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In this paper, a new enrichment scheme is proposed to model fractures and other conduits in porous media flow problems. Inserting this scheme into a partition of unity based method results in a new numerical method that does not require the mesh to honor the specific geometry of these subsurface features. The new scheme involves a specially designed integration procedure and enrichment functions, which can capture effects of local heterogeneity introduced by subsurface features on the pressure solution. The new method is also capable of modeling fractures with low as well as high conductivity. Another feature of the proposed scheme is that, even though two enrichment functions are used to model the permeability change at the two rock/fracture interfaces of a fracture, only one element partition is made for numerical integration. To demonstrate the accuracy and effectiveness of the proposed approach, production problems for wells that were stimulated or completed by longitudinal fracture, transverse fractures, and perforations are studied.

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