Use of "digital core" module in SAE Fidesis to determine effective parameters of fractured porous media
Authors: Levin Vladimir 
Published: March 2020

&lt;p&gt;Development of the homogenization algorithms for&amp;#160;the heterogeneous periodic and non-periodic materials has applications in different domains and considers different types of upscaling techniques&amp;#160;(Fish, 2008, Bagheri, Settari, 2005, Kachanov et al. 1994, Levin et al. 2003).&lt;/p&gt;&lt;p&gt;The current&amp;#160;presentation&amp;#160;discusses an algorithm implemented in CAE Fidesys (Levin, Zingerman,&amp;#160;Vershinin 2015, 2017)&amp;#160;for calculating the effective mechanical characteristics of a porous-fractured medium (Myasnikov et al., 2016) at the scale of a&amp;#160;periodicity cell dissected by a group of plane-parallel cracks modeled by elastic bonds with specified stiffnesses in the normal and tangential directions in accordance with the method of modeling cracks based on elastic bonds (Bagheri,&amp;#160;Settari, 2005, 2006) In this case, the relationship between the components of the displacement vector and the force vector (normal&amp;#160;stresses at the fracture&amp;#8217;s boundaries) in the normal and tangential directions will be diagonal, neglecting the effects of dilatancy and shear deformations as a result of normal stresses.&lt;br&gt;The presentation&amp;#160;also considers&amp;#160;the general case of the relationship between displacements and forces along the fracture&amp;#8217;s&amp;#160;boundaries, taking into account shear deformations (which leads to an increase in the effective Young's modulus by 30%), and additionally a&amp;#160;cell&amp;#8217;s geometrical model&amp;#160;is generalized&amp;#160;by the presence of pores in the matrix&amp;#8217;s&amp;#160;material. The results of numerical studies on mesh&amp;#160;convergence, the influence of periodicity cell sizes and fracture&amp;#8217;s&amp;#160;thicknesses on the computed effective properties&amp;#160;are presented. A&amp;#160;comparison between&amp;#160;analytical (Kachanov, Tsukrov 1994, 2000)&amp;#160;and numerical results&amp;#160;obtained in CAE Fidesys for&amp;#160;the effective elastic moduli estimation&amp;#160;for particular cases of geometrical models of the periodicity cell is shown.&lt;br&gt;The developed algorithm is used to evaluate the effective mechanical properties of a digital core model obtained by the results of CT-scan data interpretation. A comparison is made with the results of laboratory physical&amp;#160;core tests.&amp;#160;Additionaly an algorithm implemented in CAE Fidesys&amp;#160;and the&amp;#160;results for the effective thermal conductivity and the effective coefficient of&amp;#160;thermal expansion&amp;#160;estimation are given for the considered test rock specimen.&lt;/p&gt;&lt;p&gt;The reported study was funded by Russian Science Foundation project &amp;#8470; 19-77-10062.&amp;#160;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;ol&gt;&lt;li&gt;Bagheri, M., Settari, A. Effects of fractures on reservoir deformation and flow modeling // Can. Geotech. J. 43: 574&amp;#8211;586 (2006) doi:10.1139/T06-024&lt;/li&gt;
&lt;li&gt;Bagheri, M., Settari, A. Modeling of Geomechanics in Naturally Fractured Reservoirs &amp;#8211; SPE-93083-MS, SPE Reservoir Simulation Symposium, Houston, USA, 2005.&lt;/li&gt;
&lt;li&gt;Fish J., Fan R. Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading // International Journal for Numerical Methods in Engineering. 2008. V. 76. &amp;#8211; P. 1044&amp;#8211;1064.&lt;/li&gt;
&lt;li&gt;Kachanov M., Tsukrov I., Shafiro B. Effective moduli of a solid with holes and cavities of various shapes// Appl. Mech. Reviews. 1994. V. 47, &amp;#8470; 1, Part 2. P. S151-S174.&lt;/li&gt;
&lt;/ol&gt;