore fluid effects on shear modulus, show that the pore fluid interaction with overall shear behavior is complicated. The changes from drained to undrained behavior for shear modulus can range from being a negligible effect (as it is according to Gassmann's results for microhomogeneous and isotropic media) to being a bigger effect than the changes in bulk modulus under some circumstances (see Figures 5 and 11 showing that the ratio of compliance differences R > 1 in some cases). Influences of pore geometry can also be studied in this model if desired, but this complication was avoided here by parameterizing the fluid effects through the use of Skempton's coefficient B. All the pore microgeometry effects were thereby hidden in the present analysis, but these could be brought out in future studies of the same and/or many other related systems.

Another related result of some importance to analysis of partially and patchy saturated systems was obtained in Appendix B. The results are illustrated in Figure 12 and show that deviations from a system satisfying Hill's equation (3) need not be small if the shear modulus heterogeneity is large. The analysis does show, however, that if shear modulus variation is small, then the observed deviations from predictions of Hill's equation should also be correspondingly small.

An implicit assumption made throughout the present paper is that the porosity and -- most importantly -- the fluid permeability of the geomechanical system under consideration is relatively uniform. Then, the pore fluid pressures equilibrate on essentially the same timescale throughout the whole system. If this is not true, as it would not be in a double-porosity dual-permeability system (Berryman and Wang, 1995), then the present analysis needs to be modified to account for the presence of more than one pertinent timescale. One direction for future work along these lines will therefore be focused on this more complex, but nevertheless important, problem commonly encountered in real earth reservoirs. The random polycrystal of porous laminates model is flexible enough to allow this set of problems to be studied within a very similar framework.