**4. Conclusions**

Based on increasing interest in the use of optimised modelling techniques to simulate hydraulic fracturing, we developed a robust and computationally efficient equivalent continuum method. Our ECM method implemented using ABAQUS applies a step-like relationship between void ratio and permeability and incorporates microseismic data to define the stimulated volume of a reservoir. Anisotropy is accounted for by applying a transformation that enables the use of a standard one-dimensional modelling approach with a uniform mesh. This method is particularly useful for cases where there is insufficient data available to define parameters for other numerical approaches, including stress/strain sensitive zones in the target formation. In addition, the use of representative element volume allows the homogenisation of rock elastic and fracture properties for a modelled region. The proposed ECM is more representative compared to PKN, KGD, and diffusivity models and more efficient compared to the XFEM approach. A case study of hydraulic fracturing of tight sand in the Hoadley gas field, Alberta, illustrates the utility of our method for characterising hydraulic fracturing.

**Author Contributions:** Conceptualisation, E.A.; methodology, E.A.; writing—original draft preparation, E.A.; writing—review and editing, R.C.K.W. and D.W.E.; supervision, R.C.K.W.; funding acquisition, D.W.E. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Natural Sciences and Engineering Research Council of Canada gran<sup>t</sup> number CRDPJ/474748-2014.

**Acknowledgments:** This research was funded by Natural Sciences and Engineering Research Council of Canada gran<sup>t</sup> number CRDPJ/474748-2014. Sponsors of the Microseismic Industry Consortium are also thanked for their ongoing support of this initiative.

**Conflicts of Interest:** The authors declare no conflict of interest.
