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We consider single-phase flow in a fractured porous medium governed byDarcy's law with spatially varying hydraulic conductivity matrices in both bulkand fractures. The width-to-length ratio of a fracture is of the order of asmall parameter $\varepsilon$ and the ratio $K_\mathrm{f}^\star /K_\mathrm{b}^\star$ of the characteristic hydraulic conductivities in thefracture and bulk domains is assumed to scale with $\varepsilon^\alpha$ for aparameter $\alpha \in \mathbb{R}$. The fracture geometry is parameterized byaperture functions on a submanifold of codimension one. Given a fracture, wederive the limit models as $\varepsilon \rightarrow 0$. Depending on the valueof $\alpha$, we obtain five different limit models as $\varepsilon \rightarrow0$, for which we present rigorous convergence results.

Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture