Estimate the Effective Elastic Properties of Digitized Porous Rocks by Inverting the Cracks Unresolved

Current imaging technique such as micro X-ray CT can provide us detailed 3D micro-structures of porous rocks that can be used in numerical simulation so as to predict elastic properties of rocks saturated with different fluids. However, limited by the resolution the imaging process can provide, we usually lose the small features of rocks such as cracks and micro-pores, consequences of which can cause over-predicted effective elastic properties of porous rocks. In this paper, we present an inversion scheme to estimate the lost cracks during imaging process with Monte-Carlo algorithm. This method combines numerical simulation with theoretical models – the differential effective media model and Kuster-Toksöz model. Compared to the traditional inversion algorithms solely based on theoretical models, the algorithm presented in this paper utilizes the micro-structures of porous rocks resolved and takes the advantages of computational results from the digitized rocks, which in fact provides us much information of rocks and limits our inversion space for cracks. At end, we demonstrate the capability of this method on predicting the elastic properties of Berea sandstones measured in laboratory.