| Popis: |
Random presence of various minerals, cracks and voids in different proportion make a rock inhomogeneous. These heterogeneities may be characterized by their different elastic constants. The size of heterogeneities can vary from micro-scale to macro-scale, and therefore the elastic properties of a rock become scale dependent. There has been great deal of efforts to estimate the effective properties of the heterogeneous materials, such as upper and lower bounds, self-consistent theory, differential effective medium theory; are based on the assumption that the inclusions occur in a particular shape. The mathematical formulations, based upon the solution of singularly perturbed linear equations approximation, partial differential equations, stochastic differential equations, ordinary differential equations and Markov chains, are used to estimate effective media properties . But these approximation methods, generally, do not take into account the interaction between heterogeneities. Our upscaling method is based upon pairand multispatial correlation function. Comparison of these two methods has been done with Backus averaging and simple running window averaging. Results indicate that the upscaling based pairand multicorrelation function are in good agreement to the original data. |
