Numerical evaluation of mean-field homogenisation methods for predicting shale elastic response

Abstract

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Numerical evaluation of mean-field homogenisation methods for predicting shale elastic responseReceived: date / Accepted: date Abstract Homogenisation techniques have been successfully used to estimate the mechanical response of synthetic composite materials, due to their ability to relate the macroscopic mechanical response to the material microstructure. The adoption of these mean-field techniques in geo-composites such as shales is attractive, partly because of the practical difficulties associated with the experimental characterisation of these highly heterogeneous materials. In this paper, numerical modelling has been undertaken to investigate the applicability of homogenisation methods in predicting the macroscopic, elastic response of clayey rocks. The rocks are considered as two-level composites consisting of a porous clay matrix at the first level and a matrix-inclusion morphology at the second level . The simulated microstructures ranged from a simple system of one inclusion/void embedded in a matrix to complex, random microstructures. The effectiveness and limitations of the different homogenisation schemes were demonstrated through a comparative evaluation of the macroscopic elastic response, illustrating the appropriate schemes for upscaling the microstructure of shales. Based on the numerical simulations and existing experimental observations, a randomly distributed pore system for the micro-structure of porous clay matrix has been proposed which can be used for the subsequent development and validation of shale constitutive models and their flow properties. Finally, the homogenisation techniques were used to predict the experimental measurements of elastic response. The developed methodology is proved to be a valuable too for verifying the accuracy and performance of the homogenisation techniques.

Predicting the elastic response of organic‐rich shale using nanoscale measurements and homogenisation methods

“…The capabilities of homogenisation techniques in shales was investigated using numerical simulations in which several virtual shale microstructures were generated and studied (Goodarzi et al . ). Good agreement was obtained between the macroscopic elastic responses of the numerical rocks and the predicted values from the homogenisation methods.…”

“…As was highlighted in Section , numerical studies using SCS and MT schemes for predicting homogenised elastic response of matrix‐inclusion morphology showed that each of this elastic constant can be better predicted with one of these schemes (Goodarzi et al . ). In fact, the error observed in homogenised stiffness tensor components can be seen as the combined error of homogenised elastic constants.…”

“…Further, Goodarzi et al . () also found that, for matrix‐inclusion morphologies containing up to 40% of inclusion, the homogenised Young's modulus is better predicted using SCS, whereas the Mori–Tanaka (MT) model (Mori and Tanaka ) provides better results for the homogenised bulk modulus. For volume fractions above 40%, the prediction error for these schemes increases gradually.…”

“…Goodarzi, Rouainia and Aplin () studied the performance and accuracy of various formulations using numerical analyses. Different microstructures for the porous clay and also the matrix‐inclusion morphology were considered.…”

Quantifying Rock Weakening Due to Decreasing Calcite Mineral Content by Numerical Simulations

“…Moreover, the same rock sample can be examined under varying testing conditions or mineral composition, which can be virtually varied [ 48 ]. Present numerical models employ calculation techniques to determine static [ 49 , 50 , 51 ] and dynamic moduli [ 52 ] mainly for reservoir rocks such as sandstones [ 53 , 54 ] and carbonates [ 55 , 56 ], but also for shales [ 57 ]. However, there is still a discrepancy between the achieved numerical estimates of mechanical properties derived from micro-CT images and laboratory data, where, regardless of the numerical approach, the simulated moduli are systematically higher [ 58 , 59 ].…”