**2. Representation of the discrete fracture network**

DFNs often are characterized by statistical parameters associated with one or more identified fracture sets. These statistical parameters typically characterize the fracture size distribution, orientation distribution and density of each fracture set.

It is widely accepted that the fracture length distribution usually follows a power law distri‐ bution, which relates the probability of occurrence of a fracture with a length of *l* to the negative exponent of the length, i.e., *n*(*l*)∝*l* <sup>−</sup>*α*. Value of *α* is site specific, but often varies in the range between 2 and 4. In this two-dimensional study, P21 is used as the measure of the fracture density. (P21 is defined as the sum of fracture or trace lengths divided by the area of the sampling or mapping domain — i.e.,*P*21=∑ *l <sup>i</sup>* / *<sup>L</sup>* <sup>2</sup> , where L is the linear dimension of the DFN domain.)

Considering the computational requirements of the numerical tool used in this study, it was impractical to represent DFNs with the same level of complexity as that observed in the field. Therefore, the DFN realizations were simplified or filtered. The objective of the filtering process was to reduce the geometrical complexity while preserving the relevant characteristics of the DFN. In the adopted approach, DFN realizations were simplified first by disregarding fractures with a length smaller than a prescribed threshold. The minimum fracture length cutoff is determined based on the length scale of the analysed problem. Also, to conform to what is often observed in the field, closely spaced, sub-parallel fractures (sometimes generated by the Poisson process used for generation of the fracture locations in the synthetic DFN) are disregarded. The latter criterion is based on the field observations and the reasoning that the stress field around a fracture prevents occurrence of sub-parallel fractures in its vicinity. Finally, in this study, the variation of fracture orientation about the mean for each fracture set was disregarded.

The flow characterises of the DFN are determined by identifying the clusters and evaluating overall DFN connectivity. A cluster is a group of fractures that are connected to each other; no fracture inside a cluster intersects a fracture belonging to a different cluster. A fully connected DFN is defined as the DFN with one cluster extending to the boundaries of the domain. The partially and sparsely connected DFNs were created by decreasing the fracture density and visually inspecting the size of formed clusters relative to the size of the model.
