  This article proves the existence of solutions to a model of incompressible
miscible displacement through a porous medium, with zero molecular diffusion
and modelling wells by spatial measures. We obtain the solution by passing to
the limit on problems indexed by vanishing molecular diffusion coefficients.
The proof employs cutoff functions to excise the supports of the measures and
the discontinuities in the permeability tensor, thus enabling compensated
compactness arguments used by Y. Amirat and A. Ziani for the analysis of the
problem with $L^2$ wells [\emph{Z. Anal. Anwendungen}, 23(2):335--351, 2004].
We give a novel treatment of the diffusion-dispersion term, which requires
delicate use of the Aubin--Simon lemma to ensure the strong convergence of the
pressure gradient, owing to the troublesome lower-order terms introduced by the
localisation procedure.
