Homogenisation analysis within ParaGeo enables multi-scale investigation of material properties and upscaling, where the range of scales may encompass from SEM images to element sizes associated with field-case simulations. 
 
Data acquisition for this analysis is itself obtained at different scales; e.g. cuttings, core plugs, wellbore sonic logs and seismic cube. Our homogenization workflow, which is implemented within MATINA, facilitates incorporation of this data to be used in any of the homogenization procedures available including:

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• “Analytical models”, which evaluates the properties using standard analytical homogenisation expressions

• “Numerical Stiffness”, which from an input of a sample (e.g. a SEM image) identifies the stiffness of such sample without requiring any constitutive assumption (except the individual grain properties). In case of millimetre and centimetre scale samples, either the full (anisotropic) stiffness can be utilised, or best estimates of elastic isotropic parameters are provided. For upper scales with distinct layers, the slab model is well justified, and parameters for the transverse isotropic material model can be employed to upscale.

•  “Range Test”, where the input sample is used to perform several simulations over a range of different loading conditions using parameter values automatically evaluated by the inversion algorithm

•  “Biaxial Test", which is specifically used for upscaling properties using simulated biaxial tests on the input sample; e.g. discrete particle models

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For loadings that drive the materials to a non-linear behaviour, either the Range Test, or the Biaxial Test will provide the peak strength data required to evaluate the failure envelope for the tested range of loads.

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Our workflow deploying MATINA uses model templates for homogenisation analysis at each scale directly linked to a material database tool so that upscaled properties can be seamlessly transferred to the next scale. Additionally, a correlation module enables rationalisation of the data measurements based on the results of the homogenisation analysis.

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In addition ParaGeoInv may be used for performing inverse analysis to achieve homogenisation and upscaling of material properties. Due to the gradient-free nature of the nearest neighbour algorithm, ParaGeoInv is applicable in a variety of nonlinear problems that are common in complex and challenging geological models. Examples of upscaling applications shown here include extracting equivalent fracture permeability from fine-scale discrete fracture model under single-phase hydro-mechanical condition and homogenising stratigraphy layers that are heterogeneous in nature.