  Modeling flows in fractured porous media is important in applications. One
main challenge in numerical simulation is that the flow is strongly influenced
by the fractures, so that the solutions typically contain complex features,
which require high computational grid resolutions. Instead of using uniformly
fine mesh, a more computationally efficient adaptively refined mesh is
desirable. In this paper we design and analyze a novel residual-type a
posteriori error estimator for staggered DG methods on general polygonal meshes
for Darcy flows in fractured porous media. The method can handle fairly general
meshes and hanging nodes can be simply incorporated into the construction of
the method, which is highly appreciated for adaptive mesh refinement. The
reliability and efficiency of the error estmator are proved. The derivation of
the reliability hinges on the stability of the continuous setting in the primal
formulation. A conforming counterpart that is continuous within each bulk
domain for the discrete bulk pressure is defined to facilitate the derivation
of the reliability. Finally, several numerical experiments including multiple
non-intersecting fractures are carried out to confirm the proposed theories.
