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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 25, 2019

A Graph Theoretic Approach for Spatial Analysis of Induced Fracture Networks

Deborah Glosser and Jennifer R. Bauer


Drilling induced fractures are generated when excessive stresses around a borehole cause tensile failure of the wellbore wall. If stress concentrations are great enough, compressive failures can form in the region surrounding the wellbore, leading to wellbore breakout, and the potential compromise of wellbore integrity. Another category of induced fracture networks are hydraulically induced fractures, which are generated by the injection of pressurized fluids into the subsurface. Overlapping induced fracture networks between collocated wellbores may increase pathways in the subsurface, and create the potential for unwanted fluid leakage. The generation of induced fractures is greatly dependent upon the structural and geological characteristics. Probabilistic-based simulations are often used to model fracture systems. Several methods for modeling local fracture networks have been proposed in the literature. These models often involve the generation of randomly located fractures, and may have limited capabilities for honoring engineered fractures such as induced fracture networks. We present a graph theoretic approach for identifying geospatial regions and wellbores at increased risk for subsurface connectivity based on wellbore proximity and local lithologic characteristics. The algorithm is coded in Matlab, and transforms 3 dimensional geospatial data to graph form for rapid computation of pairwise and topological relationships between wellbores (nodes), andthe spatial radius of induced fractures (edges). Induced fracture reaches are represented as cylinders with a radius r, based on literature derived ranges for fracture lengths for different lithologies (e.g. shale, sandstone).

The topological algorithm is compared to a standard graph-based k-nearest neighbor algorithm to demonstrate the value of incorporating lithologic attributes in graph-based fracture models. The algorithms are applied to two scenarios using Pennsylvania wellbore and lithologic data: a subset of data from the Bradford field, as well as a known leakage scenario in Armstrong County. The topological algorithm presented in this paper can be used to complement existing fracture models to better account for the reach of induced fractures, and to identify spatial extents at increased risk for unwanted subsurface connectivity. As a result, the method presented in this paper can be part of a cumulative strategy to reduce uncertainty inherent to combined geologic and engineered systems. The model output provides valuable information for industry to develop environmentally safe drilling and injection plans; and for regulators to identify specific wellbores at greater risk for leakage, and to develop targeted, science-based monitoring policies for higher risk regions.


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Received: 2016-05-27
Accepted: 2016-08-26
Published Online: 2019-03-25
Published in Print: 2016-12-01

© 2016 Deborah Glosser et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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