This paper introduces a comprehensive C++ software package, HatchFrac, for stochastic modelling of fracture networks in two and three dimensions. Two main methods, the inverse CDF method and acceptance-rejection method, are applied to generate random variables from the stochastic distributions commonly used in discrete fracture network (DFN) modelling. The multilayer per-ceptron (MLP) machine learning approach, combined with the inverse CDF method, is implemented to generate random variables following any sampling distribution. To make the code faster, we extend the Newman-Ziff to determine clusters in the fracture networks. When combined with the block method, the Ziff algorithm improves the coding efficiency significantly. The software generates the T-type fracture intersections in the network, which can be used in applications involving fracture growth or incorporating geomechanics. We introduce three applications of HatchFrac that demonstrate the versatility of our software: percolation analysis, fracture intensity analysis, and flow and connectivity analysis.

Fractures play an essential role in formations with low permeability; however, fracture sealing significantly reduces the permeability of fractures. The mechanism of how fracture sealing impacts the macro-scale fluid flow is rarely investigated. Here, we simulate sealing in two- and three-dimensional orthogonal fracture networks and investigate the impact of sealing on the percolation of these fracture networks. We find that a small amount of sealing can prevent the formation of spanning clusters, which suggests that global connectivity is rarely realized. Without significant stress perturbations, most fractures are partially sealed and non-critically stressed, and they usually do not contribute much to the fluid flow. However, under a significant stress perturbation, such as hydraulic fracturing, the well-connected and critically oriented fractures become critically stressed and slide because of the increased pore pressure. Partially sealed and non-critically stressed fractures can also contribute to the fluid flow by enlarging the stimulated reservoir volume (SRV). We estimate the stimulated reservoir volume in two dimensions by dividing the target distance (LSRV) into two parts. One is the distance limiting generation of hydraulic fractures (ΔLh), and the other is the limiting distance of making natural fractures slide (ΔLs). A rough estimation yields an elongated shape of the SRV, which is consistent with observations from microseismicity maps.

The stochastic discrete fracture network (SDFN) model is a practical approach to model complex fracture systems in the subsurface. However, it is impossible to validate the correctness and quality of an SDFN model because the comprehensive subsurface structure is never known. We utilize a pixel-based fracture detection algorithm to digitize 80 published outcrop maps of different scales at different locations. The key fracture properties, including fracture lengths, orientations, intensities, topological structures, clusters and flow are then analyzed. Our findings provide significant justifications for statistical distributions used in SDFN modellings. In addition, the shortcomings of current SDFN models are discussed. We find that fracture lengths follow multiple (instead of single) power-law distributions with varying exponents. Large fractures tend to have large exponents, possibly because of a small coalescence probability. Most small-scale natural fracture networks have scattered orientations, corresponding to a small κ value (κ<3) in a von Mises–Fisher distribution. Large fracture systems collected in this research usually have more concentrated orientations with large κ values. Fracture intensities are spatially clustered at all scales. A fractal spatial density distribution, which introduces clustered fracture positions, can better capture the spatial clustering than a uniform distribution. Natural fracture networks usually have a significant proportion of T-type nodes, which is unavailable in conventional SDFN models. Thus a rule-based algorithm to mimic the fracture growth and form T-type nodes is necessary. Most outcrop maps show good topological connectivity. However, sealing patterns and stress impact must be considered to evaluate the hydraulic connectivity of fracture networks.

The fractal dimension and multifractal spectrum are widely used to characterize the complexity of natural fractures. However, a systematic investigation on the impact of different fracture properties (fracture lengths, orientations, center positions, system sizes) on the fractal and multifractal characterization of complex fracture networks is missing. We utilize an in-house developed DFN modeling software, HatchFrac, to construct stochastic fracture networks with prescribed distributions and systematically study the impact of four geometrical properties of fractures on the fractal and multifractal characterization. We calculate the single fractal dimension and multifractal spectrum with the box-counting method. The single fractal dimension, D, and the difference of singularity exponent, ∆α, are used to represent the fractal and multifractal patterns, respectively. We find that fracture lengths, orientations and system sizes have positive correlations with D and ∆α, while the system size has the most significant impact among the four parameters. D is uncorrelated with fracture positions (FD), which means that a single fractal dimension cannot capture the complexity caused by clustering effects. However, ∆α has a strong negative correlation with FD, which implies that clustering effects make fracture networks more complex, and ∆α can capture the difference. We also digitize 60 outcrop maps with a novel fracture detection algorithm and calculate their fractal dimension and multifractal spectrum. We find wide variations of D and ∆α on those outcrop maps, even for outcrops at similar scales. It means that a universal indicator for characterizing fracture networks at different scales or the same scale is almost impossible.