Comparison of geomechanical upscaling methods for prediction of elastic modulus of heterogeneous media

Geomechanical properties of rocks are essential for understanding their elastic behavior. These parameters find their applications in various fields such as petroleum engineering, and geological storage sites, of nuclear waste and carbon dioxide and other geotechnical operations. There are several methods to obtain these parameters, including experimental methods, mathematical upscaling, and numerical simulation while experimental approaches are more trusted. The aim of this study is to estimate Young's modulus of a shale sample from several major upscaling mathematical methods and compare the results to polyaxial compressive strength test and nanoindentation measurements on the same piece of sample. To achieve this, five major theoretical upscaling models, including DEM, MT, SCA, KTF, and DM, have been utilized to calculate the Young's modulus based on constituent components of the sample that was obtained from routine XRD and geochemical analysis. The calculations for each of the five methods were performed in two scenarios: without incorporating the organic matter in the model and with it, in a range of porosity values while input parameters for each constituent components were found from the literature. Young's modulus with organic materials following the upscaling schemes was in the range of 24.0661 GPa to 27.0001 GPa. Likewise, excluding the organic substances Young's modulus was calculated 25.1784 GPa and 29.1394 GPa, as the smallest and largest values, respectively. These values were compared to the Young's modulus obtained from the nanoindentation (34.15 GPa) and polyaxial test (24.36 GPa). The Young's modulus decreases of approximately 7% with considering organic matter around 2.45% and decrease of less than 5% with variation of 1% porosity. Based on the results, it was concluded that upscaling methods overall provide results in an acceptable range while they are more cost-effective and time-efficient when compared to expensive and time-consuming experimental approaches and can replace them. Furthermore, the use of upscaling methods reduces the need for destructive testing and also eliminates the requirement for expensive equipment with limited access to proper size of the samples and required preparations that should be followed. However, the lithology of the sample and presence of certain type of pore spaces and fractures should not be taken lightly in this process.